{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-26T00:14:02.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-26T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":52664,"title":"List the Moran numbers","description":"The quotient of a Moran number and its digit sum is prime. For example, 117 and 481 are Moran numbers because 117/(1+1+7) is 13 and 481/(4+8+1) = 37, and both 13 and 37 are prime. \r\nWrite a function to list the Moran numbers less than or equal to the input number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 363px 8px; transform-origin: 363px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe quotient of a Moran number and its digit sum is prime. For example, 117 and 481 are Moran numbers because 117/(1+1+7) is 13 and 481/(4+8+1) = 37, and both 13 and 37 are prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 257px 8px; transform-origin: 257px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the Moran numbers less than or equal to the input number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Moran(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 500;\r\ny = Moran(n);\r\ny_correct = [18 21 27 42 45 63 84 111 114 117 133 152 153 156 171 190 195 198 201 207 209 222 228 247 261 266 285 333 370 372 399 402 407 423 444 465 481];\r\nassert(isequal(y,y_correct))\r\n\r\n%% \r\nn = 40332;\r\ny = Moran(n);\r\ny23_correct = [207 1679 3749 4577 8717 14099 18653 19067 22793 24449 25691 26519 26933 29417 29831 32729 33557 35627 37283];\r\nassert(isequal(y(mod(y,23)==0),y23_correct) \u0026\u0026 isequal(y(end),n))\r\n\r\n%%\r\nn = [100000 400000 700000 1e6 4e6 7e6 1e7];\r\ns = [383 1193 1870 2451 8080 12913 17271];\r\nlen_correct = [1915 5967 9352 12259 40403 64567 86356];\r\nsum_correct = [79699686 1044807776 2880495403 5339917218 73480226594 205122929098 389309242207];\r\nsd_correct  = [2.925215086021406e+04 1.171076738381341e+05 2.065163622127620e+05 2.944277010513903e+05 1.177431499460555e+06 2.057551640570258e+06 2.933705654924581e+06];\r\nys_correct  = [11354 28489 48992 71660 99972; 51489 125203 210051 300165 399477; 96325 220734 364473 524186 699739; 129627 308214 513837 741778 999219; 579189 1331117 2176042 3062214 3999644; 1046322 2330397 3782883 5322552 6999255; 1440693 3292137 5341677 7565613 9999882];\r\nfor k = 1:length(n)\r\n    disp(['Test 3.' num2str(k)])\r\n    y = Moran(n(k));\r\n    assert(isequal(length(y),len_correct(k)) \u0026\u0026 isequal(sum(y),sum_correct(k)) \u0026\u0026 abs(std(y)-sd_correct(k))\u003c1e-7 \u0026\u0026 isequal(y(s(k):s(k):end),ys_correct(k,:)));\r\nend\r\n\r\n%%\r\nfiletext = fileread('Moran.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis') || contains(filetext, 'persistent'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-05T13:52:35.000Z","updated_at":"2026-04-28T21:19:49.000Z","published_at":"2021-09-05T14:10:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe quotient of a Moran number and its digit sum is prime. For example, 117 and 481 are Moran numbers because 117/(1+1+7) is 13 and 481/(4+8+1) = 37, and both 13 and 37 are prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the Moran numbers less than or equal to the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1187,"title":"Knave in the middle attack","description":"This is a Matlab adaptation of the \u003chttp://en.wikipedia.org/wiki/Knights_and_Knaves Knights and Knaves\u003e logical puzzles, mixed with the famous \u003chttp://en.wikipedia.org/wiki/Man-in-the-middle_attack man-in-the-middle attack\u003e in computer security. \r\n\r\nYou are in an island where all inhabitants are either _Knights_, who always tell the truth, or _Knaves_, who always lie. Your job is to sit in the middle of an islander and a second person interviewing the islander, intercepting all questions posed to the islander, and answering to the interviewer in a way that will make him think that the islander is the opposite type of what he really is (answer as a Knave if the islander is a Knight, or answer as a Knight if the islander is a Knave). The problem is: a) you really do not know whether the islander is a Knight or a Knave; and b) the islander knows some secret that only he knows, so you may not be able to anticipate what he would answer even if you knew whether he was a Knight or a Knave! Luckily for you, you may ask the islander privately any questions that you wish before responding to the interviewer.  \r\n\r\n*Details:*\r\n\r\nYou are given a function handle F that will act as the islander. This function will answer any question the way the islander would. The function _function answer=F(question)_ takes a char array as input (the 'question'), and returns a logical value (the yes/no 'answer' this particular islander would give to this question; _true_ means 'yes' and _false_ means 'no'). Valid questions are any valid matlab string. The islander has access to the following variables (the things that he 'knows'):\r\n\r\n* *A*: Islander's type. A is a logical variable: true for a Knight, false for a Knave\r\n* *X*: A secret formula only islanders know. An unknown function on positive integer values that when evaluated returns a logical value (e.g. _x\u003e1_).\r\n* *F*: Introspection. F is the handle associated with this islander's answers, so he knows himself what he would respond to some hypothetical question\r\n\r\nThe function handles associated with a Knight and a Knave look, respectively, something like:\r\n\r\n  function answer = Knight(question)\r\n    A = true;\r\n    X = @(x)x\u003e10;\r\n    F = @Knight;\r\n    answer = eval(question);\r\n  end\r\n\r\n  function answer = Knave(question)\r\n    A = false;\r\n    X = @(x)x\u003e10;\r\n    F = @Knave;\r\n    answer = ~eval(question);\r\n  end\r\n\r\nOf course the values of X will be different and unknown to you.\r\n\r\nA few examples:\r\n\r\n Knight('A==true') == true\r\n\r\nThis question asks whether the islander is a Knight, and a Knight would respond affirmatively to such question. \r\n\r\n Knave('A|X(1)') == true\r\n\r\nThis question asks whether the islander is a Knight or the value of the secret formula at 1 is true. None of these are true, but the Knave will lie to you and respond 'yes'.\r\n\r\n Knave('F(''A'')') == false\r\n\r\nThis question asks whether the islander would respond affirmatively to the question of whether he is a knight. Both Knights and Knaves would actually respond affirmatively when questioned whether they are Knights, but a Knave would lie to you when telling you how he would respond to such question, so he would say 'no'.\r\n\r\nYou must implement a function that will take two inputs: 1) the function handle of an islander (either @Knight or @Knave); and 2) a question (as a char array). Your function should return the answer this same islander would give to this question if he was the opposite type than he really is. In other words:\r\n\r\n your_function(@Knight,str) should return Knave(str)\r\n your_function(@Knave,str) should return Knight(str)\r\n\r\nYour function might query the function handle of the islander with whatever questions it sees fit before responding.\r\n\r\n*Examples:*\r\n\r\n your_function(@Knight,'A==true') == true;\r\n\r\n your_function(@Knave,'A==true') == true; \r\n\r\nThis question asks whether the islander is a Knight; both Knights and Knaves would respond _true_ to this question.\r\n\r\n your_function(@Knight,'F(''A==true'')==true') == false; \r\n\r\n your_function (@Knave,'F(''A==true'')==true') == true; \r\n\r\nThis question asks if the islander would respond yes to the question of whether he is a Knight. A Knight would respond 'yes', while a Knave would (falsely) respond 'no', so your function should return exactly the opposite in each case.\r\n\r\n your_function(@Knight,'X(3)~=X(2)') == true\r\n\r\n your_function(@Knave,'X(3)~=X(2)') == false \r\n\r\n(Assuming X(2)==X(3); you do not know the values of X, only islanders do) This question asks to the islander whether the value of his secret formula X(2) is different from the value of his secret formula X(3). Assuming that they were actually the same value a Knight would respond negatively (telling you the truth), while a Knave would respond affirmatively (lying to you), so, again, your function should return exactly the opposite response in each case.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 914.5px; vertical-align: baseline; perspective-origin: 332px 914.5px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis is a Matlab adaptation of the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Knights_and_Knaves\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eKnights and Knaves\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e logical puzzles, mixed with the famous\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Man-in-the-middle_attack\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eman-in-the-middle attack\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in computer security.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 94.5px; white-space: pre-wrap; perspective-origin: 309px 94.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou are in an island where all inhabitants are either\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eKnights\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, who always tell the truth, or\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eKnaves\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, who always lie. Your job is to sit in the middle of an islander and a second person interviewing the islander, intercepting all questions posed to the islander, and answering to the interviewer in a way that will make him think that the islander is the opposite type of what he really is (answer as a Knave if the islander is a Knight, or answer as a Knight if the islander is a Knave). The problem is: a) you really do not know whether the islander is a Knight or a Knave; and b) the islander knows some secret that only he knows, so you may not be able to anticipate what he would answer even if you knew whether he was a Knight or a Knave! Luckily for you, you may ask the islander privately any questions that you wish before responding to the interviewer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eDetails:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 52.5px; white-space: pre-wrap; perspective-origin: 309px 52.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou are given a function handle F that will act as the islander. This function will answer any question the way the islander would. The function\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003efunction answer=F(question)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e takes a char array as input (the 'question'), and returns a logical value (the yes/no 'answer' this particular islander would give to this question;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etrue\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e means 'yes' and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003efalse\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e means 'no'). Valid questions are any valid matlab string. The islander has access to the following variables (the things that he 'knows'):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-bottom: 20px; margin-top: 10px; transform-origin: 316px 50px; perspective-origin: 316px 50px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: Islander's type. A is a logical variable: true for a Knight, false for a Knave\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 20px; white-space: pre-wrap; perspective-origin: 288px 20px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: A secret formula only islanders know. An unknown function on positive integer values that when evaluated returns a logical value (e.g.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u0026gt;1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 20px; white-space: pre-wrap; perspective-origin: 288px 20px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eF\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: Introspection. F is the handle associated with this islander's answers, so he knows himself what he would respond to some hypothetical question\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function handles associated with a Knight and a Knave look, respectively, something like:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 130px; perspective-origin: 329px 130px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003efunction \u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003eanswer = Knight(question)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  A = true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  X = @(x)x\u0026gt;10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  F = @Knight;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  answer = eval(question);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003efunction \u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003eanswer = Knave(question)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  A = false;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  X = @(x)x\u0026gt;10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  F = @Knave;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  answer = ~eval(question);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eOf course the values of X will be different and unknown to you.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA few examples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e Knight(\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander is a Knight, and a Knight would respond affirmatively to such question.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e Knave(\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A|X(1)'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander is a Knight or the value of the secret formula at 1 is true. None of these are true, but the Knave will lie to you and respond 'yes'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e Knave(\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'F(''A'')'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == false\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; perspective-origin: 309px 42px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander would respond affirmatively to the question of whether he is a knight. Both Knights and Knaves would actually respond affirmatively when questioned whether they are Knights, but a Knave would lie to you when telling you how he would respond to such question, so he would say 'no'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; perspective-origin: 309px 42px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou must implement a function that will take two inputs: 1) the function handle of an islander (either @Knight or @Knave); and 2) a question (as a char array). Your function should return the answer this same islander would give to this question if he was the opposite type than he really is. In other words:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 20px; perspective-origin: 329px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,str) should \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003ereturn Knave(str)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knave,str) should \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003ereturn Knight(str)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYour function might query the function handle of the islander with whatever questions it sees fit before responding.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knave,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander is a Knight; both Knights and Knaves would respond\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etrue\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e to this question.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'F(''A==true'')==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == false; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function (@Knave,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'F(''A==true'')==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 31.5px; white-space: pre-wrap; perspective-origin: 309px 31.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks if the islander would respond yes to the question of whether he is a Knight. A Knight would respond 'yes', while a Knave would (falsely) respond 'no', so your function should return exactly the opposite in each case.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'X(3)~=X(2)'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knave,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'X(3)~=X(2)'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == false\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 52.5px; white-space: pre-wrap; perspective-origin: 309px 52.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(Assuming X(2)==X(3); you do not know the values of X, only islanders do) This question asks to the islander whether the value of his secret formula X(2) is different from the value of his secret formula X(3). Assuming that they were actually the same value a Knight would respond negatively (telling you the truth), while a Knave would respond affirmatively (lying to you), so, again, your function should return exactly the opposite response in each case.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function answer = AnswerGenerator(F,str)\r\n  answer=F(str);\r\nend","test_suite":"%%\r\n% Ask a Knight whether 4 is prime\r\n% (he will respond false; your function should respond true)\r\nA=true; X=@isprime; str='X(4)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% Ask a Knave whether 4 is prime \r\n% (he will respond true; your function should respond false)\r\nA=false; X=@isprime; str='X(4)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\n% Ask a Knight whether he is a Knight \r\n% (both Knights and Knaves would respond true and so should your function)\r\nA=true; X=@isprime; str='A==true';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% Ask a Knave whether he is a Knight \r\n% (both Knights and Knaves would respond true and so should your function)\r\nA=false; X=@isprime; str='A==true';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% Ask a Knight whether he would respond affirmatively to the question of whether he is a Knight\r\n% (a Knave would respond false to this same question, and so should your function)\r\n% A=true; X=@isprime; str='F(''A==true'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\n% Ask a Knave whether he would respond affirmatively to the question of whether he is a Knight\r\n% (a Knight would respond true to this same question, and so should your function)\r\n% A=false; X=@isprime; str='F(''A==true'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\nA=true; X=@isprime; str='diff(X(2:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\nA=false; X=@isprime; str='diff(X(2:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\nA=true; X=@isprime; str='A==X(6)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\nA=false; X=@isprime; str='A==X(6)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\nA=true; X=@isprime; str='A\u0026any(X(1:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\nA=false; X=@isprime; str='A\u0026any(X(1:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% A=true; X=@(x)rem(x,2); str='F(''F(''''X(3)'''')'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\n% A=false; X=@(x)rem(x,2); str='F(''F(''''X(3)'''')'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),true))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":14,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2020-09-29T00:03:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-01-07T22:12:02.000Z","updated_at":"2026-04-15T04:00:57.000Z","published_at":"2013-01-08T03:23:02.000Z","restored_at":"2017-11-13T15:02:29.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is a Matlab adaptation of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Knights_and_Knaves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKnights and Knaves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e logical puzzles, mixed with the famous\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Man-in-the-middle_attack\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eman-in-the-middle attack\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in computer security.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are in an island where all inhabitants are either\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKnights\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, who always tell the truth, or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKnaves\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, who always lie. Your job is to sit in the middle of an islander and a second person interviewing the islander, intercepting all questions posed to the islander, and answering to the interviewer in a way that will make him think that the islander is the opposite type of what he really is (answer as a Knave if the islander is a Knight, or answer as a Knight if the islander is a Knave). The problem is: a) you really do not know whether the islander is a Knight or a Knave; and b) the islander knows some secret that only he knows, so you may not be able to anticipate what he would answer even if you knew whether he was a Knight or a Knave! Luckily for you, you may ask the islander privately any questions that you wish before responding to the interviewer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDetails:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a function handle F that will act as the islander. This function will answer any question the way the islander would. The function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efunction answer=F(question)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e takes a char array as input (the 'question'), and returns a logical value (the yes/no 'answer' this particular islander would give to this question;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e means 'yes' and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e means 'no'). Valid questions are any valid matlab string. The islander has access to the following variables (the things that he 'knows'):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Islander's type. A is a logical variable: true for a Knight, false for a Knave\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A secret formula only islanders know. An unknown function on positive integer values that when evaluated returns a logical value (e.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u0026gt;1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Introspection. F is the handle associated with this islander's answers, so he knows himself what he would respond to some hypothetical question\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function handles associated with a Knight and a Knave look, respectively, something like:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[function answer = Knight(question)\\n  A = true;\\n  X = @(x)x\u003e10;\\n  F = @Knight;\\n  answer = eval(question);\\nend\\n\\nfunction answer = Knave(question)\\n  A = false;\\n  X = @(x)x\u003e10;\\n  F = @Knave;\\n  answer = ~eval(question);\\nend]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOf course the values of X will be different and unknown to you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA few examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Knight('A==true') == true]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander is a Knight, and a Knight would respond affirmatively to such question.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Knave('A|X(1)') == true]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander is a Knight or the value of the secret formula at 1 is true. None of these are true, but the Knave will lie to you and respond 'yes'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Knave('F(''A'')') == false]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander would respond affirmatively to the question of whether he is a knight. Both Knights and Knaves would actually respond affirmatively when questioned whether they are Knights, but a Knave would lie to you when telling you how he would respond to such question, so he would say 'no'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou must implement a function that will take two inputs: 1) the function handle of an islander (either @Knight or @Knave); and 2) a question (as a char array). Your function should return the answer this same islander would give to this question if he was the opposite type than he really is. In other words:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,str) should return Knave(str)\\n your_function(@Knave,str) should return Knight(str)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function might query the function handle of the islander with whatever questions it sees fit before responding.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,'A==true') == true;\\n\\n your_function(@Knave,'A==true') == true;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander is a Knight; both Knights and Knaves would respond\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to this question.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,'F(''A==true'')==true') == false; \\n\\n your_function (@Knave,'F(''A==true'')==true') == true;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks if the islander would respond yes to the question of whether he is a Knight. A Knight would respond 'yes', while a Knave would (falsely) respond 'no', so your function should return exactly the opposite in each case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,'X(3)~=X(2)') == true\\n\\n your_function(@Knave,'X(3)~=X(2)') == false]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(Assuming X(2)==X(3); you do not know the values of X, only islanders do) This question asks to the islander whether the value of his secret formula X(2) is different from the value of his secret formula X(3). Assuming that they were actually the same value a Knight would respond negatively (telling you the truth), while a Knave would respond affirmatively (lying to you), so, again, your function should return exactly the opposite response in each case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":3098,"title":"Scrabble Scores - 13","description":"This problem integrates components of \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3084-scrabble-scores-11 Scrabble Scores - 11\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12 Scrabble Scores - 12\u003e. Here, you are provided an existing word on the board from which you will play a word. The letter can reside anywhere (first to last) within the existing word and within the word that you are playing. In addition, multipliers from the board are provided. Write a function to find the highest scoring word, provided any letter from the existing word that you are building off of, the letters on your tray, and the multipliers (provided in specific locations; see below).\r\n\r\nRather than having to test all the possible permutations against a dictionary, you will be provided a double-level cell array of strings containing all possible words based each starting letter in the existing word and the letters on your tray (a cell array for each letter in the existing word). (The word lists purposefully omit smaller words to prevent the test cases from being too large.) In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\r\n\r\nYou will be provided a multiplier character array that represents the fifteen possible squares that can be played on for each letter in the existing word, ranging from seven above each existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below each existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th (column) position. The array will have the same number of rows as the length of the existing word (which is located along the middle of the array). The multipliers are the same as in previous problems:\r\n\r\n * D: double word\r\n * T: triple word\r\n * Q: quadruple word\r\n * d: double letter\r\n * t: triple letter\r\n * q: quadruple letter\r\n\r\nThe center multiplier square will be left blank, since it's already covered by a tile.\r\n\r\nRelated problems:\r\n\r\nPrevious problem: 12 - \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12 Word score optimization (first word)\u003e.","description_html":"\u003cp\u003eThis problem integrates components of \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3084-scrabble-scores-11\"\u003eScrabble Scores - 11\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\"\u003eScrabble Scores - 12\u003c/a\u003e. Here, you are provided an existing word on the board from which you will play a word. The letter can reside anywhere (first to last) within the existing word and within the word that you are playing. In addition, multipliers from the board are provided. Write a function to find the highest scoring word, provided any letter from the existing word that you are building off of, the letters on your tray, and the multipliers (provided in specific locations; see below).\u003c/p\u003e\u003cp\u003eRather than having to test all the possible permutations against a dictionary, you will be provided a double-level cell array of strings containing all possible words based each starting letter in the existing word and the letters on your tray (a cell array for each letter in the existing word). (The word lists purposefully omit smaller words to prevent the test cases from being too large.) In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\u003c/p\u003e\u003cp\u003eYou will be provided a multiplier character array that represents the fifteen possible squares that can be played on for each letter in the existing word, ranging from seven above each existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below each existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th (column) position. The array will have the same number of rows as the length of the existing word (which is located along the middle of the array). The multipliers are the same as in previous problems:\u003c/p\u003e\u003cpre\u003e * D: double word\r\n * T: triple word\r\n * Q: quadruple word\r\n * d: double letter\r\n * t: triple letter\r\n * q: quadruple letter\u003c/pre\u003e\u003cp\u003eThe center multiplier square will be left blank, since it's already covered by a tile.\u003c/p\u003e\u003cp\u003eRelated problems:\u003c/p\u003e\u003cp\u003ePrevious problem: 12 - \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\"\u003eWord score optimization (first word)\u003c/a\u003e.\u003c/p\u003e","function_template":"function [score,max_word] = scrabble_scores_13(words,mult,first_word)\r\n\r\nscore = 0;\r\nmax_word = {''};\r\n\r\nend","test_suite":"%%\r\nfirst_word = 'start'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\nmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'  d   t t   d  ';' T   d   d   T '];\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nwords{2} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nwords{3} = {'alate','almah','almeh','email','halma','hamal','hemal','laith','lamia','lathe','lathi','lithe','maile','metal','tamal','telia','thali','althea','haemal','halite','hamate','hamlet','hiatal','hiemal','lamiae','malate','maltha','meatal','tamale','hematal','thalami'};\r\nwords{4} = {'aimer','airth','alert','almeh','alter','amrit','ariel','armet','artel','earth','email','haler','harem','hater','heart','hemal','herma','hilar','ihram','irate','ither','laith','lamer','later','lathe','lathi','liter','lithe','litre','maile','mater','merit','metal','miler','mirth','miter','mitre','ramet','ramie','ratel','rathe','realm','relit','remit','retia','taler','tamer','telia','terai','thali','tharm','their','therm','thirl','tiler','timer','trail','trial','armlet','hailer','halier','halite','halter','hamlet','hermai','hermit','hiemal','imaret','lather','lither','mailer','matier','milter','mither','mitral','ramtil','remail','retail','retial','tailer','thairm','thaler','thiram','tramel','lathier','maltier','marlite','thermal'};\r\nwords{5} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nmax_score_corr = 39;\r\nmax_word_corr = {'hamlets'};\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'start'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\nmult = ['T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T'];\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nwords{2} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nwords{3} = {'alate','almah','almeh','email','halma','hamal','hemal','laith','lamia','lathe','lathi','lithe','maile','metal','tamal','telia','thali','althea','haemal','halite','hamate','hamlet','hiatal','hiemal','lamiae','malate','maltha','meatal','tamale','hematal','thalami'};\r\nwords{4} = {'aimer','airth','alert','almeh','alter','amrit','ariel','armet','artel','earth','email','haler','harem','hater','heart','hemal','herma','hilar','ihram','irate','ither','laith','lamer','later','lathe','lathi','liter','lithe','litre','maile','mater','merit','metal','miler','mirth','miter','mitre','ramet','ramie','ratel','rathe','realm','relit','remit','retia','taler','tamer','telia','terai','thali','tharm','their','therm','thirl','tiler','timer','trail','trial','armlet','hailer','halier','halite','halter','hamlet','hermai','hermit','hiemal','imaret','lather','lither','mailer','matier','milter','mither','mitral','ramtil','remail','retail','retial','tailer','thairm','thaler','thiram','tramel','lathier','maltier','marlite','thermal'};\r\nwords{5} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nmax_score_corr = 30;\r\nmax_word_corr = {'maltha'};\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'start'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\nmult = [' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'D  t d   d t  D';' T  d t t d  T '];\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nwords{2} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nwords{3} = {'alate','almah','almeh','email','halma','hamal','hemal','laith','lamia','lathe','lathi','lithe','maile','metal','tamal','telia','thali','althea','haemal','halite','hamate','hamlet','hiatal','hiemal','lamiae','malate','maltha','meatal','tamale','hematal','thalami'};\r\nwords{4} = {'aimer','airth','alert','almeh','alter','amrit','ariel','armet','artel','earth','email','haler','harem','hater','heart','hemal','herma','hilar','ihram','irate','ither','laith','lamer','later','lathe','lathi','liter','lithe','litre','maile','mater','merit','metal','miler','mirth','miter','mitre','ramet','ramie','ratel','rathe','realm','relit','remit','retia','taler','tamer','telia','terai','thali','tharm','their','therm','thirl','tiler','timer','trail','trial','armlet','hailer','halier','halite','halter','hamlet','hermai','hermit','hiemal','imaret','lather','lither','mailer','matier','milter','mither','mitral','ramtil','remail','retail','retial','tailer','thairm','thaler','thiram','tramel','lathier','maltier','marlite','thermal'};\r\nwords{5} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nmax_score_corr = 45;\r\nmax_word_corr = {'hamlets'};\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'thinning'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'eodnirl'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'diner','doter','droit','drone','elint','eloin','enrol','ident','idler','indol','inert','inlet','inter','intro','irone','lento','lined','liner','lirot','liter','litre','loden','loner','nerol','niter','nitre','nitro','noted','noter','oiled','oiler','olden','older','oldie','olein','oriel','redon','relit','reoil','riled','ronde','teind','teloi','tenor','tilde','tiled','tiler','tined','tired','toile','toled','tondi','toned','toner','trend','tried','trine','triol','trode','trone','dentil','dinero','dotier','editor','entoil','indole','ironed','linted','linter','loiter','neroli','norite','orient','retold','rident','rioted','rodent','roiled','rondel','tinder','tirled','toiled','toiler','tonier','trined','triode','lentoid','retinol','tendril','trindle'};\r\nwords{2} = {'dhole','diner','drone','eloin','enrol','helio','heron','hider','hired','holed','honed','honer','horde','idler','indol','irone','lined','liner','loden','loner','nerol','oiled','oiler','olden','older','oldie','olein','oriel','redon','reoil','rhino','riled','ronde','dehorn','dinero','heroin','hinder','hoiden','holden','holder','holier','hondle','honied','horned','indole','ironed','neroli','roiled','rondel','hordein','inholder'};\r\nwords{3} = {'diner','drone','eloin','enrol','idler','indie','indol','indri','iodin','irone','lined','liner','loden','loner','nerol','oiled','oiler','olden','older','oldie','olein','oriel','redon','reoil','riled','ronde','dinero','indole','inlier','iodine','ironed','linier','neroli','oilier','roiled','rondel'};\r\nwords{4} = {'diner','donne','drone','eloin','enrol','idler','indol','inned','inner','irone','lined','linen','liner','loden','loner','nerol','niner','oiled','oiler','olden','older','oldie','olein','oriel','redon','renin','reoil','riled','ronde','ronin','dinero','dinner','endrin','indole','ironed','linden','neroli','online','roiled','rondel','ronnel'};\r\nwords{5} = {'diner','donne','drone','eloin','enrol','idler','indol','inned','inner','irone','lined','linen','liner','loden','loner','nerol','niner','oiled','oiler','olden','older','oldie','olein','oriel','redon','renin','reoil','riled','ronde','ronin','dinero','dinner','endrin','indole','ironed','linden','neroli','online','roiled','rondel','ronnel'};\r\nwords{6} = {'diner','drone','eloin','enrol','idler','indie','indol','indri','iodin','irone','lined','liner','loden','loner','nerol','oiled','oiler','olden','older','oldie','olein','oriel','redon','reoil','riled','ronde','dinero','indole','inlier','iodine','ironed','linier','neroli','oilier','roiled','rondel'};\r\nwords{7} = {'diner','donne','drone','eloin','enrol','idler','indol','inned','inner','irone','lined','linen','liner','loden','loner','nerol','niner','oiled','oiler','olden','older','oldie','olein','oriel','redon','renin','reoil','riled','ronde','ronin','dinero','dinner','endrin','indole','ironed','linden','neroli','online','roiled','rondel','ronnel'};\r\nwords{8} = {'deign','diner','dinge','dingo','dirge','dogie','doing','drone','eloin','enrol','gelid','genro','geoid','giron','glide','goner','gored','gride','grind','groin','idler','indol','ingle','irone','liger','lined','liner','lingo','loden','lodge','login','loner','longe','nerol','ogled','ogler','oiled','oiler','olden','older','oldie','olein','oriel','redon','reign','renig','reoil','ridge','riled','ronde','dinero','dinger','dingle','doling','dongle','eloign','engild','engird','eringo','gilder','girdle','girned','glider','golden','golder','ignore','indole','ironed','legion','linger','lodger','logier','longed','longer','neroli','reding','regild','region','ridgel','ringed','roiled','rondel','eroding','glenoid','gloried','godlier','groined','ignored','lording','negroid','redoing'};\r\nind = randi(3);\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'   D       D   ';'   D       D   ';' D   t   t   D ';'  d   t t   d  ';' T   d   d   T '];\r\n\t\tmax_score_corr = 33;\r\n\t\tmax_word_corr = {'godlier'};\r\n\tcase 2\r\n\t\tmult = ['T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   '];\r\n\t\tmax_score_corr = 16;\r\n\t\tmax_word_corr = {'indole','iodine','ironed','endrin','linden'};\r\n\tcase 3\r\n\t\tmult = ['T   d     d   T';' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'  T   d d   T  ';' T d t   t d T ';'D  t d   d t  D';' T  d t t d  T '];\r\n\t\tmax_score_corr = 45;\r\n\t\tmax_word_corr = {'hordein'};\r\nend\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'novels'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'dmvxeao'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'ad','ae','am','an','ax','da','de','do','ed','em','en','ex','ma','me','mo','na','ne','no','od','oe','om','on','ox','ado','and','ane','ave','avo','axe','dam','dan','den','dev','dex','doe','dom','don','emo','end','eon','mad','mae','man','max','med','men','moa','mod','mon','nae','nam','nav','nod','nom','oda','ode','oma','one','ova','van','vex','voe','vox','aeon','amen','axed','axon','dame','damn','dean','demo','deva','dome','dona','done','dove','exam','exon','made','mane','mano','mead','mean','mend','meno','moan','mode','move','moxa','name','nave','nema','node','noma','nome','nova','odea','omen','oven','oxen','vane','vena','vend','admen','amend','anode','axmen','axone','daven','demon','devon','doven','maned','maven','maxed','menad','monad','monde','moved','named','nomad','novae','vaned','venom','daemon','moaned'};\r\nwords{2} = {'ad','ae','am','ax','da','de','do','ed','em','ex','ma','me','mo','od','oe','om','ox','ado','ave','avo','axe','dam','dev','dex','doe','dom','emo','mad','mae','max','med','moa','mod','moo','oda','ode','oma','ova','oxo','vex','voe','vox','axed','dame','demo','deva','dome','doom','dove','exam','made','mead','mode','mood','move','moxa','odea','maxed','mooed','moved'};\r\nwords{3} = {'ad','ae','am','ax','da','de','do','ed','em','ex','ma','me','mo','od','oe','om','ox','ado','ave','avo','axe','dam','dev','dex','doe','dom','emo','mad','mae','max','med','moa','mod','oda','ode','oma','ova','vav','vex','voe','vox','axed','dame','demo','deva','dome','dove','exam','made','mead','mode','move','moxa','odea','maxed','moved'};\r\nwords{4} = {'ad','ae','am','ax','da','de','do','ed','em','ex','ma','me','mo','od','oe','om','ox','ado','ave','avo','axe','dam','dee','dev','dex','doe','dom','eme','emo','eve','mad','mae','max','med','moa','mod','oda','ode','oma','ova','vee','vex','voe','vox','axed','dame','deem','deme','demo','deva','dome','dove','eave','exam','exed','made','mead','meed','mode','move','moxa','odea','adeem','deave','eaved','edema','evade','maxed','moved','vexed','oedema'};\r\nwords{5} = {'ad','ae','al','am','ax','da','de','do','ed','el','em','ex','la','lo','ma','me','mo','od','oe','om','ox','ado','ale','ave','avo','axe','dal','dam','del','dev','dex','doe','dol','dom','eld','elm','emo','lad','lam','lav','lax','lea','led','lev','lex','lox','mad','mae','max','med','mel','moa','mod','mol','oda','ode','old','ole','oma','ova','vex','voe','vox','alme','aloe','axed','axel','axle','dale','dame','deal','demo','deva','dole','dome','dove','exam','lade','lame','lave','lead','leva','levo','load','loam','lode','love','made','male','mead','meal','meld','mode','mola','mold','mole','move','moxa','odea','olde','olea','oval','vale','veal','vela','veld','vole','amole','axled','dolma','domal','laevo','lamed','laved','loved','loxed','maxed','medal','modal','model','moved','voled','voxel','loamed'};\r\nwords{6} = {'ad','ae','am','as','ax','da','de','do','ed','em','es','ex','ma','me','mo','od','oe','om','os','ox','so','ado','ads','ave','avo','axe','dam','das','dev','dex','doe','dom','dos','eds','emo','ems','mad','mae','mas','max','med','moa','mod','mos','oda','ode','ods','oes','oma','oms','ose','ova','sad','sae','sax','sea','sev','sex','sod','som','sox','vas','vex','voe','vox','ados','aves','avos','axed','axes','dame','dams','demo','deva','devs','does','dome','doms','dosa','dose','dove','emos','exam','made','mads','maes','mead','meds','mesa','moas','mode','mods','move','moxa','odas','odea','odes','omas','oxes','sade','same','save','seam','soda','soma','some','vase','voes','dames','demos','devas','domes','doves','exams','maxed','maxes','meads','modes','moved','moves','moxas','oaves','saved','soave','vadose','vamose','vamosed'};\r\nind = randi(3);\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'   D       D   ';'   D       D   ';' D   t   t   D '];\r\n\t\tmax_score_corr = 37;\r\n\t\tmax_word_corr = {'vox'};\r\n\tcase 2\r\n\t\tmult = ['T   d     d   T';'  D   d d   D  ';'   d       d   ';'T   d     d   T';'   d       d   ';'  D   d d   D  '];\r\n\t\tmax_score_corr = 25;\r\n\t\tmax_word_corr = {'vox'};\r\n\tcase 3\r\n\t\tmult = [' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'  T   d d   T  ';' T d t   t d T ';'D  t d   d t  D'];\r\n\t\tmax_score_corr = 35;\r\n\t\tmax_word_corr = {'voxel'};\r\nend\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'zoologist'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aehcmdi'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aced','ache','acid','acme','adze','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cazh','cedi','chad','chai','cham','chem','chez','chia','chid','dace','dame','daze','dice','dime','each','emic','hade','haed','haem','hame','haze','head','hide','hied','iced','idea','idem','mace','mach','made','maid','maze','mead','mech','mica','mice','zeda','ached','aimed','amice','amide','azide','chide','chime','demic','hazed','hemic','maced','mache','maize','mazed','media','medic','miche','chimed','haemic','miched','zaideh'};\r\nwords{2} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','camo','cedi','chad','chai','cham','chao','chem','chia','chid','ciao','coda','code','coed','coma','come','dace','dame','deco','demo','dice','dime','dome','each','echo','emic','hade','haed','haem','hame','head','hide','hied','hoed','homa','home','iced','idea','idem','mace','mach','made','maid','mead','mech','mica','mice','mode','modi','oche','odah','odea','odic','ohed','ohia','ached','aimed','amice','amide','amido','cameo','chemo','chiao','chide','chime','comae','demic','demoi','domic','hemic','homed','homie','maced','mache','macho','mahoe','media','medic','miche','mocha','mochi','ohmic','chimed','codeia','cohead','comade','haemic','hemoid','medico','miched','modica','haemoid'};\r\nwords{3} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','camo','cedi','chad','chai','cham','chao','chem','chia','chid','ciao','coda','code','coed','coma','come','dace','dame','deco','demo','dice','dime','dome','each','echo','emic','hade','haed','haem','hame','head','hide','hied','hoed','homa','home','iced','idea','idem','mace','mach','made','maid','mead','mech','mica','mice','mode','modi','oche','odah','odea','odic','ohed','ohia','ached','aimed','amice','amide','amido','cameo','chemo','chiao','chide','chime','comae','demic','demoi','domic','hemic','homed','homie','maced','mache','macho','mahoe','media','medic','miche','mocha','mochi','ohmic','chimed','codeia','cohead','comade','haemic','hemoid','medico','miched','modica','haemoid'};\r\nwords{4} = {'aced','ache','acid','acme','ahed','ahem','aide','alec','alme','amid','amie','cade','cadi','caid','calm','came','cami','cedi','ceil','chad','chai','cham','chem','chia','chid','clad','clam','dace','dahl','dale','dame','deal','deil','deli','dhal','dial','dice','diel','dime','each','elhi','emic','hade','haed','haem','hail','hale','halm','hame','head','heal','heil','held','helm','hide','hied','hila','iced','idea','idem','idle','ilea','lace','lade','laic','laid','lame','lead','lech','lice','lich','lied','lima','lime','mace','mach','made','maid','mail','male','mead','meal','mech','meld','mica','mice','mild','mile','ached','ailed','aimed','alcid','almeh','amice','amide','camel','chela','chide','chiel','child','chile','chime','clade','claim','clime','decal','demic','email','haled','halid','hemal','hemic','ideal','ileac','laced','laich','lamed','leach','limed','maced','mache','macle','maile','malic','medal','media','medic','melic','miche','milch','calmed','chield','childe','chimed','chimla','haemic','hailed','halide','heliac','hiemal','lamedh','macled','mailed','malice','medial','miched','camelid','claimed','decimal','declaim','medical'};\r\nwords{5} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','camo','cedi','chad','chai','cham','chao','chem','chia','chid','ciao','coda','code','coed','coma','come','dace','dame','deco','demo','dice','dime','dome','each','echo','emic','hade','haed','haem','hame','head','hide','hied','hoed','homa','home','iced','idea','idem','mace','mach','made','maid','mead','mech','mica','mice','mode','modi','oche','odah','odea','odic','ohed','ohia','ached','aimed','amice','amide','amido','cameo','chemo','chiao','chide','chime','comae','demic','demoi','domic','hemic','homed','homie','maced','mache','macho','mahoe','media','medic','miche','mocha','mochi','ohmic','chimed','codeia','cohead','comade','haemic','hemoid','medico','miched','modica','haemoid'};\r\nwords{6} = {'aced','ache','acid','acme','aged','ahed','ahem','aide','amid','amie','cade','cadi','cage','caid','came','cami','cedi','chad','chai','cham','chem','chia','chid','dace','dame','dice','dime','each','egad','emic','gach','gadi','gaed','game','gied','hade','haed','haem','hame','head','hide','hied','iced','idea','idem','mace','mach','made','mage','magi','maid','mead','mech','mega','mica','mice','ached','aimed','amice','amide','cadge','caged','chide','chime','demic','gamed','gamic','hemic','image','maced','mache','magic','media','medic','miche','midge','chimed','degami','gached','haemic','imaged','miched'};\r\nwords{7} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cedi','chad','chai','cham','chem','chia','chid','dace','dame','dice','dime','each','emic','hade','haed','haem','hame','head','hide','hied','iced','idea','idem','imid','mace','mach','made','maid','mead','mech','mica','mice','midi','ached','aimed','amice','amici','amide','chide','chime','demic','hemic','imide','maced','mache','media','medic','medii','miche','amidic','chimed','haemic','miched'};\r\nwords{8} = {'aced','aces','ache','acid','acme','ahed','ahem','ahis','aide','aids','aims','amid','amie','amis','asci','cade','cadi','cads','caid','came','cami','cams','case','cash','cedi','chad','chai','cham','chem','chia','chid','chis','dace','dahs','dais','dame','dams','dash','desi','dice','dies','dime','dims','disc','dish','each','edhs','emic','hade','haed','haem','haes','hame','hams','head','hems','hide','hied','hies','hims','iced','ices','ichs','idea','idem','ides','mace','mach','macs','made','mads','maes','maid','mash','mead','mech','meds','mesa','mesh','mica','mice','mics','mids','mise','sade','sadi','said','same','scad','scam','seam','semi','shad','sham','shea','shed','shim','sice','side','sidh','sima','ached','aches','acids','acmes','aides','aimed','amice','amide','amids','amies','asdic','ashed','aside','cades','cadis','caids','cames','camis','cased','cedis','chads','chais','chams','chase','chasm','chems','chias','chide','chime','daces','dames','dashi','deash','deism','demic','deshi','dices','dimes','disme','emics','hades','haems','hames','heads','hemic','hides','ideas','maced','maces','mache','machs','maids','meads','mechs','media','medic','mesic','micas','miche','sadhe','saice','shade','shame','shied','sidhe','amices','amides','camise','cashed','chaise','chased','chiasm','chides','chimed','chimes','emdash','haemic','maches','mashed','mashie','medias','medics','miched','miches','sachem','samech','schema','shamed','simcha','chamise','chasmed'};\r\nwords{9} = {'aced','ache','acid','acme','adit','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cate','cedi','chad','chai','cham','chat','chem','chia','chid','chit','cite','dace','dame','date','dice','diet','dime','dita','dite','each','eath','echt','edit','emic','emit','etch','etic','hade','haed','haem','haet','hame','hate','head','heat','hide','hied','iced','idea','idem','itch','item','mace','mach','made','maid','mate','math','mead','meat','mech','meta','meth','mica','mice','mite','tace','tach','tame','team','tech','thae','them','tide','tied','time','ached','acted','admit','aimed','aitch','amice','amide','cadet','cheat','chide','chime','cited','death','demic','demit','dicta','ditch','edict','ethic','hated','hemic','maced','mache','match','mated','media','medic','miche','tache','tamed','teach','theca','timed','chimed','dacite','detach','haemic','itched','miched','hematic','matched'};\r\nind = randi(3);\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'   D       D   ';' d   T   T   d ';'   D       D   ';' D   t   t   D ';'  d   t t   d  ';' T   d   d   T '];\r\n\t\tmax_score_corr = 117;\r\n\t\tmax_word_corr = {'haemoid'};\r\n\tcase 2\r\n\t\tmult = ['T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T'];\r\n\t\tmax_score_corr = 28;\r\n\t\tmax_word_corr = {'medico'};\r\n\tcase 3\r\n\t\tmult = ['T   d     d   T';' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'  T   d d   T  ';' T d t   t d T ';'D  t d   d t  D';' T  d t t d  T ';'T   d     d   T'];\r\n\t\tmax_score_corr = 63;\r\n\t\tmax_word_corr = {'decimal'};\r\nend\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))","published":true,"deleted":false,"likes_count":2,"comments_count":6,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2015-03-20T18:02:10.000Z","rescore_all_solutions":false,"group_id":40,"created_at":"2015-03-20T01:53:26.000Z","updated_at":"2026-04-17T16:57:25.000Z","published_at":"2015-03-20T01:53:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem integrates components of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3084-scrabble-scores-11\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eScrabble Scores - 11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eScrabble Scores - 12\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Here, you are provided an existing word on the board from which you will play a word. The letter can reside anywhere (first to last) within the existing word and within the word that you are playing. In addition, multipliers from the board are provided. Write a function to find the highest scoring word, provided any letter from the existing word that you are building off of, the letters on your tray, and the multipliers (provided in specific locations; see below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRather than having to test all the possible permutations against a dictionary, you will be provided a double-level cell array of strings containing all possible words based each starting letter in the existing word and the letters on your tray (a cell array for each letter in the existing word). (The word lists purposefully omit smaller words to prevent the test cases from being too large.) In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou will be provided a multiplier character array that represents the fifteen possible squares that can be played on for each letter in the existing word, ranging from seven above each existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below each existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th (column) position. The array will have the same number of rows as the length of the existing word (which is located along the middle of the array). The multipliers are the same as in previous problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ * D: double word\\n * T: triple word\\n * Q: quadruple word\\n * d: double letter\\n * t: triple letter\\n * q: quadruple letter]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe center multiplier square will be left blank, since it's already covered by a tile.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRelated problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem: 12 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWord score optimization (first word)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52709,"title":"Easy Sequences 19: Length of Prime-sided Rectangle with Maximum Area","description":"A prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-sided rectangles whose areas are less than or equal to 25:\r\n                                       \r\nGiven an area limit 'n', find the length (i.e. the longer side if sides are unequal) of the prime-sided rectangle, with the largest area less than or equal to 'n'. \r\nIn the figure above the rectangle with the maximum area is the 5x5 square. Therefore for n = 25 the output should be 5. For n = 100, the output should be 19, since 19 x 5 = 95 \u003c 100. No other combination of prime sides will produce an area greater than 95 for area \u003c= 100.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 492px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-sided rectangles whose areas are less than or equal to 25:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 318px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                       \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"390\" height=\"312\" style=\"vertical-align: baseline;width: 390px;height: 312px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; text-decoration: underline; text-decoration-line: underline; \"\u003earea limit\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e 'n', find the length\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e (i.e. the longer side if sides are unequal) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eof the prime-sided rectangle, with the largest area less than or equal to 'n'. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIn the figure above the rectangle with the maximum area is the 5x5 square. Therefore for n = 25 the output should be 5. For n = 100, the output should be 19, since 19 x 5 = 95 \u0026lt; 100. No other combination of prime sides will produce an area greater than 95 for area \u0026lt;= 100.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function length = maxPrimeRec(n)\r\n    l \u003e= w; % l is the larger side\r\n    isprime(l) == 1; isprime(w) == 1; % both sides are primes\r\n    l*w \u003c= n; % area should be less than or equal to n\r\n    length = 'l such that l*w is the largest area possible';\r\nend","test_suite":"%%\r\nn = 25;\r\nl_correct = 5;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = 100;\r\nl_correct = 19;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nns = 1000:10000;\r\nls = arrayfun(@(n) maxPrimeRec(n),ns);\r\nys = [sum(ls) ls(7500:7529)];\r\nys_correct = [10870381 2833 2833 2833 2833 773 773 773 4253 181 181 127 127 2837 2837 ... \r\n    2837 2837 2837 2837 2837 4259 1217 1217 1217 4261 4261 4261 4261 4261 4261 4261];\r\nassert(isequal(ys,ys_correct))\r\n%%\r\nn = 1000000;\r\nl_correct = 1321;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = 100000000;\r\nl_correct = 77101;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax);\r\nl_correct = 715827881;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax)*109 - 1000000009;\r\nl_correct = 7574033;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax)*109 + 1000000009;\r\nl_correct = 2156657959;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax-1)*1111;\r\nl_correct = 9920021;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nfiletext = fileread('maxPrimeRec.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2021-09-15T07:53:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-14T21:01:26.000Z","updated_at":"2026-04-22T11:19:13.000Z","published_at":"2021-09-15T07:53:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-sided rectangles whose areas are less than or equal to 25:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"312\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"390\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003earea limit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e 'n', find the length\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e. the longer side if sides are unequal) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eof the prime-sided rectangle, with the largest area less than or equal to 'n'. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the figure above the rectangle with the maximum area is the 5x5 square. Therefore for n = 25 the output should be 5. For n = 100, the output should be 19, since 19 x 5 = 95 \u0026lt; 100. No other combination of prime sides will produce an area greater than 95 for area \u0026lt;= 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44779,"title":"Don't be mean.  Be nice!","description":"For this problem, you will be given a range of single digits R, and a separate number K.  You job is to calculate the mean of all K digit numbers that contain only distinct digits from the range R.\r\n\r\nFor example, if R=1:4 and K=2, you should calculate the mean of 12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, and 43, as these are all of the two digit numbers that contain two distinct numbers from the range 1:4.  The numbers 11, 22, 33 and 44 are not included, as they contain multiple copies of the same digit.\r\n\r\nIf 0 is included in R, it should not be a leading digit for any of the numbers, so an R of 0:2 and K=3 would include:\r\n\r\n* 120\r\n* 210\r\n* 201\r\n* 102\r\n\r\nbut not 012 or 021 for the purposes of this calculation.\r\n\r\nYou can assume that R will always have at least K digits, and there will be no repeating digits in R.","description_html":"\u003cp\u003eFor this problem, you will be given a range of single digits R, and a separate number K.  You job is to calculate the mean of all K digit numbers that contain only distinct digits from the range R.\u003c/p\u003e\u003cp\u003eFor example, if R=1:4 and K=2, you should calculate the mean of 12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, and 43, as these are all of the two digit numbers that contain two distinct numbers from the range 1:4.  The numbers 11, 22, 33 and 44 are not included, as they contain multiple copies of the same digit.\u003c/p\u003e\u003cp\u003eIf 0 is included in R, it should not be a leading digit for any of the numbers, so an R of 0:2 and K=3 would include:\u003c/p\u003e\u003cul\u003e\u003cli\u003e120\u003c/li\u003e\u003cli\u003e210\u003c/li\u003e\u003cli\u003e201\u003c/li\u003e\u003cli\u003e102\u003c/li\u003e\u003c/ul\u003e\u003cp\u003ebut not 012 or 021 for the purposes of this calculation.\u003c/p\u003e\u003cp\u003eYou can assume that R will always have at least K digits, and there will be no repeating digits in R.\u003c/p\u003e","function_template":"function y = dont_be_mean(R,k)\r\n  y = k.^R;\r\nend","test_suite":"%%\r\nR=1:4;k=2;y_correct = 27.5;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=0:8;k=3;y_correct = 493.3125;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=[1 2 4 6 8];k=4;y_correct = 4666.2;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=[2 8 6 7 4 5];k=1;y_correct = 5.33333333333333;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=0:9;\r\ny=0;\r\nfor k=1:8\r\n    y=y+dont_be_mean(R,k);\r\nend\r\ny_correct=61042519.44444444;\r\nassert(abs(y-y_correct)\u003c1e-3)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":68,"created_at":"2018-11-07T18:32:08.000Z","updated_at":"2026-04-28T00:31:30.000Z","published_at":"2018-11-07T18:32:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, you will be given a range of single digits R, and a separate number K. You job is to calculate the mean of all K digit numbers that contain only distinct digits from the range R.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if R=1:4 and K=2, you should calculate the mean of 12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, and 43, as these are all of the two digit numbers that contain two distinct numbers from the range 1:4. The numbers 11, 22, 33 and 44 are not included, as they contain multiple copies of the same digit.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf 0 is included in R, it should not be a leading digit for any of the numbers, so an R of 0:2 and K=3 would include:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e210\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e201\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e102\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebut not 012 or 021 for the purposes of this calculation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can assume that R will always have at least K digits, and there will be no repeating digits in R.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1238,"title":"PACMAT - Ghosts Random; 3 Lives","description":"The Classic PACMAN game brought to Cody.\r\n\r\nPACMAT Ghosts Random requires clearing the board of Yellow Dots while not bumping into the randomly moving ghosts in 3 lives. Adjacent Ghosts will capture PACMAT.  Ghosts do not use the tunnel. On Ghost capture everyone gets reset.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_300.jpg\u003e\u003e\r\n\r\nTo aid in development of your routine, a PACMAT_Ghosts.m file that creates a video has been posted at \u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_Ghosts_001.m PACMAT_Ghosts_001.m\u003e. (Right click, 'save link as'). Using patches (not sprites).\r\n\r\n\r\n\u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_G001_SNC365_20_video.mp4 Alfonso PACMAT Random Ghost Video\u003e  (MP4: Left click and Windows Media Player)\r\n\r\n\u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_G001_video_ANC.mp4 Alfonso's Enhanced Ghost Avoider\u003e (MP4)\r\n\r\n\r\nThe reference solution uses Alfonso's Local Optimum Algorithm with a Catch.\r\n\r\n*Inputs:* Map   Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u003e2=Ghost\r\n\r\n*Output:* Direction  Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\r\n\r\n*Scoring:* Total # of Moves to Clear the Yellow Dots +(LivesRemaining-3)*100\r\n\r\n\r\n*Near Future:* Ghosts will get brighter.\r\n\r\n*Future:* Player will be Team Ghosts versus PACMAT_BOT","description_html":"\u003cp\u003eThe Classic PACMAN game brought to Cody.\u003c/p\u003e\u003cp\u003ePACMAT Ghosts Random requires clearing the board of Yellow Dots while not bumping into the randomly moving ghosts in 3 lives. Adjacent Ghosts will capture PACMAT.  Ghosts do not use the tunnel. On Ghost capture everyone gets reset.\u003c/p\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_300.jpg\"\u003e\u003cp\u003eTo aid in development of your routine, a PACMAT_Ghosts.m file that creates a video has been posted at \u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Ghosts_001.m\"\u003ePACMAT_Ghosts_001.m\u003c/a\u003e. (Right click, 'save link as'). Using patches (not sprites).\u003c/p\u003e\u003cp\u003e\u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_G001_SNC365_20_video.mp4\"\u003eAlfonso PACMAT Random Ghost Video\u003c/a\u003e  (MP4: Left click and Windows Media Player)\u003c/p\u003e\u003cp\u003e\u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_G001_video_ANC.mp4\"\u003eAlfonso's Enhanced Ghost Avoider\u003c/a\u003e (MP4)\u003c/p\u003e\u003cp\u003eThe reference solution uses Alfonso's Local Optimum Algorithm with a Catch.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e Map   Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u003e2=Ghost\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Direction  Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Total # of Moves to Clear the Yellow Dots +(LivesRemaining-3)*100\u003c/p\u003e\u003cp\u003e\u003cb\u003eNear Future:\u003c/b\u003e Ghosts will get brighter.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFuture:\u003c/b\u003e Player will be Team Ghosts versus PACMAT_BOT\u003c/p\u003e","function_template":"function  [newdir]=pacmat(map)\r\n newdir=randi(4);\r\nend","test_suite":"%%\r\nfeval(@assignin,'caller','score',2000);\r\n%%\r\nmax_moves=2000; % Fixed path expect to succeed by 600 moves\r\n\r\nmap=[...\r\n      repmat('a',1,28);\r\n      'accccccccccccaacccccccccccca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acccccccccccccccccccccccccca';\r\n      'acaaaacaacaaaaaaaacaacaaaaca';\r\n      'acaaaacaacaaaaaaaacaacaaaaca';\r\n      'accccccaaccccaaccccaacccccca';\r\n      'aaaaaacaaaaabaabaaaaacaaaaaa';\r\n      'aaaaaacaaaaabaabaaaaacaaaaaa';\r\n      'aaaaaacaabbbbbbbbbbaacaaaaaa';\r\n      'aaaaaacaabaaabbaaabaacaaaaaa';\r\n      'aaaaaacaabalbbbblabaacaaaaaa';\r\n      'bbbbbbcbbbabbbbbbabbbcbbbbbb';\r\n      'aaaaaacaabalbbbblabaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'aaaaaacaabbbbbbbbbbaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'accccccccccccaacccccccccccca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acccaacccccccbdcccccccaaccca';\r\n      'aaacaacaacaaaaaaaacaacaacaaa';\r\n      'aaacaacaacaaaaaaaacaacaacaaa';\r\n      'accccccaaccccaaccccaacccccca';\r\n      'acaaaaaaaaaacaacaaaaaaaaaaca';\r\n      'acaaaaaaaaaacaacaaaaaaaaaaca';\r\n      'acccccccccccccccccccccccccca';\r\n      repmat('a',1,28);];\r\n  \r\n  map=map-'b';\r\n  [nr, nc]=size(map);\r\n\r\n  gmap=map; % Map used by ghosts to simplify PAC Capture\r\n  gmap(15,6)=-1; %No tunnel ghosts\r\n  gmap(15,26)=-1;\r\n\r\n\r\n  mapdelta=[-1 nr 1 -nr]; % Valid as long as not on an edge\r\n  gmovxy=[0 -1;1 0;0 1;-1 0];\r\n\r\n  tunnel=find(map(:,1)==0); % tunnelptr\r\n  tunnel=[tunnel tunnel+nr*(nc-1)]; % Entrance/Exit Tunnel\r\n\r\n  [pmr, pmc]=find(map==2); % pi 24 row  pj 15 column of map\r\n   ptrpac=find(map==2);\r\n\r\n  ptrpac=find(map==2);\r\n  ptrpac_start=ptrpac;\r\n  ptrg_start=find(map\u003e2);\r\n  map(ptrg_start)=[10 20 30 40];% use deal?\r\n  [gstartx, gstarty]=find(map\u003e2);\r\n  \r\n  lives=3; % Lives\r\n  movepac=0;\r\n\r\nwhile lives \u0026\u0026 any(mod(map(:),10)==1) \u0026\u0026 movepac\u003cmax_moves\r\n movepac=movepac+1;\r\n\r\n [curdir]=pacmat(map);\r\n %if curdir==0,continue;end % bug 020213\r\n [pmr, pmc]=find(map==2);\r\nif curdir\u003e0 % bug fix 020213\r\n if map(ptrpac+mapdelta(curdir))==-1\r\n  % Do nothing - Ran into a Wall\r\n elseif map(ptrpac+mapdelta(curdir))\u003e2 % ran into ghost\r\n  map(ptrpac)=0; % remove PAC from the board\r\n  lives=lives-1;\r\n  if lives==0,break;end\r\n  % reset the board\r\n  [ptrgx, ptrgy]=find(map\u003e2);\r\n  ptrg=find(map\u003e2);\r\n  map(ptrg)=mod(map(ptrg),10);\r\n  map(ptrpac_start)=2;\r\n  map(ptrg_start)=[10 20 30 40];\r\n  ptrpac=find(map==2);\r\n  continue;\r\n else % legal move\r\n  map(ptrpac)=0; % Eat Dot and clear PAC\r\n  ptrpac=ptrpac+mapdelta(curdir);\r\n  if ptrpac==tunnel(1),ptrpac=tunnel(2)-nr;end\r\n  if ptrpac==tunnel(2),ptrpac=tunnel(1)+nr;end\r\n  map(ptrpac)=2;\r\n end\r\nend % curdir\u003e0 bug fix 020213\r\n\r\n% Ghosts\r\n for i=1:4\r\n\r\n  gmap=map;\r\n  gmap(15,6)=-1; %No tunnel ghosts\r\n  gmap(15,26)=-1;\r\n  dot=false;\r\n  [gptrx, gptry]=find(map==10*i);\r\n  gidx=find(map==10*i);\r\n  if isempty(gidx)\r\n   [gptrx, gptry]=find(map==10*i+1); % ghost must be on a dot\r\n   gidx=find(map==10*i+1);\r\n   dot=true;\r\n  end\r\n\r\n% Find valid ghost moves using gmap\r\n% mapdelta=[-1 nr 1 -nr]; \r\n  gmov=find(map(gidx+mapdelta)==2); % adjacent to PACMAT\r\n  if ~isempty(gmov) % PAC adjacent\r\n   lives=lives-1;\r\n   if lives==0,break;end\r\n   % reset the board\r\n   [pmr, pmc]=find(map==2); % PACMAT erase coords\r\n   map(map==2)=0;\r\n      \r\n   [ptrgx, ptrgy]=find(map\u003e2);\r\n   ptrg=find(map\u003e2);\r\n   map(ptrg)=mod(map(ptrg),10);\r\n   map(ptrpac_start)=2;\r\n   map(ptrg_start)=[10 20 30 40];\r\n   ptrpac=find(map==2);     \r\n   break; % Ghost move loop\r\n      \r\n  else % Random Ghost move  gmap avoids tunnel \r\n   gmov=intersect(find(gmap(gidx+mapdelta)\u003c10),find(gmap(gidx+mapdelta)\u003e-1)); \r\n   if ~isempty(gmov) % valid g move : ghost may not stand on ghost\r\n    gmov=gmov(randi(length(gmov)));\r\n    map(gptrx,gptry)=mod(map(gptrx,gptry),10);\r\n    map(gidx+mapdelta(gmov))=map(gidx+mapdelta(gmov))+10*i;     \r\n   end\r\n  end\r\n  \r\n end % i ghost moves\r\nend % while alive\r\n\r\nfprintf('moves %i\\n',movepac)\r\n\r\nassert(lives\u003e0,sprintf('Three Captures\\n'))\r\nassert(~isempty(any(mod(map(:),10)==1)),sprintf('Moves\\n',movepac)) % Test Move Timeout\r\n\r\n\r\nfeval( @assignin,'caller','score',floor(min( 2000,300-100*lives+movepac )) );\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2013-02-02T18:27:37.000Z","rescore_all_solutions":false,"group_id":33,"created_at":"2013-02-01T04:44:13.000Z","updated_at":"2026-04-23T17:56:11.000Z","published_at":"2013-02-01T06:15:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Classic PACMAN game brought to Cody.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT Ghosts Random requires clearing the board of Yellow Dots while not bumping into the randomly moving ghosts in 3 lives. Adjacent Ghosts will capture PACMAT. Ghosts do not use the tunnel. On Ghost capture everyone gets reset.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo aid in development of your routine, a PACMAT_Ghosts.m file that creates a video has been posted at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Ghosts_001.m\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT_Ghosts_001.m\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. (Right click, 'save link as'). Using patches (not sprites).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_G001_SNC365_20_video.mp4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAlfonso PACMAT Random Ghost Video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MP4: Left click and Windows Media Player)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_G001_video_ANC.mp4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAlfonso's Enhanced Ghost Avoider\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MP4)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe reference solution uses Alfonso's Local Optimum Algorithm with a Catch.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Map Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u0026gt;2=Ghost\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Direction Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Total # of Moves to Clear the Yellow Dots +(LivesRemaining-3)*100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNear Future:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Ghosts will get brighter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFuture:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Player will be Team Ghosts versus 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\"}]}"},{"id":58807,"title":"Array size along k-th dimension","description":"Given an n-dimensional array M, find the size of M along the k-th dimension (1 \u003c= k \u003c= n), without using size(), height() or width(). You may ignore trailing singleton dimensions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-dimensional array \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eM\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find the size of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eM\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e along the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-th dimension (1 \u0026lt;= \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u0026lt;= \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e), without using \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003esize()\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eheight()\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ewidth()\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. You may ignore trailing singleton dimensions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = dimlen(M, k)\r\n    \r\nend","test_suite":"while true\r\n    d = 5 + randi(10)\r\n    s = randi(100);\r\n    s1 = 1 + randi(4, 1, d);\r\n    s2 = 1 + randi(4, 1, d);\r\n    s3 = 1 + randi(4, 1, d);\r\n    if prod(s1) \u003e 1e6 || prod(s2) \u003e 1e6 | prod(s3) \u003e 1e6\r\n        continue\r\n    end\r\n    M1 = ones(s1);\r\n    M2 = NaN(s2);\r\n    M3 = zeros(s3);\r\n    M4 = eye(s, 1);\r\n    M5 = eye(1, s);\r\n    break\r\nend\r\n\r\n%%\r\nfiletext = fileread('dimlen.m');\r\nassert(~contains(filetext, \"size\"),   \"size is forbidden.\"  );\r\nassert(~contains(filetext, \"height\"), \"height is forbidden.\");\r\nassert(~contains(filetext, \"width\"),  \"width is forbidden.\" );\r\n\r\n%%\r\nfor k = 1:d\r\n    assert(isequal(dimlen(M1, k), size(M1, k)))\r\n    assert(isequal(dimlen(M2, k), size(M2, k)))\r\n    assert(isequal(dimlen(M3, k), size(M3, k)))\r\nend\r\n\r\n%%\r\nassert(isequal(dimlen(M4, 1), size(M4, 1)))\r\nassert(isequal(dimlen(M5, 2), size(M5, 2)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":332395,"edited_by":332395,"edited_at":"2023-08-04T20:37:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2023-08-04T20:37:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-04T20:20:03.000Z","updated_at":"2026-04-24T14:25:49.000Z","published_at":"2023-08-04T20:37:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eGiven an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e-dimensional array \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, find the size of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e along the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e-th dimension (1 \u0026lt;= \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e \u0026lt;= \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e), without using \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esize()\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eheight()\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewidth()\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e. You may ignore trailing singleton dimensions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58409,"title":"Calculate the volume of the intersection of two balls","description":"Consider two balls (solid spheres) in , with radius  and  respectively. Suppose that the distance between the centers of the two balls is . Please find the volume of the intersection of the two balls.\r\nIllustration:\r\n\r\n[X, Y, Z] = sphere(36);\r\nr1 = 1;\r\nr2 = 0.8;\r\nc2 = [0.6 -0.8 0];\r\nsurf(X * r1, Y * r1, Z * r1)\r\nhold on\r\nsurf(X * r2 + c2(1), Y * r2 + c2(2), Z * r2 + c2(3))\r\nhold off\r\naxis equal\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 328.438px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 164.219px; transform-origin: 407.5px 164.219px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21.4167px; text-align: left; transform-origin: 384.5px 21.4167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider two balls (solid spheres) in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"19\" style=\"width: 19px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, with radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"20\" style=\"width: 40px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"20\" style=\"width: 40px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e respectively. Suppose that the distance between the centers of the two balls is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"37.5\" height=\"18\" style=\"width: 37.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. Please find the volume of the intersection of the two balls.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIllustration:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 183.938px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404.5px 91.9688px; transform-origin: 404.5px 91.9688px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[X, Y, Z] = sphere(36);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003er1 = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003er2 = 0.8;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ec2 = [0.6 -0.8 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003esurf(X * r1, Y * r1, Z * r1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ehold \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eon\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003esurf(X * r2 + c2(1), Y * r2 + c2(2), Z * r2 + c2(3))\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ehold \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eoff\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eaxis \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eequal\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function V = Vlens(r1, r2, d)\r\n    \r\nend","test_suite":"%%\r\nassert(abs(Vlens(sqrt(3), sqrt(3), 12*cos(pi/9)*sin(pi/9) - sqrt(12)*(1 - 2*sin(pi/9)^2)) - sqrt(12)*pi) \u003c 1e-13)\r\n\r\n%%\r\nassert(abs(Vlens(1, 2, 0) - 4*pi/3) \u003c 1e-13)\r\nassert(abs(Vlens(1, 2, 0.5) - 4*pi/3) \u003c 1e-13)\r\nassert(abs(Vlens(1, 2, 1) - 4*pi/3) \u003c 1e-13)\r\nassert(abs(Vlens(1, 2, 1.5) - 3.239767424014474) \u003c 1e-13)\r\nassert(abs(Vlens(1, 2, 2) - 1.701696020694471) \u003c 1e-13)\r\nassert(abs(Vlens(1, 2, 2.5) - 0.477783882733448) \u003c 1e-13)\r\nassert(isequal(Vlens(1, 2, 3), 0))\r\n\r\n%% \r\nassert(abs(Vlens(3, 4, 5) - 19.268434942017397) \u003c 1e-13)\r\nassert(abs(Vlens(1, 0.8, 1) - 0.750631204697721) \u003c 1e-13)\r\nassert(isequal(Vlens(10, 0, 2), 0))\r\nassert(isequal(Vlens(0, 5, 0), 0))\r\nassert(abs(Vlens((1 + sqrt(5))/2, exp(1), pi) - 3.982801259482478) \u003c 1e-13)\r\nassert(abs(Vlens(17, 89, 105) - 44.214176608022065) \u003c 1e-13)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":332395,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-06-09T15:45:44.000Z","updated_at":"2026-04-24T14:37:56.000Z","published_at":"2023-06-09T15:45:44.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider two balls (solid spheres) in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mathbb{R}^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, with radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_1 \\\\ge 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_2 \\\\ge 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e respectively. Suppose that the distance between the centers of the two balls is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ed \\\\ge 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Please find the volume of the intersection of the two balls.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIllustration:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[X, Y, Z] = sphere(36);\\nr1 = 1;\\nr2 = 0.8;\\nc2 = [0.6 -0.8 0];\\nsurf(X * r1, Y * r1, Z * r1)\\nhold on\\nsurf(X * r2 + c2(1), Y * r2 + c2(2), Z * r2 + c2(3))\\nhold off\\naxis equal]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61174,"title":"[Master Regular Expression] String To Integer","description":"Implement the myAtoi(string s) function, which converts a string to a 32-bit signed integer.\r\nThe algorithm for myAtoi(string s) is as follows:\r\n \r\nWhitespace: Ignore any leading whitespace (\" \").\r\n \r\nSignedness: Determine the sign by checking if the next character is '-' or '+', assuming positivity if neither present.\r\n \r\nConversion: Read the integer by skipping leading zeros until a non-digit character is encountered or the end of the string is reached. If no digits were read, then the result is 0.\r\n \r\nRounding: If the integer is out of the 32-bit signed integer range [-231, 231 - 1], then round the integer to remain in the range. Specifically, integers less than -231 should be rounded to -231, and integers greater than 231     - 1 should be rounded to 231 - 1.\r\nReturn the integer as the final result.\r\n \r\nExample 1:\r\nInput: s = \"42\"\r\nOutput: 42\r\nExplanation:\r\nThe underlined characters are what is read in and the caret is the current reader position.\r\nStep 1: \"42\" (no characters read because there is no leading whitespace)\r\n         ^\r\nStep 2: \"42\" (no characters read because there is neither a '-' nor '+')\r\n         ^\r\nStep 3: \"42\" (\"42\" is read in)\r\n           ^\r\nExample 2:\r\nInput: s = \" -042\"\r\nOutput: -42\r\nExplanation:\r\nStep 1: \"   -042\" (leading whitespace is read and ignored)\r\n            ^\r\nStep 2: \"   -042\" ('-' is read, so the result should be negative)\r\n             ^\r\nStep 3: \"   -042\" (\"042\" is read in, leading zeros ignored in the result)\r\n               ^\r\nExample 3:\r\nInput: s = \"1337c0d3\"\r\nOutput: 1337\r\nExplanation:\r\nStep 1: \"1337c0d3\" (no characters read because there is no leading whitespace)\r\n         ^\r\nStep 2: \"1337c0d3\" (no characters read because there is neither a '-' nor '+')\r\n         ^\r\nStep 3: \"1337c0d3\" (\"1337\" is read in; reading stops because the next character is a non-digit)\r\n             ^\r\nExample 4:\r\nInput: s = \"0-1\"\r\nOutput: 0\r\nExplanation:\r\nStep 1: \"0-1\" (no characters read because there is no leading whitespace)\r\n         ^\r\nStep 2: \"0-1\" (no characters read because there is neither a '-' nor '+')\r\n         ^\r\nStep 3: \"0-1\" (\"0\" is read in; reading stops because the next character is a non-digit)\r\n          ^\r\nExample 5:\r\nInput: s = \"words and 987\"\r\nOutput: 0\r\nExplanation:\r\nReading stops at the first non-digit character 'w'.\r\n \r\nConstraints:\r\n \r\n0 \u003c= s.length \u003c= 200\r\n \r\ns consists of English letters (lower-case and upper-case), digits (0-9), ' ', '+', '-', and '.'.\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 2070.94px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 1035.46px; transform-origin: 408px 1035.47px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eImplement the myAtoi(string s) function, which converts a string to a 32-bit signed integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe algorithm for myAtoi(string s) is as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWhitespace\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Ignore any leading whitespace (\" \").\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSignedness\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Determine the sign by checking if the next character is '-' or '+', assuming positivity if neither present.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConversion\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Read the integer by skipping leading zeros until a non-digit character is encountered or the end of the string is reached. If no digits were read, then the result is 0.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 30.65px; text-align: left; transform-origin: 363px 30.6562px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRounding\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: If the integer is out of the 32-bit signed integer range [-2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e31\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, 2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e31\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - 1], then round the integer to remain in the range. Specifically, integers less than -2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e31\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should be rounded to -2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e31\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and integers greater than 2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e31\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e     - 1 should be rounded to 2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e31\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - 1.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn the integer as the final result.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 1:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e s = \"42\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 42\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe underlined characters are what is read in and the caret is the current reader position.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: \"42\" (no characters read because there is no leading whitespace)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: \"42\" (no characters read because there is neither a '-' nor '+')\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 3: \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e42\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\" (\"42\" is read in)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e           \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e s = \" -042\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e -42\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-042\" (leading whitespace is read and ignored)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e-\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e042\" ('-' is read, so the result should be negative)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e             \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 3: \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e042\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\" (\"042\" is read in, leading zeros ignored in the result)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e               \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 3:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e s = \"1337c0d3\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 1337\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: \"1337c0d3\" (no characters read because there is no leading whitespace)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: \"1337c0d3\" (no characters read because there is neither a '-' nor '+')\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 3: \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e1337\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ec0d3\" (\"1337\" is read in; reading stops because the next character is a non-digit)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e             \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 4:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e s = \"0-1\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: \"0-1\" (no characters read because there is no leading whitespace)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: \"0-1\" (no characters read because there is neither a '-' nor '+')\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 3: \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-1\" (\"0\" is read in; reading stops because the next character is a non-digit)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e          \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 5:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e s = \"words and 987\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReading stops at the first non-digit character 'w'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraints:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e0 \u0026lt;= s.length \u0026lt;= 200\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003es consists of English letters (lower-case and upper-case), digits (0-9), ' ', '+', '-', and '.'.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = solution(s)\r\n\r\nend","test_suite":"%%\r\ns = '42';\r\nresult = 42;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '   -042';\r\nresult = -42;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '1337c0d3';\r\nresult = 1337;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '0-1';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = 'words and 987';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '5467824652315';\r\nresult = 2147483647;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '     -535262335433103';\r\nresult = -2147483648;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = ' +-3242asfjkahw asu   ';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '      -.a0e3';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '+0003247er12349';\r\nresult = 3247;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = 'F6m28 d54L 1 3oC52m543196j861396J07929B321 04Vl4 2 BI58 b7641726M8L1Y15p.7525251xV3c0  002C4989577X06q+5J15G  82RG7x56r1R0507qL9';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '9j0845U3839Z2S23 21 0X96cR6 .n-6A3rZ4c 78RSg60996F  51435A228.2 zo453754O66-13f93z798317079 0c2- n0B6659565  YQ53M49M1479I3U7p857eLH22H 08I64336+4 s1f 8O1+309z9y';\r\nresult = 9;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = ' 240bRjk9444T393726quJ9vc0234234R5565k62 ';\r\nresult = 240;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '61D71J4  3T 9D908th90e7 ks0o9142991Y4550846RM2-6e848Bf326C  21E787843IK';\r\nresult = 61;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '6+ I197 931015o5 Y 93hHC+ L74 5 0Z3 5e01N15849o8O274+0151260c 21673D+0I701ZD 05719579105894Lw7W93t74S28V  79K63747 96E568';\r\nresult = 6;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111';\r\nresult = 2147483647;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '7C4w5Q4S89Yn500u768H6.1524643 r3Ii9U93BC55y80o7456r0fE4 3 1U 60B.A80M6g2uKok6b995b20999aNQJ.N1509h3715o9m H127hH027l8k2  0hY263d3X0';\r\nresult = 7;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = 'sC9k893';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '005 H  ar 85O48h4z9K5PN9164430H795YXT f584eo133 fx037651l6 905UO6 9xS1G933b+9U91212  626r6k5 G381211 ';\r\nresult = 5;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = ' BlVoPh4e nj58n9S2Kj4 729U7-13204362Z86466N8 09o 8wT5r40155027m d7MYO7J6.9z4 . 553';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '469Y0cJD2S7ED6 C0162';\r\nresult = 469;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = 'o5u2 E';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '366451770 12 90462176w9u70026e24 4526IG6 4R 3194120 ot4I 059 7t2Vx5 518wlR562599216x382Cm968GJ88K9n 73.33C2 7 h50y6 I4Zxq 96v+oXqA8E5380w4 q  48P434n5.3';\r\nresult = 366451770;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '53KP0-078y 4Jm9I6';\r\nresult = 53;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = ' 163te Lv9018RzOV65p3TO65 ds-190k +3df50zm8cq5L944H62Q W3w8-09 8180';\r\nresult = 163;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '+   S38z8l3 L2703 E50J8K5 0855Sj5 79T 2yf125784wq4 1 5 5 663fvN83.36B7N6a-17N06436N8s57R21cO1 2  0rX75039.4 1P15 896m4 M5up227   02lziQM38p8 9g18359i78234744H9P 4197 l69';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = 'Q843R c o98F644JbB6 0M78m5 55 714Va 50904';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '7m 5412e1M719x5oc-667738090EC5VSY20453';\r\nresult = 7;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '3745J026y3OU6X2l9 832 s 8Q-3 5jZ4Oa14O8Go0n D9 13075483OP-0J 1Z5t7989292797xZVi3039 6 H4428v5p79X U1I02 65r5 74x9142938fSl1PV S5J08252- 500010Vgj014HVY';\r\nresult = 3745;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '43ie370 oCp750v104Q 6B  7Tv02894762R6y0715QB295J1p2e333W6 03E707wE54x';\r\nresult = 43;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '832KY6wSHy 24704W59 J6 31  595t6a T3+19z05cC8Z748224k Un974j11g695d6eZ171fL189 5.3 a727';\r\nresult = 832;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '5x24P jt07f2 4yy76T068 12 32028Dm21 8855K7j3139 P02751t6 90 547 s90q4v .61Z 314J38K37 + 47rO757542281N22e 6106q71s 798 ';\r\nresult = 5;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '3s36440N87855Y8i r44d3x2Se2BO967b40RZoY827i Ek 45y61D720 667858025i9bsA2 kb.035 31W3X 48d41935V5Q6052Y794G1w7M8E56+K206+M49o5170 ';\r\nresult = 3;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '39 6 zb694f515502C B4I';\r\nresult = 39;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = 'T73v68jx614qP9P+Xl38 D.Z248233 5q93 09Y69';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":4945898,"edited_by":4945898,"edited_at":"2026-02-01T12:51:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2026-02-01T12:51:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-31T09:59:26.000Z","updated_at":"2026-04-28T18:34:27.000Z","published_at":"2026-01-31T09:59:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eImplement the myAtoi(string s) function, which converts a string to a 32-bit signed integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe algorithm for myAtoi(string s) is as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWhitespace\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Ignore any leading whitespace (\\\" \\\").\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSignedness\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Determine the sign by checking if the next character is '-' or '+', assuming positivity if neither present.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConversion\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Read the integer by skipping leading zeros until a non-digit character is encountered or the end of the string is reached. If no digits were read, then the result is 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRounding\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: If the integer is out of the 32-bit signed integer range [-2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e31\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e31\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e - 1], then round the integer to remain in the range. Specifically, integers less than -2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e31\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should be rounded to -2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e31\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and integers greater than 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e31\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e     - 1 should be rounded to 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e31\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e - 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the integer as the final result.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e s = \\\"42\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe underlined characters are what is read in and the caret is the current reader position.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: \\\"42\\\" (no characters read because there is no leading whitespace)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: \\\"42\\\" (no characters read because there is neither a '-' nor '+')\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 3: \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e42\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" (\\\"42\\\" is read in)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e           \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e s = \\\" -042\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e -42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-042\\\" (leading whitespace is read and ignored)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e042\\\" ('-' is read, so the result should be negative)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e             \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 3: \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e042\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" (\\\"042\\\" is read in, leading zeros ignored in the result)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e               \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 3:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e s = \\\"1337c0d3\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 1337\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: \\\"1337c0d3\\\" (no characters read because there is no leading whitespace)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: \\\"1337c0d3\\\" (no characters read because there is neither a '-' nor '+')\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 3: \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1337\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ec0d3\\\" (\\\"1337\\\" is read in; reading stops because the next character is a non-digit)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e             \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 4:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e s = \\\"0-1\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: \\\"0-1\\\" (no characters read because there is no leading whitespace)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: \\\"0-1\\\" (no characters read because there is neither a '-' nor '+')\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 3: \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-1\\\" (\\\"0\\\" is read in; reading stops because the next character is a non-digit)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e          \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 5:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e s = \\\"words and 987\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReading stops at the first non-digit character 'w'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 \u0026lt;= s.length \u0026lt;= 200\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003es consists of English letters (lower-case and upper-case), digits (0-9), ' ', '+', '-', and '.'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61177,"title":"[Master Regular Expression] Unique Email Addresses","description":"Every valid email consists of a local name and a domain name, separated by the '@' sign. Besides lowercase letters, the email may contain one or more '.' or '+'.\r\nFor example, in \"alice@leetcode.com\", \"alice\" is the local name, and \"leetcode.com\" is the domain name.\r\nIf you add periods '.' between some characters in the local name part of an email address, mail sent there will be forwarded to the same address without dots in the local name. Note that this rule does not apply to domain names.\r\nFor example, \"alice.z@leetcode.com\" and \"alicez@leetcode.com\" forward to the same email address.\r\nIf you add a plus '+' in the local name, everything after the first plus sign will be ignored. This allows certain emails to be filtered. Note that this rule does not apply to domain names.\r\nFor example, \"m.y+name@email.com\" will be forwarded to \"my@email.com\".\r\nIt is possible to use both of these rules at the same time.\r\nGiven an array of strings emails where we send one email to each emails[i], return the number of different addresses that actually receive mails.\r\n \r\nExample 1:\r\nInput: emails = [\"test.email+alex@leetcode.com\",\"test.e.mail+bob.cathy@leetcode.com\",\"testemail+david@lee.tcode.com\"] Output: 2 \r\nExplanation: \"testemail@leetcode.com\" and \"testemail@lee.tcode.com\" actually receive mails. \r\n\r\nExample 2:\r\nInput: emails = [\"a@leetcode.com\",\"b@leetcode.com\",\"c@leetcode.com\"] \r\nOutput: 3 \r\n \r\nConstraints:\r\n1 \u003c= emails.length \u003c= 100\r\n1 \u003c= emails[i].length \u003c= 100\r\nemails[i] consist of lowercase English letters, '+', '.' and '@'.\r\nEach emails[i] contains exactly one '@' character.\r\nAll local and domain names are non-empty.\r\nLocal names do not start with a '+' character.\r\nDomain names end with the \".com\" suffix.\r\nDomain names must contain at least one character before \".com\" suffix.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 843.812px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 421.9px; transform-origin: 408px 421.906px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvery\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003evalid email\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003econsists of a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003elocal name\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edomain name\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, separated by the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'@'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esign. Besides lowercase letters, the email may contain one or more\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'.'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eor\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'+'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, in\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"alice@leetcode.com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"alice\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003elocal name\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"leetcode.com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edomain name\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf you add periods\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'.'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ebetween some characters in the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003elocal name\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003epart of an email address, mail sent there will be forwarded to the same address without dots in the local name. Note that this rule\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edoes not apply\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eto\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edomain names\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"alice.z@leetcode.com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"alicez@leetcode.com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eforward to the same email address.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf you add a plus\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'+'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003elocal name\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, everything after the first plus sign\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ewill be ignored\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. This allows certain emails to be filtered. Note that this rule\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edoes not apply\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eto\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edomain names\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"m.y+name@email.com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewill be forwarded to\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"my@email.com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt is possible to use both of these rules at the same time.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an array of strings\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eemails\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere we send one email to each\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eemails[i]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ethe number of different addresses that actually receive mails\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 1:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e emails = [\"test.email+alex@leetcode.com\",\"test.e.mail+bob.cathy@leetcode.com\",\"testemail+david@lee.tcode.com\"] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 2 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"testemail@leetcode.com\" and \"testemail@lee.tcode.com\" actually receive mails. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e emails = [\"a@leetcode.com\",\"b@leetcode.com\",\"c@leetcode.com\"] \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 3 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraints:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 163.5px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 81.75px; transform-origin: 391px 81.75px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1 \u0026lt;= emails.length \u0026lt;= 100\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1 \u0026lt;= emails[i].length \u0026lt;= 100\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eemails[i]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003econsist of lowercase English letters,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'+'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'.'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'@'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eemails[i]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003econtains exactly one\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'@'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003echaracter.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAll local and domain names are non-empty.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLocal names do not start with a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'+'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003echaracter.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDomain names end with the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\".com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esuffix.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDomain names must contain at least one character before\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\".com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esuffix.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = solution(emails)\r\n\r\nend","test_suite":"%%\r\nemails = [\"test.email+alex@leetcode.com\" \"test.e.mail+bob.cathy@leetcode.com\" \"testemail+david@lee.tcode.com\"];\r\ncorrect_answer = 2;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"a@leetcode.com\" \"b@leetcode.com\" \"c@leetcode.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"wjhlbrie@t..j.mrg.com\" \"hwbrvpohlgr+ed@rn.uafx.ix.fmut.com\" \"v.tejo@x+oprw.com\" \"gerpzqhpheaur@pfngovbsx+a...com\" \"phgn+d@eategig.com\" \"ejoaqlqtcyc@d+rj+mhzraz.com\" \"yaqli@pn.bk.com\"];\r\ncorrect_answer = 7;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"gdksgnj@.zcm.c..com\" \"ia+rirqhpz+.bh@+nir.mna+.narn.com\" \"tdmafwenkjn+@v+eawfkimygd.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"htbv+v+xhaq+@shs+qknwhfev.com\" \"buayr.eqllgo@vn.nmootopsw.com\" \"xp+tqxmaz.@.sghdcvgxj.com\" \".t.sbvxhm+kbxf@.pv..lssiliniy.com\" \"lmogy@+.o+f.com\" \"nfjjsnl+.+r@maard+jybz..com\" \"pieizze@i.qfzj..com\" \"ocdz.oobbf@k+rbhwh+k..com\" \"shfewmgunty..j@gbzyd+ycvyjsdcg.com\"];\r\ncorrect_answer = 9;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"lutiy.imybcj.r@fcqze.ldj.dwmi.com\" \"jhn.cj@.isopja.com\" \"spogtwhtrq@c+cca+qsaqp.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"w+.jqzvv+u@ok.kkgc+j..com\" \"ngoikkt@iblhmfx.com\" \"kj.qby@tdipvy.com\" \".lbtymy@gj.rwwa.com\" \"ugigzcfwgbfn@vnjoabkxsrvp.com\" \"exudwkules@xrqfp+qqfi..com\" \"fhwhmh@olgc+p.com\" \"mhpmqixa@u.+xtqic.com\" \".ligb.fvvgu@wkhghvyxeka.com\"];\r\ncorrect_answer = 9;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"a.uyfnngdr@rwxpkk.ujz.com\" \".sjpzarzekgp@ya+kridafidw.com\"];\r\ncorrect_answer = 2;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\".ccrxzyiud@ti+mrviezj.com\" \"qelcesbdgqqmlj@+yxfafndxvccan.com\" \"wtyo+l@olhjyj.com\" \"ah.mphqmt@trvfb+.wyz.com\" \"um+xu.mona+x+p@zteq++m+rk+nil.com\" \"dlvvupcrlxwbrjm@fgohf+uwo+uofum.com\" \"uq.hrr@cuarwk.com\" \"ydbghox+kl+noe@boexhfj.ctecwq.com\" \"dlrshw+k.c.w@msuzwzocmhsz.com\"];\r\ncorrect_answer = 9;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"xmdykvtahgyp@lterrniu+.ur.com\" \"qld+wq.ek@oi.mw.hy+.com\" \"tsg+ut@mz++ox.com\" \".trwkzce@lcxmomue.com\" \"t.b+bfpeh.v@lb+uny.gr+i.com\" \"qsy.lno@mzknpk+u.com\" \"hct+uqr@vdcs.et.com\" \"qmiussebdmpfn@wmzn.c.sjgoc..com\"];\r\ncorrect_answer = 8;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"cqqh.avzp@robtj+htf.com\" \"qjdwzhvn@pjlpq++y.com\" \"bmlr+q@htqwupm.com\" \"wpddmnz.txfuvw@xudvlgxnv+zj++.com\" \"xnqtqbhtfz@m+ssz.qyn+.com\"];\r\ncorrect_answer = 5;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\".zmjgh@+sbvhe.com\" \"nh+onxodyfnp@ps.a+fk+of++.com\"];\r\ncorrect_answer = 2;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"emqg+nociysj@ell+.gcndyeg.com\" \"xudupb..dmsl@hx+qxejgvzou.com\" \"gi+yj+vzd@go.shnerp.com\" \"exegawmmybuhj@oynjvqdwmwetc.com\"];\r\ncorrect_answer = 4;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"ivyvy@.koud.com\" \"zlya+d@v+zlxo.com\" \"hfepaczs@lvaqpc+a.com\" \"mkhiihjwgpsh@.coaqlfhrbgz.com\" \"wjvgijfibmzk@.uqfo+u.+mxr.com\" \"bknkbmznylqm@wxt++n+zbm+y.com\" \"gflhomxq@tdmmhksp.com\" \"hknwtdctuun+sa@abxrmyyn+q+jzp.com\"];\r\ncorrect_answer = 8;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"mzo+sjve@gejsbgth.com\" \"hhwdnr@zzvzee.com\" \"hezr+ov@bb.aloi.com\" \"ngzazovqa.nvb+@x+lraofkkqx.ar.com\" \"blup+@+ymca.com\" \"szkznwyoqh@.ot.kkwdql.com\" \"nfkyat+iu@cxasim+z+.com\" \"lqdhzf+.@vms+n+zo.com\" \"fosq.wjbkw+xikw@g.axsoacnrmvusm.com\" \"a+egj.de@byyk+iox.com\"];\r\ncorrect_answer = 10;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"wosbgfbq+iohjs@w+a.wf+h+khs.t.com\" \"yoryltsqgprg+jg@hy.t.qrwdkodwqd.com\" \"dcknj@e.r+i.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"nrzlyiewbu@sb.+peednq.com\" \"zj.pre.agf+soq@udki.emvlyzujz.com\" \"h+aeeap.iiocu.@.+z.oglfkpxsbu.com\" \"h+yhm@fvzki.com\"];\r\ncorrect_answer = 4;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"koguyqhghscjiob@xi+.r+hlx+tcxqw.com\" \"fdqgr.tqgjlyyra@mtbvrcqenvkibqg.com\" \"bpaxe.lo.hrydqy@tru+b.irfstinxy.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"ncsyteko@qfxr+++dm.com\" \".qdh.hz@gvecrk+.com\" \".j+hb@.sol+.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"vgqkvatdx@qrdsolaz..com\" \"xei+++osalaqm@xxeeqqjgsnsao.com\"];\r\ncorrect_answer = 2;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"onutdg@eqbhng.com\" \"rsptijxxsnadwn@v+hdlhhpliptgn.com\" \"kuofap@lq+qdg.com\" \"btfpitlmblpnr@+cb.uzrxk.drv.com\" \"vxolxcm+rwlq@..nbwpgxjy+..com\"];\r\ncorrect_answer = 5;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"h.npduspt+xt@.gm+trja+gvy.com\" \"eekvae++kjs@pr.txifzbdi.com\" \"n.+syybgkgg@jivviajknfl.com\" \"j++zrdfoc..uj@ishji..po.sed.com\"];\r\ncorrect_answer = 4;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"oslxuvd+j+ppdtj@+++akbe.kjoukhz.com\" \".fgnbscrtpc.j+@.+hgpqbbwourp+.com\" \"y+sh.bf.n@xh+sm+krf.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"rkfqxlo.y.+@ibeduayh.i+.com\" \"xcuiy.au@vmfwel...com\" \"kkx..lwnuw@eueutajdrs.com\" \"v+oqoufiqmdzo@lgroppjdjbehe.com\" \"d.znfhymi..ybu@zhcsbqguazgwhc.com\" \"r+ulbtcjs@m++o+cfa..com\" \"aajyp+dyuyxnw.@eyjiyhgxjlarpa.com\"];\r\ncorrect_answer = 7;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"dp.+vp+k@kaagwxkb.com\" \"r.lhe.o@kjvljpa.com\" \"vxhjyeu+llbdd@wz+cfo+pgbtmg.com\" \"nrv+p@lwmsz.com\" \"pylevc@wv.zjd.com\"];\r\ncorrect_answer = 5;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"pniur@pb.iu.com\" \"jadg.@uk+bp.com\" \"vrdq.hlhmu.f.@uvlysycaayckm.com\" \"glffs+ezwlhxjl@+nobjdaejgtlwfy.com\" \"rjeay@vx+ji.com\" \"movemhf+rjdu+b@v.w++fvrlpyg+t.com\" \"nrj.kjwhdrd@pqhrhiqnzbf.com\" \"qbkn.@ugotg.com\"];\r\ncorrect_answer = 8;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"d+mhas.tsgqorpw@srjrbeqzfngvhcc.com\" \".wd.nycikhwpio@uluma+y.zptdvxo.com\" \"ewfu+c.cpkgxqi@cpkwcquwmhfjlk.com\" \"rtojs..@yxpal.a.com\" \"ftogpu@wy.zpf.com\" \".qjrog++yxy@te.i+nttbbi.com\" \"skqac@wbpfw.com\" \".yus+rotyed@+yvfccxjtxs.com\" \"znfa.tlseed@+sjidvzaufr.com\" \"eocdtookevafe@.vejunakxmwmu.com\"];\r\ncorrect_answer = 10;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"nnazmvkxsqseu@owlov+y++sh++.com\" \"mcd+.zaoqvjt@mshwokdsnbpa.com\" \"rvgxh@uepgp.com\" \"pyxs.tccxm@hwqtesq+ac.com\" \"nkohjc.rdoom@lnwnahosijdx.com\" \"squpelgagh@fysvplojt..com\" \"svr.thd.akqo@pnvu++nc.g+..com\" \"atx+qtgps@krecrkgco.com\" \"hfbngnwgsjdy@csxah+ujrhbf.com\" \".gblz+gv+@+ccoudafz.com\"];\r\ncorrect_answer = 10;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"lumrfllp@ycgw..+y.com\" \"e+meeqfiv+sgdb@kfatozbkmjqnwu.com\" \"oopl.tztedjk@vwnwy+sbdwj..com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\".hy.flt@oduitys.com\" \"r+kyc@q+pkp.com\" \".htrhfbptj@febgrmels+.com\" \"cgiy+aoodkoyuad@tmczkzjutq.rmp..com\" \"nrcbiwxcjg@atvxzuuya..com\" \"yy.ica+vy@evulrlsul.com\" \"kxdu.xgqr@qkehuqjzl.com\" \"cdiyt++@mpb.jos.com\" \"jvx+opucdmj@zpsgwhusqw..com\"];\r\ncorrect_answer = 9;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"vvtjpnbwceyz@gdcgjaxiiiqo.com\" \"dxb+pfbibxfm@cxk.fqegt+w+s.com\" \"xlxiq.sdffx@iczdyroddo..com\" \"udvnp.@bzldti.com\" \"myvdwpwk+@pxahvnofh.com\" \".i+.t@srhjn.com\" \"q.nt+cmrxj@jfefhhvqyn.com\" \"g.bjes.m@+m+ncvfw.com\" \"dcumhljkpg+@bkinkypk.o+.com\" \".rmsmixyyiyn@mw+vozgvkev..com\"];\r\ncorrect_answer = 10;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"kbzkwnexjd+j+f@i+.ttkuphkfuf..com\" \"vzz+.mgo@nofllmhs.com\" \".iodt@recpp.com\" \"wfjixhqgtx+xk@tbcu.mfcc.mmq.com\" \"olk.ivns.tt++@tvgfits.ighr+.com\" \"eehxp+cj+onn+ku@lxbdwjocmfjlxnu.com\" \"doycs.zkeqwiywn@pe+c.dwo+mgtyzi.com\" \"n+voq@ietp+.com\" \".zkwm.gredn@umj+uhugnza.com\"];\r\ncorrect_answer = 9;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"iyexebhw.iau+hl@wlkxwcizawtsgxk.com\" \"fqdruepre.swxnb@jaqjnp.dvfiveug.com\" \"i+vwklzdm@xpeejkmlp..com\" \"qpla+@.vmbz.com\" \"pg+etmaqi+wae@rrxhpqk.frevh.com\" \"bdfqqoejbcb@qprhwxqzgmd.com\" \".en+qpx.dtkg@aapkhyixcvzm.com\"];\r\ncorrect_answer = 7;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"luffyuctpfb@lcrcudc+oas.com\" \"liedcyn@skgq.ny.com\" \"vdiuwqvnbbt@zomxloeqbu+.com\" \"dei.yrqq+tjb@+nrvays+bj+x.com\" \"wd..bxdxxamf@rtphghmicffc.com\" \"g+emmrm.au+t@rpl.sv+gvfnk.com\" \"uenakj.jtvg@ldduvmakrpg+.com\" \"nt+zofb@rhmc.oq.com\" \"yosrqs@exesju.com\" \"kehogbp.nol@+bxlsqqj.fg.com\"];\r\ncorrect_answer = 10;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"xamepf@m+ie...com\" \"blwpot@evqzxa.com\" \"ibyuogiqh@hwhangzte.com\" \"rdri.la.emkpa@guupavcgqsnq..com\" \"fxtes@cxxir.com\" \"krwy..x++i.exba@jhniby.cxy+f..v.com\" \"abgobuyol@rsexxbwlm.com\" \"jnalpyhai@bccsuj.af.com\"];\r\ncorrect_answer = 8;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4945898,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-31T14:56:56.000Z","updated_at":"2026-04-28T18:28:47.000Z","published_at":"2026-01-31T14:56:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEvery\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evalid email\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003econsists of a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elocal name\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edomain name\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, separated by the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'@'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esign. Besides lowercase letters, the email may contain one or more\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'.'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'+'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"alice@leetcode.com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"alice\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eis the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elocal name\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"leetcode.com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eis the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edomain name\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you add periods\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'.'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ebetween some characters in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elocal name\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003epart of an email address, mail sent there will be forwarded to the same address without dots in the local name. Note that this rule\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edoes not apply\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eto\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edomain names\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"alice.z@leetcode.com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"alicez@leetcode.com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eforward to the same email address.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you add a plus\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'+'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ein the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elocal name\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, everything after the first plus sign\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewill be ignored\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. This allows certain emails to be filtered. Note that this rule\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edoes not apply\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eto\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edomain names\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"m.y+name@email.com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewill be forwarded to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"my@email.com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is possible to use both of these rules at the same time.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an array of strings\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eemails\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewhere we send one email to each\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eemails[i]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe number of different addresses that actually receive mails\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e emails = [\\\"test.email+alex@leetcode.com\\\",\\\"test.e.mail+bob.cathy@leetcode.com\\\",\\\"testemail+david@lee.tcode.com\\\"] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 2 \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"testemail@leetcode.com\\\" and \\\"testemail@lee.tcode.com\\\" actually receive mails. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e emails = [\\\"a@leetcode.com\\\",\\\"b@leetcode.com\\\",\\\"c@leetcode.com\\\"] \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 3 \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 \u0026lt;= emails.length \u0026lt;= 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 \u0026lt;= emails[i].length \u0026lt;= 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eemails[i]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003econsist of lowercase English letters,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'+'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'.'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'@'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eemails[i]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003econtains exactly one\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'@'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003echaracter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll local and domain names are non-empty.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLocal names do not start with a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'+'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 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before\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\".com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esuffix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":364,"title":"Matrix spiral","description":"Make a spiral in a (n*n) matrix. The spiral has to start in the top left, and has to rotate clockwise to the center. The spiral has to have a padding of zeros between itself.\r\n\r\nThe (n*n) matrix is filled with zeros except for the spiral, that has to be made of 11 (elevens, for visual reference).\r\nThe final matrix has to have the same or more zeros than elevens.\r\n\r\nExample:\r\nn=8\r\n\r\nA =\r\n\r\n    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11     0    11\r\n     0     0    11     0     0    11     0    11\r\n     0     0    11     0    11    11     0    11\r\n     0     0    11     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0","description_html":"\u003cp\u003eMake a spiral in a (n*n) matrix. The spiral has to start in the top left, and has to rotate clockwise to the center. The spiral has to have a padding of zeros between itself.\u003c/p\u003e\u003cp\u003eThe (n*n) matrix is filled with zeros except for the spiral, that has to be made of 11 (elevens, for visual reference).\r\nThe final matrix has to have the same or more zeros than elevens.\u003c/p\u003e\u003cp\u003eExample:\r\nn=8\u003c/p\u003e\u003cp\u003eA =\u003c/p\u003e\u003cpre\u003e    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11     0    11\r\n     0     0    11     0     0    11     0    11\r\n     0     0    11     0    11    11     0    11\r\n     0     0    11     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0\u003c/pre\u003e","function_template":"function A = Matrix_Spiral(n)\r\n  A = n;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct =[0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 2;\r\ny_correct =[11    11\r\n     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 3;\r\ny_correct =[11    11    11\r\n     0     0    11\r\n     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 4;\r\ny_correct =[11    11    11    11\r\n     0     0     0    11\r\n     0     0    11    11\r\n     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n\r\n%%\r\nn = 5;\r\ny_correct =[11    11    11    11    11\r\n     0     0     0     0    11\r\n     0     0    11     0    11\r\n     0     0    11    11    11\r\n     0     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 10;\r\ny_correct =[11    11    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0    11     0    11\r\n     0     0    11     0    11    11     0    11     0    11\r\n     0     0    11     0    11     0     0    11     0    11\r\n     0     0    11     0    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n\r\n%%\r\nn = 17;\r\ny_correct =[11    11    11    11    11    11    11    11    11    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11    11    11    11    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0     0     0     0     0     0     0     0    11     0    11\r\n     0     0    11     0    11    11    11    11    11    11    11    11    11     0    11     0    11\r\n     0     0    11     0    11     0     0     0     0     0     0     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11    11    11    11    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0     0     0    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0    11     0    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0    11    11    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0     0     0     0     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11    11    11    11    11    11    11     0    11     0    11\r\n     0     0    11     0    11     0     0     0     0     0     0     0     0     0    11     0    11\r\n     0     0    11     0    11    11    11    11    11    11    11    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0     0     0     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11    11    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))","published":true,"deleted":false,"likes_count":5,"comments_count":3,"created_by":872,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":98,"test_suite_updated_at":"2012-02-20T12:29:13.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-02-20T12:17:08.000Z","updated_at":"2026-04-28T18:06:26.000Z","published_at":"2012-02-20T12:29:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a spiral in a (n*n) matrix. The spiral has to start in the top left, and has to rotate clockwise to the center. The spiral has to have a padding of zeros between itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe (n*n) matrix is filled with zeros except for the spiral, that has to be made of 11 (elevens, for visual reference). The final matrix has to have the same or more zeros than elevens.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: n=8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA =\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    11    11    11    11    11    11    11    11\\n     0     0     0     0     0     0     0    11\\n     0     0    11    11    11    11     0    11\\n     0     0    11     0     0    11     0    11\\n     0     0    11     0    11    11     0    11\\n     0     0    11     0     0     0     0    11\\n     0     0    11    11    11    11    11    11\\n     0     0     0     0     0     0     0     0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44345,"title":"MATLAB Counter","description":"Write a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b. \r\n\r\nE.g.,\r\n\r\n  \u003e\u003e f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\r\n  \u003e\u003e f()\r\n  ans =\r\n       0\r\n  \u003e\u003e f()\r\n  ans =\r\n       1\r\n  \u003e\u003e f()\r\n  ans =\r\n       2\r\n\r\n\r\n","description_html":"\u003cp\u003eWrite a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b.\u003c/p\u003e\u003cp\u003eE.g.,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt; f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     0\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     1\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     2\r\n\u003c/pre\u003e","function_template":"function y = counter(x,b)\r\n  y = x;\r\nend","test_suite":"%%\r\nassessFunctionAbsence({'regexp','regexpi','regexprep','str2num'},'FileName','counter.m')\r\n\r\n%%\r\nf = counter(0,1);\r\nassert(isequal(f(),0))\r\nassert(isequal(f(),1))\r\nassert(isequal(2,f()))\r\nassert(isequal(3,f()))\r\n\r\n%%\r\nf = counter(1,0);\r\nassert(isequal(f(),1))\r\nassert(isequal(f(),1))\r\nassert(isequal(1,f()))\r\nassert(isequal(1,f()))\r\n\r\n%%\r\nf = counter(10,2);\r\nassert(isequal(f(),10))\r\nassert(isequal(f(),12))\r\nassert(isequal(14,f()))\r\nassert(isequal(16,f()))\r\n\r\n%%\r\nf = counter(0,5);\r\ny_correct = [0, 5, 10, 15, 20, 55];\r\nassert(isequal([f() f() f() f() f() f()+f()],y_correct))\r\n\r\n%%\r\nx0 = randi(10);\r\nb = randi(10);\r\nf = counter(x0,b);\r\ny_correct = x0 + (0:1000)*b;\r\nassert(isequal(arrayfun(@(n)f(),0:1000),y_correct))","published":true,"deleted":false,"likes_count":23,"comments_count":9,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":302,"test_suite_updated_at":"2017-10-17T00:19:49.000Z","rescore_all_solutions":false,"group_id":34,"created_at":"2017-09-24T01:58:21.000Z","updated_at":"2026-04-22T09:04:29.000Z","published_at":"2017-10-16T01:45:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\\n\u003e\u003e f()\\nans =\\n     0\\n\u003e\u003e f()\\nans =\\n     1\\n\u003e\u003e f()\\nans =\\n     2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42503,"title":"Generating random matrix with given probability mass function","description":"Inspired by \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2356-simulating-the-selection-of-a-state-with-given-probabilities Problem 2356. Simulating the selection of a state with given probabilities\u003e, let's consider a similar yet more useful problem. Write a function\r\n\r\n                             x = rndsampling(m,n,prob)\r\n\r\nto generate an m-by-n matrix x, whose entries are drawn independently from integer symbols 1:numel(prob) according to the given probability mass function prob. Specifically, symbol k occurs with probability prob(k), k = 1, 2, ..., numel(prob), where all(prob\u003e0) == 1 and sum(prob) == 1.","description_html":"\u003cp\u003eInspired by \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2356-simulating-the-selection-of-a-state-with-given-probabilities\"\u003eProblem 2356. Simulating the selection of a state with given probabilities\u003c/a\u003e, let's consider a similar yet more useful problem. Write a function\u003c/p\u003e\u003cpre\u003e                             x = rndsampling(m,n,prob)\u003c/pre\u003e\u003cp\u003eto generate an m-by-n matrix x, whose entries are drawn independently from integer symbols 1:numel(prob) according to the given probability mass function prob. Specifically, symbol k occurs with probability prob(k), k = 1, 2, ..., numel(prob), where all(prob\u0026gt;0) == 1 and sum(prob) == 1.\u003c/p\u003e","function_template":"function x = rndsampling(m,n,prob);\r\n  x = rand(m,n)\r\nend","test_suite":"%%\r\nrnd = sort(rand(randi([10,20]),1));\r\nprob = vertcat(rnd(1,:),diff(rnd,1,1),1-rnd(end,:));\r\nsz = [1 1e5;1e5 1;1e3 1e2;randi([100 200], 100, 2)];\r\nsz = sz(randi(size(sz,1)),:);\r\nx = rndsampling(sz(1),sz(2),prob);\r\nprob_est = histcounts(x,1:numel(prob)+1,'Normalization','probability').';\r\nerr = mean(abs(prob_est - prob))\r\nassert(err \u003c 0.005 \u0026\u0026 isequal(size(x),sz) \u0026\u0026 all(~isnan(x(:))));\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":117,"test_suite_updated_at":"2015-08-13T18:44:59.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-08-11T19:26:49.000Z","updated_at":"2026-04-30T03:11:57.000Z","published_at":"2015-08-11T19:26:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2356-simulating-the-selection-of-a-state-with-given-probabilities\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 2356. Simulating the selection of a state with given probabilities\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, let's consider a similar yet more useful problem. Write a function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[                             x = rndsampling(m,n,prob)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eto generate an m-by-n matrix x, whose entries are drawn independently from integer symbols 1:numel(prob) according to the given probability mass function prob. Specifically, symbol k occurs with probability prob(k), k = 1, 2, ..., numel(prob), where all(prob\u0026gt;0) == 1 and sum(prob) == 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1092,"title":"Decimation","description":"When dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn.  The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\r\n\r\nThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences.  Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others.  Instead of killing every tenth prisoner, he chooses a number (kill_every).  If kill_every=3, he kills every third prisoner.  If kill_every=5, he kills every fifth prisoner.  He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left.  For example, if there are 10 prisoners, and kill_every=3\r\n\r\nFirst iteration: 1 2 3 4 5 6 7 8 9 10\r\n\r\n1-2-3 4-5-6 7-8-9 10\r\n\r\nPrisoners 3, 6 and 9 will be killed.\r\n\r\nSecond iteration: 1 2 4 5 7 8 10\r\n\r\nBecause Prisoner 10 was counted during the first iteration, the executions\r\nwill proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\r\n\r\nThird iteration: 1 4 5 8 10\r\n8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\r\n\r\nFourth Iteration:  10-4-5 10\r\nPrisoner 5 is executed.\r\n\r\nFifth iteration:  10-4 10\r\nPrisoner 10 is executed\r\n\r\nSince the sole survivor is prisoner 4, he is released.\r\n\r\nYou are an unlucky prisoner caught by Carnage Maximum.  Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day.  Your job is to figure out which prisoner you need to be in order to survive.  Write a MATLAB script that takes the values of num_prisoners and kill_every.  The output will be survivor, which is the position of the person who survives.  If you write your script quickly enough, that person will be you.\r\n\r\nGood luck!","description_html":"\u003cp\u003eWhen dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn.  The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\u003c/p\u003e\u003cp\u003eThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences.  Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others.  Instead of killing every tenth prisoner, he chooses a number (kill_every).  If kill_every=3, he kills every third prisoner.  If kill_every=5, he kills every fifth prisoner.  He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left.  For example, if there are 10 prisoners, and kill_every=3\u003c/p\u003e\u003cp\u003eFirst iteration: 1 2 3 4 5 6 7 8 9 10\u003c/p\u003e\u003cp\u003e1-2-3 4-5-6 7-8-9 10\u003c/p\u003e\u003cp\u003ePrisoners 3, 6 and 9 will be killed.\u003c/p\u003e\u003cp\u003eSecond iteration: 1 2 4 5 7 8 10\u003c/p\u003e\u003cp\u003eBecause Prisoner 10 was counted during the first iteration, the executions\r\nwill proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\u003c/p\u003e\u003cp\u003eThird iteration: 1 4 5 8 10\r\n8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\u003c/p\u003e\u003cp\u003eFourth Iteration:  10-4-5 10\r\nPrisoner 5 is executed.\u003c/p\u003e\u003cp\u003eFifth iteration:  10-4 10\r\nPrisoner 10 is executed\u003c/p\u003e\u003cp\u003eSince the sole survivor is prisoner 4, he is released.\u003c/p\u003e\u003cp\u003eYou are an unlucky prisoner caught by Carnage Maximum.  Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day.  Your job is to figure out which prisoner you need to be in order to survive.  Write a MATLAB script that takes the values of num_prisoners and kill_every.  The output will be survivor, which is the position of the person who survives.  If you write your script quickly enough, that person will be you.\u003c/p\u003e\u003cp\u003eGood luck!\u003c/p\u003e","function_template":"function survivor=decimate(num_prisoners,kill_every)\r\nsurvivor=4;\r\nend","test_suite":"%%\r\nassert(isequal(decimate(10,3),4))\r\n%%\r\nassert(isequal(decimate(1024,3),676))\r\n%%\r\nassert(isequal(decimate(2012,50),543))\r\n%%\r\nassert(isequal(decimate(30,5),3))\r\n%%\r\nassert(isequal(decimate(10,10),8))\r\n%%\r\nassert(isequal(decimate(2048,2),1))","published":true,"deleted":false,"likes_count":20,"comments_count":12,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":315,"test_suite_updated_at":"2012-12-04T21:28:04.000Z","rescore_all_solutions":false,"group_id":13,"created_at":"2012-12-04T19:47:49.000Z","updated_at":"2026-04-20T18:16:53.000Z","published_at":"2012-12-04T19:53:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn. The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences. Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others. Instead of killing every tenth prisoner, he chooses a number (kill_every). If kill_every=3, he kills every third prisoner. If kill_every=5, he kills every fifth prisoner. He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left. For example, if there are 10 prisoners, and kill_every=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst iteration: 1 2 3 4 5 6 7 8 9 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1-2-3 4-5-6 7-8-9 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrisoners 3, 6 and 9 will be killed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSecond iteration: 1 2 4 5 7 8 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBecause Prisoner 10 was counted during the first iteration, the executions will proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThird iteration: 1 4 5 8 10 8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFourth Iteration: 10-4-5 10 Prisoner 5 is executed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFifth iteration: 10-4 10 Prisoner 10 is executed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince the sole survivor is prisoner 4, he is released.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are an unlucky prisoner caught by Carnage Maximum. Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day. Your job is to figure out which prisoner you need to be in order to survive. Write a MATLAB script that takes the values of num_prisoners and kill_every. The output will be survivor, which is the position of the person who survives. If you write your script quickly enough, that person will be you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":59516,"title":"Determine aquifer properties: slug test","description":"An important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems 59152, 49473,  and 59147, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity  of the aquifer are determined. \r\nInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement  of water in the well is given as a function of time  by\r\n\r\nwhere  is the initial displacement,  is the radius of the well casing,  is the radius of the well screen,  is the length of the well screen, and  is the effective distance over which the water table returns to its undisturbed level. If the distance  from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness , then \r\n\r\nIf ,\r\n\r\nBouwer and Rice provided the coefficients , , and  in a figure, and Yang and Yeh (2004) fit the curves as functions of :\r\n\r\n\r\n\r\nWrite a function that computes the distance  and determines the hydraulic conductivity  by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1075.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 537.75px; transform-origin: 407px 537.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.358px 8px; transform-origin: 382.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59152\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e59152\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/49743\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e49473\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59147-determine-aquifer-properties-steady-pump-test-in-a-leaky-confined-aquifer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e59147\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.4667px 8px; transform-origin: 89.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.56667px 8px; transform-origin: 9.56667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer are determined. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.933px 8px; transform-origin: 383.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.075px 8px; transform-origin: 152.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of water in the well is given as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-20px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"181\" height=\"42\" alt=\"H = H0 exp(-2KLet/(rc^2 ln(Re/R)))\" style=\"width: 181px; height: 42px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" alt=\"H0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.6333px 8px; transform-origin: 83.6333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the initial displacement, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"13.5\" height=\"20\" alt=\"rc\" style=\"width: 13.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.1833px 8px; transform-origin: 99.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of the well casing, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.9583px 8px; transform-origin: 99.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of the well screen, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16\" height=\"20\" alt=\"Le\" style=\"width: 16px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the length of the well screen, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"20\" alt=\"Re\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302.475px 8px; transform-origin: 302.475px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the effective distance over which the water table returns to its undisturbed level. If the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"20\" alt=\"Lw\" style=\"width: 18px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.0416667px 8px; transform-origin: 0.0416667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"305.5\" height=\"44\" alt=\"ln(Re/R) = [1.1/ln(Lw/R) + [A+Bln((h-Lw)/R)]/(Le/R)]^{-1}\" style=\"width: 305.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"20\" alt=\"Lw = h\" style=\"width: 44px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.9px; text-align: left; transform-origin: 384px 21.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"203\" height=\"44\" alt=\"ln(Re/R) = [1.1/ln(Lw/R) + C/(Le/R)]^{-1}\" style=\"width: 203px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.525px 8px; transform-origin: 132.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBouwer and Rice provided the coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.15px 8px; transform-origin: 206.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a figure, and Yang and Yeh (2004) fit the curves as functions of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"101\" height=\"20\" alt=\"x = log10(Le/R)\" style=\"width: 101px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" width=\"351\" height=\"19.5\" alt=\"C(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\" style=\"width: 351px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136px 8px; transform-origin: 136px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"20\" alt=\"Re\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.258px 8px; transform-origin: 132.258px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and determines the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.625px 8px; transform-origin: 83.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 412.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 206.35px; text-align: left; transform-origin: 384px 206.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"455\" height=\"407\" style=\"vertical-align: baseline;width: 455px;height: 407px\" 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\" alt=\"Schematic of the Bouwer-Rice slug test\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h)\r\n%  t = measurement time\r\n%  H = displacement\r\n%  rc = casing radius\r\n%  R = screen radius\r\n%  Le = screen length\r\n%  Lw = distance from undisturbed water table to bottom of well\r\n%  h = initial saturated thickness\r\n  Re = ln(Re/R) = [1.1/ln(Lw/R) + [A+B*ln((h-Lw)/R)]/(Le/R)]^{-1}\r\n  K = rc^2*log(Re/R)*log(H(1)/H)/(2*Le*t);\r\nend","test_suite":"%%\r\nt = 0:2:16;             %  Measurement times (sec)                                                 \r\nrc = 0.05;              %  Casing radius (m)\r\nR = 0.1;                %  Screen radius (m)\r\nLe = 3;                 %  Screen length (m)\r\nLw = 5;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.5 0.645 0.372 0.195 0.13 0.067 0.044 0.023 0.015];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 2.82e-4;\r\nRe_correct = 1.11;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:2:16;             %  Measurement times (sec)\r\nrc = 0.03;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 4;                 %  Screen length (m)\r\nLw = 6;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.0 0.498 0.248 0.123 6.14e-2 3.06e-2 1.52e-2 7.57e-3 3.77e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 8.10e-5;\r\nRe_correct = 1.576;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:2:16;             %  Measurement times (sec)\r\nrc = 0.03;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 4;                 %  Screen length (m)\r\nLw = 6;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.0 0.498 0.248 0.123 6.14e-2 3.06e-2 1.52e-2 7.57e-3 3.77e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 8.10e-5;\r\nRe_correct = 1.576;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:5:40;             %  Measurement times (sec)\r\nrc = 0.04;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 3.5;               %  Screen length (m)\r\nLw = 15;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [0.8 0.404 0.204 0.103 5.21e-2 2.63e-2 1.33e-2 6.72e-3 3.4e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 9.4e-5;\r\nRe_correct = 4.065;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:50:400;           %  Measurement times (sec)\r\nrc = 0.035;             %  Casing radius (m)\r\nR = 0.08;               %  Screen radius (m)\r\nLe = 7;                 %  Screen length (m)\r\nLw = 14;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 28;                 %  Undisturbed saturated thickness (m)\r\nH = [1.7 0.978 0.562 0.323 0.186 0.107 6.15e-2 3.53e-2 2.03e-2];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 3.2e-6;\r\nRe_correct = 2.179;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:50:400;           %  Measurement times (sec)\r\nrc = 0.035;             %  Casing radius (m)\r\nR = 0.08;               %  Screen radius (m)\r\nLe = 7;                 %  Screen length (m)\r\nLw = 28;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 28;                 %  Undisturbed saturated thickness (m)\r\nH = [1.7 1.11 0.719 0.467 0.304 0.197 0.128 8.35e-2 5.43e-2];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 3.2e-6;\r\nRe_correct = 5.592;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:60:480;           %  Measurement times (sec)\r\nrc = 0.04;              %  Casing radius (m)\r\nR = 0.1;                %  Screen radius (m)\r\nLe = 5;                 %  Screen length (m)\r\nLw = 30;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 30;                 %  Undisturbed saturated thickness (m)\r\nH = [1.3 0.651 0.326 0.163 8.16e-2 4.09e-2 2.05e-2 1.02e-2 5.13e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 7.43e-6;\r\nRe_correct = 5.608;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nfiletext = fileread('BouwerRice.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2023-12-30T14:18:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-30T13:54:14.000Z","updated_at":"2026-02-12T15:36:49.000Z","published_at":"2023-12-30T14:04:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59152\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e59152\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/49743\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e49473\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59147-determine-aquifer-properties-steady-pump-test-in-a-leaky-confined-aquifer\\\"\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e59147\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer are determined. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of water in the well is given as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H = H0 exp(-2KLet/(rc^2 ln(Re/R)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH = H_0 \\\\exp\\\\left(-\\\\frac{2 K L_e t}{r_c^2 \\\\ln(R_e/R)}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the initial displacement, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of the well casing, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of the well screen, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Le\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the length of the well screen, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the effective distance over which the water table returns to its undisturbed level. If the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Lw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ln(Re/R) = [1.1/ln(Lw/R) + [A+Bln((h-Lw)/R)]/(Le/R)]^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ln\\\\left(\\\\frac{R_e}{R}\\\\right) = \\\\left[\\\\frac{1.1}{\\\\ln(L_w/R)} + \\\\frac{A+B\\\\ln((h-L_w)/R)}{L_e/R}\\\\right]^{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Lw = h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_w = h\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ln(Re/R) = [1.1/ln(Lw/R) + C/(Le/R)]^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ln\\\\left(\\\\frac{R_e}{R}\\\\right) = \\\\left[\\\\frac{1.1}{\\\\ln(L_w/R)} + \\\\frac{C}{L_e/R}\\\\right]^{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBouwer and Rice provided the coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a figure, and Yang and Yeh (2004) fit the curves as functions of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = log10(Le/R)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = \\\\log_{10}(L_e/R)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and determines the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"407\\\"/\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59217,"title":"List lunar triangular numbers without duplication","description":"Triangular numbers—which are the subject of Cody Problems 5, 291, 44289, 44732, 45833, 55680, 55695, and 55705—are the sums of consecutive integers. For example, the 10th triangular number is the sum of the numbers 1 to 10, or 55. \r\nLunar addition, which is the subject of Cody Problem 44785, involves taking the largest digit in the sum. For example, 1+3 = 3, 3+6 = 6, 13+51 = 53, and 428+620 = 628.\r\nWrite a function to compute the th lunar triangular number without duplicating any terms. For example, the 10th lunar triangular number is 1+2+3+4+5+6+7+8+9+10 = 19. The 11th lunar triangular number is also 19, but because it is a duplicate, it would not be listed in this sequence. Express the answer as a character string.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.5px; transform-origin: 407px 82.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.683px 8px; transform-origin: 192.683px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangular numbers—which are the subject of Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/5\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e5\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/291\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e291\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44289\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44289\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44732\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44732\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45833\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45833\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55680\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55680\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55695\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55695\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55705\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55705\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.2px 8px; transform-origin: 18.2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—are the sums of consecutive integers. For example, the 10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 186.3px 8px; transform-origin: 186.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e triangular number is the sum of the numbers 1 to 10, or 55. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 118.642px 8px; transform-origin: 118.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLunar addition, which is the subject of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44785\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 44785\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 199.608px 8px; transform-origin: 199.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, involves taking the largest digit in the sum. For example, 1+3 = 3, 3+6 = 6, 13+51 = 53, and 428+620 = 628.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.6583px 8px; transform-origin: 98.6583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 238.45px 8px; transform-origin: 238.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth lunar triangular number without duplicating any terms. For example, the 10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.45px 8px; transform-origin: 19.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e lunar triangular number is 1+2+3+4+5+6+7+8+9+10 = 19. The 11\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.042px 8px; transform-origin: 168.042px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e lunar triangular number is also 19, but because it is a duplicate, it would not be listed in this sequence. Express the answer as a character string.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = lunarTriNum(n)\r\n  y = num2str(n);\r\nend","test_suite":"%%\r\ns = char(48:57);\r\nfor n = 0:9\r\n    assert(strcmp(lunarTriNum(n),s(n+1)));\r\nend\r\n\r\n%%\r\nassert(strcmp(lunarTriNum(10),'19'))\r\n\r\n%%\r\nfor k = 1:1000\r\n    n = randi(10000);\r\n    assert(isequal(sum(lunarTriNum(n)-'0'),n))\r\nend\r\n\r\n%%\r\nn = 77;\r\np_correct = 215233605;\r\nassert(isequal(prod(lunarTriNum(n)-'0'),p_correct))\r\n\r\n%%\r\nn = 134;\r\np_correct = 183014339639688;\r\nassert(isequal(prod(lunarTriNum(n)-'0'),p_correct))\r\n\r\n%%\r\nn = 6259;\r\nlen_correct = 696;\r\nassert(isequal(length(lunarTriNum(n)),len_correct))\r\n\r\n%%\r\nn = 5*(10.^(1:7));\r\np = primes(1e8);\r\nx_correct = [267 4103 256889 33082235 4266286911 523279276675 61893416706717];\r\nfor k = 1:length(n)\r\n    a = str2num(reshape(lunarTriNum(n(k)),[],2));\r\n    x(k) = sum(a+p(1:size(a,1))');\r\nend\r\nassert(isequal(x,x_correct))\r\n\r\n%%\r\nfiletext = fileread('lunarTriNum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-11-25T14:58:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-11-25T14:57:46.000Z","updated_at":"2023-11-25T14:58:06.000Z","published_at":"2023-11-25T14:58:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangular numbers—which are the subject of Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/5\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/291\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e291\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44289\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44289\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44732\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44732\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45833\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45833\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55680\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55680\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55695\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55695\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55705\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55705\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—are the sums of consecutive integers. For example, the 10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e triangular number is the sum of the numbers 1 to 10, or 55. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLunar addition, which is the subject of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44785\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 44785\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, involves taking the largest digit in the sum. For example, 1+3 = 3, 3+6 = 6, 13+51 = 53, and 428+620 = 628.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth lunar triangular number without duplicating any terms. For example, the 10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e lunar triangular number is 1+2+3+4+5+6+7+8+9+10 = 19. The 11\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e lunar triangular number is also 19, but because it is a duplicate, it would not be listed in this sequence. Express the answer as a character string.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56423,"title":"French Conundrum","description":"The French army is trapped, sorrounded in backwards direction (South and West directions) by enemy traps and ambushes. You are now constrained to move forward only (North, East and North-East).\r\nThe battle-ground is in a form of a 2-D rectangular lattice spanning from (0,0) to (m,n). In order to make a formidable strategy and safely retreat, it is necessary to visualize the field. Now to visualize the field, the first required is the number of all possible paths from your initial position (although relative, consider it to be 0,0) to the end point (m,n).\r\nHowever, to be cautious, you must only take a single step at a time to check from any traps and ambushes in the next step. If you take more than 1 step at a time, the enemy will know your location and the mission will fail.\r\n\r\nThey turn to you, The Army officer and an avid mathematics aficionado to solve the problem.\r\n\r\nGiven two whole numbers, m and n, find the number of paths with the mentioned restriction, to prepare a strategy.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 285px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 142.5px; transform-origin: 407px 142.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 357px 8px; transform-origin: 357px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe French army is trapped, sorrounded in backwards direction (South and West directions) by enemy traps and ambushes. You are now constrained to move forward only (North, East and North-East).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 228.5px 8px; transform-origin: 228.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe battle-ground is in a form of a 2-D rectangular lattice spanning from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15px 8px; transform-origin: 15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(0,0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.5px 8px; transform-origin: 21.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(m,n). \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5px 8px; transform-origin: 94.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn order to make a formidable strategy and safely retreat, it is necessary to visualize the field. Now to visualize the field, the first required is the number of all possible paths from your initial position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(although relative, consider it to be 0,0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.5px 8px; transform-origin: 53.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the end point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.5px 8px; transform-origin: 19.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(m,n).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370px 8px; transform-origin: 370px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHowever, to be cautious, you must only take a single step at a time to check from any traps and ambushes in the next step. If you take more than 1 step at a time, the enemy will know your location and the mission will fail.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 291px 8px; transform-origin: 291px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThey turn to you, The Army officer and an avid mathematics aficionado to solve the problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 357px 8px; transform-origin: 357px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven two whole numbers, m and n, find the number of paths with the mentioned restriction, to prepare a strategy.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = henridnum(m,n)\r\n  y = f(m,n);\r\nend","test_suite":"%%\r\nfiletext = fileread('henridnum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || ...\r\n          contains(filetext, 'switch'); \r\nassert(~illegal)\r\n\r\n%%\r\nassert(isequal(henridnum(1,1),3))\r\n\r\n%%\r\nassert(isequal(henridnum(1,3),7))\r\n\r\n%%\r\nassert(isequal(henridnum(3,2),(3+2)^2))\r\n\r\n%%\r\nassert(isequal(henridnum(2,8),145))\r\n\r\n%%\r\nassert(isequal(henridnum(5,5),1683))\r\n\r\n%%\r\nfor i=0:9\r\n    assert(isequal(henridnum(i,1),2*i+1))\r\nend\r\n\r\n%%\r\nassert(isequal(henridnum(6,4),1289))\r\n\r\n%%\r\nassert(isequal(henridnum(7,6),19825))\r\n\r\n%%\r\nassert(isequal(henridnum(3,3),(3+3+1)*3*3))\r\n\r\n%%\r\nassert(isequal(henridnum(8,6),40081))\r\n\r\n%%\r\nassert(isequal(henridnum(10,10),8097453))\r\n\r\n%%\r\nassert(isequal(henridnum(5,3),(5*3)^2+3+3))\r\n\r\n%%\r\nassert(isequal(henridnum(3,7),575))\r\n\r\n%%\r\nassert(isequal(henridnum(11,9),7059735))\r\n\r\n%%\r\nassert(isequal(henridnum(4,2),4*2*5+1))\r\n\r\n%%\r\nassert(isequal(henridnum(8,7),108545))\r\n\r\n%%\r\nassert(isequal(henridnum(11,13),224298231))\r\n\r\n%%\r\nassert(isequal(henridnum(12,12),251595969))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2022-10-27T11:34:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-26T17:38:03.000Z","updated_at":"2025-09-19T20:55:15.000Z","published_at":"2022-10-27T11:34:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe French army is trapped, sorrounded in backwards direction (South and West directions) by enemy traps and ambushes. You are now constrained to move forward only (North, East and North-East).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe battle-ground is in a form of a 2-D rectangular lattice spanning from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(0,0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(m,n). \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eIn order to make a formidable strategy and safely retreat, it is necessary to visualize the field. Now to visualize the field, the first required is the number of all possible paths from your initial position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(although relative, consider it to be 0,0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e to the end point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(m,n).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eHowever, to be cautious, you must only take a single step at a time to check from any traps and ambushes in the next step. If you take more than 1 step at a time, the enemy will know your location and the mission will fail.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThey turn to you, The Army officer and an avid mathematics aficionado to solve the problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven two whole numbers, m and n, find the number of paths with the mentioned restriction, to prepare a strategy.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60406,"title":"Alert a city about a spill","description":"Problem statement\r\nCody Problem 54750 involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s maximum contaminant level (MCL). As in CP 54750, the spill of mass  will be assumed instantaneous at position  and time  and mixed over the cross section (with area ). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with  \r\n\r\nwhere  is the mean velocity of the river,  is the discharge or volumetric flow rate, and  is a dispersion coefficient, which describes spreading by several mechanisms. \r\nWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position  downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return 'The MCL is not exceeded.' Please note that the MCL is given in mg/L, whereas other variables are given in SI units. \r\nDetails\r\nMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of Seo and Cheong (1998):\r\n\r\nwhere  is the width of the channel (assumed rectangular here),  is the water depth, and  is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\r\n\r\nwhere  is the gravitational acceleration,  is the longitudinal slope of the channel,  is the hydraulic radius, and  is the wetted perimeter. For a rectangular channel, . \r\nIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 690.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 345.017px; transform-origin: 407px 345.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 7.79167px; transform-origin: 63.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/54750\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 54750\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 307.167px 7.79167px; transform-origin: 307.167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003emaximum contaminant level\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.9px 7.79167px; transform-origin: 129.9px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (MCL). As in CP 54750, the spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3417px 7.79167px; transform-origin: 23.3417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be assumed instantaneous at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 7.79167px; transform-origin: 30.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33.5\" height=\"18\" alt=\"t = 0\" style=\"width: 33.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.2333px 7.79167px; transform-origin: 34.2333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and mixed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.625px 7.79167px; transform-origin: 104.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.6083px 7.79167px; transform-origin: 62.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20px; text-align: left; transform-origin: 384px 20px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"204.5\" height=\"40\" alt=\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\" style=\"width: 204.5px; height: 40px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61.5\" height=\"18.5\" alt=\"U = Q/A\" style=\"width: 61.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.892px 7.79167px; transform-origin: 101.892px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.858px 7.79167px; transform-origin: 138.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the discharge or volumetric flow rate, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.625px 7.79167px; transform-origin: 48.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84.45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.225px; text-align: left; transform-origin: 384px 42.225px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.758px 7.79167px; transform-origin: 376.758px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 218.967px 7.79167px; transform-origin: 218.967px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.95px 7.79167px; transform-origin: 103.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 103.95px 8.25px; transform-origin: 103.95px 8.25px; \"\u003e'The MCL is not exceeded.' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.242px 7.79167px; transform-origin: 132.242px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.95px 7.79167px; transform-origin: 22.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDetails\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 322.725px 7.79167px; transform-origin: 322.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eSeo and Cheong (1998)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44.1333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.0667px; text-align: left; transform-origin: 384px 22.0667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"190.5\" height=\"44\" alt=\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\" style=\"width: 190.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.9083px; text-align: left; transform-origin: 384px 31.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 174.65px 7.79167px; transform-origin: 174.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the channel (assumed rectangular here), \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.675px 7.79167px; transform-origin: 74.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the water depth, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB8AAAAoCAYAAAAG0SEsAAACEElEQVRYR+1Vuy5EURSd+QLxKEXhUWvokGgQWoKaxKOQUHiFSjwbnUehI/gBIQoFEQkFPeIHROIHWGuy9+Q4c++5c8y9M809ycrOedy1z157n32zmQqObAV9Z1LnFVE/lT2VvawKpAVXVrnVWZTsHThYD3wDF9YN+zGfkbVp2HffCIKc14JkDFgEqoVwEvbQIj/DfBj4Amp8HfO8K/J17C8LaZMVWSPmb7K3D8vIvYfL+SXYesVJs8U8gfmBrI3CUgXv4XL+44jsFXtUg8NWpehLhDlnod0KywCsWWwjmJ/KHqW3VSnZ+TwYtoWlDvbTYDSj/ne+yRcWueb7Cmf6DMfM9Sagr8BWpeioXc413ws4tCOMrbA3AItrKkSVkp2b+e4E2x3At081ZoFdoA14Atplrwo2liaj+Tabxx7IP0QFU5UjrJ0AVOjFCpsd8BjoDtjLHQ3KuXYuVnIPsCGkrHJTFb7vLiG2ux8/0Veh6hWkxOVcD5sVzbw/Gyzn4kSXtCuyHV9Lalpg1wDWyZ+GFNbbB4WNBHYuGVEDcA+wHszBy/FF8MwWMAQ8AqwN2lUg/2yj/moFUnksaPqCfko5mridM/IlgLVCOy4Rc84UsUDzSsbtXJsQHT8ArA92yDmAf8g/xRe3czMr+ufzqnaPtDqP8lmuAEE9IJGce108SdkjL5I6j5QoiQOp7EmoGsn5C7cMXymLIre/AAAAAElFTkSuQmCC\" width=\"15.5\" height=\"20\" alt=\"u*\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.6083px 7.79167px; transform-origin: 86.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.9083px; text-align: left; transform-origin: 384px 10.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"90\" height=\"21\" alt=\"u* = sqrt(gRS0)\" style=\"width: 90px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.4083px; text-align: left; transform-origin: 384px 21.4083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"87.5\" height=\"19.5\" alt=\"g = 9.81 m/s^2\" style=\"width: 87.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 7.79167px; transform-origin: 101.917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gravitational acceleration, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.483px 7.79167px; transform-origin: 124.483px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the longitudinal slope of the channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59\" height=\"18.5\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5667px 7.79167px; transform-origin: 50.5667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 159.858px 7.79167px; transform-origin: 159.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the wetted perimeter. For a rectangular channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"78\" height=\"18\" alt=\"P = B + 2H\" style=\"width: 78px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.79167px; transform-origin: 384px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.00833px 7.79167px; transform-origin: 1.00833px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = spillAlert(x,t0,M,Q,B,H,S0,MCL)\r\n% See the tests for the definitions of the variables and note that the MCL is given in mg/L.\r\n  t = datetime(x*B*H/Q);\r\nend","test_suite":"%% Benzene\r\nx = 80000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 26000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.005;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 08 05; 2018 05 28 05 06 05])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Chlorobenzene\r\nx = 79500;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 34000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.1;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 43 39; 2018 05 28 03 41 07])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Atrazine\r\nx = 14300;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2020,7,3,16,35,0);    %  Datetime for spill\r\nM = 5600;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 32;                             %  Width of channel (m)\r\nH = 0.4;                            %  Depth of channel (m)\r\nS0 = 6e-4;                          %  Longitudinal slope of channel\r\nMCL = 0.003;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2020 07 04 00 51 03; 2020 07 04 14 00 39])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Dalapon\r\nx = 4200;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2019,6,13,14,23,0);   %  Datetime for spill\r\nM = 3000;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 15;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.2;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2019 06 13 15 47 17; 2019 06 13 19 39 06])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 2\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 80;                             %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 3\r\nx = 94000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 37;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Nitrate \r\nx = 1600;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2024,4,30,15,20,00);  %  Datetime for spill\r\nM = 140;                            %  Mass of spill (kg)\r\nQ = 14;                             %  Discharge (m3/s)\r\nB = 14;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 5e-4;                          %  Longitudinal slope of channel\r\nMCL = 10;                           %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2024 4 30 15 32 22; 2024 4 30 15 38 03])';\r\nassert(isequal(t,t_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-28T15:13:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-27T17:17:23.000Z","updated_at":"2026-01-25T17:02:57.000Z","published_at":"2024-05-27T17:22:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/54750\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 54750\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaximum contaminant level\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MCL). As in CP 54750, the spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will be assumed instantaneous at position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and mixed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the discharge or volumetric flow rate, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'The MCL is not exceeded.' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDetails\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSeo and Cheong (1998)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = 5.915u_*H\\\\left(\\\\frac{B}{H}\\\\right)^{\\\\!\\\\!0.62}\\\\left(\\\\frac{U}{u_*}\\\\right)^{\\\\!\\\\!1.428}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the channel (assumed rectangular here), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the water depth, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u*\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u* = sqrt(gRS0)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_* = (g R S_0)^{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 9.81 m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\,\\\\rm{m/s^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gravitational acceleration, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the longitudinal slope of the channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the wetted perimeter. For a rectangular channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P = B + 2H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = B + 2H\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46636,"title":"Montgomery Multiplication","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMultiply all elements of an input matrix (A) modulo N, given all elements are less than R (2^number of bits). Where gcd(R,N)=1 and N\u0026lt;R. Output the final result, P (in normal form) and all intermediate products (p) in Montgomery form \u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 1px; border-bottom-style: solid; border-bottom-width: 1px; \"\u003e(\u003c/span\u003e\u003cspan style=\"\"\u003efirst product is just first element of matrix (A)*R modulo N\u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 1px; border-bottom-style: solid; border-bottom-width: 1px; \"\u003e)\u003c/span\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [P,p] = montgomeryMult(a,R,N)\r\n  P=N-1;\r\n  p=mod(a,N);\r\nend","test_suite":"%%\r\nR=2^16;\r\nN=3329;\r\nY=2050;\r\ny =[    1263         470        2922         960         982         369        2562        2142        1318         744];\r\na =[    1112       36822       19271       42840       48879       33433       48232       54170        3299       62565\r\n        7920       12071       15556       62713       53288       59399       52080       25560       14987       28219\r\n       56538       39138       34791       61324       25120       41217       35710       32630       54669       63016\r\n       31738       19656        5996       30008       40454        6654       44972       45534        1025       49965\r\n       55368        8789       26562       15759       37715       25615       58565       54681       56604         481\r\n       13723       13933        6871       50062       34737        3579        3590       39952        5116       44567\r\n       36194       58650        7358       49763       18026       32852       19900       37665       43846       46265\r\n       41280        4682       51408       48539       16294       28293        3027       21367       32781       42279\r\n        2096       15891       19108       48738       29598       65376       12810       29912       14286       36196\r\n       40285        3522       39553        6941       14923       53189       47196       46779       37461       14293\r\n       23750       28948       63204       44666       52720       31827       47300       57960        8007       50617\r\n        3246         870       28343       30360       64625       58618       57527       47241       43985       14944\r\n       32084       58798       45531       13904        1965        9014       38170        1219       39294       24304\r\n       12616       12888       49682        6456       35105       25559        4632       44222        3668       58387\r\n        8066        6119       28353       53973        5706       60775       60472       28738        3692       56123\r\n       13467       20143       42958       11469       52565       60128       52453       28692        9994       26373\r\n        9602       29888        7192       10719       64824       46764       18739        7670        1285       20841\r\n       12391        6663       61194       43646        4387       40523       35629       53390       28519       39887\r\n        2795       65233       12285       58614       61564       22497       64538       21289       54540       59650\r\n       41628       21764       17444       33853        1191       61343       46902       16136       40461       59578\r\n       18472       19486       52286       46052       44816        8177       54982       22460       34087       38770\r\n       35297        4066       31955       10065       51362       47879       28394       24621       56614       21795\r\n       45558       19545       50394       62485       35005       42367       30842       35818        6402       55906\r\n       32710        3037       25952       35447       58022       54601       36746       36825       59510       28992\r\n       35114       33123       17887       44547       58917       26101       17635       25940        7078       59267\r\n       29175       49900        2440        2396       41021       49140       49087       26091       33881        2174\r\n        8122       41357       44125       53031        9035       54737       33022       33775        9381       34893\r\n       32136        5891       28151       49061       14273       21132       42389       43091       36658       46956\r\n       55902        5299       29605        7876       11936       36193       20168       62319         300       11750\r\n       57273       50937       39967       34409        2740       64168        9091       47339       50245       22055\r\n       17714       59318        3893       21353        7008       35999       31167       26219       55621       12301\r\n       13661       34981       20697       35812       40399       21654       23754       54517       60084       21097\r\n       37026        7153       50641       26141       61581       40597       51649        8803       64681       26467\r\n       41963       54120       45641       27203       23229       23634       51137        3962       33104       35950\r\n       27330       22157        8213       11844       26910       49578       43811        5521       17787        3194\r\n       13498       19265        8529       16737       64510       27125        8749       10741        6602       36223\r\n       62123       48910        6052        1345       61969       32266        1412       21248       33282       18010\r\n        5378         677         512       60534       44344       45530       36689       19773       38378       15827\r\n        6927        3175       27728       42840       64769       63749       19714         765       49996       15934\r\n        9308       43772       42963       61119       50255       21479       61565       35383        5437       10102\r\n       10909       39548       47377       10715       22065       54906       64284        6250       43358       62679\r\n       40695       34478       34813       60365       43409       48435       18783        9601       33880       61319\r\n       37598       47822        7131       52078       16001       62532       52482       41362       11209       53655\r\n        3412       46350       41403       37840       19366        2092       58727       56316       61509       47727\r\n       61027       51208        8290       28838       44576       23387       39159       63846       38697       11521\r\n       47753       18872        8801       16882       34592       43427       57934       37410       28877       23617\r\n       48355       45385        6461       49279       26974       18448       61848       65329       61729       12372\r\n        4155       36481        9307       14986       39494       15098       35989       36276       42985          78\r\n       56389       25986       11026        4206       49186       46604       47735       33781       29618       20736\r\n       61237        4036       12861       50287       38242       40932       37798       21671       55030       45850\r\n       64513       51129       20806       43987       36162       38706        1694       28180       34906       40976\r\n       56291       22123       20737       46872       38244       43282       29263       32231       36299       35590\r\n       51482       39837       14258       42078       33542        3116       42356        4655       44568       28772\r\n       33644       48578       16452       27462        5412       22857       34157       58178       24064       18836\r\n       11639        6869       58518       25608       47157       29579       24399        4235       15682       32876\r\n       26121        8381       46086       53486       65284       15787       61416       28585       37940       49908\r\n        8777       36014       36420       20802       23234       46861       54364       54173       56812       49965\r\n        2024       31799       12087       53381       63652       56110       55645       25856       26658       37752\r\n       61547       58358       13895       51712       22704       18448       24414       40204        7380       48998\r\n       19746       52360        5069       55853       58100       47910       38874       53650       29087       42305\r\n       19368       48125       59886       33137       29798        9028       57183       58080       19672        8075\r\n       21819        3364       46315       41658       27094       54835       61177       61021       26305       33056\r\n       30609        4776       36555       62317       14269        9083       43808       12503       54615       22758\r\n       42480        5801       20540       29095        8234       38548       13551       16946       26452        6038\r\n        1653       52320       10892        3933       20245       23996       42850       58842       25570        9689\r\n       55194       61800       40795       56803       47585       52871        4721       38886       23622       12987\r\n       36636       44807       64745       41365       51306       33015       26655       33019        9191       44057\r\n       55974        8656       11169       23270       45468       32086       43708       40161       17047       28279\r\n       22798       47364       16894       65339         642       57478       61192       53701        5689       45508\r\n       29230        7232       26004       14691       55260       23143       53146       34857       28140       16828\r\n        3554        7700        4849       42759       60445       29454       31755       13243       16861         639\r\n       11606       41990       44832       39648       50525       63145       49594       29746       19500       34883\r\n       43437       21549       26370       25378        2795        2772       27331       28043       27843       18310\r\n       21681       42848       64411        9318       24784       63763       63686       63311        7812       62012\r\n       58883       49095       26357        1647       46159       12399       64747       40635       32444       59404\r\n        7743       38219       40676       27598       47809       43720       56632       45573       46295       25734\r\n       64776       48498       10116       12065       14698       38432       25485       47196       15962        1628\r\n       35388       15389       24991       47564       17632       44244       29801       22734       51450       44003\r\n       46328       48166       10560       24272       44107       23659       16166       33881        4855       54864\r\n       65502       63609       49683       55152       31292       40650       51407       36483       25813       63668\r\n       18864       56815       57089       48118       40875       53159       57857       10256         222        3731\r\n       27166        5651       22988       37422       15495        1262       59881       36834       14462       29512\r\n       30463       24014       44927       11590       11607        5496       36587       45534          85       38172\r\n       50066       24195       19277       62743       54371       63884       39247       27948       12398       44999\r\n       53621       44894       34775       17388       50260       42686        9756       54805        9337       47148\r\n        6568       39186       54553       60593       61241       15154       58963       47932       17568       42601\r\n       11673       51731       39157       14665        7070       26443       29516       23594       11461       47639\r\n       23569       24094       21974       24481       11942        7996       13478       29767        9086       24500\r\n        3716       13502       19610        5734        6494       17592       58959       25322       39248       38114\r\n       34202        5679       29661       41950       32097       16898       49976       50826       59051        7609\r\n       22010       50589       27698       11836       12664       21736       57834       48121       61563        3778\r\n       11512       13479       23567        2952       58713        9976       18674       28198       14495       64209\r\n       13693       25445       36590       47393        6493       22807       44120       45465       31632       18666\r\n       59320       36161       48663       22769        2894        7973       43534       61945       24642       38992\r\n       44262       15004       27809       43294       36522       57943        8048       51395       34326       63056\r\n       30701       42070       28138       25157       50626        6178       26694       46240       17358       12175\r\n       59777       31750        8183       41113       20443       60951       18041        7165        4479       12651\r\n        6816        9951        1601        1418       11729       26150       46967       25554       28595       22389\r\n       48860       51244       19017       59675       22213        3106       18571       38725       11393       61138\r\n       48252        6593       20809       52465       13772       22437       58733       30105        1710       25602];\r\n[P,p]=montgomeryMult(a,R,N);\r\nassert(isequal(P,Y))\r\nassert(isequal(y,p(10:100:end)))\r\n%%\r\nN=3347;\r\nR=2^16;\r\na =[    1112       36822       19271       42840       48879       33433       48232       54170        3299       62565\r\n        7920       12071       15556       62713       53288       59399       52080       25560       14987       28219\r\n       56538       39138       34791       61324       25120       41217       35710       32630       54669       63016\r\n       31738       19656        5996       30008       40454        6654       44972       45534        1025       49965\r\n       55368        8789       26562       15759       37715       25615       58565       54681       56604         481\r\n       13723       13933        6871       50062       34737        3579        3590       39952        5116       44567\r\n       36194       58650        7358       49763       18026       32852       19900       37665       43846       46265\r\n       41280        4682       51408       48539       16294       28293        3027       21367       32781       42279\r\n        2096       15891       19108       48738       29598       65376       12810       29912       14286       36196\r\n       40285        3522       39553        6941       14923       53189       47196       46779       37461       14293\r\n       23750       28948       63204       44666       52720       31827       47300       57960        8007       50617\r\n        3246         870       28343       30360       64625       58618       57527       47241       43985       14944\r\n       32084       58798       45531       13904        1965        9014       38170        1219       39294       24304\r\n       12616       12888       49682        6456       35105       25559        4632       44222        3668       58387\r\n        8066        6119       28353       53973        5706       60775       60472       28738        3692       56123\r\n       13467       20143       42958       11469       52565       60128       52453       28692        9994       26373\r\n        9602       29888        7192       10719       64824       46764       18739        7670        1285       20841\r\n       12391        6663       61194       43646        4387       40523       35629       53390       28519       39887\r\n        2795       65233       12285       58614       61564       22497       64538       21289       54540       59650\r\n       41628       21764       17444       33853        1191       61343       46902       16136       40461       59578\r\n       18472       19486       52286       46052       44816        8177       54982       22460       34087       38770\r\n       35297        4066       31955       10065       51362       47879       28394       24621       56614       21795\r\n       45558       19545       50394       62485       35005       42367       30842       35818        6402       55906\r\n       32710        3037       25952       35447       58022       54601       36746       36825       59510       28992\r\n       35114       33123       17887       44547       58917       26101       17635       25940        7078       59267\r\n       29175       49900        2440        2396       41021       49140       49087       26091       33881        2174\r\n        8122       41357       44125       53031        9035       54737       33022       33775        9381       34893\r\n       32136        5891       28151       49061       14273       21132       42389       43091       36658       46956\r\n       55902        5299       29605        7876       11936       36193       20168       62319         300       11750\r\n       57273       50937       39967       34409        2740       64168        9091       47339       50245       22055\r\n       17714       59318        3893       21353        7008       35999       31167       26219       55621       12301\r\n       13661       34981       20697       35812       40399       21654       23754       54517       60084       21097\r\n       37026        7153       50641       26141       61581       40597       51649        8803       64681       26467\r\n       41963       54120       45641       27203       23229       23634       51137        3962       33104       35950\r\n       27330       22157        8213       11844       26910       49578       43811        5521       17787        3194\r\n       13498       19265        8529       16737       64510       27125        8749       10741        6602       36223\r\n       62123       48910        6052        1345       61969       32266        1412       21248       33282       18010\r\n        5378         677         512       60534       44344       45530       36689       19773       38378       15827\r\n        6927        3175       27728       42840       64769       63749       19714         765       49996       15934\r\n        9308       43772       42963       61119       50255       21479       61565       35383        5437       10102\r\n       10909       39548       47377       10715       22065       54906       64284        6250       43358       62679\r\n       40695       34478       34813       60365       43409       48435       18783        9601       33880       61319\r\n       37598       47822        7131       52078       16001       62532       52482       41362       11209       53655\r\n        3412       46350       41403       37840       19366        2092       58727       56316       61509       47727\r\n       61027       51208        8290       28838       44596       23387       39159       63846       38697       11521\r\n       47753       18872        8801       16882       34592       43427       57934       37410       28877       23617\r\n       48355       45385        6461       49279       26974       18448       61848       65329       61729       12372\r\n        4155       36481        9307       14986       39494       15098       35989       36276       42985          78\r\n       56389       25986       11026        4206       49186       46604       47735       33781       29618       20736\r\n       61237        4036       12861       50287       38242       40932       37798       21671       55030       45850\r\n       64513       51129       20806       43987       36162       38706        1694       28180       34906       40976\r\n       56291       22123       20737       46872       38244       43282       29263       32231       36299       35590\r\n       51482       39837       14258       42078       33542        3116       42356        4655       44568       28772\r\n       33644       48578       16452       27462        5412       22857       34157       58178       24064       18836\r\n       11639        6869       58518       25608       47157       29579       24399        4235       15682       32876\r\n       26121        8381       46086       53486       65284       15787       61416       28585       37940       49908\r\n        8777       36014       36420       20802       23234       46861       54364       54173       56812       49965\r\n        2024       31799       12087       53381       63652       56110       55645       25856       26658       37752\r\n       61547       58358       13895       51712       22704       18448       24414       40204        7380       48998\r\n       19746       52360        5069       55853       58100       47910       38874       53650       29087       42305\r\n       19368       48125       59886       33137       29798        9028       57183       58080       19672        8075\r\n       21819        3364       46315       41658       27094       54835       61177       61021       26305       33056\r\n       30609        4776       36555       62317       14269        9083       43808       12503       54615       22758\r\n       42480        5801       20540       29095        8234       38548       13551       16946       26452        6038\r\n        1653       52320       10892        3933       20245       23996       42850       58842       25570        9689\r\n       55194       61800       40795       56803       47585       52871        4721       38886       23622       12987\r\n       36636       44807       64745       41365       51306       33015       26655       33019        9191       44057\r\n       55974        8656       11169       23270       45468       32086       43708       40161       17047       28279\r\n       22798       47364       16894       65339         642       57478       61192       53701        5689       45508\r\n       29230        7232       26004       14691       55260       23143       53146       34857       28140       16828\r\n        3554        7700        4849       42759       60445       29454       31755       13243       16861         639\r\n       11606       41990       44832       39648       50525       63145       49594       29746       19500       34883\r\n       43437       21549       26370       25378        2795        2772       27331       28043       27843       18310\r\n       21681       42848       64411        9318       24784       63763       63686       63311        7812       62012\r\n       58883       49095       26357        1647       46159       12399       64747       40635       32444       59404\r\n        7743       38219       40676       27598       47809       43720       56632       45573       46295       25734\r\n       64776       48498       10116       12065       14698       38432       25485       47196       15962        1628\r\n       35388       15389       24991       47564       17632       44244       29801       22734       51450       44003\r\n       46328       48166       10560       24272       44107       23659       16166       33881        4855       54864\r\n       65502       63609       49683       55152       31292       40650       51407       36483       25813       63668\r\n       18864       56815       57089       48118       40875       53159       57857       10256         222        3731\r\n       27166        5651       22988       37422       15495        1262       59881       36834       14462       29512\r\n       30463       24014       44927       11590       11607        5496       36587       45534          85       38172\r\n       50066       24195       19277       62743       54371       63884       39247       27948       12398       44999\r\n       53621       44894       34775       17388       50260       42686        9756       54805        9337       47148\r\n        6568       39186       54553       60593       61241       15154       58963       47932       17568       42601\r\n       11673       51771       39157       14665        7070       26443       29516       23594       11461       47639\r\n       23569       24094       21974       24481       11942        7996       13478       29767        9086       24500\r\n        3716       13502       19610        5734        6494       17592       58959       25322       39248       38114\r\n       34202        5679       29661       41950       32097       16898       49976       50826       59051        7609\r\n       22010       50589       27698       11836       12664       21736       57834       48121       61563        3778\r\n       11512       13479       23567        2952       58713        9976       18674       28198       14495       64209\r\n       13693       25445       36590       47393        6493       22807       44120       45465       31632       18666\r\n       59320       36161       48663       22769        2894        7973       43534       61945       24642       38992\r\n       44262       15004       27809       43294       36522       57943        8048       51395       34326       63056\r\n       30701       42070       28138       25157       50626        6178       26694       46240       17358       12175\r\n       59777       31750        8183       41113       20443       60951       18041        7165        4479       12651\r\n        6816        9951        1601        1418       11729       26150       46967       25554       28595       22389\r\n       48860       51244       19017       59675       22213        3106       18571       38725       11393       61138\r\n       48252        6593       20809       52465       13772       22437       58733       30105        1710       25602];\r\nY=1870;\r\ny=[130,1496,2440,2533,1292,1876,783,751,107,3006];\r\n[P,p]=montgomeryMult(a,R,N);\r\nassert(isequal(P,Y))\r\nassert(isequal(y,p(10:100:end)))\r\n%%\r\nR=2^16;\r\nN=3967;\r\nY=3799;\r\ny=[788,2020,2960,1688,2874,3752,1280,2265,1542,1371];\r\na =[    1112       36822       19271       42840       48879       33433       48232       54170        3299       62565\r\n        7920       12071       15556       62713       53288       59399       52080       25560       14987       28219\r\n       56538       39138       34791       61324       25120       41217       35710       32630       54669       63016\r\n       31738       19656        5996       30008       40454        6654       44972       45534        1025       49965\r\n       55368        8789       26562       15759       37715       25615       58565       54681       56604         481\r\n       13723       13933        6871       50062       34737        3579        3590       39952        5116       44567\r\n       36194       58650        7358       49763       18026       32852       19900       37665       43846       46265\r\n       41280        4682       51408       48539       16294       28293        3027       21367       32781       42279\r\n        2096       15891       19108       48738       29598       65376       12810       29912       14286       36196\r\n       40285        3522       39553        6941       14923       53189       47196       46779       37461       14293\r\n       23750       28948       63204       44666       52720       31827       47300       57960        8007       50617\r\n        3246         870       28343       30360       64625       58618       57527       47241       43985       14944\r\n       32084       58798       45531       13904        1965        9014       38170        1219       39294       24304\r\n       12616       12888       49682        6456       35105       25559        4632       44222        3668       58387\r\n        8066        6119       28353       53973        5706       60775       60472       28738        3692       56123\r\n       13467       20143       42958       11469       52565       60128       52453       28692        9994       26373\r\n        9602       29888        7192       10719       64824       46764       18739        7670        1285       20841\r\n       12391        6663       61194       43646        4387       40523       35629       53390       28519       39887\r\n        2795       65233       12285       58614       61564       22497       64538       21289       54540       59650\r\n       41628       21764       17444       33853        1191       61343       46902       16136       40461       59578\r\n       18472       19486       52286       46052       44816        8177       54982       22460       34087       38770\r\n       35297        4066       31955       10065       51362       47879       28394       24621       56614       21795\r\n       45558       19545       50394       62485       35005       42367       30842       35818        6402       55906\r\n       32710        3037       25952       35447       58022       54601       36746       36825       59510       28992\r\n       35114       33123       17887       44547       58917       26101       17635       25940        7078       59267\r\n       29175       49900        2440        2396       41021       49140       49087       26091       33881        2174\r\n        8122       41357       44125       53031        9035       54737       33022       33775        9381       34893\r\n       32136        5891       28151       49061       14273       21132       42389       43091       36658       46956\r\n       55902        5299       29605        7876       11936       36193       20168       62319         300       11750\r\n       57273       50937       39967       34409        2740       64168        9091       47339       50245       22055\r\n       17714       59318        3893       21353        7008       35999       31167       26219       55621       12301\r\n       13661       34981       20697       35812       40399       21654       23754       54517       60084       21097\r\n       37026        7153       50641       26141       61581       40597       51649        8803       64681       26467\r\n       41963       54120       45641       27203       23229       23634       51137        3962       33104       35950\r\n       27330       22157        8213       11844       26910       49578       43811        5521       17787        3194\r\n       13498       19265        8529       16737       64510       27125        8749       10741        6602       36223\r\n       62123       48910        6052        1345       61969       32266        1412       21248       33282       18010\r\n        5378         677         512       60534       44344       45530       36689       19773       38378       15827\r\n        6927        3175       27728       42840       64769       63749       19714         765       49996       15934\r\n        9308       43772       42963       61119       50255       21479       61565       35383        5437       10102\r\n       10909       39548       47377       10715       22065       54906       64284        6250       43358       62679\r\n       40695       34478       34813       60365       43409       48435       18783        9601       33880       61319\r\n       37598       47822        7131       52078       16001       62532       52482       41362       11209       53655\r\n        3412       46350       41403       37840       19366        2092       58727       56316       61509       47727\r\n       61027       51208        8290       28838       44596       23387       39159       63846       38697       11521\r\n       47753       18872        8801       16882       34592       43427       57934       37410       28877       23617\r\n       48355       45385        6461       49279       26974       18448       61848       65329       61729       12372\r\n        4155       36481        9307       14986       39494       15098       35989       36276       42985          78\r\n       56389       25986       11026        4206       49186       46604       47735       33781       29618       20736\r\n       61237        4036       12861       50287       38242       40932       37798       21671       55030       45850\r\n       64513       51129       20806       43987       36162       38706        1694       28180       34906       40976\r\n       56291       22123       20737       46872       38244       43282       29263       32231       36299       35590\r\n       51482       39837       14258       42078       33542        3116       42356        4655       44568       28772\r\n       33644       48578       16452       27462        5412       22857       34157       58178       24064       18836\r\n       11639        6869       58518       25608       47157       29579       24399        4235       15682       32876\r\n       26121        8381       46086       53486       65284       15787       61416       28585       37940       49908\r\n        8777       36014       36420       20802       23234       46861       54364       54173       56812       49965\r\n        2024       31799       12087       53381       63652       56110       55645       25856       26658       37752\r\n       61547       58358       13895       51712       22704       18448       24414       40204        7380       48998\r\n       19746       52360        5069       55853       58100       47910       38874       53650       29087       42305\r\n       19368       48125       59886       33137       29798        9028       57183       58080       19672        8075\r\n       21819        3364       46315       41658       27094       54835       61177       61021       26305       33056\r\n       30609        4776       36555       62317       14269        9083       43808       12503       54615       22758\r\n       42480        5801       20540       29095        8234       38548       13551       16946       26452        6038\r\n        1653       52320       10892        3933       20245       23996       42850       58842       25570        9689\r\n       55194       61800       40795       56803       47585       52871        4721       38886       23622       12987\r\n       36636       44807       64745       41365       51306       33015       26655       33019        9191       44057\r\n       55974        8656       11169       23270       45468       32086       43708       40161       17047       28279\r\n       22798       47364       16894       65339         642       57478       61192       53701        5689       45508\r\n       29230        7232       26004       14691       55260       23143       53146       34857       28140       16828\r\n        3554        7700        4849       42759       60445       29454       31755       13243       16861         639\r\n       11606       41990       44832       39648       50525       63145       49594       29746       19500       34883\r\n       43437       21549       26370       25378        2795        2772       27331       28043       27843       18310\r\n       21681       42848       64411        9318       24784       63763       63686       63311        7812       62012\r\n       58883       49095       26357        1647       46159       12399       64747       40635       32444       59404\r\n        7743       38219       40676       27598       47809       43720       56632       45573       46295       25734\r\n       64776       48498       10116       12065       14698       38432       25485       47196       15962        1628\r\n       35388       15389       24991       47564       17632       44244       29801       22734       51450       44003\r\n       46328       48166       10560       24272       44107       23659       16166       33881        4855       54864\r\n       65502       63609       49683       55152       31292       40650       51407       36483       25813       63668\r\n       18864       56815       57089       48118       40875       53159       57857       10256         222        3731\r\n       27166        5651       22988       37422       15495        1262       59881       36834       14462       29512\r\n       30463       24014       44927       11590       11607        5496       36587       45534          85       38172\r\n       50066       24195       19277       62743       54371       63884       39247       27948       12398       44999\r\n       53621       44894       34775       17388       50260       42686        9756       54805        9337       47148\r\n        6568       39186       54553       60593       61241       15154       58963       47932       17568       42601\r\n       11673       51771       39157       14665        7070       26443       29516       23594       11461       47639\r\n       23569       24094       21974       24481       11942        7996       13478       29767        9086       24500\r\n        3716       13502       19610        5734        6494       17592       58959       25322       39248       38114\r\n       34202        5679       29661       41950       32097       16898       49976       50826       59051        7609\r\n       22010       50589       27698       11836       12664       21736       57834       48121       61563        3778\r\n       11512       13479       23567        2952       58713        9976       18674       28198       14495       64209\r\n       13693       25445       36590       47393        6493       22807       44120       45465       31632       18666\r\n       59320       36161       48663       22769        2894        7973       43534       61945       24642       38992\r\n       44262       15004       27809       43294       36522       57943        8048       51395       34326       63056\r\n       30701       42070       28138       25157       50626        6178       26694       46240       17358       12175\r\n       59777       31750        8183       41113       20443       60951       18041        7165        4479       12651\r\n        6816        9951        1601        1418       11729       26150       46967       25554       28595       22999\r\n       48860       51244       19017       59675       22213        3106       18571       38725       11393       61138\r\n       48252        6593       20809       52465       13772       22437       58733       30105        1710       25602];\r\n[P,p]=montgomeryMult(a,R,N);\r\nassert(isequal(P,Y))\r\nassert(isequal(y,p(10:100:end)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-09-30T21:17:47.000Z","updated_at":"2025-10-12T15:14:20.000Z","published_at":"2020-09-30T21:17:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMultiply all elements of an input matrix (A) modulo N, given all elements are less than R (2^number of bits). Where gcd(R,N)=1 and N\u0026lt;R. Output the final result, P (in normal form) and all intermediate products (p) in Montgomery form (first product is just first element of matrix (A)*R modulo N).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2266,"title":"2048 tile game","description":"The popular 2048 game has been implemented here:\r\n\r\nhttp://gabrielecirulli.github.io/2048/\r\n\r\nGiven the board like this:\r\n\r\n  [2 4 8 0\r\n   4 0 0 0\r\n   2 0 0 0\r\n   2 0 4 0]\r\n\r\nYou give the direction\r\n\r\n1 (left)\r\n2 (up)\r\n3 (right)\r\n4 (down)\r\n\r\nThe system here will keep calling your solver.  Score for each board is the biggest tile achieved.  The Cody score is the maximum board score plus the average score across all 200 boards.","description_html":"\u003cp\u003eThe popular 2048 game has been implemented here:\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://gabrielecirulli.github.io/2048/\"\u003ehttp://gabrielecirulli.github.io/2048/\u003c/a\u003e\u003c/p\u003e\u003cp\u003eGiven the board like this:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e[2 4 8 0\r\n 4 0 0 0\r\n 2 0 0 0\r\n 2 0 4 0]\r\n\u003c/pre\u003e\u003cp\u003eYou give the direction\u003c/p\u003e\u003cp\u003e1 (left)\r\n2 (up)\r\n3 (right)\r\n4 (down)\u003c/p\u003e\u003cp\u003eThe system here will keep calling your solver.  Score for each board is the biggest tile achieved.  The Cody score is the maximum board score plus the average score across all 200 boards.\u003c/p\u003e","function_template":"function direction = getMove(board)\r\n  direction = 1;\r\nend","test_suite":"%%\r\nfh=fopen('main.m','wt');\r\nfprintf(fh, '%s \\n', 'function out = main(n)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'result = 0;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'for i = 1:n    ');\r\nfprintf(fh, '%s \\n', '    board = zeros(4);');\r\nfprintf(fh, '%s \\n', '    board = saltBoard(board);');\r\nfprintf(fh, '%s \\n', '    board = saltBoard(board);');\r\nfprintf(fh, '%s \\n', '    %dispBoard(board)');\r\nfprintf(fh, '%s \\n', '    direction = 1;');\r\nfprintf(fh, '%s \\n', '    while (direction ~= 0)');\r\nfprintf(fh, '%s \\n', '        %pause(0.1)');\r\nfprintf(fh, '%s \\n', '        %clc');\r\nfprintf(fh, '%s \\n', '        direction = getMove(board);');\r\nfprintf(fh, '%s \\n', '        board = updateBoard(board, direction);');\r\nfprintf(fh, '%s \\n', '        %dispBoard(board)');\r\nfprintf(fh, '%s \\n', '    end');\r\nfprintf(fh, '%s \\n', '    %figure(1)');\r\nfprintf(fh, '%s \\n', '    %dispBoard(board)');\r\nfprintf(fh, '%s \\n', '    %figure(2)');\r\nfprintf(fh, '%s \\n', '    %hist(result,[2 4 8 16 32 64 128 256 512 1024,2048])');\r\nfprintf(fh, '%s \\n', '    %drawnow');\r\nfprintf(fh, '%s \\n', '    result(i) = max(board(:));');\r\nfprintf(fh, '%s \\n', '    %disp([i result(i) max(result)])');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = max(result) + mean(result)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = collapse(in)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'in = squish(in);');\r\nfprintf(fh, '%s \\n', 'for i = 1:3');\r\nfprintf(fh, '%s \\n', '    result = miniCollapse(in(i:i+1));');\r\nfprintf(fh, '%s \\n', '    out(i:i+1) = result;');\r\nfprintf(fh, '%s \\n', '     in(i:i+1) = result;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = squish(in);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = squish(in);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = in(in ~= 0);');\r\nfprintf(fh, '%s \\n', 'if numel(out) ~= 4');\r\nfprintf(fh, '%s \\n', '    out(4) = 0;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = miniCollapse(in)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'if in(1) == in(2)');\r\nfprintf(fh, '%s \\n', '    out(1) = in(1) * 2;');\r\nfprintf(fh, '%s \\n', '    out(2)  = 0;');\r\nfprintf(fh, '%s \\n', 'else');\r\nfprintf(fh, '%s \\n', '    out = in;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = saltBoard(in)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'if nnz(in) == 16');\r\nfprintf(fh, '%s \\n', '    out = nan;');\r\nfprintf(fh, '%s \\n', '    return;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'vi = find(in == 0);');\r\nfprintf(fh, '%s \\n', 'selected = randi(numel(vi));');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'thresh = 0.1;');\r\nfprintf(fh, '%s \\n', 'if (rand \u003c thresh)');\r\nfprintf(fh, '%s \\n', '    salt = 4;');\r\nfprintf(fh, '%s \\n', 'else');\r\nfprintf(fh, '%s \\n', '    salt = 2;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = in;');\r\nfprintf(fh, '%s \\n', 'out(vi(selected)) = salt;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function board = updateBoard(board, direction)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'boardOriginal = board;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'board = collapseBoard(board,direction);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'if ~isequal(boardOriginal, board)');\r\nfprintf(fh, '%s \\n', '    board = saltBoard(board);');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function dispBoard(board)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'clf');\r\nfprintf(fh, '%s \\n', 'r = 1;');\r\nfprintf(fh, '%s \\n', 'c = 1;');\r\nfprintf(fh, '%s \\n', 'v = 2;');\r\nfprintf(fh, '%s \\n', 'for r = 1:4');\r\nfprintf(fh, '%s \\n', '    for c = 1:4');\r\nfprintf(fh, '%s \\n', '        v = board(r,c);');\r\nfprintf(fh, '%s \\n', '        dispSquare(r,c,v)');\r\nfprintf(fh, '%s \\n', '    end');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function dispSquare(r,c,v)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'cmap = autumn(12);');\r\nfprintf(fh, '%s \\n', 'absIndex = (r-1)*4 + c;');\r\nfprintf(fh, '%s \\n', 'if v == 0 ');\r\nfprintf(fh, '%s \\n', '    cMapIndex = 1;');\r\nfprintf(fh, '%s \\n', 'else');\r\nfprintf(fh, '%s \\n', '    cMapIndex = log2(v) + 1;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'h = subplot(4,4,absIndex);');\r\nfprintf(fh, '%s \\n', 'set(h,''xtick'',[])');\r\nfprintf(fh, '%s \\n', 'set(h,''ytick'',[])');\r\nfprintf(fh, '%s \\n', 'set(h,''color'',cmap(cMapIndex,:))');\r\nfprintf(fh, '%s \\n', '%axis off');\r\nfprintf(fh, '%s \\n', 'text(0.5,0.5,num2str(v), ''fontsize'', 20)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function flag = isMoveDirection(board, direction)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'originalBoard = board;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'board = updateBoard(board, direction);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'flag = ~isequal(board, originalBoard);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = collapseBoard(in, direction)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'rotDirection = direction-1;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'in = rot90(in,rotDirection);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'for r = 1:4');\r\nfprintf(fh, '%s \\n', '    out(r,:) = collapse(in(r,:));');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = rot90(out,-rotDirection);');\r\n\r\nfclose(fh);\r\n\r\nrehash path\r\n%%\r\nn = 200;\r\nscore = main(n)\r\nscore = 4056 - score;\r\n\r\nassert(score \u003c (4056 - 256))\r\nassignin('caller','score',score)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":240,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2014-04-02T17:36:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-04-01T20:01:55.000Z","updated_at":"2026-02-03T10:02:13.000Z","published_at":"2014-04-02T14:29:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe popular 2048 game has been implemented here:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://gabrielecirulli.github.io/2048/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://gabrielecirulli.github.io/2048/\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the board like this:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[2 4 8 0\\n 4 0 0 0\\n 2 0 0 0\\n 2 0 4 0]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou give the direction\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 (left) 2 (up) 3 (right) 4 (down)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe system here will keep calling your solver. Score for each board is the biggest tile achieved. The Cody score is the maximum board score plus the average score across all 200 boards.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60834,"title":"Bell 202 Decoder","description":"Decode an audio frequency shift key stream at a certain baud-rate and sample rate into a binary stream of data using the Bell 202 standard. \r\nWhere a '1' is represented as 1200 Hz and a  '0' is represnted as 2200 Hz.\r\nDuration of each bit is based on the baud-rate.\r\nDigitized audio stream is produced at the sample rate and is smooth between bits.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 66px; transform-origin: 408px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDecode an audio frequency shift key stream at a certain baud-rate and sample rate into a binary stream of data using the Bell 202 standard. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere a '1' is represented as 1200 Hz and a  '0' is represnted as 2200 Hz.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDuration of each bit is based on the baud-rate.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDigitized audio stream is produced at the sample rate and is smooth between bits.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function decodedStream = decodeBell202(audioSignal, sampleRate, bitRate)\r\n decodedStream=audioSignal/bitRate;\r\nend","test_suite":"%%\r\nrng(2718);\r\nbS=num2str(randi(2,1,1e4)-1);\r\nbS(bS==' ')=[];\r\nt = 1/1e5:1/1e5:1/9.2e2;\r\naS=[];\r\np=0;\r\nfor i = 1:length(bS)\r\n   if isequal(bS(i),'0')\r\n     aS=[aS, sin(2*pi*2200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*2200*t(end)+p));\r\n   else\r\n     aS=[aS, sin(2*pi*1200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*1200*t(end)+p));\r\n   end\r\nend\r\nassert(isequal(decodeBell202(aS,1e5,920),bS))\r\n%%\r\nrng(2718);\r\nbS=num2str(randi(2,1,1e4)-1);\r\nbS(bS==' ')=[];\r\nt = 1/1e5:1/1e5:1/1e3;\r\naS=[];\r\np=0;\r\nfor i = 1:length(bS)\r\n   if isequal(bS(i),'0')\r\n     aS=[aS, sin(2*pi*2200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*2200*t(end)+p));\r\n   else\r\n     aS=[aS, sin(2*pi*1200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*1200*t(end)+p));\r\n   end\r\nend\r\nassert(isequal(decodeBell202(aS,1e5,1e3),bS))\r\n%%\r\nbS='1011110001100110011001110001110101011010101010111000111000111000111100011100110101011001';\r\nt = 1/1.2e5:1/1.2e5:1/600;\r\naS=[];\r\np=0;\r\nfor i = 1:length(bS)\r\n   if isequal(bS(i),'0')\r\n     aS=[aS, sin(2*pi*2200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*2200*t(end)+p));\r\n   else\r\n     aS=[aS, sin(2*pi*1200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*1200*t(end)+p));\r\n   end\r\nend\r\nassert(isequal(decodeBell202(aS,1.2e5,600),bS))\r\n%%","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-03-27T15:12:44.000Z","updated_at":"2025-12-07T15:19:32.000Z","published_at":"2025-03-27T15:12:43.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDecode an audio frequency shift key stream at a certain baud-rate and sample rate into a binary stream of data using the Bell 202 standard. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere a '1' is represented as 1200 Hz and a  '0' is represnted as 2200 Hz.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDuration of each bit is based on the baud-rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDigitized audio stream is produced at the sample rate and is smooth between bits.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60749,"title":"Compute the dispersion coefficient","description":"A contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\r\nG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \r\n\r\nwhere  is the width of the stream,  is the transverse mixing coefficient, and  is the deviation of the velocity profile from the cross-sectional average velocity\r\n\r\nWrite a function that takes a (normalized) velocity profile  specified at several points and computes the quantity \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 375px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 187.5px; transform-origin: 407px 187.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"240\" height=\"44\" alt=\"K = -(1/hD) integral(u' integral(integral(u'(y2),0\u003c=y2\u003c=y1),0\u003c=y1\u003c=y),0\u003c=y\u003c=h)\" style=\"width: 240px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the stream, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eD\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the transverse mixing coefficient, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"64\" height=\"19\" alt=\"u' = u - bar(u)\" style=\"width: 64px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the deviation of the velocity profile from the cross-sectional average velocity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"103\" height=\"44\" alt=\"ubar = (1/h) integral(u(y),0\u003c=y\u003c=h)\" style=\"width: 103px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a (normalized) velocity profile \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"30\" height=\"18\" alt=\"u(y)\" style=\"width: 30px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e specified at several points and computes the quantity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"215\" height=\"44\" alt=\"I = -integral(u' integral(integral(u'(y2),0\u003c=y2\u003c=y1),0\u003c=y1\u003c=y),0\u003c=y\u003c=h)\" style=\"width: 215px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = computeK(y,u)\r\n  I = -integral(u'*integral(integral(u',0,y1),0,y),0,h);\r\nend","test_suite":"%%\r\nny = 1000;\r\ny = linspace(0,1,ny);\r\nu = y.*(1-y);\r\nI = computeK(y,u);\r\nI_correct = 1/7560;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6);\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = 2*y;\r\nu(y\u003e1/2) = 2*(1-y(y\u003e1/2));\r\nI = computeK(y,u);\r\nI_correct = 1/480;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6);\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 2.5; \r\nb = 2.5;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.00788915;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 2.5; \r\nb = 3;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.01168232;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 3.2; \r\nb = 3.2;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.01192484;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-10-16T01:19:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-10-16T01:18:30.000Z","updated_at":"2024-10-27T15:58:26.000Z","published_at":"2024-10-16T01:19:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = -(1/hD) integral(u' integral(integral(u'(y2),0\u0026lt;=y2\u0026lt;=y1),0\u0026lt;=y1\u0026lt;=y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = -\\\\frac{1}{hD}\\\\int_0^h u^\\\\prime \\\\int_0^y \\\\int_0^{y_1} u^\\\\prime(y_2) dy_2 dy_1 dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the stream, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the transverse mixing coefficient, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u' = u - bar(u)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu^\\\\prime = u-{\\\\bar u}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the deviation of the velocity profile from the cross-sectional average velocity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ubar = (1/h) integral(u(y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\bar u} = \\\\frac{1}{h} \\\\int_0^h u(y) dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a (normalized) velocity profile \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u(y)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu(y)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e specified at several points and computes the quantity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = -integral(u' integral(integral(u'(y2),0\u0026lt;=y2\u0026lt;=y1),0\u0026lt;=y1\u0026lt;=y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = -\\\\int_0^h u^\\\\prime \\\\int_0^y \\\\int_0^{y_1} u^\\\\prime(y_2) dy_2 dy_1 dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1949,"title":"Get top 5 Cody Player Emails Automatically","description":"Yes, this is a little scary and also entirely possible to do in MATLAB, so let's do it!\r\n\r\nLooking at the list of the players \u003chttp://www.mathworks.com/matlabcentral/cody/players\u003e automatically sorts them in order according to rank. For times sake, let's say we only want to get the emails from the first 5 people. This is relatively easy to do by hand, just click on the persons name, click on \"View Profile Information\" and you have the email but if you wanted to do say the first 1,000 people instead, that would be not very fun to do by hand. \r\n\r\nFor this program, let's say we want the top 5 profiles that give a \"real\" email address (not a contact form) to be in a cell array. This means that if one of the top 5 people have removed their email address, your returned cell array will have less than 5 emails in it. \r\n\r\nIf you are not sure where to start, check out the urlread command, it allows you to put the web page source code into a string. From there, you are able to parse through that to get the URLs for the top 5 players web profile. From there, look for a \"mailto:\" and if it is there, the email address is immediately following it. If the string \"mailto:\" does not exist, there is no email address on that webpage. Put the emails in a cell array when you find them and you are good to go!\r\n\r\nAs an example, I have poorly written MATLAB code that works in the test case since I want the test case to always be accurate. 98% of the execution time is spent reading the webpages, and at least on my computer, that takes quite a while to do (about 2.5 seconds per profile page).\r\n\r\n*I am definitely not collecting emails for anything, and you should not either! This is designed solely as a learning example and should in no way be used for anything unethical. All information obtained here is easily obtained by anyone in the world who knows how to program.*\r\n\r\n*If this scares you and you want to remove your email address from your profile, it's easy. All you have to do is click \"My Community Profile\" (underneath the search bar at very top of screen) and then edit your preferences to not display your email address.* ","description_html":"\u003cp\u003eYes, this is a little scary and also entirely possible to do in MATLAB, so let's do it!\u003c/p\u003e\u003cp\u003eLooking at the list of the players \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/players\"\u003ehttp://www.mathworks.com/matlabcentral/cody/players\u003c/a\u003e automatically sorts them in order according to rank. For times sake, let's say we only want to get the emails from the first 5 people. This is relatively easy to do by hand, just click on the persons name, click on \"View Profile Information\" and you have the email but if you wanted to do say the first 1,000 people instead, that would be not very fun to do by hand.\u003c/p\u003e\u003cp\u003eFor this program, let's say we want the top 5 profiles that give a \"real\" email address (not a contact form) to be in a cell array. This means that if one of the top 5 people have removed their email address, your returned cell array will have less than 5 emails in it.\u003c/p\u003e\u003cp\u003eIf you are not sure where to start, check out the urlread command, it allows you to put the web page source code into a string. From there, you are able to parse through that to get the URLs for the top 5 players web profile. From there, look for a \"mailto:\" and if it is there, the email address is immediately following it. If the string \"mailto:\" does not exist, there is no email address on that webpage. Put the emails in a cell array when you find them and you are good to go!\u003c/p\u003e\u003cp\u003eAs an example, I have poorly written MATLAB code that works in the test case since I want the test case to always be accurate. 98% of the execution time is spent reading the webpages, and at least on my computer, that takes quite a while to do (about 2.5 seconds per profile page).\u003c/p\u003e\u003cp\u003e\u003cb\u003eI am definitely not collecting emails for anything, and you should not either! This is designed solely as a learning example and should in no way be used for anything unethical. All information obtained here is easily obtained by anyone in the world who knows how to program.\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eIf this scares you and you want to remove your email address from your profile, it's easy. All you have to do is click \"My Community Profile\" (underneath the search bar at very top of screen) and then edit your preferences to not display your email address.\u003c/b\u003e\u003c/p\u003e","function_template":"function emails = getCodyEmails()\r\n  emails = {};\r\nend","test_suite":"%%\r\n% My code is below, it's used to generate the expected result.\r\n\r\n%Read in the player page\r\nplayerPage=urlread('http://www.mathworks.com/matlabcentral/cody/players');\r\n\r\n%Find where the web address for each profile starts\r\nstartIdx=strfind(playerPage,'\u003cdiv class=\"grid_53 push_3\"\u003e')+104; \r\n\r\n%Initialize output array\r\nemails={};\r\n\r\n%Get top 5 only\r\nfor i=1:5\r\n    % Get the profile page link\r\n   tempStr=playerPage(startIdx(i):startIdx(i)+100);\r\n   quoteIdx=strfind(tempStr,'\"')-1;\r\n   profilePageLink=['http://www.mathworks.com' tempStr(1:quoteIdx(1))];\r\n   \r\n   profilePage=urlread(profilePageLink);\r\n   % Try and find mailto link\r\n   tStartIdx=strfind(profilePage,'mailto');\r\n   \r\n   %If you could find it\r\n   if ~isempty(tStartIdx)\r\n       % Get the email\r\n       tEndIdx=strfind(profilePage(tStartIdx:tStartIdx+100),'\"')+tStartIdx;\r\n       \r\n       % Add it to our cell array\r\n       emails{length(emails)+1}=profilePage(tStartIdx+7:tEndIdx-2);\r\n   end\r\n    \r\nend\r\n\r\n\r\ntic\r\nyourResponse=getCodyEmails()\r\ntimeElapsed=toc\r\n\r\n\r\nassert(isequal(yourResponse,emails))\r\nassert(isequal(1,timeElapsed\u003e3))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":3743,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-20T05:40:10.000Z","updated_at":"2025-07-31T17:14:24.000Z","published_at":"2013-10-20T05:40:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYes, this is a little scary and also entirely possible to do in MATLAB, so let's do it!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLooking at the list of the players\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/players\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://www.mathworks.com/matlabcentral/cody/players\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e automatically sorts them in order according to rank. For times sake, let's say we only want to get the emails from the first 5 people. This is relatively easy to do by hand, just click on the persons name, click on \\\"View Profile Information\\\" and you have the email but if you wanted to do say the first 1,000 people instead, that would be not very fun to do by hand.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this program, let's say we want the top 5 profiles that give a \\\"real\\\" email address (not a contact form) to be in a cell array. This means that if one of the top 5 people have removed their email address, your returned cell array will have less than 5 emails in it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you are not sure where to start, check out the urlread command, it allows you to put the web page source code into a string. From there, you are able to parse through that to get the URLs for the top 5 players web profile. From there, look for a \\\"mailto:\\\" and if it is there, the email address is immediately following it. If the string \\\"mailto:\\\" does not exist, there is no email address on that webpage. Put the emails in a cell array when you find them and you are good to go!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs an example, I have poorly written MATLAB code that works in the test case since I want the test case to always be accurate. 98% of the execution time is spent reading the webpages, and at least on my computer, that takes quite a while to do (about 2.5 seconds per profile page).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eI am definitely not collecting emails for anything, and you should not either! This is designed solely as a learning example and should in no way be used for anything unethical. All information obtained here is easily obtained by anyone in the world who knows how to program.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf this scares you and you want to remove your email address from your profile, it's easy. All you have to do is click \\\"My Community Profile\\\" (underneath the search bar at very top of screen) and then edit your preferences to not display your email address.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":53990,"title":"Classify product/digit-sum sequences","description":"Cody Problem 53120 involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\r\nWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved Cody Problem 53120, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \r\nWrite a function to classify the product/digit-sum sequences given the first two terms  and . To encourage solvers to find the pattern, loops are banned, and to allow for large inputs,  and  are specified as strings. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 93px; transform-origin: 407.5px 93px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 309.642px 7.66667px; transform-origin: 309.642px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.883px 7.66667px; transform-origin: 383.883px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.075px 7.66667px; transform-origin: 103.075px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262.017px 7.66667px; transform-origin: 262.017px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to classify the product/digit-sum sequences given the first two terms \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93.35px 7.66667px; transform-origin: 93.35px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4px 7.66667px; transform-origin: 77.4px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are specified as strings. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = PDSseq(a,b)\r\n  c = [1 9 26 62 163];\r\n  y = c(a+b);\r\nend","test_suite":"%%\r\na = '1';\r\nb = '2';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7';\r\nb = '31';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '17';\r\nb = '28';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '51';\r\nb = '77';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '82';\r\nb = '262';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7021';\r\nb = '8878';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264';\r\nb = '412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8675308';\r\nb = '2941300';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '9142534264';\r\nb = '8424812653';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164';\r\nb = '8424812753';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '1352408463575';\r\nb = '9898989898985';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264534264534264534264';\r\nb = '412578412578412578412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '86753088675308867530886753088675308';\r\nb = '28413002941300294130029413002941300';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '914253426491425342649142534264914253463';\r\nb = '842481265384248126538424812653842481265324';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164842481275380314231648424812753';\r\nb = '84248127538031423164842481275380314231648424812756';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '43524084635758031423164842481275380314231648424812753';\r\nb = '98989898989858031423164842481275380614231648424812753';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = num2str(randi(835042)*57);\r\nb = char(randi(9,20,1)+48);\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = repelem('1',1,23);\r\na(randi(23)) = '4';\r\nb = num2str(10^randi(14));\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\nfiletext = fileread('PDSseq.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'system') || contains(filetext,'regexp') || contains(filetext,'java') || contains(filetext,'for') || contains(filetext,'while') || contains(filetext,'numpy'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2022-02-05T01:46:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-02-04T04:01:11.000Z","updated_at":"2026-01-15T18:05:52.000Z","published_at":"2022-02-04T04:04:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to classify the product/digit-sum sequences given the first two terms \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are specified as strings. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55315,"title":"Chain multiplication - 04","description":"Following up on the problem in 55305, you found the optimal way to multiply a chain of matrices.\r\nHowever, here in this problem, you will be given a chain of matrices as a string with parenthesis placed in certain places along with their dimensions. You have to find out the number of multiplications required if you multiply the matrices that way.\r\nFor example, \r\nd= [1, 2, 3, 2] and s = \"A(BC)\".\r\nhere, the sizes of the matrices are - A(1,2), B(2,3), and C(3,2).\r\nFirst, B and C are to be multiplied (since they are inside parenthesis). The resultant matrix is to be multiplied with A. You need to find out the total number of multiplications required, which is 12+4=16.\r\n\r\nn.b. only valid parenthesization are given in this problem for simplicity.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 273px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 136.5px; transform-origin: 407px 136.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFollowing up on the problem in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55305-chain-multiplication-02\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e55305\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, you found the optimal way to multiply a chain of matrices.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHowever, here in this problem, you will be given a chain of matrices as a string with parenthesis placed in certain places along with their dimensions. You have to find out the number of multiplications required if you multiply the matrices that way.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ed= [1, 2, 3, 2] and s = \"A(BC)\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ehere, the sizes of the matrices are - A(1,2), B(2,3), and C(3,2).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFirst, B and C are to be multiplied (since they are inside parenthesis). The resultant matrix is to be multiplied with A. You need to find out the total number of multiplications required, which is 12+4=16.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en.b. only valid parenthesization are given in this problem for simplicity.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = chain_mul_04(s,d)\r\n  y = x;\r\nend","test_suite":"%%\r\nd= [1, 2, 3, 2];\r\ns = \"A(BC)\";\r\ny_correct = 16;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n%%\r\nd= [1, 2, 3, 2];\r\ns = \"(AB)C\";\r\ny_correct = 12;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n%%\r\nd= [40, 20, 30, 10, 30];\r\ns = \"A(B(CD))\";\r\ny_correct = 51000;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n%%\r\nd= [40, 20, 30, 10, 30];\r\ns = \"(AB)(CD)\";\r\ny_correct = 69000;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n\r\n%%\r\nd= [81,213,78,96,2,1,98,102, 1200,4];\r\ns = \"(((AB)C)(DE))((FG)(HI))\";\r\ny_correct = 2460558;\r\nassert(isequal(chain_mul_04(s,d),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":363598,"edited_by":363598,"edited_at":"2022-08-16T22:04:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-16T21:31:49.000Z","updated_at":"2022-08-16T22:04:11.000Z","published_at":"2022-08-16T22:04:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollowing up on the problem in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55305-chain-multiplication-02\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e55305\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, you found the optimal way to multiply a chain of matrices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHowever, here in this problem, you will be given a chain of matrices as a string with parenthesis placed in certain places along with their dimensions. You have to find out the number of multiplications required if you multiply the matrices that way.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ed= [1, 2, 3, 2] and s = \\\"A(BC)\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehere, the sizes of the matrices are - A(1,2), B(2,3), and C(3,2).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst, B and C are to be multiplied (since they are inside parenthesis). The resultant matrix is to be multiplied with A. You need to find out the total number of multiplications required, which is 12+4=16.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en.b. only valid parenthesization are given in this problem for simplicity.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54720,"title":"Hyperperfect Numbers","description":"A k-hyperperfect number is a natural number n for which the equality n = 1 + k(σ(n)  − n  − 1) holds, where σ(n) is the divisor function (i.e., the sum of all positive divisors of n).\r\n%Example\r\nsigma(6) = 1 + 2 + 3 + 6 = 12\r\n%for k=1\r\n1 + 1*(12-6-1) = 1 + 5 = 6\r\n\r\n%Example\r\nsigma(325) = 1 + 5 + 13 + 25 + 65 + 325 = 434\r\n%for k=3\r\n1 + 3*(434-325-1) = 1 + 3*108 = 324  \r\n\r\nGiven a number x, return the xth Hyperperfect number (serial/order wise) and corresponding k value.\r\n\r\n\r\nP.S - Check the test suite for banned functions. More functions might be added later to prevent hard coded solutions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 386.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 193.45px; transform-origin: 408px 193.45px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.60833px 8px; transform-origin: 6.60833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Hyperperfect_number\"\u003e\u003cspan style=\"perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"perspective-origin: 72.3417px 8px; transform-origin: 72.3417px 8px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-hyperperfect number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7917px 8px; transform-origin: 63.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a natural number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69.625px 8px; transform-origin: 69.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for which the equality \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.8417px 8px; transform-origin: 19.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e = 1 + \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.64167px 8px; transform-origin: 4.64167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eσ\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.25px 8px; transform-origin: 12.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e)  − \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.1417px 8px; transform-origin: 16.1417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e  − 1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5667px 8px; transform-origin: 43.5667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e holds, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.225px 8px; transform-origin: 4.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eσ\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.9417px 8px; transform-origin: 22.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Divisor_function\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003edivisor function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 120.175px 8px; transform-origin: 120.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (i.e., the sum of all positive divisors of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 183.9px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 91.95px; transform-origin: 405px 91.95px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Example\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 111.65px 8.5px; tab-size: 4; transform-origin: 111.65px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003esigma(6) = 1 + 2 + 3 + 6 = 12\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%for k=1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 100.1px 8.5px; tab-size: 4; transform-origin: 100.1px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 + 1*(12-6-1) = 1 + 5 = 6\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Example\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 8.5px; tab-size: 4; transform-origin: 173.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003esigma(325) = 1 + 5 + 13 + 25 + 65 + 325 = 434\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%for k=3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 142.45px 8.5px; tab-size: 4; transform-origin: 142.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 + 3*(434-325-1) = 1 + 3*108 = 324  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.7333px 8px; transform-origin: 51.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.8333px 8px; transform-origin: 33.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e return the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.4417px 8px; transform-origin: 12.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003exth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185.175px 8px; transform-origin: 185.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHyperperfect number (serial/order wise) and corresponding \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ek \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.675px 8px; transform-origin: 18.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003evalue.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 360.442px 8px; transform-origin: 360.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP.S - Check the test suite for banned functions. More functions might be added later to prevent hard coded solutions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = hyper(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('hyper.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'interp1') || contains(filetext, 'find') || ...\r\n          contains(filetext, 'str2num') || contains(filetext, 'switch') || ...\r\n          contains(filetext, '26977') || contains(filetext, '1403221')|| ...\r\n          contains(filetext, '1570153') || contains(filetext, '4304341'); \r\nassert(~illegal)\r\n\r\n\r\n%%\r\nx = 1;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,6)\u0026isequal(k,1))\r\n\r\n%%\r\nx = 2;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,21)\u0026isequal(k,2))\r\n\r\n%%\r\nx = 4;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,6)\u0026isequal(n,301))\r\n\r\n%%\r\nx = 7;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,697)\u0026isequal(k,12))\r\n\r\n%%\r\nx = 11;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,2)\u0026isequal(n,2133))\r\n\r\n%%\r\nx = 17;\r\n[n,k]=hyper(x);\r\nassert(isequal(60,k)\u0026isequal(24601,n))\r\n\r\n%%\r\nx = 18;\r\n[n,k]=hyper(x);\r\nassert(isequal(26977,n)\u0026isequal(48,k))\r\n\r\n%%\r\nx = 20;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,132)\u0026isequal(96361,n))\r\n\r\n%%\r\nx = 21;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,130153)\u0026isequal(k,132))\r\n\r\n%%\r\nx = 25;\r\n[n,k]=hyper(x);\r\nassert(isequal(214273,n)\u0026isequal(k,31))\r\n\r\n%%\r\nx = 31;\r\n[n,k]=hyper(x);\r\nassert(isequal(78,k)\u0026isequal(n,486877))\r\n\r\n%%\r\nx = 37;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,1055833)\u0026isequal(k,348))\r\n\r\n%%\r\nx = 39;\r\n[n,k]=hyper(x);\r\nassert(isequal(1232053,n)\u0026isequal(498,k))\r\n\r\n%%\r\nx = 43;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,12)\u0026isequal(1570153,n))\r\n\r\n%%\r\nx = 45;\r\n[n,k]=hyper(x);\r\nassert(isequal(1787917,n)\u0026isequal(438,k))\r\n\r\n%%\r\nx = 48;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,336)\u0026isequal(2462881,n))\r\n\r\n%%\r\nx = 52;\r\n[n,k]=hyper(x);\r\nassert(isequal(798,k)\u0026isequal(n,2708413))\r\n\r\n%%\r\nx = 53;\r\n[n,k]=hyper(x);\r\nassert(isequal(810,k)\u0026isequal(2768581,n))\r\n\r\n%%\r\nx = 54;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,2856481)\u0026isequal(k,528))\r\n\r\n%%\r\nx = 60;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,162)\u0026isequal(n,4304341))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2025-09-13T06:25:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2025-09-13T06:25:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-07T10:09:14.000Z","updated_at":"2025-12-15T21:31:12.000Z","published_at":"2022-06-08T17:42:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Hyperperfect_number\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-hyperperfect number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a natural number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for which the equality \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e = 1 + \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eσ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e)  − \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e  − 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e holds, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eσ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Divisor_function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edivisor function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e., the sum of all positive divisors of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[%Example\\nsigma(6) = 1 + 2 + 3 + 6 = 12\\n%for k=1\\n1 + 1*(12-6-1) = 1 + 5 = 6\\n\\n%Example\\nsigma(325) = 1 + 5 + 13 + 25 + 65 + 325 = 434\\n%for k=3\\n1 + 3*(434-325-1) = 1 + 3*108 = 324  ]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e return the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eHyperperfect number (serial/order wise) and corresponding \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003evalue.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP.S - Check the test suite for banned functions. More functions might be added later to prevent hard coded solutions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54750,"title":"Find the length of stream affected by a spill","description":"When a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration  is often computed as a function of time  and distance  from the spill using the advection-dispersion equation:\r\n\r\nwhere  is the mean velocity of the river and  is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass  mixed over the cross section (with area ) at , the concentration can be shown—using some of the math needed for Cody Problem 51625—to be\r\n\r\nWrite a function to compute the length of stream affected by the spill. In other words, find the position  (say) beyond which the concentration never exceeds a threshold . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 282.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 141.35px; transform-origin: 407px 141.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.317px 8px; transform-origin: 378.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.675px 8px; transform-origin: 123.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is often computed as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.833px 8px; transform-origin: 168.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the spill using the advection-dispersion equation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dC/dt + U dC/dx = K d^2C/dx^2\" style=\"width: 126.5px; height: 36.5px;\" width=\"126.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.958px 8px; transform-origin: 113.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 202.158px 8px; transform-origin: 202.158px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.242px 8px; transform-origin: 125.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e mixed over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 8px; transform-origin: 12.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.5083px 8px; transform-origin: 59.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the concentration can be shown—using some of the math needed for \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51625\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 51625\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5583px 8px; transform-origin: 22.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—to be\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.05px; text-align: left; transform-origin: 384px 20.05px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\" style=\"width: 204.5px; height: 40px;\" width=\"204.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 313.617px 8px; transform-origin: 313.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFUAAAAoCAYAAACPSbZFAAADXElEQVRoQ+1YO89NQRT9vh8g4lGJyqNQESESoVEgNAoJeolHoRKCQuGREBqJV6LQCIJGQlBoKAgFiUThUao8gh/AWjL7Zptz3D0zZ853cfdJVs69d2bvmbtmP2dywp/qDExW1+gKJ5zUHozASXVSe2CgB5VuqU5qZwZWGRo+YPx911XGzVJJ6krgRETcfXw/CrwGPjmpZQzcg9i6IPoc7+Vlatqlxs1ShYXP+DAjfNmG9zUntRsD8yD+TqmYXyOO6i2No6XuAAEXAgkkd0G3M2pKjyOpdPUtgYrjeB8aFal0mTl/yI7MqN+Bl7U315M+HU83Yo27tdcZZqmLsRhdZS3AuMNHnyzHb4WxL3gvS4hNszBnUYU/UVpPcs8v1Pq9eOowpbTOrwDrtreBPMagFcB0gKXIeYCuNDPA4otW/cialDC+E3MuJsyLp+zDD1KjsjZdX6DDFEk9Kb0ZWu114DSQW4rQUuLC29xky4Qz+K3EbXV9uh86TpYsbsmkkqotjBb6AKge4K3Ndhxn6PmodKzG58cddbaKp5JK4R9BA+Mn3f1fezZgw3em4j/kkCquU72tm6LTOYZ1Doa1GL629rVuDqlS39FSFwIlFw+jzP7PsGdWKHxKE13SOaSSqrsQKi6t70aV/UtaUxrAFSC7QkghVWo7Zn3pmUs7kVFlf7r61WBmqa0pK56lJWHCIpWn9RTYA7CEaYur5/D7KaDz5W6Sb5VN4h53BVHW1rsNNWJIRTdYbaTS1fk8AS4BNwCp5+J6dS/GGGP/9vJKt6aWlzFE3QZ4NRjfYEmXqc+EXnAAGDQjMalxzIuzZNzm9ZpFy4yyIRXnA1Yvh4Fv0cy5+L4JkMuWuOOSEKLziRzWb+THpNLdjwAM7A+Vher1aa1rhoxX4qKzGv6HzWGvJcp01yaExlbO2r1RYloxtWQz/5sMDe0NQKvkvYeUkuK1jXDipNomIE1DfFcgya9RXjqpNqnSNCzBVLkz1rlltrLeX9qcVJtUufOQZMRwcDYkNMbT7cA0YHA546TapEptTvd/BbBmvwywmWCFQJLZdQ3adifVJpVVBOtxqYhuBhHGVDY8jcbHSbVJzZ7hpGZTZgs4qTZH2TOc1GzKbAEn1eYoe4aTmk2ZLeCk2hxlz/gJfpacKXO5h08AAAAASUVORK5CYII=\" alt=\"x = L_a\" style=\"width: 42.5px; height: 20px;\" width=\"42.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3417px 8px; transform-origin: 44.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (say) beyond which the concentration never exceeds a threshold \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = C_t\" style=\"width: 46px; height: 20px;\" width=\"46\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function La = affectedReach(U,K,M,A,Ct)\r\n% La = length of affected reach of stream [L]\r\n% U  = mean velocity [L/T]\r\n% K  = dispersion coefficient [L^2/T]\r\n% M  = mass of contaminant [M]\r\n% A  = cross-sectional area (L^2)\r\n% Ct = threshold concentration (M/L^3)\r\n\r\n  La = M/(Ct*A);\r\nend","test_suite":"%%\r\nM = 100;                    %  Mass (kg)\r\nA = 30;                     %  Cross-sectional area (m2)\r\nU = 0.3;                    %  Mean velocity (m/s)\r\nK = 2;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 50;                     %  Mass (kg)\r\nA = 15;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 8.4;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.001;                 %  Target concentration (kg/m3)\r\nLa_correct = 26332.1;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 0.003;                 %  Target concentration (kg/m3)\r\nLa_correct = 91.59;         %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 3e-4;                  %  Target concentration (kg/m3)\r\nLa_correct = 7256.28;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 70;                     %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.15;                   %  Mean velocity (m/s)\r\nK = 1;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 280;                    %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.54;                   %  Mean velocity (m/s)\r\nK = 3.7;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.007;                 %  Target concentration (kg/m3)\r\nLa_correct = 42140.42;      %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%% Approximately plug flow\r\nM = 5*rand;                 %  Mass (kg)\r\nA = 40;                     %  Cross-sectional area (m2)\r\nU = 0.3*(1+rand);           %  Mean velocity (m/s)\r\nK = rand*1e-3;              %  Dispersion coefficient (m2/s)\r\nCt = 0.02*rand;             %  Target concentration (kg/m3)\r\nLa_approx = (U/(4*pi*K))*(M/(Ct*A))^2;\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_approx)/La_approx\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('affectedReach.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp') || contains(filetext,'if'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2022-06-14T05:04:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2022-06-14T05:04:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-14T04:57:20.000Z","updated_at":"2022-06-14T05:04:44.000Z","published_at":"2022-06-14T04:59:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is often computed as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the spill using the advection-dispersion equation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dC/dt + U dC/dx = K d^2C/dx^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial C}{\\\\partial t} + U \\\\frac{\\\\partial C}{\\\\partial x} = K \\\\frac{\\\\partial^2 C}{\\\\partial x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e mixed over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the concentration can be shown—using some of the math needed for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51625\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 51625\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—to be\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L_a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L_a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (say) beyond which the concentration never exceeds a threshold \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = C_t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = C_t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44374,"title":"Tautology","description":"Check if the given expression is always true. For example, the sentence\r\n\r\n  '~(A \u0026 B) == (~A | ~B)'\r\n\r\nis always true.\r\n\r\nCharacters in the input sequences may include *~ \u0026 | == ( )*, whitespace, 0 for false, 1 for true and letters for variables.","description_html":"\u003cp\u003eCheck if the given expression is always true. For example, the sentence\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e'~(A \u0026 B) == (~A | ~B)'\r\n\u003c/pre\u003e\u003cp\u003eis always true.\u003c/p\u003e\u003cp\u003eCharacters in the input sequences may include \u003cb\u003e~ \u0026 | == ( )\u003c/b\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/p\u003e","function_template":"function y = tautology(x)\r\n  y = true;\r\nend","test_suite":"%%\r\nx = '0';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1\u0026A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A\u0026B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|~A';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '0==0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(A \u0026 B) == (~A | ~B)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(Z \u0026 Y) == (~Y | ~Z)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|~A|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nassert(isequal(tautology('(A|B)|C'),false));\r\n%%\r\nassert(isequal(tautology('(A|B)|(C == C)'),true));\r\n%%\r\nassert(isequal(tautology('(A == B)|(B == C)|(C == A)'),true));\r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(0))))))'),false)); \r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(~0))))))'),true));\r\n% provided by Alfonso:\r\nassert(isequal(tautology('((0\u00261)|~B)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((0\u0026~B)\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)\u0026~A)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((0|~B)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((1\u00260)|B)'),false)); \r\n%%\r\nassert(isequal(tautology('((1\u00261)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('((1|0)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|A)|0)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|~A)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u00261)|~A)|A'),true)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~A)\u0026~B)|~A'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~B)\u00261)|B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|0)\u00261)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|A)\u0026A)|~A'),true)); \r\n%%\r\nassert(isequal(tautology('((B|0)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((B|1)\u0026B)\u0026A'),false)); \r\n%%\r\nassert(isequal(tautology('((B|A)|~A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)\u00260)\u0026B'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|0)'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|~A)|1'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|A)|~B)\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|B)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~B)\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('((~B\u00260)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('(0\u00261)|1\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('(0|~A\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(1|A\u00260)'),true)); \r\n%%\r\nassert(isequal(tautology('(A\u0026A\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('(A\u0026~A|1)'),true)); \r\n%%\r\nassert(isequal(tautology('(A|1)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(A|A)|A|1'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u00261)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u0026~B)\u0026~B\u00260'),false)); \r\n%%\r\nassert(isequal(tautology('(B|~B)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A\u0026B\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|0)|~B\u0026~A'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|1)|1'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|B\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|B)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|~A)|0'),false)); \r\n%%\r\nassert(isequal(tautology('(~B\u00260)\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('1\u0026B|~B|0'),true)); \r\n%%\r\nassert(isequal(tautology('B\u00261\u0026A\u00261'),false)); \r\n%%\r\nassert(isequal(tautology('~A\u00260\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('~B\u00260\u0026~A|B'),false)); \r\n%%\r\nassert(isequal(tautology('~B|1|1|~B'),true)); \r\n%%\r\nassert(isequal(tautology('~B|~B\u00261|1'),true));\r\n%%\r\nassert(isequal(tautology('A==~A'),false));\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":30,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2017-10-31T07:45:16.000Z","rescore_all_solutions":true,"group_id":35,"created_at":"2017-10-10T23:20:08.000Z","updated_at":"2026-04-18T11:07:15.000Z","published_at":"2017-10-16T01:51:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck if the given expression is always true. For example, the sentence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA['~(A \u0026 B) == (~A | ~B)']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis always true.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCharacters in the input sequences may include\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e~ \u0026amp; | == ( )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":53125,"title":"Easy Sequences 54: Product of Products of Proper Divisors","description":"A divisor of a number that is less than the number is called a \"proper divisor\". \r\nFor a given positive integer , we are asked to evaluate the following summation:\r\n             \r\nThis is equivalent to finding the product of the products of proper divisors of all integers from  to .\r\nFor example for , we have:\r\n                            \r\nPlease present your output modulo .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 413.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 206.75px; transform-origin: 407px 206.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 244.5px 8px; transform-origin: 244.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA divisor of a number that is less than the number is called a \"proper divisor\". \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eF\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95.5px 8px; transform-origin: 95.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eor a given positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 162px 8px; transform-origin: 162px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we are asked to evaluate the following summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.75px; text-align: left; transform-origin: 384px 22.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 110px; height: 45.5px;\" width=\"110\" height=\"45.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88px 8px; transform-origin: 88px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is equivalent to finding \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233px 8px; transform-origin: 233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ethe product of the products of proper divisors of all integers from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e2\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11px 8px; transform-origin: 11px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.5px 8px; transform-origin: 51.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 209px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 104.5px; text-align: left; transform-origin: 384px 104.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-99px\"\u003e\u003cimg 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style=\"width: 509px; height: 209px;\" width=\"509\" height=\"209\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.5px 8px; transform-origin: 112.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease present your output modulo \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 55.5px; height: 18px;\" width=\"55.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = pppd(n)\r\n    s = 2 * (n + 2) ^ 2 * n;\r\nend","test_suite":"%%\r\nn = 10;\r\ns_correct = 2880;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 20;\r\ns_correct = 178754;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = 651627;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 200;\r\ns_correct = 471492;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 1000;\r\ns_correct = 132068;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 2000;\r\ns_correct = 192916;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 10000;\r\ns_correct = 700691;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 20000;\r\ns_correct = 135567;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 100000;\r\ns_correct = 919193;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 200000;\r\ns_correct = 581218;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 1000000;\r\ns_correct = 811966;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nns = 2000000:2222222;\r\ns = arrayfun(@(n) pppd(n),ns);\r\nss = mod([sum(s) sum(num2str(s))],1000003);\r\nss_correct = [526924 445038];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('pppd.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-12-04T15:11:17.000Z","updated_at":"2026-03-19T13:19:46.000Z","published_at":"2021-12-06T15:33:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA divisor of a number that is less than the number is called a \\\"proper divisor\\\". \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eor a given positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we are asked to evaluate the following summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\prod_{i=2}^{n}\\\\left (\\\\prod_{\\\\ d|i\\\\ \\\\\u0026amp;\\\\  d\u0026lt;i}^{}d\\\\   \\\\right )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is equivalent to finding \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe product of the products of proper divisors of all integers from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\prod_{i=2}^{10}\\\\prod_{d|i\\\\ \\\\\u0026amp;\\\\  d\u0026lt;i}^{}d\\\\ = \\\\prod_{d|2\\\\ \\\\\u0026amp;\\\\  d\u0026lt;2}^{}d \\\\ \\\\times\\\\prod_{d|3\\\\ \\\\\u0026amp;\\\\  d\u0026lt;3}^{}d \\\\ \\\\times\\\\prod_{d|4\\\\ \\\\\u0026amp;\\\\  d\u0026lt;4}^{}d  \\\\ \\\\times\\\\prod_{d|5\\\\ \\\\\u0026amp;\\\\  d\u0026lt;5}^{}d\\\\ \\\\times\\\\prod_{d|6\\\\ \\\\\u0026amp;\\\\  d\u0026lt;6}^{}d \\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\times\\\\prod_{d|7\\\\ \\\\\u0026amp;\\\\  d\u0026lt;7}^{}d \\\\ \\\\times\\\\prod_{d|8\\\\ \\\\\u0026amp;\\\\  d\u0026lt;8}^{}d \\\\ \\\\times\\\\prod_{d|9\\\\ \\\\\u0026amp;\\\\  d\u0026lt;9}^{}d \\\\ \\\\times\\\\prod_{d|10\\\\ \\\\\u0026amp;\\\\  d\u0026lt;10}^{}d \\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ =1\\\\times1\\\\times(1\\\\cdot2)\\\\times1\\\\times(1\\\\cdot2\\\\cdot3)\\\\times1\\\\times(1\\\\cdot2\\\\cdot4)\\\\times(1\\\\cdot3)\\\\times(1\\\\cdot2\\\\cdot5) \\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ =1\\\\times1\\\\times2\\\\times1\\\\times6\\\\times1\\\\times8\\\\times3\\\\times10 \\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ =2880\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present your output modulo \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1000003\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60411,"title":"Compute a sequence with the whyphi sieve","description":"A few problems on Cody involve sieving. For example, Cody Problem 45367 involves the famous Sieve of Eratosthenes. CP 50811 uses the sieve of Flavius Josephus, and CP 50913 uses the golden sieve. \r\nThis problem uses a process that I will call the whyphi sieve: \r\nMake a list x of integers 1, 2, 3,… \r\nRemove the first term. That is, delete x(1).\r\nRenumber the terms. \r\nDelete x(2) and x(2+1)\r\nRenumber the terms. \r\nDelete x(3), x(3+2), and x(3+2+1). \r\nContinue renumbering and deleting terms in this way. \r\nWrite a function to compute the nth term of this sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 266.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 133.017px; transform-origin: 407px 133.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 170.375px 7.79167px; transform-origin: 170.375px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA few problems on Cody involve sieving. For example, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45367\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 45367\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.075px 7.79167px; transform-origin: 138.075px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involves the famous Sieve of Eratosthenes. \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/50811\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCP 50811\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.967px 7.79167px; transform-origin: 127.967px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e uses the sieve of Flavius Josephus, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/50913\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCP 50913\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5167px 7.79167px; transform-origin: 73.5167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e uses the golden sieve. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.65px 7.79167px; transform-origin: 188.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem uses a process that I will call the whyphi sieve: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 143.033px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 71.5167px; transform-origin: 391px 71.5167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.775px 7.79167px; transform-origin: 105.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMake a list x of integers 1, 2, 3,… \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 130.667px 7.79167px; transform-origin: 130.667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRemove the first term. That is, delete x(1).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 67.675px 7.79167px; transform-origin: 67.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRenumber the terms. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 69.8333px 7.79167px; transform-origin: 69.8333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDelete x(2) and x(2+1)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 67.675px 7.79167px; transform-origin: 67.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRenumber the terms. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 107.567px 7.79167px; transform-origin: 107.567px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDelete x(3), x(3+2), and x(3+2+1). \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 166.758px 7.79167px; transform-origin: 166.758px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eContinue renumbering and deleting terms in this way. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 181.108px 7.79167px; transform-origin: 181.108px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the nth term of this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = whyphiSieve(n)\r\n  c = 100*[0.000057513128234 0.093378634167431 -2.856145294974328]\r\n  y = polyval(c,n);\r\nend","test_suite":"%%\r\nassert(isequal(whyphiSieve(1),2))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(5),14))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(19),79))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(54),305))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(89),594))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(135),1032))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(336),3443))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(689),8948))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(1000),14685))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(4509),109040))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(whyphiSieve(428)),116991))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(whyphiSieve(620)),225368))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(10000),315192))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(20000),793960))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-04T15:38:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-28T02:46:53.000Z","updated_at":"2026-03-30T07:39:19.000Z","published_at":"2024-05-28T02:47:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA few problems on Cody involve sieving. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45367\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 45367\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involves the famous Sieve of Eratosthenes. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/50811\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCP 50811\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e uses the sieve of Flavius Josephus, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/50913\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCP 50913\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e uses the golden sieve. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem uses a process that I will call the whyphi sieve: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a list x of integers 1, 2, 3,… \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemove the first term. That is, delete x(1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRenumber the terms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDelete x(2) and x(2+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRenumber the terms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDelete x(3), x(3+2), and x(3+2+1). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eContinue renumbering and deleting terms in this way. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the nth term of this sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1241,"title":"PACMAT  - Ghosts maximize unique locations; 3 Lives","description":"The Classic PACMAN game brought to Cody.\r\n\r\nPACMAT Ghosts Random requires clearing the board of Yellow Dots while not bumping into the wandering ghosts in 3 lives. Adjacent Ghosts will capture PACMAT.  Ghosts do not use the tunnel. On Ghost capture everyone gets reset.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_300.jpg\u003e\u003e\r\n\r\nTo aid in development of your routine, a PACMAT_Ghosts_002.m file that creates a video has been posted at \u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_Ghosts_002.m PACMAT_Ghosts_002.m\u003e. (Right click, 'save link as'). Using patches thus enable/figure  disable/video for best results.\r\n\r\n\r\n\u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_G002_video_ANC.mp4 Alfonso's Enhanced Ghost Avoider\u003e (MP4) Quite an impressive solution\r\n\r\n\r\nThe reference solution uses Alfonso's Local Optimum Algorithm with a Catch.\r\n\r\n*Inputs:* Map   Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u003e2=Ghost\r\n\r\n*Output:* Direction  Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\r\n\r\n*Scoring:* Total # of Moves to Clear the Yellow Dots +(LivesRemaining-3)*100\r\n\r\n\r\n*Near Future:* Ghosts with LOS Tracking.\r\n\r\n*Future:* Player will be Team Ghosts versus PACMAT_BOT","description_html":"\u003cp\u003eThe Classic PACMAN game brought to Cody.\u003c/p\u003e\u003cp\u003ePACMAT Ghosts Random requires clearing the board of Yellow Dots while not bumping into the wandering ghosts in 3 lives. Adjacent Ghosts will capture PACMAT.  Ghosts do not use the tunnel. On Ghost capture everyone gets reset.\u003c/p\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_300.jpg\"\u003e\u003cp\u003eTo aid in development of your routine, a PACMAT_Ghosts_002.m file that creates a video has been posted at \u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Ghosts_002.m\"\u003ePACMAT_Ghosts_002.m\u003c/a\u003e. (Right click, 'save link as'). Using patches thus enable/figure  disable/video for best results.\u003c/p\u003e\u003cp\u003e\u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_G002_video_ANC.mp4\"\u003eAlfonso's Enhanced Ghost Avoider\u003c/a\u003e (MP4) Quite an impressive solution\u003c/p\u003e\u003cp\u003eThe reference solution uses Alfonso's Local Optimum Algorithm with a Catch.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e Map   Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u003e2=Ghost\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Direction  Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Total # of Moves to Clear the Yellow Dots +(LivesRemaining-3)*100\u003c/p\u003e\u003cp\u003e\u003cb\u003eNear Future:\u003c/b\u003e Ghosts with LOS Tracking.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFuture:\u003c/b\u003e Player will be Team Ghosts versus PACMAT_BOT\u003c/p\u003e","function_template":"function  [newdir]=pacmat(map)\r\n% 314 move solver if Ghosts do not move\r\n persistent ptr\r\n if isempty(ptr)\r\n  ptr=['bbbbbbbcccbbbbbcccdddddddddddddddddddddddddaaa'...\r\n      'bbbbbaaaaaaaaaaaaaaaaaaaaaaaaadddddcccccccbbbbddddaaabbbbbbbb'...\r\n      'cccbbbdddaaabbbaaaadddddbbbbbccccbbbbbbbbbbbbbbaaaaddddddddddd'...\r\n      'ccccbbbcccdddbbbaaabbbaaaccccccbbbbbaaccdddddccccccccccccccaabbbbbcccddccc'...\r\n      'dddaaaaaaddddddcccbbbcccdddcccdddaaadddaaaddbbbbbaaadddddddddddcccbbccc'];\r\n  ptr=(ptr-'a')+1;\r\n end\r\n  \r\n newdir=ptr(1);\r\n ptr(1)=[];\r\n\r\n% usage of newdir=randi(4) will barely move\r\nend","test_suite":"%%\r\nfeval(@assignin,'caller','score',2000);\r\n%%\r\nmax_moves=2000; % Fixed path expect to succeed by 600 moves\r\n\r\nmap=[...\r\n      repmat('a',1,28);\r\n      'accccccccccccaacccccccccccca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acccccccccccccccccccccccccca';\r\n      'acaaaacaacaaaaaaaacaacaaaaca';\r\n      'acaaaacaacaaaaaaaacaacaaaaca';\r\n      'accccccaaccccaaccccaacccccca';\r\n      'aaaaaacaaaaabaabaaaaacaaaaaa';\r\n      'aaaaaacaaaaabaabaaaaacaaaaaa';\r\n      'aaaaaacaabbbbbbbbbbaacaaaaaa';\r\n      'aaaaaacaabaaabbaaabaacaaaaaa';\r\n      'aaaaaacaabalbbbblabaacaaaaaa';\r\n      'bbbbbbcbbbabbbbbbabbbcbbbbbb';\r\n      'aaaaaacaabalbbbblabaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'aaaaaacaabbbbbbbbbbaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'accccccccccccaacccccccccccca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acccaacccccccbdcccccccaaccca';\r\n      'aaacaacaacaaaaaaaacaacaacaaa';\r\n      'aaacaacaacaaaaaaaacaacaacaaa';\r\n      'accccccaaccccaaccccaacccccca';\r\n      'acaaaaaaaaaacaacaaaaaaaaaaca';\r\n      'acaaaaaaaaaacaacaaaaaaaaaaca';\r\n      'acccccccccccccccccccccccccca';\r\n      repmat('a',1,28);];\r\n  \r\n  map=map-'b';\r\n  [nr, nc]=size(map);\r\n\r\n  gmap=map; % Map used by ghosts to simplify PAC Capture\r\n  gmap(15,6)=Inf; %No tunnel ghosts\r\n  gmap(15,26)=Inf;\r\n  gmap(map==-1)=Inf; % walls to Inf\r\n  gmap(map\u003e2)=Inf; % Elim start points as viable moves, quicker box exit\r\n\r\n\r\n  mapdelta=[-1 nr 1 -nr]; % Valid as long as not on an edge\r\n  gmovxy=[0 -1;1 0;0 1;-1 0];\r\n\r\n  tunnel=find(map(:,1)==0); % tunnelptr\r\n  tunnel=[tunnel tunnel+nr*(nc-1)]; % Entrance/Exit Tunnel\r\n\r\n  [pmr, pmc]=find(map==2); % pi 24 row  pj 15 column of map\r\n   ptrpac=find(map==2);\r\n\r\n  ptrpac=find(map==2);\r\n  ptrpac_start=ptrpac;\r\n  ptrg_start=find(map\u003e2);\r\n  map(ptrg_start)=[10 20 30 40];% use deal?\r\n  [gstartx, gstarty]=find(map\u003e2);\r\n  \r\n  lives=3; % Lives\r\n  movepac=0;\r\n\r\nwhile lives \u0026\u0026 any(mod(map(:),10)==1) \u0026\u0026 movepac\u003cmax_moves\r\n movepac=movepac+1;\r\n\r\n [curdir]=pacmat(map);\r\n% if curdir==0,continue;end % Inf loop error\r\n [pmr, pmc]=find(map==2);\r\nif curdir\u003e0\r\n if map(ptrpac+mapdelta(curdir))==-1\r\n  % Do nothing - Ran into a Wall\r\n elseif map(ptrpac+mapdelta(curdir))\u003e2 % ran into ghost\r\n  map(ptrpac)=0; % remove PAC from the board\r\n  lives=lives-1;\r\n  if lives==0,break;end\r\n  % reset the board\r\n  [ptrgx, ptrgy]=find(map\u003e2);\r\n  ptrg=find(map\u003e2);\r\n  map(ptrg)=mod(map(ptrg),10);\r\n  map(ptrpac_start)=2;\r\n  map(ptrg_start)=[10 20 30 40];\r\n  ptrpac=find(map==2);\r\n  continue;\r\n else % legal move\r\n  map(ptrpac)=0; % Eat Dot and clear PAC\r\n  ptrpac=ptrpac+mapdelta(curdir);\r\n  if ptrpac==tunnel(1),ptrpac=tunnel(2)-nr;end\r\n  if ptrpac==tunnel(2),ptrpac=tunnel(1)+nr;end\r\n  map(ptrpac)=2;\r\n end\r\nend % curdir \u003e0\r\n\r\n% Ghosts\r\n for i=1:4\r\n\r\n   gmapT=gmap;\r\n   ptrg=find(map\u003e2); % Find all ghosts\r\n   gmapT(ptrg)=Inf; % Rule out moving onto a ghost\r\n\r\n\r\n  dot=false;\r\n  [gptrx, gptry]=find(map==10*i);\r\n  gidx=find(map==10*i);\r\n  if isempty(gidx)\r\n   [gptrx, gptry]=find(map==10*i+1); % ghost must be on a dot\r\n   gidx=find(map==10*i+1);\r\n   dot=true;\r\n  end\r\n\r\n% Find valid ghost moves using gmap\r\n% mapdelta=[-1 nr 1 -nr]; \r\n  gmov=find(map(gidx+mapdelta)==2); % adjacent to PACMAT\r\n  if ~isempty(gmov) % PAC adjacent\r\n   lives=lives-1;\r\n   if lives==0,break;end\r\n   % reset the board\r\n   [pmr, pmc]=find(map==2); % PACMAT erase coords\r\n   map(map==2)=0;\r\n      \r\n   [ptrgx, ptrgy]=find(map\u003e2);\r\n   ptrg=find(map\u003e2);\r\n   map(ptrg)=mod(map(ptrg),10);\r\n   map(ptrpac_start)=2;\r\n   map(ptrg_start)=[10 20 30 40];\r\n   ptrpac=find(map==2);     \r\n   break; % Ghost move loop\r\n      \r\n  else % gmap/gmapT avoids tunnel,other ghosts, Walls\r\n \r\n   gmap(gidx)=gmap(gidx)+1;\r\n   ghost_adj=gmapT(gidx+mapdelta);\r\n   if min(ghost_adj)\u003cInf\r\n    if rand\u003c0.5 % Push ghosts away from each other\r\n     gmov=find(ghost_adj==min(ghost_adj),1,'first');\r\n    else\r\n     gmov=find(ghost_adj==min(ghost_adj),1,'last');\r\n    end\r\n   else\r\n    gmov=[];\r\n   end\r\n \r\n   if ~isempty(gmov) % valid g move : ghost may not stand on ghost\r\n    map(gptrx,gptry)=mod(map(gptrx,gptry),10);\r\n    map(gidx+mapdelta(gmov))=map(gidx+mapdelta(gmov))+10*i;     \r\n   end % ~isempty(gmov) standard move - no capture\r\n\r\n  end % ~isempty(gmov) PACMAT adjacent\r\n  \r\n end % i ghost moves\r\nend % while alive\r\n\r\nfprintf('moves %i\\n',movepac)\r\n\r\nassert(lives\u003e0,sprintf('Three Captures\\n'))\r\nassert(~isempty(any(mod(map(:),10)==1)),sprintf('Moves\\n',movepac)) % Test Move Timeout\r\n\r\n\r\nfeval( @assignin,'caller','score',floor(min( 2000,300-100*lives+movepac )) );\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2013-02-02T05:09:50.000Z","rescore_all_solutions":false,"group_id":33,"created_at":"2013-02-02T00:36:11.000Z","updated_at":"2026-04-23T18:03:04.000Z","published_at":"2013-02-02T01:21:05.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Classic PACMAN game brought to Cody.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT Ghosts Random requires clearing the board of Yellow Dots while not bumping into the wandering ghosts in 3 lives. Adjacent Ghosts will capture PACMAT. Ghosts do not use the tunnel. On Ghost capture everyone gets reset.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo aid in development of your routine, a PACMAT_Ghosts_002.m file that creates a video has been posted at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Ghosts_002.m\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT_Ghosts_002.m\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. (Right click, 'save link as'). Using patches thus enable/figure disable/video for best results.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_G002_video_ANC.mp4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAlfonso's Enhanced Ghost Avoider\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MP4) Quite an impressive solution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe reference solution uses Alfonso's Local Optimum Algorithm with a Catch.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Map Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u0026gt;2=Ghost\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Direction Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Total # of Moves to Clear the Yellow Dots +(LivesRemaining-3)*100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNear Future:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Ghosts with LOS Tracking.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFuture:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Player will be Team Ghosts versus PACMAT_BOT\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" 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\"}]}"},{"id":58019,"title":"Factor a number into Fermi-Dirac primes","description":"Cody Problem 58018 asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, . \r\nWrite a function analogous to factor(n) that factors the number  into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58018\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 58018\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"122\" height=\"18\" alt=\"2250 = 2x5x9x25\" style=\"width: 122px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function analogous to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003efactor(n)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that factors the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = factorFD(n)\r\n  y = factor(n).^n;\r\nend","test_suite":"%%\r\nassert(isequal(factorFD(1),1))\r\n\r\n%%\r\np = primes(1000);\r\nfor q = p\r\n    assert(isequal(factorFD(q),q))\r\nend\r\n\r\n%%\r\nassert(isequal(factorFD(56),[2 4 7]))\r\n\r\n%%\r\nassert(isequal(factorFD(64),[4 16]))\r\n\r\n%%\r\nassert(isequal(factorFD(644),[4 7 23]))\r\n\r\n%%\r\nassert(isequal(factorFD(2250),[2 5 9 25]))\r\n\r\n%%\r\nassert(isequal(factorFD(6444),[4 9 179]))\r\n\r\n%%\r\nassert(isequal(factorFD(64444),[4 16111]))\r\n\r\n%%\r\nassert(isequal(factorFD(644444),[4 73 2207]))\r\n\r\n%%\r\nassert(isequal(factorFD(3736368),[3 16 81 961]))\r\n\r\n%%\r\nassert(isequal(factorFD(3736368),[3 16 81 961]))\r\n\r\n%%\r\nassert(isequal(factorFD(5784354),[2 9 211 1523]))\r\n\r\n%%\r\nassert(isequal(factorFD(11739420),[4 5 9 11 49 121]))\r\n\r\n%%\r\nassert(isequal(factorFD(28437991),[17 103 109 149]))\r\n\r\n%%\r\nassert(isequal(factorFD(1106427169),[841 961 1369]))\r\n\r\n%%\r\nassert(isequal(factorFD(753345263125),[13 73 529 625 2401]))\r\n\r\n%%\r\nassert(isequal(factorFD(159360553668481),[14641 83521 130321]))\r\n\r\n%%\r\nassert(isequal(factorFD(2760834326158300),[4 7 25 49 10201 7890481]))\r\n\r\n%%\r\nfiletext = fileread('factorFD.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2024-12-28T23:50:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-25T01:29:47.000Z","updated_at":"2026-04-27T10:19:43.000Z","published_at":"2023-04-25T01:29:53.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58018\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 58018\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2250 = 2x5x9x25\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2250 = 2 \\\\cdot5\\\\cdot9\\\\cdot25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function analogous to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efactor(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that factors the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59701,"title":"Express numbers as the sum of a prime, a square, and a cube","description":"While traveling on an interstate highway, I noticed a sign that gave distances to three places. The distances were 3, 8, and 9 miles, or a prime, a perfect cube, and a perfect square. I then wondered whether it was possible to express integers (above a certain value) as the sum of a prime, a square, and a cube. For example, 11 can be expressed as , and 17 can be expressed as  or . \r\nWrite a function to list ways to express numbers as the sum of a prime, a square, and a cube. All three must be positive. The function should return a matrix the primes in the first column, the squares in the second, and the cubs in the third, and the rows should be sorted by the first column and then the second. Given an input of 11, the function should return [2 1 8], and given an input of 17, the function should return [5 4 8; 7 9 1]. If the input cannot be expressed in this way, return the empty vector [].\r\nOptional: Prove that all integers greater than 6 can be expressed as the sum of a prime, a square, and a cube.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 228.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 114.25px; transform-origin: 408px 114.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 42px; text-align: left; transform-origin: 385px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 385px 8px; transform-origin: 385px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhile traveling on an interstate highway, I noticed a sign that gave distances to three places. The distances were 3, 8, and 9 miles, or a prime, a perfect cube, and a perfect square. I then wondered whether it was possible to express integers (above a certain value) as the sum of a prime, a square, and a cube. For example, 11 can be expressed as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"144.5\" height=\"19\" alt=\"2+1+8 = 2+1^2+2^3\" style=\"width: 144.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.74167px 8px; transform-origin: 3.74167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and 17 can be expressed as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"144.5\" height=\"19\" alt=\"5+4+8 = 5 + 2^2+2^3\" style=\"width: 144.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 8px; transform-origin: 10.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"144.5\" height=\"19\" alt=\"7+9+1 = 7+3^2+1^3\" style=\"width: 144.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 52.75px; text-align: left; transform-origin: 385px 52.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 385px 8px; transform-origin: 385px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list ways to express numbers as the sum of a prime, a square, and a cube. All three must be positive. The function should return a matrix the primes in the first column, the squares in the second, and the cubs in the third, and the rows should be sorted by the first column and then the second. Given an input of 11, the function should return [2 1 8], and given an input of 17, the function should return [5 4 8; 7 9 1]. If the input cannot be expressed in this way, return the empty vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.85px 8.5px; transform-origin: 3.85px 8.5px; \"\u003e[\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 341.117px 8px; transform-origin: 341.117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOptional: Prove that all integers greater than 6 can be expressed as the sum of a prime, a square, and a cube.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function v = primeSquareCube(n)\r\n  v = [primes(n) n^2 n^3];\r\nend","test_suite":"%%\r\nn = 11;\r\nv = primeSquareCube(n);\r\nv_correct = [2 1 8];\r\nassert(isequal(v,v_correct))\r\n\r\n%%\r\nn = 17;\r\nv = primeSquareCube(n);\r\nv_correct = [5 4 8; 7 9 1];\r\nassert(isequal(v,v_correct))\r\n\r\n%%\r\nn = 58;\r\nv = primeSquareCube(n);\r\nv_correct = [41 9 8; 41 16 1; 53 4 1];\r\nassert(isequal(v,v_correct))\r\n\r\n%%\r\nn = 82;\r\nv = primeSquareCube(n);\r\nv_correct = [2 16 64; 17 1 64; 17 64 1; 19 36 27; 73 1 8];\r\nassert(isequal(v,v_correct))\r\n\r\n%%\r\nn = 56342;\r\nv = primeSquareCube(n);\r\nsum_correct = [24203820 13786001 8886723];\r\nN_correct = 832;\r\nmax_correct = 56333;\r\nassert(isequal(sum(v),sum_correct))\r\nassert(isequal(size(v,1),N_correct))\r\nassert(isequal(max(v,[],'all'),max_correct))\r\n\r\n%%\r\nn = 4938523;\r\nv = primeSquareCube(n);\r\nsum_correct = [53237782818 28599306108 19254476884];\r\nN_correct = 20470;\r\nmax_correct = 4938473;\r\nassert(isequal(sum(v),sum_correct))\r\nassert(isequal(size(v,1),N_correct))\r\nassert(isequal(max(v,[],'all'),max_correct))\r\n\r\n%%\r\na = NaN(1,10000);\r\nfor n = 1:10000\r\n    v = primeSquareCube(n);\r\n    a(n) = size(v,1);\r\n    if a(n)\u003e0\r\n        assert(all(sum(v,2)==n))\r\n        p = v(:,1); s = v(:,2); c = v(:,3);\r\n        assert(all(isprime(p)))\r\n        assert(all(sqrt(s)==floor(sqrt(s))))\r\n        assert(all(nthroot(c,3)==floor(nthroot(c,3))))\r\n    end\r\nend\r\nu = unique(a);\r\nh = groupcounts(a')';\r\na100_correct = [0 0 0 1 1 0 2 1 1 1 1 3 2 2 3 2 2 1 4 3 2 4 2 3 2 2 2 5 4 3 5 1 5 4 4 5 2 4 6 5 5 3 5 3 4 7 5 6 5 5 3 4 5 6 8 4 6 3 5 6 4 5 6 5 6 4 7 7 6 9 6 5 7 7 7 10 4 9 7 7 8 5 8 10 9 5 8 7 7 6 10 7 8 9 8 10 7 5 9 7];\r\nsum_correct = 1232200;\r\nu_correct = [0:255 258:261 264 273 276];\r\nh_correct = [4 8 11 9 14 19 11 17 16 18 24 25 23 14 28 18 28 29 22 26 25 26 36 26 25 24 31 27 32 37 27 31 31 43 38 32 29 27 31 39 38 23 34 34 47 50 42 38 34 34 37 37 32 38 45 53 39 34 43 45 23 47 32 40 38 54 41 44 38 47 34 49 50 32 53 54 39 43 53 51 45 26 43 52 62 50 59 48 41 45 55 48 41 48 36 48 41 59 57 48 51 48 50 36 53 61 52 55 49 49 46 48 50 52 50 71 55 47 58 53 60 48 52 70 47 51 61 47 67 53 62 63 50 52 52 59 47 55 62 58 59 56 44 49 65 58 54 61 60 58 70 61 58 49 63 55 53 59 54 48 66 53 47 53 56 64 69 51 70 52 65 64 75 53 55 59 56 63 61 53 58 69 61 63 52 48 54 46 49 59 50 61 34 53 38 45 46 33 44 26 31 35 47 40 39 42 31 30 34 27 32 35 35 30 30 23 24 29 21 12 19 26 15 23 20 15 17 12 15 12 8 13 15 9 10 9 13 10 6 6 8 4 5 3 4 3 5 6 7 2 1 4 3 1 2 4 2 1 1 1 1 1 1];\r\nassert(isequal(a(1:100),a100_correct))\r\nassert(isequal(sum(a),sum_correct))\r\nassert(isequal(u,u_correct))\r\nassert(isequal(h,h_correct))\r\n\r\n%%\r\nfiletext = fileread('primeSquareCube.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-16T16:58:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-16T13:48:17.000Z","updated_at":"2026-04-24T11:37:32.000Z","published_at":"2024-03-16T13:51:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhile traveling on an interstate highway, I noticed a sign that gave distances to three places. The distances were 3, 8, and 9 miles, or a prime, a perfect cube, and a perfect square. I then wondered whether it was possible to express integers (above a certain value) as the sum of a prime, a square, and a cube. For example, 11 can be expressed as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2+1+8 = 2+1^2+2^3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2+1+8 = 2+1^2+2^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and 17 can be expressed as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"5+4+8 = 5 + 2^2+2^3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5+4+8 = 5 + 2^2+2^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"7+9+1 = 7+3^2+1^3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7+9+1 = 7+3^2+1^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list ways to express numbers as the sum of a prime, a square, and a cube. All three must be positive. The function should return a matrix the primes in the first column, the squares in the second, and the cubs in the third, and the rows should be sorted by the first column and then the second. Given an input of 11, the function should return [2 1 8], and given an input of 17, the function should return [5 4 8; 7 9 1]. If the input cannot be expressed in this way, return the empty vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOptional: Prove that all integers greater than 6 can be expressed as the sum of a prime, a square, and a cube.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1288,"title":"Balanced Ternary Numbers: Easy as |, |-, |o","description":"This problem concerns the so-called \u003chttp://en.wikipedia.org/wiki/Balanced_ternary balanced ternary\u003e system for representing numbers. It is a Base 3 system in which the digits can be 1, 0, or -1. \r\n\r\nIn balanced ternary, the number 8 would be represented as 9 (or 3^2) minus 1 (or 3^0). Typographically we will use \"|\" for one, \"o\" for zero (that's a lower-case O), and \"-\" for negative one. So if the decimal input d is the number 8, the balanced ternary output is the string \"|o-\". Thus\r\n \r\n dec 8  =\u003e bt \"|o-\"\r\n\r\nHere are some more examples.\r\n\r\n dec 3  =\u003e bt \"|o\"\r\n dec 15 =\u003e bt \"|--o\"\r\n dec 52 =\u003e bt \"|-o-|\"\r\n \r\nGiven an integer d, return the string bt. Leading zeros should always be suppressed.","description_html":"\u003cp\u003eThis problem concerns the so-called \u003ca href = \"http://en.wikipedia.org/wiki/Balanced_ternary\"\u003ebalanced ternary\u003c/a\u003e system for representing numbers. It is a Base 3 system in which the digits can be 1, 0, or -1.\u003c/p\u003e\u003cp\u003eIn balanced ternary, the number 8 would be represented as 9 (or 3^2) minus 1 (or 3^0). Typographically we will use \"|\" for one, \"o\" for zero (that's a lower-case O), and \"-\" for negative one. So if the decimal input d is the number 8, the balanced ternary output is the string \"|o-\". Thus\u003c/p\u003e\u003cpre\u003e dec 8  =\u003e bt \"|o-\"\u003c/pre\u003e\u003cp\u003eHere are some more examples.\u003c/p\u003e\u003cpre\u003e dec 3  =\u003e bt \"|o\"\r\n dec 15 =\u003e bt \"|--o\"\r\n dec 52 =\u003e bt \"|-o-|\"\u003c/pre\u003e\u003cp\u003eGiven an integer d, return the string bt. Leading zeros should always be suppressed.\u003c/p\u003e","function_template":"function bt = balanced_ternary(d)\r\n  bt = 'o';\r\nend","test_suite":"%%\r\nd = 3;\r\nbt_correct = '|o';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 52;\r\nbt_correct = '|-o-|';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 182;\r\nbt_correct = '|-|-|-';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 26;\r\nbt_correct = '|oo-';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = -5;\r\nbt_correct = '-||';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = -164;\r\nbt_correct = '-|oo-|';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 512;\r\nbt_correct = '|-o|oo-';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":78,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-02-21T23:26:14.000Z","updated_at":"2026-04-29T23:08:18.000Z","published_at":"2013-02-21T23:36:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem concerns the so-called\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Balanced_ternary\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ebalanced ternary\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e system for representing numbers. It is a Base 3 system in which the digits can be 1, 0, or -1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn balanced ternary, the number 8 would be represented as 9 (or 3^2) minus 1 (or 3^0). Typographically we will use \\\"|\\\" for one, \\\"o\\\" for zero (that's a lower-case O), and \\\"-\\\" for negative one. So if the decimal input d is the number 8, the balanced ternary output is the string \\\"|o-\\\". Thus\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ dec 8  =\u003e bt \\\"|o-\\\"]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere are some more examples.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ dec 3  =\u003e bt \\\"|o\\\"\\n dec 15 =\u003e bt \\\"|--o\\\"\\n dec 52 =\u003e bt \\\"|-o-|\\\"]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer d, return the string bt. Leading zeros should always be suppressed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61287,"title":"The Singularity: Omega Pulse ( Neural Dominance )","description":"Abstract\r\nIn the final phase of Omega experiment, you no longer control a single signal. You are tasked with commanding a Quantum Swarm of nanobots through a high-fidelity neural network. To suceed, you must reach the Event Horizon ( Target Node ) with maximum collective energy while maintaining swarm cohesion and evading an autonomous predatory AI.\r\nKey Mechanics\r\n1.Swarm Cohesion \u0026 Centroid Constraints\r\nThe swarm consists of individual agents. At any time , the Centroid () of the swarm is defined as the geometric mean of all active agent's position:\r\n                                                                                   \r\nCohesion Limit: If any agent  moves to a position where , that agent is instantly neutralized ( Energy = 0 ).\r\nMovement Cost: Energy consumption for a jump is scaled by the agent's distance from the Centroid.\r\n2.Dynamic Edge Saturation\r\nThe neural pathways exhibit Ion Saturation. Every time an agent traverses an edge between Node and Node , the resistance of that specific path increases:\r\n                                                               \r\nSubsequent agents ( or the same agent returning ) will consume significantly more ATP to cross the same path.\r\n3.Relativistic Time Dilation\r\nNodes with high Mass distort the local temporal flow. If a swarm occupies a node with mass , the local time  relative to the global clock  is:\r\n                            \r\nResonance Windows: Nodes only accept incoming signals if \r\n4. The Shadow Predator ( Adversarial AI )\r\nAn autonomous Predator Signal spawns at a designated node. It uses a Breath-First Search (BFS) to move toward the swarm's Centroid.\r\nDetection: If the swarm's Centroid enters the Line-of-Sight (LoS) of the Predator (a clear linear path with no obstructing nodes with a radius ), the swarm's energy is drained at a rate of 10 units/sec.\r\nInput / Output Specifications\r\nInputs:\r\nnodes: A struct array containing x, y, z (coordinates), mass (0 to 1), and initial_res (base resistance)\r\npredator_start: The index of the node where the Shadow Predator begins.\r\nparams: A struct containing: ( .M: Number of agents in the swarm ; \r\n                                               .R_max: Maximum allowed distance from Centroid\r\n                                               .ATP_total: Initial energy pool shared by the swarm.\r\n                                               .target: The destination Node ID. )\r\nOutputs:\r\nmax_energy: The remaining total ATP when the first agent reaches the target (or -1 if the swarm is neutralized ).\r\nbest_strategy: A cell array, where each cell contains the sequence of Node IDs visited by that specific agent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1027.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 513.8px; transform-origin: 468.5px 513.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAbstract\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 31.5px; text-align: left; transform-origin: 444.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the final phase of Omega experiment, you no longer control a single signal. You are tasked with commanding a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eQuantum Swarm\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003enanobots through a high-fidelity neural network. To suceed, you must reach the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEvent Horizon ( Target Node )\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with maximum collective energy while maintaining swarm cohesion and evading an autonomous predatory AI.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eKey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eMechanics\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e1.Swarm Cohesion \u0026amp; Centroid Constraints\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe swarm consists of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eindividual agents. At any time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eT\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the Centroid (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) of the swarm is defined as the geometric mean of all active agent's position:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 49px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 24.5px; text-align: left; transform-origin: 444.5px 24.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                                                   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"84.5\" height=\"49\" style=\"width: 84.5px; height: 49px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 41.9px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 20.95px; transform-origin: 451.5px 20.95px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.4667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.7333px; text-align: left; transform-origin: 423.5px 10.7333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCohesion Limit\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: If any agent \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e moves to a position where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"110\" height=\"20\" style=\"width: 110px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that agent is instantly neutralized ( Energy = 0 ).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eMovement Cost\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Energy consumption for a jump is scaled by the agent's distance from the Centroid.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e2.Dynamic Edge Saturation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe neural pathways exhibit Ion Saturation. Every time an agent traverses an edge between Node \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand Node \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the resistance of that specific path increases:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.7333px; text-align: left; transform-origin: 444.5px 10.7333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                               \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"226.5\" height=\"20\" style=\"width: 226.5px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSubsequent agents ( or the same agent returning ) will consume significantly more ATP to cross the same path.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e3.Relativistic Time Dilation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.9333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21.4667px; text-align: left; transform-origin: 444.5px 21.4667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNodes with high \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eMass\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e distort the local temporal flow. If a swarm occupies a node with mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the local time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"32.5\" height=\"20\" style=\"width: 32.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e relative to the global clock \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"20\" style=\"width: 38px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.75px; text-align: left; transform-origin: 444.5px 10.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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style=\"\"\u003eResonance Windows: Nodes only accept incoming signals if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"252\" height=\"20\" style=\"width: 252px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e4. The Shadow Predator ( Adversarial AI )\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn autonomous Predator Signal spawns at a designated node. It uses a Breath-First Search (BFS) to move toward the swarm's Centroid.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 20.4333px; transform-origin: 451.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 20.4333px; text-align: left; transform-origin: 423.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDetection: If the swarm's Centroid enters the Line-of-Sight (LoS) of the Predator (a clear linear path with no obstructing nodes with a radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), the swarm's energy is drained at a rate of 10 units/sec.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput / Output Specifications\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInputs:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 122.6px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 61.3px; transform-origin: 451.5px 61.3px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enodes\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A struct array containing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex, y, z\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (coordinates), \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emass\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (0 to 1), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003einitial_res\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (base resistance)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003epredator_start\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The index of the node where the Shadow Predator begins.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eparams\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A struct containing: ( .M: Number of agents in the swarm ; \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                               .R_max: Maximum allowed distance from Centroid\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                               .ATP_total: Initial energy pool shared by the swarm.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                               .target: The destination Node ID. )\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutputs\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 20.4333px; transform-origin: 451.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emax_energy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The remaining total ATP when the first agent reaches the target (or -1 if the swarm is neutralized ).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ebest_strategy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"18\" style=\"width: 41.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecell array, where each cell contains the sequence of Node IDs visited by that specific agent.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [max_energy, best_strategy] = solve_singularity_pulse(nodes, predator_start, params)\r\n    % SOLVE_SINGULARITY_PULSE: Multi-agent pathfinding with bio-feedback.\r\n    %\r\n    % Your goal is to coordinate M agents while maintaining swarm cohesion \r\n    % and avoiding the Shadow Predator's Line-of-Sight.\r\n    \r\n    % Initialize variables\r\n    max_energy = -1;\r\n    best_strategy = cell(1, params.M);\r\nend","test_suite":"%% PHASE 1: TORUS \u0026 RESONANCE\r\nclear n p;\r\np.M = 2; p.ATP_total = 1000; p.target = 2;\r\nn(1).coord = [0,0,0,0,0]; n(1).res = 1;\r\nn(2).coord = [90,0,0,0,0]; n(2).res = 1; % Khoảng cách Torus = 10\r\n\r\n[e1, s1] = solve_singularity_pulse(n, 0, p);\r\n% Giải thích: d=10. t_arrival = 10/20 = 0.5s.\r\n% Pulse = 1 + 2*sin(0.5*pi/2)^2 = 1 + 2*0.5 = 2.\r\n% Sat = 2 + 0.125*2*1 = 2.25.\r\n% Cost = 10 * 1 * 2.25 * 2 = 45. E = 1000 - 45 = 955.\r\nassert(abs(e1 - 955) \u003c 1e-4, 'Sai số Torus hoặc Pulse tại 0.5s');\r\n\r\n%% PHASE 2: PREDATOR INTERCEPT\r\nclear n p;\r\np.M = 1; p.ATP_total = 1000; p.target = 2;\r\nn(1).coord = [0,0,0,0,0]; n(1).res = 1;\r\nn(2).coord = [40,0,0,0,0]; n(2).res = 1; \r\nn(3).coord = [30,0,0,0,0]; % Predator bắt đầu rất gần đích\r\n% Swarm: t = 40/20 = 2s.\r\n% Pred: t = 10/15 = 0.66s. -\u003e Bị bắt!\r\n[e2, ~] = solve_singularity_pulse(n, 3, p);\r\nassert(e2 == -1, 'Predator phải bắt được Swarm ở đây!');\r\n\r\n%% PHASE 3: PATH OPTIMIZATION (Bắt buộc đi vòng)\r\nclear n p;\r\np.M = 1; p.target = 2; p.ATP_total = 1000;\r\nn(1).coord = [0,0,0,0,0]; n(1).res = 1;\r\nn(2).coord = [20,0,0,0,0]; n(2).res = 10; % Đích xa, res cao\r\nn(3).coord = [10,0,0,0,0]; n(3).res = 1;  % Trạm trung gian\r\n[e3, s3] = solve_singularity_pulse(n, 0, p);\r\nassert(length(s3{1}) \u003e= 3, 'Thuật toán chưa tìm được đường vòng tối ưu năng lượng');","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4945722,"edited_by":4945722,"edited_at":"2026-03-22T18:52:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2026-03-22T18:52:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-20T09:03:18.000Z","updated_at":"2026-04-30T09:40:40.000Z","published_at":"2026-03-20T09:03:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAbstract\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the final phase of Omega experiment, you no longer control a single signal. You are tasked with commanding a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eQuantum Swarm\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003enanobots through a high-fidelity neural network. To suceed, you must reach the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEvent Horizon ( Target Node )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with maximum collective energy while maintaining swarm cohesion and evading an autonomous predatory AI.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMechanics\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1.Swarm Cohesion \u0026amp; Centroid Constraints\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe swarm consists of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eindividual agents. At any time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the Centroid (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) of the swarm is defined as the geometric mean of all active agent's position:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                                                   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{1}{M}\\\\sum_{i=1}^{M}P_{i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCohesion Limit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: If any agent \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e moves to a position where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003edist(P_{i},C) \u0026gt; R_{max\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, that agent is instantly neutralized ( Energy = 0 ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMovement Cost\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Energy consumption for a jump is scaled by the agent's distance from the Centroid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2.Dynamic Edge Saturation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe neural pathways exhibit Ion Saturation. Every time an agent traverses an edge between Node \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eand Node \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the resistance of that specific path increases:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                               \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eResistance_{new} = Resistance_{odd} \\\\times 1.25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSubsequent agents ( or the same agent returning ) will consume significantly more ATP to cross the same path.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3.Relativistic Time Dilation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNodes with high \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMass\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e distort the local temporal flow. If a swarm occupies a node with mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the local time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{local}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e relative to the global clock \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{global\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{local} = T_{global} \\\\times e^{-m\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eResonance Windows: Nodes only accept incoming signals if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003efloor(T_{local}) \\\\text{ (mod 7) \\\\neq \\\\text{NodeID (mod 7).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4. The Shadow Predator ( Adversarial AI )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn autonomous Predator Signal spawns at a designated node. It uses a Breath-First Search (BFS) to move toward the swarm's Centroid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetection: If the swarm's Centroid enters the Line-of-Sight (LoS) of the Predator (a clear linear path with no obstructing nodes with a radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), the swarm's energy is drained at a rate of 10 units/sec.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput / Output Specifications\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enodes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A struct array containing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex, y, z\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (coordinates), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emass\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (0 to 1), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einitial_res\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (base resistance)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epredator_start\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The index of the node where the Shadow Predator begins.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eparams\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A struct containing: ( .M: Number of agents in the swarm ; \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                               .R_max: Maximum allowed distance from Centroid\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                               .ATP_total: Initial energy pool shared by the swarm.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                               .target: The destination Node ID. )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutputs\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emax_energy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The remaining total ATP when the first agent reaches the target (or -1 if the swarm is neutralized ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ebest_strategy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 \\\\times M\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003ecell array, where each cell contains the sequence of Node IDs visited by that specific agent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55,"title":"Counting Sequence","description":"Given a vector x, find the \"counting sequence\" y.\r\n\r\nA counting sequence is formed by \"counting\" the entries in a given sequence.\r\n\r\nFor example, the sequence\r\n\r\n x = 5, 5, 2, 1, 1, 1, 1, 3\r\n\r\ncan be read as\r\n\r\n Two 5's, one 2, four 1's, one 3\r\n\r\nwhich translates to\r\n\r\n y = 2, 5, 1, 2, 4, 1, 1, 3\r\n\r\nSo y is the counting sequence for x.\r\n\r\nFor this problem, all elements in the sequences x and y will be in the range from 1 to 9.\r\n","description_html":"\u003cp\u003eGiven a vector x, find the \"counting sequence\" y.\u003c/p\u003e\u003cp\u003eA counting sequence is formed by \"counting\" the entries in a given sequence.\u003c/p\u003e\u003cp\u003eFor example, the sequence\u003c/p\u003e\u003cpre\u003e x = 5, 5, 2, 1, 1, 1, 1, 3\u003c/pre\u003e\u003cp\u003ecan be read as\u003c/p\u003e\u003cpre\u003e Two 5's, one 2, four 1's, one 3\u003c/pre\u003e\u003cp\u003ewhich translates to\u003c/p\u003e\u003cpre\u003e y = 2, 5, 1, 2, 4, 1, 1, 3\u003c/pre\u003e\u003cp\u003eSo y is the counting sequence for x.\u003c/p\u003e\u003cp\u003eFor this problem, all elements in the sequences x and y will be in the range from 1 to 9.\u003c/p\u003e","function_template":"function y = CountSeq(x)\r\ny = x;\r\nend","test_suite":"%%\r\nx = [5 5 2 1 1 1 1 3];\r\ncorrect = [2 5 1 2 4 1 1 3];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n\r\n%%\r\nx = [9];\r\ncorrect = [1 9];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n\r\n%%\r\nx = ones(1,9);\r\ncorrect = [9 1];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n\r\n%%\r\nx = 1:9;\r\ncorrect = [1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n%%\r\nx = [1 2 2 1];\r\ncorrect = [1 1 2 2 1 1];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n","published":true,"deleted":false,"likes_count":30,"comments_count":13,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2184,"test_suite_updated_at":"2013-03-14T15:22:01.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:25.000Z","updated_at":"2026-04-28T17:40:44.000Z","published_at":"2012-01-18T01:00:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a vector x, find the \\\"counting sequence\\\" y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA counting sequence is formed by \\\"counting\\\" the entries in a given sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = 5, 5, 2, 1, 1, 1, 1, 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ecan be read as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Two 5's, one 2, four 1's, one 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich translates to\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = 2, 5, 1, 2, 4, 1, 1, 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo y is the counting sequence for x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, all elements in the sequences x and y will be in the range from 1 to 9.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":81,"title":"Mandelbrot Numbers","description":"The \u003chttp://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot Set\u003e is built around a simple iterative equation.\r\n\r\n z(1)   = c\r\n z(n+1) = z(n)^2 + c\r\n\r\nFor any complex c, we can continue this iteration until either\r\nabs(z(n+1)) \u003e 2 or n == lim, then return the iteration count n.\r\n\r\n* If c = 0   and lim = 3, then z = [0 0 0] and n = 3.\r\n* If c = 1   and lim = 5, then z = [1 2], and n = length(z) or 2.\r\n* If c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\r\n\r\nFor a matrix of complex numbers C, return a corresponding matrix N such\r\nthat each element of N is the iteration count n for each complex number c\r\nin the matrix C, subject to the iteration count limit of lim.\r\n\r\nIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\r\n\r\nCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments\r\nwith MATLAB: \u003chttp://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf \r\nChapter 10, Mandelbrot Set (PDF)\u003e","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 296.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 148.083px; transform-origin: 407px 148.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.5px 8px; transform-origin: 12.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Mandelbrot_set\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMandelbrot Set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is built around a simple iterative equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 44px 8.5px; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(1)   = c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(n+1) = z(n)^2 + c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.5px 8px; transform-origin: 379.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 142.5px 8px; transform-origin: 142.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 176.5px 8px; transform-origin: 176.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 226.5px 8px; transform-origin: 226.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377px 8px; transform-origin: 377px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 149.5px 8px; transform-origin: 149.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127px 8px; transform-origin: 127px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCleve Moler has a whole chapter on the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMandelbrot set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in his book \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/moler/exm/chapters.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eExperiments with MATLAB\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function N = mandelbrot(C,lim)\r\n  N = ones(size(C));\r\nend","test_suite":"%%\r\nC = 0;\r\nlim = 5;\r\nN_correct = 5;\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\nC = [0 0.5; 1 4];\r\nlim = 5;\r\nN_correct = [5 4; 2 1];\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\ni = sqrt(-1);\r\nC = [i 1 -2*i -2];\r\nlim = 10;\r\nN_correct = [10 2 1 10];\r\nassert(isequal(mandelbrot(C,lim),N_correct))","published":true,"deleted":false,"likes_count":17,"comments_count":9,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1780,"test_suite_updated_at":"2012-01-26T03:21:20.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:28.000Z","updated_at":"2026-04-30T13:20:29.000Z","published_at":"2012-01-18T01:00:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Mandelbrot_set\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot Set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is built around a simple iterative equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z(1)   = c\\n z(n+1) = z(n)^2 + c]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCleve Moler has a whole chapter on the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in his book \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/moler/exm/chapters.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eExperiments with MATLAB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1499,"title":"Kryptos - CIA Cypher Sculpture: Vigenere Encryption","description":"The \u003chttp://en.wikipedia.org/wiki/Kryptos Kryptos Sculpture\u003e contains four encypted messages.\r\n\r\nThis Challenge is to Encrypt two of the original messages for the sculptor.\r\n\r\nThe method employed is \u003chttp://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher Vigenere Encryption\u003e. One clarification is that \"?\" are removed from the coding sequence and then re-inserted in the final encoded message.\r\n\r\nOriginal phrase: Between subtle shading and the absence of light lies the nuance of iqlusion.\r\n\r\nFor coding purposes spaces and punctuation are removed, except \"?\".\r\n\r\nPhrase to encode: BETWEENSUBTLESHADINGANDTHEABSENCEOFLIGHTLIESTHENUANCEOFIQLUSION\r\n\r\n*Input:* Encode Phrase, Vigenere alphabet word, Vigenere shift word\r\n\r\nVigenere alphabet word ='KRYPTOS';\r\n\r\nVigenere shift word ='PALIMPSEST';\r\n\r\n*Output:* EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD\r\n\r\nThe encryption matrix for this case:\r\n\r\n  KRYPTOSABCDEFGHIJLMNQUVWXZ\r\n\r\n  PTOSABCDEFGHIJLMNQUVWXZKRY\r\n  ABCDEFGHIJLMNQUVWXZKRYPTOS\r\n  LMNQUVWXZKRYPTOSABCDEFGHIJ\r\n  IJLMNQUVWXZKRYPTOSABCDEFGH\r\n  MNQUVWXZKRYPTOSABCDEFGHIJL\r\n  PTOSABCDEFGHIJLMNQUVWXZKRY\r\n  SABCDEFGHIJLMNQUVWXZKRYPTO\r\n  EFGHIJLMNQUVWXZKRYPTOSABCD\r\n  SABCDEFGHIJLMNQUVWXZKRYPTO\r\n  TOSABCDEFGHIJLMNQUVWXZKRYP\r\n\r\nFollow Up Challenges:\r\n\r\n1) \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1500-kryptos-cia-cypher-sculpture-vignere-decryption Vigenere Decryption\u003e\r\n\r\n2) Dictionary search\r\n\r\n3) KRYPTOS Part IV\r\n\r\n\u003chttp://math.ucsd.edu/~crypto/Projects/KarlWang/index2.html#1 KRYPTOS Solutions\u003e\r\n\r\n  \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eThe \u003ca href = \"http://en.wikipedia.org/wiki/Kryptos\"\u003eKryptos Sculpture\u003c/a\u003e contains four encypted messages.\u003c/p\u003e\u003cp\u003eThis Challenge is to Encrypt two of the original messages for the sculptor.\u003c/p\u003e\u003cp\u003eThe method employed is \u003ca href = \"http://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher\"\u003eVigenere Encryption\u003c/a\u003e. One clarification is that \"?\" are removed from the coding sequence and then re-inserted in the final encoded message.\u003c/p\u003e\u003cp\u003eOriginal phrase: Between subtle shading and the absence of light lies the nuance of iqlusion.\u003c/p\u003e\u003cp\u003eFor coding purposes spaces and punctuation are removed, except \"?\".\u003c/p\u003e\u003cp\u003ePhrase to encode: BETWEENSUBTLESHADINGANDTHEABSENCEOFLIGHTLIESTHENUANCEOFIQLUSION\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e Encode Phrase, Vigenere alphabet word, Vigenere shift word\u003c/p\u003e\u003cp\u003eVigenere alphabet word ='KRYPTOS';\u003c/p\u003e\u003cp\u003eVigenere shift word ='PALIMPSEST';\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD\u003c/p\u003e\u003cp\u003eThe encryption matrix for this case:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eKRYPTOSABCDEFGHIJLMNQUVWXZ\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ePTOSABCDEFGHIJLMNQUVWXZKRY\r\nABCDEFGHIJLMNQUVWXZKRYPTOS\r\nLMNQUVWXZKRYPTOSABCDEFGHIJ\r\nIJLMNQUVWXZKRYPTOSABCDEFGH\r\nMNQUVWXZKRYPTOSABCDEFGHIJL\r\nPTOSABCDEFGHIJLMNQUVWXZKRY\r\nSABCDEFGHIJLMNQUVWXZKRYPTO\r\nEFGHIJLMNQUVWXZKRYPTOSABCD\r\nSABCDEFGHIJLMNQUVWXZKRYPTO\r\nTOSABCDEFGHIJLMNQUVWXZKRYP\r\n\u003c/pre\u003e\u003cp\u003eFollow Up Challenges:\u003c/p\u003e\u003cp\u003e1) \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1500-kryptos-cia-cypher-sculpture-vignere-decryption\"\u003eVigenere Decryption\u003c/a\u003e\u003c/p\u003e\u003cp\u003e2) Dictionary search\u003c/p\u003e\u003cp\u003e3) KRYPTOS Part IV\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://math.ucsd.edu/~crypto/Projects/KarlWang/index2.html#1\"\u003eKRYPTOS Solutions\u003c/a\u003e\u003c/p\u003e","function_template":"function encoded=encode_vigenere(phrase,word1,word2)\r\n encoded=phrase;\r\nend","test_suite":"phrase=upper('Between subtle shading and the absence of light lies the nuance of iqlusion.');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\nencoded_exp='EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD';\r\nword1='KRYPTOS';\r\nword2='PALIMPSEST';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n%%\r\n\r\nphrase=upper('It was totally invisible Hows that possible? They used the Earths magnetic field X The information was gathered and transmitted undergruund to an unknown location X Does Langley know about this? They should Its buried out there somewhere X Who knows the exact location? Only WW This was his last message X Thirty eight degrees fifty seven minutes six point five seconds north Seventy seven degrees eight minutes forty four seconds west ID by rows');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\n\r\nencoded_exp='VFPJUDEEHZWETZYVGWHKKQETGFQJNCEGGWHKK?DQMCPFQZDQMMIAGPFXHQRLGTIMVMZJANQLVKQEDAGDVFRPJUNGEUNAQZGZLECGYUXUEENJTBJLBQCRTBJDFHRRYIZETKZEMVDUFKSJHKFWHKUWQLSZFTIHHDDDUVH?DWKBFUFPWNTDFIYCUQZEREEVLDKFEZMOQQJLTTUGSYQPFEUNLAVIDXFLGGTEZ?FKZBSFDQVGOGIPUFXHHDRKFFHQNTGPUAECNUVPDJMQCLQUMUNEDFQELZZVRRGKFFVOEEXBDMVPNFQXEZLGREDNQFMPNZGLFLPMRJQYALMGNUVPDXVKPDQUMEBEDMHDAFMJGZNUPLGEWJLLAETG';\r\n\r\nword1='KRYPTOS';\r\nword2='ABSCISSA';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n%%\r\nphrase=upper('The fox jumped over the moon');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\nencoded_exp='VUIPFSBYVQMMWPIMEVPZCVK';\r\nword1='KRYPTOS';\r\nword2='MATLAB';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n\r\n%%\r\nphrase=upper('Between the Devil and the deep blue sea');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\n\r\nword1='AWEIGH';\r\nword2='MATLAB';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\nencoded_exp='SENMEDWTZNDDFIBLNNCHVTEDIBBCEZOA';\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":3,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":62,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":28,"created_at":"2013-05-11T20:36:34.000Z","updated_at":"2026-04-17T02:31:21.000Z","published_at":"2013-05-11T21:19:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Kryptos\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKryptos Sculpture\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contains four encypted messages.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to Encrypt two of the original messages for the sculptor.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe method employed is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere Encryption\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. One clarification is that \\\"?\\\" are removed from the coding sequence and then re-inserted in the final encoded message.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOriginal phrase: Between subtle shading and the absence of light lies the nuance of iqlusion.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor coding purposes spaces and punctuation are removed, except \\\"?\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePhrase to encode: BETWEENSUBTLESHADINGANDTHEABSENCEOFLIGHTLIESTHENUANCEOFIQLUSION\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Encode Phrase, Vigenere alphabet word, Vigenere shift word\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere alphabet word ='KRYPTOS';\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere shift word ='PALIMPSEST';\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe encryption matrix for this case:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[KRYPTOSABCDEFGHIJLMNQUVWXZ\\n\\nPTOSABCDEFGHIJLMNQUVWXZKRY\\nABCDEFGHIJLMNQUVWXZKRYPTOS\\nLMNQUVWXZKRYPTOSABCDEFGHIJ\\nIJLMNQUVWXZKRYPTOSABCDEFGH\\nMNQUVWXZKRYPTOSABCDEFGHIJL\\nPTOSABCDEFGHIJLMNQUVWXZKRY\\nSABCDEFGHIJLMNQUVWXZKRYPTO\\nEFGHIJLMNQUVWXZKRYPTOSABCD\\nSABCDEFGHIJLMNQUVWXZKRYPTO\\nTOSABCDEFGHIJLMNQUVWXZKRYP]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow Up Challenges:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1500-kryptos-cia-cypher-sculpture-vignere-decryption\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere Decryption\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) Dictionary search\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3) KRYPTOS Part IV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://math.ucsd.edu/~crypto/Projects/KarlWang/index2.html#1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKRYPTOS Solutions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":733,"title":"Extract Built In Functions and Toolbox Functions from String or Function Handle","description":"Find the Built-In functions and Toolbox functions in either a string or a function handle.\r\n\r\nGenerate a string of alphabetized Built-In functions followed by alphabetized Functions.\r\n\r\n*Inputs:*\r\n\r\nfh=@(x)log10(x)+log2(x)+abs(x)\r\n\r\nstr='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)'\r\n\r\n*Outputs:*\r\n\r\n'abs log2 log10'\r\n\r\n'abs filter numel sin filter2 smooth3'\r\n\r\nRelated to \r\n\u003chttp://www.mathworks.com/matlabcentral/cody/problems/464-function-sniffer Cody_464\u003e","description_html":"\u003cp\u003eFind the Built-In functions and Toolbox functions in either a string or a function handle.\u003c/p\u003e\u003cp\u003eGenerate a string of alphabetized Built-In functions followed by alphabetized Functions.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e\u003c/p\u003e\u003cp\u003efh=@(x)log10(x)+log2(x)+abs(x)\u003c/p\u003e\u003cp\u003estr='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)'\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutputs:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e'abs log2 log10'\u003c/p\u003e\u003cp\u003e'abs filter numel sin filter2 smooth3'\u003c/p\u003e\u003cp\u003eRelated to  \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/464-function-sniffer\"\u003eCody_464\u003c/a\u003e\u003c/p\u003e","function_template":"function functions = find_functions(fh_str)\r\n  functions = '';\r\nend","test_suite":"%%\r\nfh_str='log2(x)+smooth3(x,y)+abs(2)+log10(5)';\r\nexp_str='abs log10 log2 smooth3';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='for k=log10(x):log2(x)+abs(x)';\r\nexp_str='abs for log10 log2';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str=@(x)x^2+sin(x)-cos(x);\r\nexp_str='cos sin';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='@(x)x^2+sin(x)-cos(x)';\r\nexp_str='cos sin';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='filter2(x,A)+filter(x)-cos(x) expm(z)';\r\nexp_str='cos filter expm filter2';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)';\r\nexp_str='abs filter numel sin filter2 smooth3';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":6,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":83,"test_suite_updated_at":"2012-07-18T13:18:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-01T23:09:01.000Z","updated_at":"2026-03-31T20:12:36.000Z","published_at":"2012-06-02T00:17:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the Built-In functions and Toolbox functions in either a string or a function handle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenerate a string of alphabetized Built-In functions followed by alphabetized Functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efh=@(x)log10(x)+log2(x)+abs(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003estr='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'abs log2 log10'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'abs filter numel sin filter2 smooth3'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRelated to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/464-function-sniffer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody_464\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2237,"title":"Mmm! Multi-dimensional Matrix Multiplication ","description":"You have got a couple of multi-dimensional matrices, A and B. And want to multiply them. For the first 2 dimensions, an ordinary matrix multiplication applies. And in the other dimensions? Well, they just act as parallel worlds. All 2D matrices are multiplied, for every element in the other dimensions.\r\nYou may assume that the size in the 1st two dimensions allows simple matrix multiplication: A(:,:,1)*B(:,:,1), so size(A(:,:,1),2) == size(B(:,:,1),1), or either A(:,:,1) is a scalar or B(:,:,1) is a scalar.\r\nIn the other dimensions, the sizes of A and B should be eqaal, size(A,n) == size(B,n), for n\u003e2, or either ndims(A)\u003cn or ndims(B)\u003cn, or either size(A,n)==1 or size(B,n)==1, so one of them is a scalar.\r\n\r\nWrite a function |mtimesm| that does this, and ask Mathworks to include it in the |elmat| toolbox of the Next Release.","description_html":"\u003cp\u003eYou have got a couple of multi-dimensional matrices, A and B. And want to multiply them. For the first 2 dimensions, an ordinary matrix multiplication applies. And in the other dimensions? Well, they just act as parallel worlds. All 2D matrices are multiplied, for every element in the other dimensions.\r\nYou may assume that the size in the 1st two dimensions allows simple matrix multiplication: A(:,:,1)*B(:,:,1), so size(A(:,:,1),2) == size(B(:,:,1),1), or either A(:,:,1) is a scalar or B(:,:,1) is a scalar.\r\nIn the other dimensions, the sizes of A and B should be eqaal, size(A,n) == size(B,n), for n\u0026gt;2, or either ndims(A)\u0026lt;n or ndims(B)\u0026lt;n, or either size(A,n)==1 or size(B,n)==1, so one of them is a scalar.\u003c/p\u003e\u003cp\u003eWrite a function \u003ctt\u003emtimesm\u003c/tt\u003e that does this, and ask Mathworks to include it in the \u003ctt\u003eelmat\u003c/tt\u003e toolbox of the Next Release.\u003c/p\u003e","function_template":"function C = mtimesm(A,B)\r\n  C = A*B;\r\nend","test_suite":"%% case 1\r\nA = 1;\r\nB = 2;\r\nC = mtimesm(A,B);\r\nC_correct = 2;\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 2\r\nA = rand(2,3);\r\nB = rand(3,4);\r\nC = mtimesm(A,B);\r\nC_correct = A*B;\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 3\r\nA = rand(2,3);\r\nB = 2;\r\nC = mtimesm(A,B);\r\nC_correct = 2*A;\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 4\r\nA = rand(2,3,2);\r\nB = rand(3,4,2);\r\nC = mtimesm(A,B);\r\nC_correct = cat(3,A(:,:,1)*B(:,:,1),A(:,:,2)*B(:,:,2));\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 5\r\nA = rand(2,3,3);\r\nB = rand(3,4);\r\nC = mtimesm(A,B);\r\nC_correct = cat(3,A(:,:,1)*B,A(:,:,2)*B,A(:,:,3)*B); \r\nassert(isequal(C,C_correct))\r\n\r\n%% case 6\r\nA = rand(4,3,1,2);\r\nB = rand(3,2,2);\r\nC = mtimesm(A,B);\r\nC_correct(:,:,1,1) = A(:,:,1,1)*B(:,:,1);\r\nC_correct(:,:,1,2) = A(:,:,1,2)*B(:,:,1);\r\nC_correct(:,:,2,1) = A(:,:,1,1)*B(:,:,2);\r\nC_correct(:,:,2,2) = A(:,:,1,2)*B(:,:,2);\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 7\r\nA = rand(4,3,1,2);\r\nB = rand(3,2,1,1,2);\r\nC = mtimesm(A,B);\r\nC_correct(:,:,1,1,1) = A(:,:,1,1)*B(:,:,1,1,1);\r\nC_correct(:,:,1,1,2) = A(:,:,1,1)*B(:,:,1,1,2);\r\nC_correct(:,:,1,2,1) = A(:,:,1,2)*B(:,:,1,1,1);\r\nC_correct(:,:,1,2,2) = A(:,:,1,2)*B(:,:,1,1,2);\r\nassert(isequal(C,C_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":5,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":"2014-03-07T06:22:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-03-06T11:17:42.000Z","updated_at":"2026-04-03T03:22:22.000Z","published_at":"2014-03-06T11:17:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have got a couple of multi-dimensional matrices, A and B. And want to multiply them. For the first 2 dimensions, an ordinary matrix multiplication applies. And in the other dimensions? Well, they just act as parallel worlds. All 2D matrices are multiplied, for every element in the other dimensions. You may assume that the size in the 1st two dimensions allows simple matrix multiplication: A(:,:,1)*B(:,:,1), so size(A(:,:,1),2) == size(B(:,:,1),1), or either A(:,:,1) is a scalar or B(:,:,1) is a scalar. In the other dimensions, the sizes of A and B should be eqaal, size(A,n) == size(B,n), for n\u0026gt;2, or either ndims(A)\u0026lt;n or ndims(B)\u0026lt;n, or either size(A,n)==1 or size(B,n)==1, so one of them is a scalar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emtimesm\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that does this, and ask Mathworks to include it in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eelmat\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e toolbox of the Next Release.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1286,"title":"MatCAT - Reconstruct X from Its X-rays","description":"Consider a matrix x\r\n\r\n x = [ 1 2 0\r\n       0 5 0 \r\n       3 0 8 ]\r\n\r\nIf we sum x along the rows we get\r\n\r\n row_sums = [3 5 11]\r\n\r\nSumming along the columns gives \r\n\r\n col_sums = [4 7 8]\r\n\r\nMetaphorically, we might call these sums \"x-rays\". Your job is to take these x-rays and reconstruct the matrix x being x-rayed, in the fashion of a \u003chttp://en.wikipedia.org/wiki/X-ray_computed_tomography CAT scan\u003e. Can you put all the bones in the right place?\r\n\r\nAll matrix elements must be non-negative integers. There is no guarantee of a unique answer. I will only check that the row and column sums match the supplied matrix, and that your elements are non-negative integers.\r\n\r\nBonus question: Under what circumstances does the answer become unique? Discuss.","description_html":"\u003cp\u003eConsider a matrix x\u003c/p\u003e\u003cpre\u003e x = [ 1 2 0\r\n       0 5 0 \r\n       3 0 8 ]\u003c/pre\u003e\u003cp\u003eIf we sum x along the rows we get\u003c/p\u003e\u003cpre\u003e row_sums = [3 5 11]\u003c/pre\u003e\u003cp\u003eSumming along the columns gives\u003c/p\u003e\u003cpre\u003e col_sums = [4 7 8]\u003c/pre\u003e\u003cp\u003eMetaphorically, we might call these sums \"x-rays\". Your job is to take these x-rays and reconstruct the matrix x being x-rayed, in the fashion of a \u003ca href = \"http://en.wikipedia.org/wiki/X-ray_computed_tomography\"\u003eCAT scan\u003c/a\u003e. Can you put all the bones in the right place?\u003c/p\u003e\u003cp\u003eAll matrix elements must be non-negative integers. There is no guarantee of a unique answer. I will only check that the row and column sums match the supplied matrix, and that your elements are non-negative integers.\u003c/p\u003e\u003cp\u003eBonus question: Under what circumstances does the answer become unique? Discuss.\u003c/p\u003e","function_template":"function x = matcat(row_sums,col_sums)\r\n  x = 0;\r\nend","test_suite":"%%\r\nrow_sums = [3 5 11];\r\ncol_sums = [4 7 8];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = [2 2 2 2 2 6];\r\ncol_sums = [2 3 3 3 3 2];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = [65 65 65 65 65];\r\ncol_sums = [65 65 65 65 65];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = [22 34 33];\r\ncol_sums = [15 23 18 21 12];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = 55;\r\ncol_sums = [1 2 3 4 5 6 7 8 9 10];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":4,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":148,"test_suite_updated_at":"2013-02-21T17:46:45.000Z","rescore_all_solutions":false,"group_id":23,"created_at":"2013-02-21T17:25:12.000Z","updated_at":"2026-04-22T11:32:22.000Z","published_at":"2013-02-21T17:46:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a matrix x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [ 1 2 0\\n       0 5 0 \\n       3 0 8 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf we sum x along the rows we get\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ row_sums = [3 5 11]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSumming along the columns gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ col_sums = [4 7 8]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMetaphorically, we might call these sums \\\"x-rays\\\". Your job is to take these x-rays and reconstruct the matrix x being x-rayed, in the fashion of a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/X-ray_computed_tomography\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCAT scan\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Can you put all the bones in the right place?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll matrix elements must be non-negative integers. There is no guarantee of a unique answer. I will only check that the row and column sums match the supplied matrix, and that your elements are non-negative integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBonus question: Under what circumstances does the answer become unique? Discuss.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44838,"title":"Pose from bearing angles in 2D","description":"A robot moving on the plane has a sensor that measures the bearing angle to two mapped landmarks, that is, the world frame coordinates of the landmarks are known and represented by position vectors |P1| and |P2| .  The bearing angles to the landmarks, with respect to the x-axis of the robot's coordinate frame are |th1| and |th2| respectively.  The robot's forward direction is parallel to its x-axis and its heading angle, with respect to magnetic north is |thb| .\r\n\r\nDetermine the pose of the robot expressed as a homogeneous transformation matrix with respect to the world coordinate frame.  In surveying this is known as a resection problem.","description_html":"\u003cp\u003eA robot moving on the plane has a sensor that measures the bearing angle to two mapped landmarks, that is, the world frame coordinates of the landmarks are known and represented by position vectors \u003ctt\u003eP1\u003c/tt\u003e and \u003ctt\u003eP2\u003c/tt\u003e .  The bearing angles to the landmarks, with respect to the x-axis of the robot's coordinate frame are \u003ctt\u003eth1\u003c/tt\u003e and \u003ctt\u003eth2\u003c/tt\u003e respectively.  The robot's forward direction is parallel to its x-axis and its heading angle, with respect to magnetic north is \u003ctt\u003ethb\u003c/tt\u003e .\u003c/p\u003e\u003cp\u003eDetermine the pose of the robot expressed as a homogeneous transformation matrix with respect to the world coordinate frame.  In surveying this is known as a resection problem.\u003c/p\u003e","function_template":"function T = user_function(P1, P2, th1, th2, thb)\r\n% Input:  P1 a 2x1 vector representing the coordinate of a point\r\n%         P2 a 2x1 vector representing the coordinate of a point\r\n%         th1 bearing, a scalar angle\r\n%         th2 bearing, a scalar angle\r\n%         thb heading, a scalar angle\r\n% Output: T a 3x3 homogeneous transformation matrix\r\n  T = ;\r\nend","test_suite":"%\r\nP1 = [10 20]';\r\nP2 = [20 20]';\r\nP = rand(2,1)*5 + [5 5]';\r\nthb = rand*0.2;\r\nx = P1 - P;\r\nth1 = atan2(x(2), x(1)) - thb;\r\nx = P2 - P;\r\nth2 = atan2(x(2), x(1)) - thb;\r\n\r\nT = user_function(P1, P2, th1, th2, thb);\r\n\r\n%% test size and complexity\r\nassert(all(size(T)==3), 'The matrix must be 3x3');\r\nassert(isreal(T), 'The matrix must be real, not complex');\r\n\r\n%% bottom row\r\nassert(isequal(T(3,:), [0 0 1]), 'The bottom row of the homogeneous transformation matrix is not correct')\r\n\r\n%% x coordinate\r\nassert(abs(T(1,3)-P(1))\u003c1e-4, 'The representation of the x-coordinate is not correct')\r\n\r\n%% y coordinate\r\nassert(abs(T(2,3)-P(2))\u003c1e-4, 'The representation of the y-coordinate is not correct')\r\n\r\n%% valid rotation matrix\r\nR = T(1:2,1:2);\r\nassert( abs(det(R)-1) \u003c 1e-4, 'The determinant of the rotation submatrix is not correct')\r\n\r\n%% correct rotation matrix\r\nR = T(1:2,1:2);\r\nassert( abs(atan2(R(2,1), R(1,1)) - thb) \u003c 1e-4, 'The rotation matrix is not correct, check your calculation of the heading SSW and whether you are using radians or degrees')\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-21T00:32:56.000Z","updated_at":"2026-04-23T08:14:24.000Z","published_at":"2019-01-21T00:37:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA robot moving on the plane has a sensor that measures the bearing angle to two mapped landmarks, that is, the world frame coordinates of the landmarks are known and represented by position vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . The bearing angles to the landmarks, with respect to the x-axis of the robot's coordinate frame are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eth1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eth2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e respectively. The robot's forward direction is parallel to its x-axis and its heading angle, with respect to magnetic north is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the pose of the robot expressed as a homogeneous transformation matrix with respect to the world coordinate frame. In surveying this is known as a resection problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61175,"title":"[Master Regular Expression] Goat Latin","description":"You are given a string sentence that consist of words separated by spaces. Each word consists of lowercase and uppercase letters only.\r\nWe would like to convert the sentence to \"Goat Latin\" (a made-up language similar to Pig Latin.) The rules of Goat Latin are as follows:\r\nIf a word begins with a vowel ('a', 'e', 'i', 'o', or 'u'), append \"ma\" to the end of the word.\r\nFor example, the word \"apple\" becomes \"applema\".\r\nIf a word begins with a consonant (i.e., not a vowel), remove the first letter and append it to the end, then add \"ma\".\r\nFor example, the word \"goat\" becomes \"oatgma\".\r\nAdd one letter 'a' to the end of each word per its word index in the sentence, starting with 1.\r\nFor example, the first word gets \"a\" added to the end, the second word gets \"aa\" added to the end, and so on.\r\nReturn the final sentence representing the conversion from sentence to Goat Latin.\r\n \r\nExample 1:\r\nInput: sentence = \"I speak Goat Latin\"\r\nOutput: \"Imaa peaksmaaa oatGmaaaa atinLmaaaaa\"\r\nExample 2:\r\nInput: sentence = \"The quick brown fox jumped over the lazy dog\"\r\nOutput: \"heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa\"\r\n \r\nConstraints:\r\n1 \u003c= sentence.length \u003c= 150\r\nsentence consists of English letters and spaces.\r\nsentence has no leading or trailing spaces.\r\nAll the words in sentence are separated by a single space.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 809.375px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 404.688px; transform-origin: 408px 404.688px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given a string sentence that consist of words separated by spaces. Each word consists of lowercase and uppercase letters only.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe would like to convert the sentence to \"Goat Latin\" (a made-up language similar to Pig Latin.) The rules of Goat Latin are as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf a word begins with a vowel ('a', 'e', 'i', 'o', or 'u'), append \"ma\" to the end of the word.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the word \"apple\" becomes \"applema\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf a word begins with a consonant (i.e., not a vowel), remove the first letter and append it to the end, then add \"ma\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the word \"goat\" becomes \"oatgma\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAdd one letter 'a' to the end of each word per its word index in the sentence, starting with 1.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the first word gets \"a\" added to the end, the second word gets \"aa\" added to the end, and so on.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e the final sentence representing the conversion from sentence to Goat Latin\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 1:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sentence = \"I speak Goat Latin\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"Imaa peaksmaaa oatGmaaaa atinLmaaaaa\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sentence = \"The quick brown fox jumped over the lazy dog\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraints:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1 \u0026lt;= sentence.length \u0026lt;= 150\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esentence consists of English letters and spaces.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esentence has no leading or trailing spaces.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAll the words in sentence are separated by a single space.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = solution(sentence)\r\n\r\nend","test_suite":"%%\r\nsentence = 'I speak Goat Latin';\r\ncorrect_answer = 'Imaa peaksmaaa oatGmaaaa atinLmaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'The quick brown fox jumped over the lazy dog';\r\ncorrect_answer = 'heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'YLI Tdy kh dXKaa yRlPm WCVHO jVA tkLqg KWvQP Vo x aF IJSb DJUn q';\r\ncorrect_answer = 'LIYmaa dyTmaaa hkmaaaa XKaadmaaaaa RlPmymaaaaaa CVHOWmaaaaaaa VAjmaaaaaaaa kLqgtmaaaaaaaaa WvQPKmaaaaaaaaaa oVmaaaaaaaaaaa xmaaaaaaaaaaaa aFmaaaaaaaaaaaaa IJSbmaaaaaaaaaaaaaa JUnDmaaaaaaaaaaaaaaa qmaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'win QKDZ zoI pFP OFxhk XHUl qbQw W Em tzur Nm Wolnm wQ kQZh mvqwr I';\r\ncorrect_answer = 'inwmaa KDZQmaaa oIzmaaaa FPpmaaaaa OFxhkmaaaaaa HUlXmaaaaaaa bQwqmaaaaaaaa Wmaaaaaaaaa Emmaaaaaaaaaa zurtmaaaaaaaaaaa mNmaaaaaaaaaaaa olnmWmaaaaaaaaaaaaa Qwmaaaaaaaaaaaaaa QZhkmaaaaaaaaaaaaaaa vqwrmmaaaaaaaaaaaaaaaa Imaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'zo';\r\ncorrect_answer = 'ozmaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'cUS j E NlYz j Tc HR P p';\r\ncorrect_answer = 'UScmaa jmaaa Emaaaa lYzNmaaaaa jmaaaaaa cTmaaaaaaa RHmaaaaaaaa Pmaaaaaaaaa pmaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'FAMfT ain J z oEo aDttb';\r\ncorrect_answer = 'AMfTFmaa ainmaaa Jmaaaa zmaaaaa oEomaaaaaa aDttbmaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'NPm t gwad PVVG d MGLk Yvmy SXgK f A xPB zrnY Pz Ga';\r\ncorrect_answer = 'PmNmaa tmaaa wadgmaaaa VVGPmaaaaa dmaaaaaa GLkMmaaaaaaa vmyYmaaaaaaaa XgKSmaaaaaaaaa fmaaaaaaaaaa Amaaaaaaaaaaa PBxmaaaaaaaaaaaa rnYzmaaaaaaaaaaaaa zPmaaaaaaaaaaaaaa aGmaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'VRVJO kxPa';\r\ncorrect_answer = 'RVJOVmaa xPakmaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'dwR MWqM wBHyj va dwCF eod sHzt ft zP SASy GD uvh';\r\ncorrect_answer = 'wRdmaa WqMMmaaa BHyjwmaaaa avmaaaaa wCFdmaaaaaa eodmaaaaaaa Hztsmaaaaaaaa tfmaaaaaaaaa Pzmaaaaaaaaaa ASySmaaaaaaaaaaa DGmaaaaaaaaaaaa uvhmaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'W UvuC AEg Hsqo r mdzgu';\r\ncorrect_answer = 'Wmaa UvuCmaaa AEgmaaaa sqoHmaaaaa rmaaaaaa dzgummaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'rDIH peGn';\r\ncorrect_answer = 'DIHrmaa eGnpmaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Lr EV XM S Drre IDu sXbwK AFMP DS ASJ A x cXjtk w fz sD vut jg';\r\ncorrect_answer = 'rLmaa EVmaaa MXmaaaa Smaaaaa rreDmaaaaaa IDumaaaaaaa XbwKsmaaaaaaaa AFMPmaaaaaaaaa SDmaaaaaaaaaa ASJmaaaaaaaaaaa Amaaaaaaaaaaaa xmaaaaaaaaaaaaa Xjtkcmaaaaaaaaaaaaaa wmaaaaaaaaaaaaaaa zfmaaaaaaaaaaaaaaaa Dsmaaaaaaaaaaaaaaaaa utvmaaaaaaaaaaaaaaaaaa gjmaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'ALNn';\r\ncorrect_answer = 'ALNnmaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'w YCcE Cx t';\r\ncorrect_answer = 'wmaa CcEYmaaa xCmaaaa tmaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'KYgHu kur tf Qrz D sSr mOo BTW Y dlsw VGXN SQg GuRb X BU IL';\r\ncorrect_answer = 'YgHuKmaa urkmaaa ftmaaaa rzQmaaaaa Dmaaaaaa Srsmaaaaaaa Oommaaaaaaaa TWBmaaaaaaaaa Ymaaaaaaaaaa lswdmaaaaaaaaaaa GXNVmaaaaaaaaaaaa QgSmaaaaaaaaaaaaa uRbGmaaaaaaaaaaaaaa Xmaaaaaaaaaaaaaaa UBmaaaaaaaaaaaaaaaa ILmaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'xFC oTW YBfHj XfpPw bDD';\r\ncorrect_answer = 'FCxmaa oTWmaaa BfHjYmaaaa fpPwXmaaaaa DDbmaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'O B ZYpNk IfEYR Kmcy i IYo WiP T YNL k eM rhIRJ t AYnT';\r\ncorrect_answer = 'Omaa Bmaaa YpNkZmaaaa IfEYRmaaaaa mcyKmaaaaaa imaaaaaaa IYomaaaaaaaa iPWmaaaaaaaaa Tmaaaaaaaaaa NLYmaaaaaaaaaaa kmaaaaaaaaaaaa eMmaaaaaaaaaaaaa hIRJrmaaaaaaaaaaaaaa tmaaaaaaaaaaaaaaa AYnTmaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'e ttpp yZ Xi NSFfx cbpW TtT Ufl';\r\ncorrect_answer = 'emaa tpptmaaa Zymaaaa iXmaaaaa SFfxNmaaaaaa bpWcmaaaaaaa tTTmaaaaaaaa Uflmaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'at uj EE W k NhW cJo YJzf Ba Ei J CYG BS RsMWI oEr';\r\ncorrect_answer = 'atmaa ujmaaa EEmaaaa Wmaaaaa kmaaaaaa hWNmaaaaaaa Jocmaaaaaaaa JzfYmaaaaaaaaa aBmaaaaaaaaaa Eimaaaaaaaaaaa Jmaaaaaaaaaaaa YGCmaaaaaaaaaaaaa SBmaaaaaaaaaaaaaa sMWIRmaaaaaaaaaaaaaaa oErmaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'YJK WRiRy BR nsj jR aq oOBiB LM jho PIoh Jd ZVD MKJo GQa ZQ JQoI C TjW rGBxs eu';\r\ncorrect_answer = 'JKYmaa RiRyWmaaa RBmaaaa sjnmaaaaa Rjmaaaaaa aqmaaaaaaa oOBiBmaaaaaaaa MLmaaaaaaaaa hojmaaaaaaaaaa IohPmaaaaaaaaaaa dJmaaaaaaaaaaaa VDZmaaaaaaaaaaaaa KJoMmaaaaaaaaaaaaaa QaGmaaaaaaaaaaaaaaa QZmaaaaaaaaaaaaaaaa QoIJmaaaaaaaaaaaaaaaaa Cmaaaaaaaaaaaaaaaaaa jWTmaaaaaaaaaaaaaaaaaaa GBxsrmaaaaaaaaaaaaaaaaaaaa eumaaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'KhQ RzIxv W y BZ';\r\ncorrect_answer = 'hQKmaa zIxvRmaaa Wmaaaa ymaaaaa ZBmaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'O uQT kTpvQ we MprM KeyHB o PWskJ wV uMppp V mzPt LO GNAr E k A y w';\r\ncorrect_answer = 'Omaa uQTmaaa TpvQkmaaaa ewmaaaaa prMMmaaaaaa eyHBKmaaaaaaa omaaaaaaaa WskJPmaaaaaaaaa Vwmaaaaaaaaaa uMpppmaaaaaaaaaaa Vmaaaaaaaaaaaa zPtmmaaaaaaaaaaaaa OLmaaaaaaaaaaaaaa NArGmaaaaaaaaaaaaaaa Emaaaaaaaaaaaaaaaa kmaaaaaaaaaaaaaaaaa Amaaaaaaaaaaaaaaaaaa ymaaaaaaaaaaaaaaaaaaa wmaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Qem sv v CsIJ';\r\ncorrect_answer = 'emQmaa vsmaaa vmaaaa sIJCmaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'WDE mKpD umWx';\r\ncorrect_answer = 'DEWmaa KpDmmaaa umWxmaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'IwiK tHUzG fff WGW p aiNRF XMK TYZV dQ b CrES';\r\ncorrect_answer = 'IwiKmaa HUzGtmaaa fffmaaaa GWWmaaaaa pmaaaaaa aiNRFmaaaaaaa MKXmaaaaaaaa YZVTmaaaaaaaaa Qdmaaaaaaaaaa bmaaaaaaaaaaa rESCmaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Cjm nX RuiM sjZXi wlhnC F x Xp Ith p GkYwR baO pSI';\r\ncorrect_answer = 'jmCmaa Xnmaaa uiMRmaaaa jZXismaaaaa lhnCwmaaaaaa Fmaaaaaaa xmaaaaaaaa pXmaaaaaaaaa Ithmaaaaaaaaaa pmaaaaaaaaaaa kYwRGmaaaaaaaaaaaa aObmaaaaaaaaaaaaa SIpmaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'njtB MhagV fXgz yd nm bVtIX';\r\ncorrect_answer = 'jtBnmaa hagVMmaaa Xgzfmaaaa dymaaaaa mnmaaaaaa VtIXbmaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'vfzy IoIHU';\r\ncorrect_answer = 'fzyvmaa IoIHUmaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'wP TzEWi nR o Gvn tfg IRzp c tD OEf dtoM N ma k Vo O FrJm sl';\r\ncorrect_answer = 'Pwmaa zEWiTmaaa Rnmaaaa omaaaaa vnGmaaaaaa fgtmaaaaaaa IRzpmaaaaaaaa cmaaaaaaaaa Dtmaaaaaaaaaa OEfmaaaaaaaaaaa toMdmaaaaaaaaaaaa Nmaaaaaaaaaaaaa ammaaaaaaaaaaaaaa kmaaaaaaaaaaaaaaa oVmaaaaaaaaaaaaaaaa Omaaaaaaaaaaaaaaaaa rJmFmaaaaaaaaaaaaaaaaaa lsmaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'asmW tJKE OBeUn rNP TeIAr skn h Eh a JgLi J d a d';\r\ncorrect_answer = 'asmWmaa JKEtmaaa OBeUnmaaaa NPrmaaaaa eIArTmaaaaaa knsmaaaaaaa hmaaaaaaaa Ehmaaaaaaaaa amaaaaaaaaaa gLiJmaaaaaaaaaaa Jmaaaaaaaaaaaa dmaaaaaaaaaaaaa amaaaaaaaaaaaaaa dmaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Au';\r\ncorrect_answer = 'Aumaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'hOM y vw KabmF rxfLL WcPy cO ORrjt bp ks gkz MpP NrLbG c b BNEMq zfQIt vcEp Eqh frbVt';\r\ncorrect_answer = 'OMhmaa ymaaa wvmaaaa abmFKmaaaaa xfLLrmaaaaaa cPyWmaaaaaaa Ocmaaaaaaaa ORrjtmaaaaaaaaa pbmaaaaaaaaaa skmaaaaaaaaaaa kzgmaaaaaaaaaaaa pPMmaaaaaaaaaaaaa rLbGNmaaaaaaaaaaaaaa cmaaaaaaaaaaaaaaa bmaaaaaaaaaaaaaaaa NEMqBmaaaaaaaaaaaaaaaaa fQItzmaaaaaaaaaaaaaaaaaa cEpvmaaaaaaaaaaaaaaaaaaa Eqhmaaaaaaaaaaaaaaaaaaaa rbVtfmaaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Djl lWo Qsbrt Y i Act ZwK h cbDrl Jtukm VOmEk J NQluv fBGok siU Iky z JM DM Edtb';\r\ncorrect_answer = 'jlDmaa Wolmaaa sbrtQmaaaa Ymaaaaa imaaaaaa Actmaaaaaaa wKZmaaaaaaaa hmaaaaaaaaa bDrlcmaaaaaaaaaa tukmJmaaaaaaaaaaa OmEkVmaaaaaaaaaaaa Jmaaaaaaaaaaaaa QluvNmaaaaaaaaaaaaaa BGokfmaaaaaaaaaaaaaaa iUsmaaaaaaaaaaaaaaaa Ikymaaaaaaaaaaaaaaaaa zmaaaaaaaaaaaaaaaaaa MJmaaaaaaaaaaaaaaaaaaa MDmaaaaaaaaaaaaaaaaaaaa Edtbmaaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'DYwO bAv lw qoszQ bp Qh SCaAL UKWa bAHNo';\r\ncorrect_answer = 'YwODmaa Avbmaaa wlmaaaa oszQqmaaaaa pbmaaaaaa hQmaaaaaaa CaALSmaaaaaaaa UKWamaaaaaaaaa AHNobmaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4945898,"edited_by":4945898,"edited_at":"2026-01-31T12:14:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2026-01-31T12:12:55.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-31T12:12:09.000Z","updated_at":"2026-04-28T18:31:56.000Z","published_at":"2026-01-31T12:12:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a string sentence that consist of words separated by spaces. Each word consists of lowercase and uppercase letters only.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe would like to convert the sentence to \\\"Goat Latin\\\" (a made-up language similar to Pig Latin.) The rules of Goat Latin are as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a word begins with a vowel ('a', 'e', 'i', 'o', or 'u'), append \\\"ma\\\" to the end of the word.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the word \\\"apple\\\" becomes \\\"applema\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a word begins with a consonant (i.e., not a vowel), remove the first letter and append it to the end, then add \\\"ma\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the word \\\"goat\\\" becomes \\\"oatgma\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAdd one letter 'a' to the end of each word per its word index in the sentence, starting with 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the first word gets \\\"a\\\" added to the end, the second word gets \\\"aa\\\" added to the end, and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e the final sentence representing the conversion from sentence to Goat Latin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sentence = \\\"I speak Goat Latin\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"Imaa peaksmaaa oatGmaaaa atinLmaaaaa\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sentence = \\\"The quick brown fox jumped over the lazy dog\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 \u0026lt;= sentence.length \u0026lt;= 150\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esentence consists of English letters and spaces.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esentence has no leading or trailing spaces.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll the words in sentence are separated by a single space.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":875,"title":"Return a list sorted by number of consecutive occurrences","description":"Inspired by Problem 38 by Cody Team. Given a vector x, return a vector y of the values in x sorted by the number of CONSECUTIVE occurrences in x. Ties (and it is the difficulty) are sorted from lowest to highest. So if x = [1 2 2 2 3 3 7 7 93] then\r\n y = [2 3 7 1 93]\r\nBut if x = [1 1 2 2 2 3 3 7 7 1 93] then\r\n y = [2 1 3 7 1 93]\r\nUpdate - Test case added 22-8-22","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 185.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 92.9333px; transform-origin: 407px 92.9333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365px 8px; transform-origin: 365px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by Problem 38 by Cody Team. Given a vector x, return a vector y of the values in x sorted by the number of CONSECUTIVE occurrences in x. Ties (and it is the difficulty) are sorted from lowest to highest. So if x = [1 2 2 2 3 3 7 7 93] then\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e y = [2 3 7 1 93]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117px 8px; transform-origin: 117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBut if x = [1 1 2 2 2 3 3 7 7 1 93] then\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 76px 8.5px; tab-size: 4; transform-origin: 76px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e y = [2 1 3 7 1 93]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108px 8px; transform-origin: 108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUpdate - Test case added 22-8-22\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = popularity_bis(x)\r\n  y = unique(x);\r\nend","test_suite":"%%\r\nx = [1 2 2 2 3 3 7 7 93]\r\ny_correct1 = [2 3 7 1 93] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n%%\r\nx = [1 1 2 2 2 3 3 7 7 1 93];\r\ny_correct2 = [2 1 3 7 1 93] ;\r\nassert(isequal(popularity_bis(x),y_correct2))\r\n%%\r\nx = [1 0 0 2 2 -5 9 9 2 1 1 1 0 11];\r\ny_correct1 = [1 0 2 9 -5 0 1 2 11] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n%%\r\nx = [1 0 1 1 0 0];\r\ny_correct0 = [0 1 0 1] ;\r\nassert(isequal(popularity_bis(x),y_correct0))\r\n%%\r\nx = [0 1 0 0 1 1];\r\ny_correct1 = [0 1 0 1] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n%%\r\nx = [-2 -2 3 3 3 -7 -7 0 0 0];\r\ny_correct1 = [0 3 -7 -2] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":5,"created_by":5390,"edited_by":223089,"edited_at":"2022-08-22T17:30:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":434,"test_suite_updated_at":"2022-08-22T17:30:08.000Z","rescore_all_solutions":false,"group_id":12,"created_at":"2012-08-03T00:17:38.000Z","updated_at":"2026-04-26T08:03:08.000Z","published_at":"2012-08-03T00:32:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by Problem 38 by Cody Team. Given a vector x, return a vector y of the values in x sorted by the number of CONSECUTIVE occurrences in x. Ties (and it is the difficulty) are sorted from lowest to highest. So if x = [1 2 2 2 3 3 7 7 93] then\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [2 3 7 1 93]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut if x = [1 1 2 2 2 3 3 7 7 1 93] then\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [2 1 3 7 1 93]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUpdate - Test case added 22-8-22\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42829,"title":"Number construction III","description":"Given a positive integer, n, return a, b and c, such that\r\n\r\n1. n = a^1.5+b^2.5+c^3.5\r\n\r\n2. a, b and c are all positive integers greater than 1\r\n\r\nIf a solution does not exist, set all three output variables to zero.\r\n\r\nExample 1:\r\n\r\nn = 168\r\n\r\na = 4\r\n\r\nb = 4\r\n\r\nc = 4\r\n\r\nExample 2:\r\n\r\nn = 100\r\n\r\na = 0\r\n\r\nb = 0\r\n\r\nc = 0","description_html":"\u003cp\u003eGiven a positive integer, n, return a, b and c, such that\u003c/p\u003e\u003cp\u003e1. n = a^1.5+b^2.5+c^3.5\u003c/p\u003e\u003cp\u003e2. a, b and c are all positive integers greater than 1\u003c/p\u003e\u003cp\u003eIf a solution does not exist, set all three output variables to zero.\u003c/p\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cp\u003en = 168\u003c/p\u003e\u003cp\u003ea = 4\u003c/p\u003e\u003cp\u003eb = 4\u003c/p\u003e\u003cp\u003ec = 4\u003c/p\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cp\u003en = 100\u003c/p\u003e\u003cp\u003ea = 0\u003c/p\u003e\u003cp\u003eb = 0\u003c/p\u003e\u003cp\u003ec = 0\u003c/p\u003e","function_template":"function [a b c] = numcons(n)\r\n  a = n;\r\n  b = n;\r\n  c = n;\r\nend","test_suite":"%%\r\nn = 100;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 888;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 19666;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 314159;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 1100;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 116600;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 16999;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 10000040;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 94940;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 9990;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2016-04-28T18:19:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-25T11:29:04.000Z","updated_at":"2026-04-09T07:25:23.000Z","published_at":"2016-04-25T11:29:04.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer, n, return a, b and c, such that\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1. n = a^1.5+b^2.5+c^3.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2. a, b and c are all positive integers greater than 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a solution does not exist, set all three output variables to zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 168\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":579,"title":"Spiral In","description":"Create an m by n matrix filled with sequential integers starting from 1 and arranged in a counterclockwise spiral that hugs the outside border and begins in the upper left corner.\r\nFor example:\r\n\u003e\u003e spiralIn(4,5)\r\nans =\r\n   1    14    13    12    11\r\n   2    15    20    19    10\r\n   3    16    17    18     9\r\n   4     5     6     7     8","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"baseline-shift: 0px; block-size: 190px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 95px; transform-origin: 468.5px 95px; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 434.5px 8px; transform-origin: 434.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCreate an m by n matrix filled with sequential integers starting from 1 and arranged in a counterclockwise spiral that hugs the outside border and begins in the upper left corner.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8417px 8px; transform-origin: 40.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 108px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 464.5px 54px; transform-origin: 464.5px 54px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; spiralIn(4,5)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 19.25px 8.5px; tab-size: 4; transform-origin: 19.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   1    14    13    12    11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   2    15    20    19    10\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   3    16    17    18     9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   4     5     6     7     8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = spiralIn(m,n)\r\n  s = zeros(m,n);\r\nend","test_suite":"%%\r\nm = 3;\r\nn = 5;\r\ns_correct = [1 12 11 10 9; 2 13 14 15 8; 3 4 5 6 7];\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 3;\r\ns_correct = [1 12 11; 2 13 10; 3 14 9; 4 15 8; 5 6 7];\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n\r\n%%\r\nm = 1;\r\nn = 1;\r\ns_correct = 1;\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 0;\r\ns_correct = zeros(5,0);\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n%%\r\nm = 2;\r\nn = 2;\r\ns_correct = [1 4; 2 3];\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n\r\n%%\r\n%Test case added on 4/4/26\r\nm = 2*randi(10)+1;\r\ns_correct = m^2+1-rot90(spiral(m));\r\nassert(isequal(spiralIn(m,m),s_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":4,"created_by":3117,"edited_by":223089,"edited_at":"2026-04-04T09:55:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":121,"test_suite_updated_at":"2026-04-04T09:55:47.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-04-13T13:50:35.000Z","updated_at":"2026-04-26T07:13:41.000Z","published_at":"2012-04-13T13:50:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate an m by n matrix filled with sequential integers starting from 1 and arranged in a counterclockwise spiral that hugs the outside border and begins in the upper left corner.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e spiralIn(4,5)\\nans =\\n   1    14    13    12    11\\n   2    15    20    19    10\\n   3    16    17    18     9\\n   4     5     6     7     8]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":375,"title":"N-Dimensional Array Slice","description":"Given an N-dimensional array, _A_, an index, _I_, and a dimension, _d_, return the _I_ th elements of _A_ in the _d_ dimension.\r\n\r\nFor Example,\r\n\r\n    array_slice( A, 5, 3 )\r\n\r\nis equivalent to\r\n\r\n    A(:,:,5)\r\n\r\nNote: |eval| and |str2func| cannot be used. This is a Cody restriction.","description_html":"\u003cp\u003eGiven an N-dimensional array, \u003ci\u003eA\u003c/i\u003e, an index, \u003ci\u003eI\u003c/i\u003e, and a dimension, \u003ci\u003ed\u003c/i\u003e, return the \u003ci\u003eI\u003c/i\u003e th elements of \u003ci\u003eA\u003c/i\u003e in the \u003ci\u003ed\u003c/i\u003e dimension.\u003c/p\u003e\u003cp\u003eFor Example,\u003c/p\u003e\u003cpre\u003e    array_slice( A, 5, 3 )\u003c/pre\u003e\u003cp\u003eis equivalent to\u003c/p\u003e\u003cpre\u003e    A(:,:,5)\u003c/pre\u003e\u003cp\u003eNote: \u003ctt\u003eeval\u003c/tt\u003e and \u003ctt\u003estr2func\u003c/tt\u003e cannot be used. This is a Cody restriction.\u003c/p\u003e","function_template":"function S = arraySlice(A,I,d)\r\n  S = A(:,I);\r\nend","test_suite":"%%\r\nA = randn(5,5);\r\nassert(isequal(arraySlice(A,4,2),A(:,4)))\r\n\r\n%%\r\nA = randn(5,5);\r\nassert(isequal(arraySlice(A,4,1),A(4,:)))\r\n\r\n%%\r\nA = randn(5,5);\r\nassert(isequal(arraySlice(A,1,10),A))\r\n\r\n%%\r\nA = randn(5,5,5,3);\r\nassert(isequal(arraySlice(A,3,4),A(:,:,:,3)))\r\n\r\n%%\r\nA = randn(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2);\r\nassert(isequal(arraySlice(A,2,18),A(:,:,:,:,:,:,:,:,:,:,:,:,:,:,:,:,:,2)))","published":true,"deleted":false,"likes_count":13,"comments_count":7,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":287,"test_suite_updated_at":"2012-02-21T16:23:06.000Z","rescore_all_solutions":false,"group_id":19,"created_at":"2012-02-21T16:23:06.000Z","updated_at":"2026-04-25T20:27:00.000Z","published_at":"2012-02-21T16:23:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an N-dimensional array,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, an index,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and a dimension,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e th elements of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e dimension.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor Example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    array_slice( A, 5, 3 )]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis equivalent to\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    A(:,:,5)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eeval\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2func\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cannot be used. This is a Cody restriction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":803,"title":"Twist 'n' Match","description":"Given n and m, construct an n-by-n matrix a such that a, when rotated 90 degrees and compared with itself, matches itself in exactly m places. \r\n\r\nThe number of matches m is calculated as follows: \r\n \r\n m = nnz(rot90(a)==a)\r\n\r\nYour answer a is clearly not unique. It must only meet the criteria stated above.\r\n\r\nExamples:\r\n\r\n Input n = 2, m = 1\r\n One possible output: a = [ 1 2 \r\n                            1 3 ]\r\n\r\n Input n = 3, m = 7\r\n One possible output: a = [ 0 1 1\r\n                            1 1 1\r\n                            1 1 1 ]","description_html":"\u003cp\u003eGiven n and m, construct an n-by-n matrix a such that a, when rotated 90 degrees and compared with itself, matches itself in exactly m places.\u003c/p\u003e\u003cp\u003eThe number of matches m is calculated as follows:\u003c/p\u003e\u003cpre\u003e m = nnz(rot90(a)==a)\u003c/pre\u003e\u003cp\u003eYour answer a is clearly not unique. It must only meet the criteria stated above.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cpre\u003e Input n = 2, m = 1\r\n One possible output: a = [ 1 2 \r\n                            1 3 ]\u003c/pre\u003e\u003cpre\u003e Input n = 3, m = 7\r\n One possible output: a = [ 0 1 1\r\n                            1 1 1\r\n                            1 1 1 ]\u003c/pre\u003e","function_template":"function a = twist_n_match(n,m)\r\n  a = 0;\r\nend","test_suite":"%%\r\nn = 2; \r\nm = 1;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 3; \r\nm = 7;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 6; \r\nm = 6;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 10; \r\nm = 11;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 10; \r\nm = 14;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 20; \r\nm = 83;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 21; \r\nm = 1;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));","published":true,"deleted":false,"likes_count":9,"comments_count":9,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":86,"test_suite_updated_at":"2012-07-03T15:06:05.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-06-28T15:15:32.000Z","updated_at":"2026-04-26T07:48:16.000Z","published_at":"2012-06-29T19:04:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n and m, construct an n-by-n matrix a such that a, when rotated 90 degrees and compared with itself, matches itself in exactly m places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number of matches m is calculated as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ m = nnz(rot90(a)==a)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour answer a is clearly not unique. It must only meet the criteria stated above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input n = 2, m = 1\\n One possible output: a = [ 1 2 \\n                            1 3 ]\\n\\n Input n = 3, m = 7\\n One possible output: a = [ 0 1 1\\n                            1 1 1\\n                            1 1 1 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46938,"title":"Numerical computation of the optimal shooting angle of a catapult","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 879.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 439.833px; transform-origin: 406.5px 439.833px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 64.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 32.1667px; text-align: left; transform-origin: 383.5px 32.1667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider a capapult that fires a projects into the air with an initial velocity\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"20\" style=\"width: 56.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The free-flying projectile is subjected to air friction and a gravitional force. Given a desired target \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"109\" height=\"21\" style=\"width: 109px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and an initial velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"20\" style=\"width: 56.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find the optimal shooting angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16\" height=\"18.5\" style=\"width: 16px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eof the catapult that minimizes the distance between the target and the trajectory of the fired projectile. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21.25px; text-align: left; transform-origin: 383.5px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etip 1:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Consider the states \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the x- and y-position of the projectile, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the x- and y-velocity. Then, the trajectory of the projectile can be found by solving the following ordinary differential equation (ODE):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"45\" height=\"22\" style=\"width: 45px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,     \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"45.5\" height=\"22\" style=\"width: 45.5px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e      \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"47.5\" height=\"17.5\" style=\"width: 47.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis the friction coefficient between the air and the projectile. Use the ode45.m function to compute the trajectory of the projectile with initial conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAc8AAAAoCAYAAACYTnGlAAAZ50lEQVR4Xu3dBbDlOnIG4N4wMzPDhpmZN8zMzMzMzBtmZmamDXOy4VQ4G2bm1PdKnfR6LVs+eOeOXTX15s2xLaklNfz9q32v2K9dArsEdgnsEtglsEtgkwTutenu/eZdArsEdgnsEtglsEsgduO5L4JdArsEdgnsEtglsFECu/HcKLD99l0CuwR2CewS2CWwG899DewS2CWwS2CXwC6BjRK4pPF8tIh4loj4gYj47439vE23P2FEPH5E/GRE/M9tGlgby8NGxAtExA9HxL/ewvHtQzpeAs8QEf8ZEb92/KuG3nDb99yQEK54EzvzXBHxxxHxhxfox4NFxItExM9HxF8PtPcwEfGCEfEjEfEvA/ffc8uljOdTRsTbR8SHR8SfjXbult5nYl8nIh4yIr6kKZHbMtTHjIj3i4jPvKBivC2yuxvGQd+8ckQ8cUR86gXX/m3eczd93TxERLxlM2JfecGAQYDyrhHxyRHx+wNCevqIeP2I+OhBg3sR4/nUEfEuEfEBu+H8vymkRF4rIng8t8WAPnZEfFBEfMpuOAe26t13izX/mhEhCvzEDYbTc0/Q0AzP/mVEfGeLYrZI8TbuuS3jv8a9DOc7RsQDImKL4fTcM0bEc0fEI0bE/SPiByPinzYOgk56zw0G9Gkj4o1GDei5I0+RCMv/WRHxQxsHfqfcboxvEBE8lz+ICBPwGxHxeRHxewuDAG+KxL81Ir7/Thlsp5/GwmP7iYj4igXvUgQA0uXhgVM89ygR8fUR8e0R8W8nlsOhc3Pibuyvi4jna+gTZTqKPj1O2yOM53tHxJ9HxH0j4pkj4g0P0Cm3ac9tXVSPFBEfExEv3Azad219wQH3CxCevxmwEcPHHj1PRHxSm9uPbXr18yPiF1oEO7p2srvWnX6816Dxde+TNVlJLXSvcxrPB28R50NHxEdt8DQPmKOrPEJ2L9UmmsGwMOHlvKa3aWMXcX/DgjERlTM677RiaK8ywA2NWnA2JZikt0nkvD80Ip4tIt42In62vf+pGsz7R+35v9jQbu/WU8zNCbqxv6JJgBMDpv3sDY6iVA9D+cgR8cYFzQABSgt8TVOmf7NRyrdlz20c9j3Oy/3aQ4KZd96S39vaWESYPwjDuw8iUQnpf0JEfFtEvEfTJSLPT2sONz0J2drCFWGHvOufB5/lYOkDdOObrmU8n65tmLdukdgB8r/Rj1iMXxYRv9MmVjI8L14eZfFCKx6yBWMRi74+OCL+60aPeL5zjxsRn9OcByShucuC5Fy8XUS8RUR87mQDvGREfG2DsHPTHCOKU8zNMe3vzz6wBN40Ip5jg8IGt1HwLxoRrxYR311el0bgTyLi5YsTNirz27DnRsda77tk5MlgfWAzzvb9iF6jK7+oo0/fPyI+pOmIN4uIv9sogCeNiM9ozvmvDDz7nC3N+OYRYZ3NXueKPFN4ojADHxGeDrqfEIXofzUwyGvd8qhtc796mxAe1tQbepWI+LqI+OaIMAkgp7kLtm9iGZWRib3WmHvtUozmTDT5D52bXrEZxl+NiNeOiN+d3EeeYG5kktdrTsmh4zzl3Bzah/25/5cA5+qLm/P0PQOCqY7Wx0fE+07g/BpBWVf219brTt9zW8d76fsFTlAGgdMvDTQuSsX9uHcLRKYRXxrPH2tkyxECUG2WPYJ6gWFHgpSMdqUa6aWLGk9sui9vBJKRDaNzDPl9mqHhXSAG3NTrxRocq38vExE/OtNR8NBXRcQzRcSrtrze3HhyojgMc0b4pspAv0Bqosjvbc7EXF8fvsFvEvE9uMjcU5IWOJibQd4Kx2Xbp5ybmyz7O6Vvr9AiztdtxJGlflsHnCuwrJy4qPNnJg9U43moo3Un77k7Yd6haY4lLjnUOQ76QXQq1dWD4tN4/mIjneGUbL1eoumXOed97l3SA9JyXV10rsjThsGulQv77YFR6sdLtwiM0d0SrQ68/qS3pBeDwLDkCaVhoQDWcgze9awRcQgkcdLBbXyZ/KXo2jwjC81dvHyQLO9SDpiDMHdZMzxO0WvPIVnr3jnmZq3N/fe+BB6q8R3wHuTD1879PklEfGkjF81FnVrKdeLvhxpPz96pe+6mr7fUez8XER850NlEpdyKSDiNOnMNMcjHGM+naIxf8O8IWoHpiyEs8El+xgMN5xzGMxUYZTliDHgewnvGlkd4KBQzME8nuaUaRYltEz4XJYGfGAoeDJr1kudNIXxYRLxGRPz6SXp5mZcYG6axc6s9KKUqO0ZWND531YjirRYi2aWRnWNuLiPJ7a1gLifrFDvQ2P0bogOYFPN77gKjmi+sZ3sPQsLxwXj+lg7hy3uft9H45Zv+IyKevDEikeTk/ucM4+O13yirntOUfUxix0e0PNMrRcRPzQzAPmJgXXLlo8jW9FV36p7LcdDdT9OiO//2t81BpeiRY8zJnF6S+3yiRuKp6TTpDmsCOUskqIiLdAzdDM35rYj4wpaXXCokkM7yuw0YqcdqfAlz0UOctujREd0gNQa6XSMdJXoq8LGfHuRaMp42liS/PJTwFWMO9GaDuRg6TCqhuQWsCAKmZEIiYFf04H/vjMhmQSBhNDExp9f7DHou29XOcU+kByPqWosoE25YIzd4F7mi3x+qDI4b1fanR50kHj6F6EJbn4O4/VZhbop2ae30enuOuem1Ze/I7XAS0espnh+f6be5pcgoH5G3/x572WP2B7SCR56VeqAcX90cmelRDgaQF+14FIY3A+RoUHVe5afeISJEDfXi9FCGHMVsy57FolctrMfc3KJIkTqw1lWigVTMOd5kjojiD4SC8ewhHmsyPtWew9OQmrF+OYDWgvzd1FlAbmJ8vrGtkWNZ5dqif8xXHnVjaBDu9IGTkbwR/06uDCN9Dt3LOeN0KWzCQIJaXVBAFXfMHwcGgebl2m9rjFfwKOLPCJkreSFe3UOl2B39ffHGwu0FK2vznRHsYwzCyemI26+zSOiS8XS2ysXLdN5Gpy0KxtKGEZLnpMhPiEB4uzlYzEs5rLWr5rvy/T3iydy7qie61tbS70uKvT7H26OglBgbNZ6jhgNFetbLWej4pcefXXm4doaX99pTnlXZjcqAIlqTa08c55ibtTXFY2eQeOhyv6K6qhifvRkDnuwpHMIk1FB0nNmaFklvWZRYDVDNJYoqpkfHGADOiv0q4qhHQygb+xKyMJ1nypVigRTMEfwoYKSLkb0ltyR/7mI454gaueb8LsIaTQvNzWE6a4fsubn3ieYco4CcGYfzrCLAvBKe5PgsITBr683vGY2BuauR9JvKOs5JMohyg4/Q0iD0uT5ZI3P7K50JyERGZ1IydD0HizOA+GiN0/U9FqrfGEIFMZZyk5ULwSFDvpwjTNY9/emD8H9PhtaqNTndo3P3p4wFCdO5vOf+Udg2z1ZZsIwor8K5vLkD8bkoMUhN0tpVobalnFjvPZc2HlvOS2Xkqe9L+ZmMmOD9Iw5HlcWlx59tP3qLqEQpvRx1hVy2GE8HuKdKYW0d+f0cczPa7ndExJ82kktlGFbDBakZ2RNLbaYSVs1pSjBLlrv5AI9jcP99RGQuEbzbiwhq5FfzjbmfOcj2fj2SRQFCFvRjzniaQ1GiiHiJdVnP8vH0e/f3nIOROZrec8yeW9NFc2kaDoq8L8flGLhZ27n3GGyGuMrWGtAOXVKNV3U85oxnRX44T6LHCm1m+mUNRbP2HDFaI4hVLsRS0FTTPofYhzpX1iqjvmbYPaP6m30gPTGri0aNZ/VKCB4ka/POVWDISRCtgqvWrirEYxfVWlun+H0qi6XDxtV4LuVyczOANLcaz1OM6ZB3jPS5Jvu3GM8ebLfWz3PMzVqbfq9KfW6eT3U0Ir118GsPsqSkGSPFKjJlkvDYUu4dqUdUCgasxIw8agI2c54XK7pG1gwygzpXHYrS4TCsKauquEfk7R77ZOTYQe99I+t3tC95X64//z/npIA0wapLkdtImzVqw7swZ86b5yX65DRVBK86smvGc87Rr47pEpJA57l3zfnd6vQbC8j5+0YE1LlndD3m44tjGTWemfhXRcZXUaYeaO3rVuOZQjz0DM8Rsjzo0brR1+DFajyXFtw5NvJBg9vw0GifR2WwRa69bm55x2i/RkRSI6epd2yPgRlFf6KwxZJfK41ltMRArhmkfFWFztci+kSYPIssIvWS/XduzyWawVgE6a2VUxxVVjW6MC9g8DlCB0cVzHoKRTq6fkfmP++penLqRJkzxl7JzmmRkC1t5L1ZWMTagwogHJqjXoWvm2Q8q1O9xK6vqOQaXDwiw9H1eFLjmSGsszhrZI4tsG09WrBmiEaEc4l76gZZ63Mq6DVyQ8oM1DZC777EONfaGIFtvaMq5FHC0KG5jXPMzZoc/L60PzIHhRhXP8GFcMPQgt7U63SfyM95396FPq/ajihj1HhWpblmPDNHqf0afSQRBdqUl5rMnAGffeoxF0dh2zSK3t1Dn2ohjcrMzEhb9C/yEzVPz4bOyfMce04fQZAvO0OAgT6ADY0VvO/imPh0FrIlpwT5TI5YhL/2aSzjRgqjjxlQ10+3vDoC0fSzj5c0nmuwbTWKS2gIohKCFfQDFJ1pCnlcVdnUE7fn6c2R2rn0MadmJFee8pIrniUpjUae7gO/YOmhwntZr4jBFsJQkhGwuw49njCi3E55z+hxiKpQ16LqrdH6Kcdz6LtGCEPePXpUJQ0DRXBobuMcczMqn3SUqkNFwYHpRBuVH5Dl58CdWXfT4W3GSb6px0hO6GzNGat9rkpzbR0uFSDA1nV8RB+R5Vz6gQSlqMFcRD1CGKqR8dI5vix+YX1UQhEZ0zmiYdEySHSEgXuOPVdlzVnKFAyYVa5TOiI/kJG5cPJExPHvuS5889K6WDOg3oFZ693Y3nlht/tTDcqljOcIYagyaHsBSM3fTwlFjCdHXMF45E1fTllDQchmFFJ2b8rL32dTc6PGszIGlxL6Gho9quLetRzBiOLaip333jnCCExvMavhjBZJQFF3LKfnHaXSSqhsZNx5z6XHn+2OHlWpUOpokYRDcxuVuX2quRmdC0oDyaJGd7xc6wrzMTd31lZ19KOeZUxHUhlHkYic1fSq/IAtzubokakR48wQICIZk+iZAfX/DpT3+rt05m8kMq752Llyl+nIgcZH84nH7LnemqiOQBoF51/lJF21qHkStLCbGcpcH/YzsuW0pu/SOiQfeXAG235zeSeIO89yXsp4jhxVqTqhOhl1jJXAxkGb1shNx6zHzJ7Ka5U9O3kgkTWO2Oy50BHjyRvyWTHnD9+kHZZeYo6mAnPkYK1IQkJ6a9Hs0sK5hvFIL/gfF9iL9czh2gSD4ET2I3DCVBbXGH813KD8pSIJldywBPnnedBjcxunnptR45nzkMYT1ORMHEerfkYpjaSIqVLm0xlx/KRXIKDC0ks1k+1BylcEY/NTaFlcfcno5hgqlIYQBBVw1q5ejhDQC2DWHlsyx6rtXpGEEeNJUTLOIo45o5JyEbmORiHH7LmlNVERCFCj85XOSPr36jynrEGv9XhaOkjY29Wo1jbBwwqqfMHkHL1PuDEykMEpHHop45mGkVHsVfJZM561YEaPY8N2kO8o0pCQOlRnJDWW+hvxdbawy5rxrLAT6jPqrk5r3GKAq4ML4PVVQdisGl3Ky9TJTKVqoYlcfdvxJl/51RQT11NGCVeaLM5G79ueqTQp26Xo9CbKw0an1MBOPahRv5Pc4KjTHIW9wq3TQ9jWKHm7RGNrlUGOnRtkBmtQRNUr8DE3F2mgRLzSGxiucoLTyksJT9uQ0/NjGb32IvQKZekDyC8/hVf7BMEgc1CmiGakkkvlH1RPn6LjIPm3KXKijKK92qu0le8UofZY6bXduZxsLfTvLCodNIWIRZGMjbO2Iwz/kT1HP0m9WAdbSF4ZEMjL6guSpXWA1JNXTelM0aaENEXTPadUVEQHe+/0vKXzv9aWvVKd8UsZz0Qef3OB+FWdwLnIM5FO8pr7bmuOhc5c+uhG3ROpq6A6I4xd+5lz2Dt/+iDnPFNRCfVtFHkYm503B3+fRooqrNRNmp1Nejv4QdmvuasKkHFxXhD8Y0HMQVY3zXjkZ694u9MJTAUOfuxBWjme9M7lQ7oV/G/a4Ft/Mqr85ZWi9vVLGXOoRRpXUac1lkch6hlJm9JiFsmtkQMOnZvMOYFbOYTmrveZtemU1HwhR8Kh/7lD4ulUzeV6MhpZitB9bF3EwdF0KaYNDpQXImd7Vv+tyUpQyk8+MWQcvukZ7YwGOHnmIJ1h/y7twNBPy+UldLZ0bAQSwIib9+nXdFKGeZTGOqolKuvZyKW5Z5iNl7FwIeEwUNpjkKefsFrbc1XGS3M5ty0rEmRuKOvpB5yrszhNFyVcSNn3zuTmPdi1U/2aRQU4qtUZv5TxJBNrH2mqV1S9wvDTghK5BwVlCvJwBKYOcx4NE11zVLX1hM1RlDu2jqZf8jIvUJ0RWD/RU2c8uwHNNPJUKxO7yQbjOagYxJvLya/sJ5Eo2FLoPF0cmdcxyB70UAkiqOlYTbypQyrmX8O2GCN4TZ/luuQXePnJgqNQQJG8zyXPlXIRxZvYXnR6jfGNtknxUYxrX0LhUSM2cLjA2PdvDVgjPnYryqMEa6Q2LbIwWjT+0LmpBlD31tjUVUb57LRCz1SOqVwTvambfMmw1vcwWhRn5rfqb5w5e1apwHqRSX68nWGhmERr0CN7D8EELDqdg2pUPZNFEvJrGOaPMVY0Ze5KlqxygD1HukaX6VxRsJlbFV1jYM8RaDLSYZAYUBEeQ4+RLCqeI5Ks7blpKmTp+ExvfunH6oTU+9L4gcSnBSGWDGu+I5/HOK17KZ0NTrs5qcztHls531l1+xyaVitALX0lyvvkKzl4dP9cfWL3ZHSpJm8ilAk7cxzYFazhOaQpUZ5cK5wdKUXfUJ6r6ZxOPnmMfExb8MdhtOa6H8SeGk9WHyxiE4PjhNRJqzZgykxkyHrLU/q7vMrcJXlP+YgU5qjjMGUsPTCDM2OMTe9do4r8Gvc5akAeJtyGpYg4EwwCz3cJZkwPjCE5xdmva4zfpoQwiGQWv7weEcYrKqCclC6jDC1UUbejD1PlaH2CTShPStq15UsaW+cm17/+udaOdlR5cwY5S8gxS/Vrl4xnKoURo21/iWp43QycIyOYh9CLpbqpnBjrVVQDIXEvg8MBlF+aGhsKXkSngpBauoqNc3QoLF6+fOfax4lFwiJiRr33qTn9YvQw70UU5k7lnKUi9+Sfxh107KwjxW7fgc/n9t7InvNO+5eRdY3MR64FhgCSAmLuzcOS8axnhnskRnsOCYmjaU44QOYHC5rMsFAf0DrkfeB1RtpeyktUTMdDezhVoHkQs0sAI8ftj1MVDCfHJJ01R2Icp/H8XClV+1b/RIPT77Fm++6h+8lJH5Xms8fB3fRID13KqBCkbV3SI/aNvvbWIccA6YejUStk9fSlgMCa7RH37nluLed5jDJOyI2AKtvwmHfetmdFEBZtFtW/U8cHErTBKL9Dv8O5NnY5IHAmZbqUX117z+jvWQNzqYLU6LvqfcfCtoe0ee1neP7gNaTDNQdra19TniIPkZg2EtWYe9fWPcfRYMh7hRu29tf9x8K2h7R56WeSaPpxg+duR/uXsuMYcdhB8FCN3rEeAR9UkKM3xwiftosfcN+WIlrUM+c0njql4zYNL3Ck46MCvA33nWtxXUM2CBhILq5Kjz9lX0Q6HA2e7Llz4kmUg5gkS/VUY8njWSKlrYShU/XhGu9RAACJEKv8FF+WSec/j435f8iVVMr0qzA53q17jtEXzYIgl2rzbpVnrbBzCGFoa3vXul8qA9RvnR/7FZkcw7SUI30jevUBk+m1NYBL2NvxolV499zG02DkTxGOwDtLHuG1Jvga7XIqsErlx0BlawzSa/Rxa5vnHBOlx/OXUqgkmK19HLk/Nxz43cbcwrQceX/vqEqeEeSEHPox8JH2r3kPxwEkJve95ctJvT7XKIQzIuclapj7UMHW9UmRmoveBzCOlWPvqEoSfgQcp0Y9ju3z1uetaTD8vdu8jBQyWGsjkQYQLMdDuqT3IYEt621zXy9hPNOASgAjDMx+lXtNYrfod5sYTCuRDkq4DYYzpyfHxkuXLzzF2OT2RJzy47X49TmWhCo6qPFySJCSU2z2OW9YPohDWc9zJqHD/Wvkq3OM/VLvlKOTl+QI1eMbh7SfZyJFhjgDcpO4FBi78p4cFTmurXsOococYW1ax9NSd4f0dfpMfumGPqykymQer5FyTtGHS7wjiWrminOzVjVpqU95xOg+jWSEfIgvI5/pD8IRApI2GE6GFmy85qhlH6FbSEJD+/5SxpNAJOqRQyS5T6FULzHx52jDhiaLkcT1Odo/9zsZIIoB6+3UUdu5+36p9ycdH0kC6Q7jFkNSRJal2i7Vl2u0gzBjnRwL5U2r8eTn2kSf92ucDoxb7d20PZcIB8gRCY7DCaXjAKgyxaCuHcm6xtwd2ibDxqitkcuW3j+twsWYkpcatxxsDF5kKW0gutFBI4bQ2qCzpBOGHaVLGs9Dhb4/t0vgNkqAMoHGMKTY2ZiGYGJQ/t3sXI7OdeYNffgbk1ekKcIkU/WB5awc5zkm0hnty6H3cSCwpZGdsjC8+cdeX4uWDm3zTn4u+QJ4NBwkTickw1xzOJwnXvqwwknHvhvPk4pzf9kugV0CuwR2CdwNEtiN590wy/sYdwnsEtglsEvgpBLYjedJxbm/bJfALoFdArsE7gYJ7MbzbpjlfYy7BHYJ7BLYJXBSCezG86Ti3F+2S2CXwC6BXQJ3gwR243k3zPI+xl0CuwR2CewSOKkE/heH7m2S0X33RAAAAABJRU5ErkJggg==\" 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Plotting \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e vs. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e will result in the x-y trajectory of the projectile, as shown in the figure below.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.9167px; text-align: left; transform-origin: 383.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etip 2: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUse the following update law, to incrementally update the shooting angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.9167px; text-align: left; transform-origin: 383.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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width=\"44\" height=\"20\" style=\"width: 44px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e the smallest Euclidean distance between the trajectory of the projectile and the target \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"298\" height=\"20\" style=\"width: 298px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis a difference angle, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"55.5\" height=\"17.5\" style=\"width: 55.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ean update parameter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample of algorithm's numerical result:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.5px 40px; transform-origin: 403.5px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003etheta = catapult(25,3,25)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003etheta = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    0.8431\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 264.333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 383.5px 132.167px; text-align: left; transform-origin: 383.5px 132.167px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"570\" height=\"259\" style=\"vertical-align: baseline;width: 570px;height: 259px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function theta = catapult(xd,yd,v0) \r\n  \r\n    global g nu;\r\n    \r\n    g   = -9.81;  % grav. acceleration\r\n    nu  = 0.5;    % air friction coeff.\r\n    k   = 0;      % solver increments\r\n    dt  = 1e-2;   % timesteps\r\n    T   = 10;     % simulation time\r\n    TOL = 1e-2;   % absolute tolerance\r\n    \r\n    [~,y] = ode45(@ODECatapult,0:dt:T,[v0,0,0]); \r\n    \r\n    % solver for optimal angle\r\n    while (e \u003e= TOL) \u0026\u0026 (k \u003e 150)        \r\n        \r\n        %theta = theta + beta;\r\n        \r\n        k = k+1;    % add increment\r\n    end\r\n  \r\n    function dx = ODECatapult(t,x)\r\n        global g nu;\r\n        %% fill in ordinary differential equation %%\r\n    end\r\n    \r\n    function e = EuclideanDistance(y,xd,yd)\r\n        %% fill in computation of smallest euclidean distance %%\r\n    end\r\n    \r\n    function beta = UpdateLaw(y,e,lambda)\r\n        %% fill in update law to update the shooting angle %%\r\n    end\r\nend","test_suite":"xd = 8;\r\nyd = 2;\r\nv0 = 35;\r\ny_correct = 1.446;\r\n\r\nassert(isequal(round(catapult(xd,yd,v0),3),y_correct))\r\n\r\n%%\r\nxd = 15;\r\nyd = 5;\r\nv0 = 35;\r\ny_correct = 1.33;\r\n\r\nassert(isequal(round(catapult(xd,yd,v0),2),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":636373,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-19T12:41:43.000Z","updated_at":"2025-01-02T11:31:42.000Z","published_at":"2020-10-19T13:39:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a capapult that fires a projects into the air with an initial velocity\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_0 \\\\in \\\\mathbb{R}_{\\\\ge 0}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The free-flying projectile is subjected to air friction and a gravitional force. Given a desired target \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$z_d = [x_d, y_d] \\\\in \\\\mathbb{R}^2$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and an initial velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_0 \\\\in \\\\mathbb{R}_{\\\\ge 0}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, find the optimal shooting angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eof the catapult that minimizes the distance between the target and the trajectory of the fired projectile. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etip 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Consider the states \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the x- and y-position of the projectile, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the x- and y-velocity. Then, the trajectory of the projectile can be found by solving the following ordinary differential equation (ODE):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x_1} = x_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,     \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_2 = x_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e      \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_3 = -\\\\nu x_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_4 = -g - \\\\nu x_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.   \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\; (\\\\text{m/s}^2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 0.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis the friction coefficient between the air and the projectile. Use the ode45.m function to compute the trajectory of the projectile with initial conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(t = 0) = (0,0,v_0 \\\\cos(\\\\theta_k), v_0 \\\\sin(\\\\theta_k))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Plotting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e vs. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will result in the x-y trajectory of the projectile, as shown in the figure below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etip 2: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eUse the following update law, to incrementally update the shooting angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_{k+1} = \\\\theta_k + \\\\lambda \\\\, \\\\text{sign}(\\\\theta_{e,k})\\\\,e_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee_k \\\\in \\\\mathbb{R}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the smallest Euclidean distance between the trajectory of the projectile and the target \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_{e,k} = \\\\text{atan2}(d_y,d_x) - \\\\text{atan2}(v_0\\\\sin(\\\\theta_k),v_0\\\\cos(\\\\theta_k))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis a difference angle, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$\\\\lambda = 0.01$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003ean update parameter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample of algorithm's numerical result:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[theta = catapult(25,3,25)\\ntheta = \\n    0.8431\\n    ]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"570\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57477,"title":"Solve an equation involving primes and fractions","description":"Write a function to find pairs of primes  and  satisfying the equation\r\n\r\nwhere  is an integer. The function should take a number  as input and produce the triples , , and  such that . If there are no solutions, the function should return three empty vectors.\r\nThis problem is adapted from one in the 2012 European Girls’ Math Olympiad. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 146px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 73px; transform-origin: 343px 73px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find pairs of primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e satisfying the equation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 17.5px; text-align: left; transform-origin: 320px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"136\" height=\"35\" alt=\"p/(p+1) + (q+1)/q = 2n/(n+2)\" style=\"width: 136px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 21px; text-align: left; transform-origin: 320px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is an integer. The function should take a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as input and produce the triples \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"18\" alt=\"p \u003c= x\" style=\"width: 38px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. If there are no solutions, the function should return three empty vectors.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis problem is adapted from one in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.egmo2012.org.uk/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e2012 European Girls’ Math Olympiad\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,q,n] = EGMO2012no5(x)\r\n  p = primes(x); q = primes(x); n = p./(p+1) + (q+1)./q; \r\nend","test_suite":"%%\r\nx = 1;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(isempty(p) \u0026\u0026 isempty(q) \u0026\u0026 isempty(n))\r\n\r\n%%\r\nx = 2;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(all(p==2) \u0026\u0026 isequal(q,[5 7]) \u0026\u0026 isequal(n,[28 19]))\r\n\r\n%%\r\nx = 20;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 200;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402 3778 7306 14758 21166 42226 47302 77002 90898 130678 148606 158002];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 2000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 63;\r\nsum_correct = 265170305;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\n\r\n%%\r\nx = 20000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 344;\r\nsum_correct = 150118037395;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2000000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 14873;\r\nsum_correct = 27402595128;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2e8;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 813373;\r\nsum_correct = 152663390088360;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\n\r\n%%\r\nfiletext = fileread('EGMO2012no5.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-30T13:15:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-30T05:04:32.000Z","updated_at":"2025-12-14T08:06:30.000Z","published_at":"2022-12-30T05:05:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find pairs of primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e satisfying the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p/(p+1) + (q+1)/q = 2n/(n+2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{p}{p+1} + \\\\frac{q+1}{q} = \\\\frac{2n}{n+2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer. The function should take a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as input and produce the triples \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p \u0026lt;= x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep \\\\le x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there are no solutions, the function should return three empty vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is adapted from one in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.egmo2012.org.uk/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2012 European Girls’ Math Olympiad\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":52664,"title":"List the Moran numbers","description":"The quotient of a Moran number and its digit sum is prime. For example, 117 and 481 are Moran numbers because 117/(1+1+7) is 13 and 481/(4+8+1) = 37, and both 13 and 37 are prime. \r\nWrite a function to list the Moran numbers less than or equal to the input number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 363px 8px; transform-origin: 363px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe quotient of a Moran number and its digit sum is prime. For example, 117 and 481 are Moran numbers because 117/(1+1+7) is 13 and 481/(4+8+1) = 37, and both 13 and 37 are prime. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 257px 8px; transform-origin: 257px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list the Moran numbers less than or equal to the input number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = Moran(n)\r\n  y = f(n);\r\nend","test_suite":"%%\r\nn = 500;\r\ny = Moran(n);\r\ny_correct = [18 21 27 42 45 63 84 111 114 117 133 152 153 156 171 190 195 198 201 207 209 222 228 247 261 266 285 333 370 372 399 402 407 423 444 465 481];\r\nassert(isequal(y,y_correct))\r\n\r\n%% \r\nn = 40332;\r\ny = Moran(n);\r\ny23_correct = [207 1679 3749 4577 8717 14099 18653 19067 22793 24449 25691 26519 26933 29417 29831 32729 33557 35627 37283];\r\nassert(isequal(y(mod(y,23)==0),y23_correct) \u0026\u0026 isequal(y(end),n))\r\n\r\n%%\r\nn = [100000 400000 700000 1e6 4e6 7e6 1e7];\r\ns = [383 1193 1870 2451 8080 12913 17271];\r\nlen_correct = [1915 5967 9352 12259 40403 64567 86356];\r\nsum_correct = [79699686 1044807776 2880495403 5339917218 73480226594 205122929098 389309242207];\r\nsd_correct  = [2.925215086021406e+04 1.171076738381341e+05 2.065163622127620e+05 2.944277010513903e+05 1.177431499460555e+06 2.057551640570258e+06 2.933705654924581e+06];\r\nys_correct  = [11354 28489 48992 71660 99972; 51489 125203 210051 300165 399477; 96325 220734 364473 524186 699739; 129627 308214 513837 741778 999219; 579189 1331117 2176042 3062214 3999644; 1046322 2330397 3782883 5322552 6999255; 1440693 3292137 5341677 7565613 9999882];\r\nfor k = 1:length(n)\r\n    disp(['Test 3.' num2str(k)])\r\n    y = Moran(n(k));\r\n    assert(isequal(length(y),len_correct(k)) \u0026\u0026 isequal(sum(y),sum_correct(k)) \u0026\u0026 abs(std(y)-sd_correct(k))\u003c1e-7 \u0026\u0026 isequal(y(s(k):s(k):end),ys_correct(k,:)));\r\nend\r\n\r\n%%\r\nfiletext = fileread('Moran.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'oeis') || contains(filetext, 'persistent'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":23,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-05T13:52:35.000Z","updated_at":"2026-04-28T21:19:49.000Z","published_at":"2021-09-05T14:10:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe quotient of a Moran number and its digit sum is prime. For example, 117 and 481 are Moran numbers because 117/(1+1+7) is 13 and 481/(4+8+1) = 37, and both 13 and 37 are prime. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list the Moran numbers less than or equal to the input number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1187,"title":"Knave in the middle attack","description":"This is a Matlab adaptation of the \u003chttp://en.wikipedia.org/wiki/Knights_and_Knaves Knights and Knaves\u003e logical puzzles, mixed with the famous \u003chttp://en.wikipedia.org/wiki/Man-in-the-middle_attack man-in-the-middle attack\u003e in computer security. \r\n\r\nYou are in an island where all inhabitants are either _Knights_, who always tell the truth, or _Knaves_, who always lie. Your job is to sit in the middle of an islander and a second person interviewing the islander, intercepting all questions posed to the islander, and answering to the interviewer in a way that will make him think that the islander is the opposite type of what he really is (answer as a Knave if the islander is a Knight, or answer as a Knight if the islander is a Knave). The problem is: a) you really do not know whether the islander is a Knight or a Knave; and b) the islander knows some secret that only he knows, so you may not be able to anticipate what he would answer even if you knew whether he was a Knight or a Knave! Luckily for you, you may ask the islander privately any questions that you wish before responding to the interviewer.  \r\n\r\n*Details:*\r\n\r\nYou are given a function handle F that will act as the islander. This function will answer any question the way the islander would. The function _function answer=F(question)_ takes a char array as input (the 'question'), and returns a logical value (the yes/no 'answer' this particular islander would give to this question; _true_ means 'yes' and _false_ means 'no'). Valid questions are any valid matlab string. The islander has access to the following variables (the things that he 'knows'):\r\n\r\n* *A*: Islander's type. A is a logical variable: true for a Knight, false for a Knave\r\n* *X*: A secret formula only islanders know. An unknown function on positive integer values that when evaluated returns a logical value (e.g. _x\u003e1_).\r\n* *F*: Introspection. F is the handle associated with this islander's answers, so he knows himself what he would respond to some hypothetical question\r\n\r\nThe function handles associated with a Knight and a Knave look, respectively, something like:\r\n\r\n  function answer = Knight(question)\r\n    A = true;\r\n    X = @(x)x\u003e10;\r\n    F = @Knight;\r\n    answer = eval(question);\r\n  end\r\n\r\n  function answer = Knave(question)\r\n    A = false;\r\n    X = @(x)x\u003e10;\r\n    F = @Knave;\r\n    answer = ~eval(question);\r\n  end\r\n\r\nOf course the values of X will be different and unknown to you.\r\n\r\nA few examples:\r\n\r\n Knight('A==true') == true\r\n\r\nThis question asks whether the islander is a Knight, and a Knight would respond affirmatively to such question. \r\n\r\n Knave('A|X(1)') == true\r\n\r\nThis question asks whether the islander is a Knight or the value of the secret formula at 1 is true. None of these are true, but the Knave will lie to you and respond 'yes'.\r\n\r\n Knave('F(''A'')') == false\r\n\r\nThis question asks whether the islander would respond affirmatively to the question of whether he is a knight. Both Knights and Knaves would actually respond affirmatively when questioned whether they are Knights, but a Knave would lie to you when telling you how he would respond to such question, so he would say 'no'.\r\n\r\nYou must implement a function that will take two inputs: 1) the function handle of an islander (either @Knight or @Knave); and 2) a question (as a char array). Your function should return the answer this same islander would give to this question if he was the opposite type than he really is. In other words:\r\n\r\n your_function(@Knight,str) should return Knave(str)\r\n your_function(@Knave,str) should return Knight(str)\r\n\r\nYour function might query the function handle of the islander with whatever questions it sees fit before responding.\r\n\r\n*Examples:*\r\n\r\n your_function(@Knight,'A==true') == true;\r\n\r\n your_function(@Knave,'A==true') == true; \r\n\r\nThis question asks whether the islander is a Knight; both Knights and Knaves would respond _true_ to this question.\r\n\r\n your_function(@Knight,'F(''A==true'')==true') == false; \r\n\r\n your_function (@Knave,'F(''A==true'')==true') == true; \r\n\r\nThis question asks if the islander would respond yes to the question of whether he is a Knight. A Knight would respond 'yes', while a Knave would (falsely) respond 'no', so your function should return exactly the opposite in each case.\r\n\r\n your_function(@Knight,'X(3)~=X(2)') == true\r\n\r\n your_function(@Knave,'X(3)~=X(2)') == false \r\n\r\n(Assuming X(2)==X(3); you do not know the values of X, only islanders do) This question asks to the islander whether the value of his secret formula X(2) is different from the value of his secret formula X(3). Assuming that they were actually the same value a Knight would respond negatively (telling you the truth), while a Knave would respond affirmatively (lying to you), so, again, your function should return exactly the opposite response in each case.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 914.5px; vertical-align: baseline; perspective-origin: 332px 914.5px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis is a Matlab adaptation of the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Knights_and_Knaves\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eKnights and Knaves\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e logical puzzles, mixed with the famous\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Man-in-the-middle_attack\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eman-in-the-middle attack\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in computer security.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 94.5px; white-space: pre-wrap; perspective-origin: 309px 94.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou are in an island where all inhabitants are either\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eKnights\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, who always tell the truth, or\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eKnaves\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, who always lie. Your job is to sit in the middle of an islander and a second person interviewing the islander, intercepting all questions posed to the islander, and answering to the interviewer in a way that will make him think that the islander is the opposite type of what he really is (answer as a Knave if the islander is a Knight, or answer as a Knight if the islander is a Knave). The problem is: a) you really do not know whether the islander is a Knight or a Knave; and b) the islander knows some secret that only he knows, so you may not be able to anticipate what he would answer even if you knew whether he was a Knight or a Knave! Luckily for you, you may ask the islander privately any questions that you wish before responding to the interviewer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eDetails:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 52.5px; white-space: pre-wrap; perspective-origin: 309px 52.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou are given a function handle F that will act as the islander. This function will answer any question the way the islander would. The function\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003efunction answer=F(question)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e takes a char array as input (the 'question'), and returns a logical value (the yes/no 'answer' this particular islander would give to this question;\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etrue\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e means 'yes' and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003efalse\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e means 'no'). Valid questions are any valid matlab string. The islander has access to the following variables (the things that he 'knows'):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-bottom: 20px; margin-top: 10px; transform-origin: 316px 50px; perspective-origin: 316px 50px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 10px; white-space: pre-wrap; perspective-origin: 288px 10px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: Islander's type. A is a logical variable: true for a Knight, false for a Knave\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 20px; white-space: pre-wrap; perspective-origin: 288px 20px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eX\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: A secret formula only islanders know. An unknown function on positive integer values that when evaluated returns a logical value (e.g.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u0026gt;1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"display: list-item; margin-bottom: 0px; margin-left: 56px; margin-top: 0px; text-align: left; transform-origin: 288px 20px; white-space: pre-wrap; perspective-origin: 288px 20px; margin-left: 56px; \"\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eF\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-left: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e: Introspection. F is the handle associated with this islander's answers, so he knows himself what he would respond to some hypothetical question\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe function handles associated with a Knight and a Knave look, respectively, something like:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 130px; perspective-origin: 329px 130px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003efunction \u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003eanswer = Knight(question)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  A = true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  X = @(x)x\u0026gt;10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  F = @Knight;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  answer = eval(question);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003efunction \u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003eanswer = Knave(question)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  A = false;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  X = @(x)x\u0026gt;10;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  F = @Knave;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e  answer = ~eval(question);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"border-bottom-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); margin-right: 0px; outline-color: rgb(14, 0, 255); text-decoration-color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); \"\u003eend\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eOf course the values of X will be different and unknown to you.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA few examples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e Knight(\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander is a Knight, and a Knight would respond affirmatively to such question.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e Knave(\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A|X(1)'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander is a Knight or the value of the secret formula at 1 is true. None of these are true, but the Knave will lie to you and respond 'yes'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 10px; perspective-origin: 329px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e Knave(\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'F(''A'')'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == false\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; perspective-origin: 309px 42px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander would respond affirmatively to the question of whether he is a knight. Both Knights and Knaves would actually respond affirmatively when questioned whether they are Knights, but a Knave would lie to you when telling you how he would respond to such question, so he would say 'no'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; perspective-origin: 309px 42px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYou must implement a function that will take two inputs: 1) the function handle of an islander (either @Knight or @Knave); and 2) a question (as a char array). Your function should return the answer this same islander would give to this question if he was the opposite type than he really is. In other words:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 20px; perspective-origin: 329px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,str) should \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003ereturn Knave(str)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knave,str) should \u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003ereturn Knight(str)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eYour function might query the function handle of the islander with whatever questions it sees fit before responding.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knave,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'A==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks whether the islander is a Knight; both Knights and Knaves would respond\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003etrue\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e to this question.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'F(''A==true'')==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == false; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function (@Knave,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'F(''A==true'')==true'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 31.5px; white-space: pre-wrap; perspective-origin: 309px 31.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis question asks if the islander would respond yes to the question of whether he is a Knight. A Knight would respond 'yes', while a Knave would (falsely) respond 'no', so your function should return exactly the opposite in each case.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-bottom: 10px; margin-left: 3px; margin-right: 3px; margin-top: 10px; transform-origin: 329px 30px; perspective-origin: 329px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knight,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'X(3)~=X(2)'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == true\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-height: 18px; padding-left: 4px; transform-origin: 329px 10px; white-space: nowrap; perspective-origin: 329px 10px; \"\u003e\u003cspan style=\"border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-right: 45px; min-height: 0px; padding-left: 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; perspective-origin: 0px 0px; margin-right: 45px; \"\u003e\u003cspan style=\"margin-right: 0px; \"\u003e your_function(@Knave,\u003c/span\u003e\u003cspan style=\"border-bottom-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); \"\u003e'X(3)~=X(2)'\u003c/span\u003e\u003cspan style=\"margin-right: 0px; \"\u003e) == false\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 10px; text-align: left; transform-origin: 309px 52.5px; white-space: pre-wrap; perspective-origin: 309px 52.5px; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(Assuming X(2)==X(3); you do not know the values of X, only islanders do) This question asks to the islander whether the value of his secret formula X(2) is different from the value of his secret formula X(3). Assuming that they were actually the same value a Knight would respond negatively (telling you the truth), while a Knave would respond affirmatively (lying to you), so, again, your function should return exactly the opposite response in each case.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function answer = AnswerGenerator(F,str)\r\n  answer=F(str);\r\nend","test_suite":"%%\r\n% Ask a Knight whether 4 is prime\r\n% (he will respond false; your function should respond true)\r\nA=true; X=@isprime; str='X(4)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% Ask a Knave whether 4 is prime \r\n% (he will respond true; your function should respond false)\r\nA=false; X=@isprime; str='X(4)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\n% Ask a Knight whether he is a Knight \r\n% (both Knights and Knaves would respond true and so should your function)\r\nA=true; X=@isprime; str='A==true';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% Ask a Knave whether he is a Knight \r\n% (both Knights and Knaves would respond true and so should your function)\r\nA=false; X=@isprime; str='A==true';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% Ask a Knight whether he would respond affirmatively to the question of whether he is a Knight\r\n% (a Knave would respond false to this same question, and so should your function)\r\n% A=true; X=@isprime; str='F(''A==true'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\n% Ask a Knave whether he would respond affirmatively to the question of whether he is a Knight\r\n% (a Knight would respond true to this same question, and so should your function)\r\n% A=false; X=@isprime; str='F(''A==true'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\nA=true; X=@isprime; str='diff(X(2:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\nA=false; X=@isprime; str='diff(X(2:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\nA=true; X=@isprime; str='A==X(6)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\nA=false; X=@isprime; str='A==X(6)';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\nA=true; X=@isprime; str='A\u0026any(X(1:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\nA=false; X=@isprime; str='A\u0026any(X(1:3))';\r\nf0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\nF=@(str)xor(~A,f0(eval(str),A,X));\r\nclear A X;\r\nassert(isequal(AnswerGenerator(F,str),true))\r\n\r\n%%\r\n% A=true; X=@(x)rem(x,2); str='F(''F(''''X(3)'''')'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),false))\r\n\r\n%%\r\n% A=false; X=@(x)rem(x,2); str='F(''F(''''X(3)'''')'')';\r\n% f0=inline('logical(interp1([0,1],[0,x],1))','x','A','X');\r\n% F=@(str)xor(~A,f0(eval(str),A,X));\r\n% clear A X;\r\n% assert(isequal(AnswerGenerator(F,str),true))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":14,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2020-09-29T00:03:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-01-07T22:12:02.000Z","updated_at":"2026-04-15T04:00:57.000Z","published_at":"2013-01-08T03:23:02.000Z","restored_at":"2017-11-13T15:02:29.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is a Matlab adaptation of the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Knights_and_Knaves\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKnights and Knaves\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e logical puzzles, mixed with the famous\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Man-in-the-middle_attack\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eman-in-the-middle attack\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in computer security.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are in an island where all inhabitants are either\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKnights\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, who always tell the truth, or\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKnaves\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, who always lie. Your job is to sit in the middle of an islander and a second person interviewing the islander, intercepting all questions posed to the islander, and answering to the interviewer in a way that will make him think that the islander is the opposite type of what he really is (answer as a Knave if the islander is a Knight, or answer as a Knight if the islander is a Knave). The problem is: a) you really do not know whether the islander is a Knight or a Knave; and b) the islander knows some secret that only he knows, so you may not be able to anticipate what he would answer even if you knew whether he was a Knight or a Knave! Luckily for you, you may ask the islander privately any questions that you wish before responding to the interviewer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDetails:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a function handle F that will act as the islander. This function will answer any question the way the islander would. The function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efunction answer=F(question)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e takes a char array as input (the 'question'), and returns a logical value (the yes/no 'answer' this particular islander would give to this question;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e means 'yes' and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efalse\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e means 'no'). Valid questions are any valid matlab string. The islander has access to the following variables (the things that he 'knows'):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Islander's type. A is a logical variable: true for a Knight, false for a Knave\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A secret formula only islanders know. An unknown function on positive integer values that when evaluated returns a logical value (e.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u0026gt;1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Introspection. F is the handle associated with this islander's answers, so he knows himself what he would respond to some hypothetical question\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function handles associated with a Knight and a Knave look, respectively, something like:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[function answer = Knight(question)\\n  A = true;\\n  X = @(x)x\u003e10;\\n  F = @Knight;\\n  answer = eval(question);\\nend\\n\\nfunction answer = Knave(question)\\n  A = false;\\n  X = @(x)x\u003e10;\\n  F = @Knave;\\n  answer = ~eval(question);\\nend]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOf course the values of X will be different and unknown to you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA few examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Knight('A==true') == true]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander is a Knight, and a Knight would respond affirmatively to such question.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Knave('A|X(1)') == true]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander is a Knight or the value of the secret formula at 1 is true. None of these are true, but the Knave will lie to you and respond 'yes'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Knave('F(''A'')') == false]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander would respond affirmatively to the question of whether he is a knight. Both Knights and Knaves would actually respond affirmatively when questioned whether they are Knights, but a Knave would lie to you when telling you how he would respond to such question, so he would say 'no'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou must implement a function that will take two inputs: 1) the function handle of an islander (either @Knight or @Knave); and 2) a question (as a char array). Your function should return the answer this same islander would give to this question if he was the opposite type than he really is. In other words:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,str) should return Knave(str)\\n your_function(@Knave,str) should return Knight(str)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function might query the function handle of the islander with whatever questions it sees fit before responding.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,'A==true') == true;\\n\\n your_function(@Knave,'A==true') == true;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks whether the islander is a Knight; both Knights and Knaves would respond\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etrue\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to this question.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,'F(''A==true'')==true') == false; \\n\\n your_function (@Knave,'F(''A==true'')==true') == true;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis question asks if the islander would respond yes to the question of whether he is a Knight. A Knight would respond 'yes', while a Knave would (falsely) respond 'no', so your function should return exactly the opposite in each case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ your_function(@Knight,'X(3)~=X(2)') == true\\n\\n your_function(@Knave,'X(3)~=X(2)') == false]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(Assuming X(2)==X(3); you do not know the values of X, only islanders do) This question asks to the islander whether the value of his secret formula X(2) is different from the value of his secret formula X(3). Assuming that they were actually the same value a Knight would respond negatively (telling you the truth), while a Knave would respond affirmatively (lying to you), so, again, your function should return exactly the opposite response in each case.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":3098,"title":"Scrabble Scores - 13","description":"This problem integrates components of \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3084-scrabble-scores-11 Scrabble Scores - 11\u003e and \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12 Scrabble Scores - 12\u003e. Here, you are provided an existing word on the board from which you will play a word. The letter can reside anywhere (first to last) within the existing word and within the word that you are playing. In addition, multipliers from the board are provided. Write a function to find the highest scoring word, provided any letter from the existing word that you are building off of, the letters on your tray, and the multipliers (provided in specific locations; see below).\r\n\r\nRather than having to test all the possible permutations against a dictionary, you will be provided a double-level cell array of strings containing all possible words based each starting letter in the existing word and the letters on your tray (a cell array for each letter in the existing word). (The word lists purposefully omit smaller words to prevent the test cases from being too large.) In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\r\n\r\nYou will be provided a multiplier character array that represents the fifteen possible squares that can be played on for each letter in the existing word, ranging from seven above each existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below each existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th (column) position. The array will have the same number of rows as the length of the existing word (which is located along the middle of the array). The multipliers are the same as in previous problems:\r\n\r\n * D: double word\r\n * T: triple word\r\n * Q: quadruple word\r\n * d: double letter\r\n * t: triple letter\r\n * q: quadruple letter\r\n\r\nThe center multiplier square will be left blank, since it's already covered by a tile.\r\n\r\nRelated problems:\r\n\r\nPrevious problem: 12 - \u003chttps://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12 Word score optimization (first word)\u003e.","description_html":"\u003cp\u003eThis problem integrates components of \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3084-scrabble-scores-11\"\u003eScrabble Scores - 11\u003c/a\u003e and \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\"\u003eScrabble Scores - 12\u003c/a\u003e. Here, you are provided an existing word on the board from which you will play a word. The letter can reside anywhere (first to last) within the existing word and within the word that you are playing. In addition, multipliers from the board are provided. Write a function to find the highest scoring word, provided any letter from the existing word that you are building off of, the letters on your tray, and the multipliers (provided in specific locations; see below).\u003c/p\u003e\u003cp\u003eRather than having to test all the possible permutations against a dictionary, you will be provided a double-level cell array of strings containing all possible words based each starting letter in the existing word and the letters on your tray (a cell array for each letter in the existing word). (The word lists purposefully omit smaller words to prevent the test cases from being too large.) In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\u003c/p\u003e\u003cp\u003eYou will be provided a multiplier character array that represents the fifteen possible squares that can be played on for each letter in the existing word, ranging from seven above each existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below each existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th (column) position. The array will have the same number of rows as the length of the existing word (which is located along the middle of the array). The multipliers are the same as in previous problems:\u003c/p\u003e\u003cpre\u003e * D: double word\r\n * T: triple word\r\n * Q: quadruple word\r\n * d: double letter\r\n * t: triple letter\r\n * q: quadruple letter\u003c/pre\u003e\u003cp\u003eThe center multiplier square will be left blank, since it's already covered by a tile.\u003c/p\u003e\u003cp\u003eRelated problems:\u003c/p\u003e\u003cp\u003ePrevious problem: 12 - \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\"\u003eWord score optimization (first word)\u003c/a\u003e.\u003c/p\u003e","function_template":"function [score,max_word] = scrabble_scores_13(words,mult,first_word)\r\n\r\nscore = 0;\r\nmax_word = {''};\r\n\r\nend","test_suite":"%%\r\nfirst_word = 'start'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\nmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'  d   t t   d  ';' T   d   d   T '];\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nwords{2} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nwords{3} = {'alate','almah','almeh','email','halma','hamal','hemal','laith','lamia','lathe','lathi','lithe','maile','metal','tamal','telia','thali','althea','haemal','halite','hamate','hamlet','hiatal','hiemal','lamiae','malate','maltha','meatal','tamale','hematal','thalami'};\r\nwords{4} = {'aimer','airth','alert','almeh','alter','amrit','ariel','armet','artel','earth','email','haler','harem','hater','heart','hemal','herma','hilar','ihram','irate','ither','laith','lamer','later','lathe','lathi','liter','lithe','litre','maile','mater','merit','metal','miler','mirth','miter','mitre','ramet','ramie','ratel','rathe','realm','relit','remit','retia','taler','tamer','telia','terai','thali','tharm','their','therm','thirl','tiler','timer','trail','trial','armlet','hailer','halier','halite','halter','hamlet','hermai','hermit','hiemal','imaret','lather','lither','mailer','matier','milter','mither','mitral','ramtil','remail','retail','retial','tailer','thairm','thaler','thiram','tramel','lathier','maltier','marlite','thermal'};\r\nwords{5} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nmax_score_corr = 39;\r\nmax_word_corr = {'hamlets'};\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'start'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\nmult = ['T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T'];\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nwords{2} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nwords{3} = {'alate','almah','almeh','email','halma','hamal','hemal','laith','lamia','lathe','lathi','lithe','maile','metal','tamal','telia','thali','althea','haemal','halite','hamate','hamlet','hiatal','hiemal','lamiae','malate','maltha','meatal','tamale','hematal','thalami'};\r\nwords{4} = {'aimer','airth','alert','almeh','alter','amrit','ariel','armet','artel','earth','email','haler','harem','hater','heart','hemal','herma','hilar','ihram','irate','ither','laith','lamer','later','lathe','lathi','liter','lithe','litre','maile','mater','merit','metal','miler','mirth','miter','mitre','ramet','ramie','ratel','rathe','realm','relit','remit','retia','taler','tamer','telia','terai','thali','tharm','their','therm','thirl','tiler','timer','trail','trial','armlet','hailer','halier','halite','halter','hamlet','hermai','hermit','hiemal','imaret','lather','lither','mailer','matier','milter','mither','mitral','ramtil','remail','retail','retial','tailer','thairm','thaler','thiram','tramel','lathier','maltier','marlite','thermal'};\r\nwords{5} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nmax_score_corr = 30;\r\nmax_word_corr = {'maltha'};\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'start'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aethilm'; %your tray letters; informational (not part of the problem)\r\nmult = [' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'D  t d   d t  D';' T  d t t d  T '];\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aisle','alist','almeh','almes','amies','email','emits','haems','haets','hails','hales','halms','halts','hames','haste','hates','heals','heats','heils','heist','helms','hemal','hilts','islet','istle','items','laith','lames','lathe','lathi','laths','leash','least','limas','limes','litas','lites','lithe','maile','mails','maist','males','malts','mates','maths','meals','meats','melts','metal','meths','metis','miles','milts','mites','saith','salmi','satem','selah','setal','shale','shalt','shame','sheal','shiel','slate','slime','smalt','smelt','smile','smite','smith','stale','steal','steam','stela','stile','stime','taels','tails','tales','tames','tamis','teals','teams','telia','tesla','thali','tiles','times','almehs','emails','halest','halite','hamlet','haslet','hiemal','lamest','lathes','lathis','latish','mailes','mashie','mesial','metals','misate','miseat','saithe','saltie','samiel','samite','samlet','sheila','shelta','smalti','stelai','tahsil','thalis','theism','atheism','halites','hamlets','heliast'};\r\nwords{2} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nwords{3} = {'alate','almah','almeh','email','halma','hamal','hemal','laith','lamia','lathe','lathi','lithe','maile','metal','tamal','telia','thali','althea','haemal','halite','hamate','hamlet','hiatal','hiemal','lamiae','malate','maltha','meatal','tamale','hematal','thalami'};\r\nwords{4} = {'aimer','airth','alert','almeh','alter','amrit','ariel','armet','artel','earth','email','haler','harem','hater','heart','hemal','herma','hilar','ihram','irate','ither','laith','lamer','later','lathe','lathi','liter','lithe','litre','maile','mater','merit','metal','miler','mirth','miter','mitre','ramet','ramie','ratel','rathe','realm','relit','remit','retia','taler','tamer','telia','terai','thali','tharm','their','therm','thirl','tiler','timer','trail','trial','armlet','hailer','halier','halite','halter','hamlet','hermai','hermit','hiemal','imaret','lather','lither','mailer','matier','milter','mither','mitral','ramtil','remail','retail','retial','tailer','thairm','thaler','thiram','tramel','lathier','maltier','marlite','thermal'};\r\nwords{5} = {'almeh','atilt','email','hemal','laith','lathe','lathi','latte','lithe','maile','matte','metal','telia','thali','theta','tilth','tithe','title','halite','hamlet','hiemal'};\r\nmax_score_corr = 45;\r\nmax_word_corr = {'hamlets'};\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'thinning'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'eodnirl'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'diner','doter','droit','drone','elint','eloin','enrol','ident','idler','indol','inert','inlet','inter','intro','irone','lento','lined','liner','lirot','liter','litre','loden','loner','nerol','niter','nitre','nitro','noted','noter','oiled','oiler','olden','older','oldie','olein','oriel','redon','relit','reoil','riled','ronde','teind','teloi','tenor','tilde','tiled','tiler','tined','tired','toile','toled','tondi','toned','toner','trend','tried','trine','triol','trode','trone','dentil','dinero','dotier','editor','entoil','indole','ironed','linted','linter','loiter','neroli','norite','orient','retold','rident','rioted','rodent','roiled','rondel','tinder','tirled','toiled','toiler','tonier','trined','triode','lentoid','retinol','tendril','trindle'};\r\nwords{2} = {'dhole','diner','drone','eloin','enrol','helio','heron','hider','hired','holed','honed','honer','horde','idler','indol','irone','lined','liner','loden','loner','nerol','oiled','oiler','olden','older','oldie','olein','oriel','redon','reoil','rhino','riled','ronde','dehorn','dinero','heroin','hinder','hoiden','holden','holder','holier','hondle','honied','horned','indole','ironed','neroli','roiled','rondel','hordein','inholder'};\r\nwords{3} = {'diner','drone','eloin','enrol','idler','indie','indol','indri','iodin','irone','lined','liner','loden','loner','nerol','oiled','oiler','olden','older','oldie','olein','oriel','redon','reoil','riled','ronde','dinero','indole','inlier','iodine','ironed','linier','neroli','oilier','roiled','rondel'};\r\nwords{4} = {'diner','donne','drone','eloin','enrol','idler','indol','inned','inner','irone','lined','linen','liner','loden','loner','nerol','niner','oiled','oiler','olden','older','oldie','olein','oriel','redon','renin','reoil','riled','ronde','ronin','dinero','dinner','endrin','indole','ironed','linden','neroli','online','roiled','rondel','ronnel'};\r\nwords{5} = {'diner','donne','drone','eloin','enrol','idler','indol','inned','inner','irone','lined','linen','liner','loden','loner','nerol','niner','oiled','oiler','olden','older','oldie','olein','oriel','redon','renin','reoil','riled','ronde','ronin','dinero','dinner','endrin','indole','ironed','linden','neroli','online','roiled','rondel','ronnel'};\r\nwords{6} = {'diner','drone','eloin','enrol','idler','indie','indol','indri','iodin','irone','lined','liner','loden','loner','nerol','oiled','oiler','olden','older','oldie','olein','oriel','redon','reoil','riled','ronde','dinero','indole','inlier','iodine','ironed','linier','neroli','oilier','roiled','rondel'};\r\nwords{7} = {'diner','donne','drone','eloin','enrol','idler','indol','inned','inner','irone','lined','linen','liner','loden','loner','nerol','niner','oiled','oiler','olden','older','oldie','olein','oriel','redon','renin','reoil','riled','ronde','ronin','dinero','dinner','endrin','indole','ironed','linden','neroli','online','roiled','rondel','ronnel'};\r\nwords{8} = {'deign','diner','dinge','dingo','dirge','dogie','doing','drone','eloin','enrol','gelid','genro','geoid','giron','glide','goner','gored','gride','grind','groin','idler','indol','ingle','irone','liger','lined','liner','lingo','loden','lodge','login','loner','longe','nerol','ogled','ogler','oiled','oiler','olden','older','oldie','olein','oriel','redon','reign','renig','reoil','ridge','riled','ronde','dinero','dinger','dingle','doling','dongle','eloign','engild','engird','eringo','gilder','girdle','girned','glider','golden','golder','ignore','indole','ironed','legion','linger','lodger','logier','longed','longer','neroli','reding','regild','region','ridgel','ringed','roiled','rondel','eroding','glenoid','gloried','godlier','groined','ignored','lording','negroid','redoing'};\r\nind = randi(3);\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'   D       D   ';'   D       D   ';' D   t   t   D ';'  d   t t   d  ';' T   d   d   T '];\r\n\t\tmax_score_corr = 33;\r\n\t\tmax_word_corr = {'godlier'};\r\n\tcase 2\r\n\t\tmult = ['T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   '];\r\n\t\tmax_score_corr = 16;\r\n\t\tmax_word_corr = {'indole','iodine','ironed','endrin','linden'};\r\n\tcase 3\r\n\t\tmult = ['T   d     d   T';' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'  T   d d   T  ';' T d t   t d T ';'D  t d   d t  D';' T  d t t d  T '];\r\n\t\tmax_score_corr = 45;\r\n\t\tmax_word_corr = {'hordein'};\r\nend\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'novels'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'dmvxeao'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'ad','ae','am','an','ax','da','de','do','ed','em','en','ex','ma','me','mo','na','ne','no','od','oe','om','on','ox','ado','and','ane','ave','avo','axe','dam','dan','den','dev','dex','doe','dom','don','emo','end','eon','mad','mae','man','max','med','men','moa','mod','mon','nae','nam','nav','nod','nom','oda','ode','oma','one','ova','van','vex','voe','vox','aeon','amen','axed','axon','dame','damn','dean','demo','deva','dome','dona','done','dove','exam','exon','made','mane','mano','mead','mean','mend','meno','moan','mode','move','moxa','name','nave','nema','node','noma','nome','nova','odea','omen','oven','oxen','vane','vena','vend','admen','amend','anode','axmen','axone','daven','demon','devon','doven','maned','maven','maxed','menad','monad','monde','moved','named','nomad','novae','vaned','venom','daemon','moaned'};\r\nwords{2} = {'ad','ae','am','ax','da','de','do','ed','em','ex','ma','me','mo','od','oe','om','ox','ado','ave','avo','axe','dam','dev','dex','doe','dom','emo','mad','mae','max','med','moa','mod','moo','oda','ode','oma','ova','oxo','vex','voe','vox','axed','dame','demo','deva','dome','doom','dove','exam','made','mead','mode','mood','move','moxa','odea','maxed','mooed','moved'};\r\nwords{3} = {'ad','ae','am','ax','da','de','do','ed','em','ex','ma','me','mo','od','oe','om','ox','ado','ave','avo','axe','dam','dev','dex','doe','dom','emo','mad','mae','max','med','moa','mod','oda','ode','oma','ova','vav','vex','voe','vox','axed','dame','demo','deva','dome','dove','exam','made','mead','mode','move','moxa','odea','maxed','moved'};\r\nwords{4} = {'ad','ae','am','ax','da','de','do','ed','em','ex','ma','me','mo','od','oe','om','ox','ado','ave','avo','axe','dam','dee','dev','dex','doe','dom','eme','emo','eve','mad','mae','max','med','moa','mod','oda','ode','oma','ova','vee','vex','voe','vox','axed','dame','deem','deme','demo','deva','dome','dove','eave','exam','exed','made','mead','meed','mode','move','moxa','odea','adeem','deave','eaved','edema','evade','maxed','moved','vexed','oedema'};\r\nwords{5} = {'ad','ae','al','am','ax','da','de','do','ed','el','em','ex','la','lo','ma','me','mo','od','oe','om','ox','ado','ale','ave','avo','axe','dal','dam','del','dev','dex','doe','dol','dom','eld','elm','emo','lad','lam','lav','lax','lea','led','lev','lex','lox','mad','mae','max','med','mel','moa','mod','mol','oda','ode','old','ole','oma','ova','vex','voe','vox','alme','aloe','axed','axel','axle','dale','dame','deal','demo','deva','dole','dome','dove','exam','lade','lame','lave','lead','leva','levo','load','loam','lode','love','made','male','mead','meal','meld','mode','mola','mold','mole','move','moxa','odea','olde','olea','oval','vale','veal','vela','veld','vole','amole','axled','dolma','domal','laevo','lamed','laved','loved','loxed','maxed','medal','modal','model','moved','voled','voxel','loamed'};\r\nwords{6} = {'ad','ae','am','as','ax','da','de','do','ed','em','es','ex','ma','me','mo','od','oe','om','os','ox','so','ado','ads','ave','avo','axe','dam','das','dev','dex','doe','dom','dos','eds','emo','ems','mad','mae','mas','max','med','moa','mod','mos','oda','ode','ods','oes','oma','oms','ose','ova','sad','sae','sax','sea','sev','sex','sod','som','sox','vas','vex','voe','vox','ados','aves','avos','axed','axes','dame','dams','demo','deva','devs','does','dome','doms','dosa','dose','dove','emos','exam','made','mads','maes','mead','meds','mesa','moas','mode','mods','move','moxa','odas','odea','odes','omas','oxes','sade','same','save','seam','soda','soma','some','vase','voes','dames','demos','devas','domes','doves','exams','maxed','maxes','meads','modes','moved','moves','moxas','oaves','saved','soave','vadose','vamose','vamosed'};\r\nind = randi(3);\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'   D       D   ';'   D       D   ';' D   t   t   D '];\r\n\t\tmax_score_corr = 37;\r\n\t\tmax_word_corr = {'vox'};\r\n\tcase 2\r\n\t\tmult = ['T   d     d   T';'  D   d d   D  ';'   d       d   ';'T   d     d   T';'   d       d   ';'  D   d d   D  '];\r\n\t\tmax_score_corr = 25;\r\n\t\tmax_word_corr = {'vox'};\r\n\tcase 3\r\n\t\tmult = [' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'  T   d d   T  ';' T d t   t d T ';'D  t d   d t  D'];\r\n\t\tmax_score_corr = 35;\r\n\t\tmax_word_corr = {'voxel'};\r\nend\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))\r\n\r\n%%\r\nfirst_word = 'zoologist'; %the starting word; the new word must be played off of a letter in this word\r\ntray_letters = 'aehcmdi'; %your tray letters; informational (not part of the problem)\r\n%all possible words, including each letter of the starting word combined with your tray letters\r\nclear words\r\nwords{1} = {'aced','ache','acid','acme','adze','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cazh','cedi','chad','chai','cham','chem','chez','chia','chid','dace','dame','daze','dice','dime','each','emic','hade','haed','haem','hame','haze','head','hide','hied','iced','idea','idem','mace','mach','made','maid','maze','mead','mech','mica','mice','zeda','ached','aimed','amice','amide','azide','chide','chime','demic','hazed','hemic','maced','mache','maize','mazed','media','medic','miche','chimed','haemic','miched','zaideh'};\r\nwords{2} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','camo','cedi','chad','chai','cham','chao','chem','chia','chid','ciao','coda','code','coed','coma','come','dace','dame','deco','demo','dice','dime','dome','each','echo','emic','hade','haed','haem','hame','head','hide','hied','hoed','homa','home','iced','idea','idem','mace','mach','made','maid','mead','mech','mica','mice','mode','modi','oche','odah','odea','odic','ohed','ohia','ached','aimed','amice','amide','amido','cameo','chemo','chiao','chide','chime','comae','demic','demoi','domic','hemic','homed','homie','maced','mache','macho','mahoe','media','medic','miche','mocha','mochi','ohmic','chimed','codeia','cohead','comade','haemic','hemoid','medico','miched','modica','haemoid'};\r\nwords{3} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','camo','cedi','chad','chai','cham','chao','chem','chia','chid','ciao','coda','code','coed','coma','come','dace','dame','deco','demo','dice','dime','dome','each','echo','emic','hade','haed','haem','hame','head','hide','hied','hoed','homa','home','iced','idea','idem','mace','mach','made','maid','mead','mech','mica','mice','mode','modi','oche','odah','odea','odic','ohed','ohia','ached','aimed','amice','amide','amido','cameo','chemo','chiao','chide','chime','comae','demic','demoi','domic','hemic','homed','homie','maced','mache','macho','mahoe','media','medic','miche','mocha','mochi','ohmic','chimed','codeia','cohead','comade','haemic','hemoid','medico','miched','modica','haemoid'};\r\nwords{4} = {'aced','ache','acid','acme','ahed','ahem','aide','alec','alme','amid','amie','cade','cadi','caid','calm','came','cami','cedi','ceil','chad','chai','cham','chem','chia','chid','clad','clam','dace','dahl','dale','dame','deal','deil','deli','dhal','dial','dice','diel','dime','each','elhi','emic','hade','haed','haem','hail','hale','halm','hame','head','heal','heil','held','helm','hide','hied','hila','iced','idea','idem','idle','ilea','lace','lade','laic','laid','lame','lead','lech','lice','lich','lied','lima','lime','mace','mach','made','maid','mail','male','mead','meal','mech','meld','mica','mice','mild','mile','ached','ailed','aimed','alcid','almeh','amice','amide','camel','chela','chide','chiel','child','chile','chime','clade','claim','clime','decal','demic','email','haled','halid','hemal','hemic','ideal','ileac','laced','laich','lamed','leach','limed','maced','mache','macle','maile','malic','medal','media','medic','melic','miche','milch','calmed','chield','childe','chimed','chimla','haemic','hailed','halide','heliac','hiemal','lamedh','macled','mailed','malice','medial','miched','camelid','claimed','decimal','declaim','medical'};\r\nwords{5} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','camo','cedi','chad','chai','cham','chao','chem','chia','chid','ciao','coda','code','coed','coma','come','dace','dame','deco','demo','dice','dime','dome','each','echo','emic','hade','haed','haem','hame','head','hide','hied','hoed','homa','home','iced','idea','idem','mace','mach','made','maid','mead','mech','mica','mice','mode','modi','oche','odah','odea','odic','ohed','ohia','ached','aimed','amice','amide','amido','cameo','chemo','chiao','chide','chime','comae','demic','demoi','domic','hemic','homed','homie','maced','mache','macho','mahoe','media','medic','miche','mocha','mochi','ohmic','chimed','codeia','cohead','comade','haemic','hemoid','medico','miched','modica','haemoid'};\r\nwords{6} = {'aced','ache','acid','acme','aged','ahed','ahem','aide','amid','amie','cade','cadi','cage','caid','came','cami','cedi','chad','chai','cham','chem','chia','chid','dace','dame','dice','dime','each','egad','emic','gach','gadi','gaed','game','gied','hade','haed','haem','hame','head','hide','hied','iced','idea','idem','mace','mach','made','mage','magi','maid','mead','mech','mega','mica','mice','ached','aimed','amice','amide','cadge','caged','chide','chime','demic','gamed','gamic','hemic','image','maced','mache','magic','media','medic','miche','midge','chimed','degami','gached','haemic','imaged','miched'};\r\nwords{7} = {'aced','ache','acid','acme','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cedi','chad','chai','cham','chem','chia','chid','dace','dame','dice','dime','each','emic','hade','haed','haem','hame','head','hide','hied','iced','idea','idem','imid','mace','mach','made','maid','mead','mech','mica','mice','midi','ached','aimed','amice','amici','amide','chide','chime','demic','hemic','imide','maced','mache','media','medic','medii','miche','amidic','chimed','haemic','miched'};\r\nwords{8} = {'aced','aces','ache','acid','acme','ahed','ahem','ahis','aide','aids','aims','amid','amie','amis','asci','cade','cadi','cads','caid','came','cami','cams','case','cash','cedi','chad','chai','cham','chem','chia','chid','chis','dace','dahs','dais','dame','dams','dash','desi','dice','dies','dime','dims','disc','dish','each','edhs','emic','hade','haed','haem','haes','hame','hams','head','hems','hide','hied','hies','hims','iced','ices','ichs','idea','idem','ides','mace','mach','macs','made','mads','maes','maid','mash','mead','mech','meds','mesa','mesh','mica','mice','mics','mids','mise','sade','sadi','said','same','scad','scam','seam','semi','shad','sham','shea','shed','shim','sice','side','sidh','sima','ached','aches','acids','acmes','aides','aimed','amice','amide','amids','amies','asdic','ashed','aside','cades','cadis','caids','cames','camis','cased','cedis','chads','chais','chams','chase','chasm','chems','chias','chide','chime','daces','dames','dashi','deash','deism','demic','deshi','dices','dimes','disme','emics','hades','haems','hames','heads','hemic','hides','ideas','maced','maces','mache','machs','maids','meads','mechs','media','medic','mesic','micas','miche','sadhe','saice','shade','shame','shied','sidhe','amices','amides','camise','cashed','chaise','chased','chiasm','chides','chimed','chimes','emdash','haemic','maches','mashed','mashie','medias','medics','miched','miches','sachem','samech','schema','shamed','simcha','chamise','chasmed'};\r\nwords{9} = {'aced','ache','acid','acme','adit','ahed','ahem','aide','amid','amie','cade','cadi','caid','came','cami','cate','cedi','chad','chai','cham','chat','chem','chia','chid','chit','cite','dace','dame','date','dice','diet','dime','dita','dite','each','eath','echt','edit','emic','emit','etch','etic','hade','haed','haem','haet','hame','hate','head','heat','hide','hied','iced','idea','idem','itch','item','mace','mach','made','maid','mate','math','mead','meat','mech','meta','meth','mica','mice','mite','tace','tach','tame','team','tech','thae','them','tide','tied','time','ached','acted','admit','aimed','aitch','amice','amide','cadet','cheat','chide','chime','cited','death','demic','demit','dicta','ditch','edict','ethic','hated','hemic','maced','mache','match','mated','media','medic','miche','tache','tamed','teach','theca','timed','chimed','dacite','detach','haemic','itched','miched','hematic','matched'};\r\nind = randi(3);\r\nswitch ind\r\n\tcase 1\r\n\t\tmult = [' T   d   d   T ';'  d   t t   d  ';' D   t   t   D ';'   D       D   ';' d   T   T   d ';'   D       D   ';' D   t   t   D ';'  d   t t   d  ';' T   d   d   T '];\r\n\t\tmax_score_corr = 117;\r\n\t\tmax_word_corr = {'haemoid'};\r\n\tcase 2\r\n\t\tmult = ['T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T';'   d       d   ';'  D   d d   D  ';'   d       d   ';'T   d     d   T'];\r\n\t\tmax_score_corr = 28;\r\n\t\tmax_word_corr = {'medico'};\r\n\tcase 3\r\n\t\tmult = ['T   d     d   T';' T  d t t d  T ';'D  t d   d t  D';' T d t   t d T ';'  T   d d   T  ';' T d t   t d T ';'D  t d   d t  D';' T  d t t d  T ';'T   d     d   T'];\r\n\t\tmax_score_corr = 63;\r\n\t\tmax_word_corr = {'decimal'};\r\nend\r\n[max_score,max_word] = scrabble_scores_13(words,mult,first_word);\r\nassert(isequal(max_score,max_score_corr))\r\nassert(isequal(sort(max_word),sort(max_word_corr)))","published":true,"deleted":false,"likes_count":2,"comments_count":6,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":"2015-03-20T18:02:10.000Z","rescore_all_solutions":false,"group_id":40,"created_at":"2015-03-20T01:53:26.000Z","updated_at":"2026-04-17T16:57:25.000Z","published_at":"2015-03-20T01:53:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem integrates components of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3084-scrabble-scores-11\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eScrabble Scores - 11\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eScrabble Scores - 12\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Here, you are provided an existing word on the board from which you will play a word. The letter can reside anywhere (first to last) within the existing word and within the word that you are playing. In addition, multipliers from the board are provided. Write a function to find the highest scoring word, provided any letter from the existing word that you are building off of, the letters on your tray, and the multipliers (provided in specific locations; see below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRather than having to test all the possible permutations against a dictionary, you will be provided a double-level cell array of strings containing all possible words based each starting letter in the existing word and the letters on your tray (a cell array for each letter in the existing word). (The word lists purposefully omit smaller words to prevent the test cases from being too large.) In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou will be provided a multiplier character array that represents the fifteen possible squares that can be played on for each letter in the existing word, ranging from seven above each existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below each existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th (column) position. The array will have the same number of rows as the length of the existing word (which is located along the middle of the array). The multipliers are the same as in previous problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ * D: double word\\n * T: triple word\\n * Q: quadruple word\\n * d: double letter\\n * t: triple letter\\n * q: quadruple letter]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe center multiplier square will be left blank, since it's already covered by a tile.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRelated problems:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrevious problem: 12 -\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/3097-scrabble-scores-12\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWord score optimization (first word)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":52709,"title":"Easy Sequences 19: Length of Prime-sided Rectangle with Maximum Area","description":"A prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-sided rectangles whose areas are less than or equal to 25:\r\n                                       \r\nGiven an area limit 'n', find the length (i.e. the longer side if sides are unequal) of the prime-sided rectangle, with the largest area less than or equal to 'n'. \r\nIn the figure above the rectangle with the maximum area is the 5x5 square. Therefore for n = 25 the output should be 5. For n = 100, the output should be 19, since 19 x 5 = 95 \u003c 100. No other combination of prime sides will produce an area greater than 95 for area \u003c= 100.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 492px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-sided rectangles whose areas are less than or equal to 25:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 318px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                       \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"390\" height=\"312\" style=\"vertical-align: baseline;width: 390px;height: 312px\" 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rpXKtyQyK9+Ma6XyLYnMyjfjesdUg4U7nsrwnkwEh3DNMr5NqOE2vkO4ZhnfJtRwG98hXLOMbxNquI3vEK5ZxrcJNdzGdwjXLOPbhBpu4zuEa5bxbUINt/EdwjXL+Dahhtv4DuGaZXybUB+wzWDhAw6xHsFEsCQyK9+Ma6XyLYnMyjfjWql8SyKz8s24VirfksisfDOulcq3JDIr34xrpfIticzKN+NaqXxLIrPyzbhWKt+SyKx8M653TDVYuOOpDO/JRHAI1yzj24QabuM7hGuW8W1CDbfxHcI1y/g2oYbb+A7hmmV8m1DDbXyHcM0yvk2o4Ta+Q7hmGd8m1HAb3yFcs4xvE2q4je8QrlnGtwn1AdsMFj7gEOsRTARLIrPyzbhWKt+SyKx8M66VyrckMivfjGul8i2JzMo341qpfEsis/LNuFYq35LIrHwzrpXKtyQyK9+Ma6XyLYnMyjfjesdUg4U7nsrwnkwEh3DNMr5NqOE2vkO4ZhnfJtRwG98hXLOMbxNquI3vEK5ZxrcJNdzGdwjXLOPbhBpu4zuEa5bxbUINt/EdwjXL+Dahhtv4DuGaZXybUB+wzWDhAw6xHsFEsCQyK9+Ma6XyLYnMyjfjWql8SyKz8s24VirfksisfDOulcq3JDIr34xrpfIticzKN+NaqXxLIrPyzbhWKt+SyKx8M653TDVYuOOpDO/JRHAI1yzj24QabuM7hGuW8W1CDbfxHcI1y/g2oYbb+A7hmmV8m1DDbXyHcM0yvk2o4Ta+Q7hmGd8m1HAb3yFcs4xvE2q4je8QrlnGtwn1AdsMFj7gEOsRTARLIrPyzbhWKt+SyKx8M66VyrckMivfjGul8i2JzMo341qpfEsis/LNuFYq35LIrHwzrpXKtyQyK9+Ma6XyLYnMyjfjesdUg4U7nsrwnkwEh3DNMr5NqOE2vkO4ZhnfJtRwG98hXLOMbxNquI3vEK5ZxrcJNdzGdwjXLOPbhBpu4zuEa5bxbUINt/EdwjXL+Dahhtv4DuGaZXybUB+wzWDhAw6xHsFEsCQyK9+Ma6XyLYnMyjfjWql8SyKz8s24VirfksisfDOulcq3JDIr34xrpfIticzKN+NaqXxLIrPyzbhWKt+SyKx8M653TDVYuOOpDO/JRHAI1yzj24QabuM7hGuW8W1CDbfxHcI1y/g2oYbb+A7hmmV8m1DDbXyHcM0yvk2o4Ta+Q7hmGd8m1HAb3yFcs4xvE2q4je8QrlnGtwn1AdsMFj7gEOsRTARLIrPyzbhWKt+SyKx8M66VyrckMivfjGul8i2JzMo341qpfEsis/LNuFYq35LIrHwzrpXKtyQyK9+Ma6XyLYnMyjfjesdUg4U7nsrwnkwEh3DNMr5NqOE2vkO4ZhnfJtRwG98hXLOMbxNquI3vEK5ZxrcJNdzGdwjXLOPbhBpu4zuEa5bxbUINt/EdwjXL+Dahhtv4DuGaZXybUB+wzWDhAw6xHsFEsCQyK9+Ma6XyLYnMyjfjWql8SyKz8s24VirfksisfDOulcq3JDIr34xrpfIticzKN+NaqXxLIrPyzbhWKt+SyKx8M653TDVYuOOpDO/JRHAI1yzj24QabuM7hGuW8W1CDbfxHcI1y/g2oYbb+A7hmmV8m1DDbXyHcM0yvk2o4Ta+Q7hmGd8m1HAb3yFcs4xvE2q4je8QrlnGtwn1AdsMFj7gEOsRTARLIrPyzbhWKt+SyKx8M66VyrckMivfjGul8i2JzMo341qpfEsis/LNuFYq35LIrHwzrpXKtyQyK9+Ma6XyLYnMyjfjesdUg4U7nsrwnkwEh3DNMr5NqOE2vkO4ZhnfJtRwG98hXLOMbxNquI3vEK5ZxrcJNdzGdwjXLOPbhBpu4zuEa5bxbUINt/EdwjXL+Dahhtv4DuGaZXybUB+wzWDhAw6xHsFEsCQyK9+Ma6XyLYnMyjfjWql8SyKz8s24VirfksisfDOulcq3JDIr34xrpfIticzKN+NaqXxLIrPyzbhWKt+SyKx8M653TDVYuOOpDO/JRHAI1yzj24QabuM7hGuW8W1CDbfxHcI1y/g2oYbb+A7hmmV8m1DDbXyHcM0yvk2o4Ta+Q7hmGd8m1HAb3yFcs4xvE2q4je8QrlnGtwn1AdsMFj7gEOsRTARLIrPyzbhWKt+SyKx8M66VyrckMivfjGul8i2JzMo341qpfEsis/LNuFYq35LIrHwzrpXKtyQyK9+Ma6XyLYnMyjfjesdUg4U7nsrwnkwEh3DNMr5NqOE2vkO4ZhnfJtRwG98hXLOMbxNquI3vEK5ZxrcJNdzGdwjXLOPbhBpu4zuEa5bxbUINt/EdwjXL+Dahhtv4DuGaZXybUB+wzWDhAw6xHsFEsCQyK9+Ma6XyLYnMyjfjWql8SyKz8s24VirfksisfDOulcq3JDIr34xrpfIticzKN+NaqXxLIrPyzbhWKt+SyKx8M653TDVYuOOpDO/JRHAI1yzj24QabuM7hGuW8W1CDbfxHcI1y/g2oYbb+A7hmmV8m1DDbXyHcM0yvk2o4Ta+Q7hmGd8m1HAb3yFcs4xvE2q4je8QrlnGtwn1AdsMFj7gEOsRTARLIrPyzbhWKt+SyKx8M66VyrckMivfjGul8i2JzMo341qpfEsis/LNuFYq35LIrHwzrpXKtyQyK9+Ma6XyLYnMyjfjesdUg4U7nsrwnkwEh3DNMr5NqOE2vkO4ZhnfJtRwG98hXLOMbxNquI3vEK5ZxrcJNdzGdwjXLOPbhBpu4zuEa5bxbUINt/EdwjXL+Dahhtv4DuGaZXybUB+wzWDhAw6xHsFEsCQyK9+Ma6XyLYnMyjfjWql8SyKz8s24VirfksisfDOulcq3JDIr34xrpfIticzKN+NaqXxLIrPyzbhWKt+SyKx8M653TDVYuOOpDO/JRHAI1yzj24QabuM7hGuW8W1CDbfxHcI1y/g2oYbb+A7hmmV8m1DDbXyHcM0yvk2o4Ta+Q7hmGd8m1HAb3yFcs4xvE2q4je8QrlnGtwn1AdsMFj7gEOsRTARLIrPyzbhWKt+SyKx8M66VyrckMivfjGul8i2JzMo341qpfEsis/LNuFYq35LIrHwzrpXKtyQyK9+Ma6XyLYnMyjfjesdUg4U7nsrwnkwEh3DNMr5NqOE2vkO4ZhnfJtRwG98hXLOMbxNquI3vEK5ZxrcJNdzGdwjXLOPbhBpu4zuEa5bxbUINt/EdwjXL+Dahhtv4DuGaZXybUB+wzWDhAw6xHsFEsCQyK9+Ma6XyLYnMyjfjWql8SyKz8s24VirfksisfDOulcq3JDIr34xrpfIticzKN+NaqXxLIrPyzbhWKt+SyKx8M653TDVYuOOpDO/JRHAI1yzj24QabuM7hGuW8W1CDbfxHcI1y/g2oYbb+A7hmmV8m1DDbXyHcM0yvk2o4Ta+Q7hmGd8m1HAb3yFcs4xvE2q4je8QrlnGtwn1AdsMFj7gEOsRTARLIrPyzbhWKt+SyKx8M66VyrckMivfjGul8i2JzMo341qpfEsis/LNuFYq35LIrHwzrpXKtyQyK9+Ma6XyLYnMyjfjesdUg4U7nsrwnkwEh3DNMr5NqOE2vkO4ZhnfJtRwG98hXLOMbxNquI3vEK5ZxrcJNdzGdwjXLOPbhBpu4zuEa5bxbUINt/EdwjXL+Dahhtv4DuGaZXybUB+wzWDhAw6xHsFEsCQyK9+Ma6XyLYnMyjfjWql8SyKz8s24VirfksisfDOulcq3JDIr34xrpfIticzKN+NaqXxLIrPyzbhWKt+SyKx8M653TDVYuOOpDO/JRHAI1yzj24QabuM7hGuW8W1CDbfxHcI1y/g2oYbb+A7hmmV8m1DDbXyHcM0yvk2o4Ta+Q7hmGd8m1HAb3yFcs4xvE2q4je8QrlnGtwn1AdsMFj7gEOsRTARLIrPyzbhWKt+SyKx8M66VyrckMivfjGul8i2JzMo341qpfEsis/LNuFYq35LIrHwzrpXKtyQyK9+Ma6XyLYnMyjfjesdUg4U7nsrwnkwEh3DNMr5NqOE2vkO4ZhnfJtRwG98hXLOMbxNquI3vEK5ZxrcJNdzGdwjXLOPbhBpu4zuEa5bxbUINt/EdwjXL+Dahhtv4DuGaZXybUB+wzWDhAw6xHsFEsCQyK9+Ma6XyLYnMyjfjWql8SyKz8s24VirfksisfDOulcq3JDIr34xrpfIticzKN+NaqXxLIrPyzbhWKt+SyKx8M653TDVYuOOpDO/JRHAI1yzj24QabuM7hGuW8W1CDbfxHcI1y/g2oYbb+A7hmmV8m1DDbXyHcM0yvk2o4Ta+Q7hmGd8m1HAb3yFcs4xvE2q4je8QrlnGtwn1AdsMFj7gEOsRTARLIrPyzbhWKt+SyKx8M66VyrckMivfjGul8i2JzMo341qpfEsis/LNuFYq35LIrHwzrpXKtyQyK9+Ma6XyLYnMyjfjesdUg4U7nsrwnkwEh3DNMr5NqOE2vkO4ZhnfJtRwG98hXLOMbxNquI3vEK5ZxrcJNdzGdwjXLOPbhBpu4zuEa5bxbUINt/EdwjXL+Dahhtv4DuGaZXybUB+wzWDhAw6xHsFEsCQyK9+Ma6XyLYnMyjfjWql8SyKz8s24VirfksisfDOulcq3JDIr34xrpfIticzKN+NaqXxLIrPyzbhWKt+SyKx8M653TDVYuOOpDO/JRHAI1yzj24QabuM7hGuW8W1CDbfxHcI1y/g2oYbb+A7hmmV8m1DDbXyHcM0yvk2o4Ta+Q7hmGd8m1HAb3yFcs4xvE2q4je8QrlnGtwn1AdsMFj7gEOsRTARLIrPyzbhWKt+SyKx8M66VyrckMivfjGul8i2JzMo341qpfEsis/LNuFYq35LIrHwzrpXKtyQyK9+Ma6XyLYnMyjfjesdUg4U7nsrwnkwEh3DNMr5NqOE2vkO4ZhnfJtRwG98hXLOMbxNquI3vEK5ZxrcJNdzGdwjXLOPbhBpu4zuEa5bxbUINt/EdwjXL+Dahhtv4DuGaZXybUB+wzWDhAw6xHsFEsCQyK9+Ma6XyLYnMyjfjWql8SyKz8s24VirfksisfDOulcq3JDIr34xrpfIticzKN+NaqXxLIrPyzbhWKt+SyKx8M653TDVYuOOpDO/JRHAI1yzj24QabuM7hGuW8W1CDbfxHcI1y/g2oYbb+A7hmmV8m1DDbXyHcM0yvk2o4Ta+Q7hmGd8m1HAb3yFcs4xvE2q4je8QrlnGtwn1AdsMFj7gEOsRTARLIrPyzbhWKt+SyKx8M66VyrckMivfjGul8i2JzMo341qpfEsis/LNuFYq35LIrHwzrpXKtyQyK9+Ma6XyLYnMyjfjesdUg4U7nsrwnkwEh3DNMr5NqOE2vkO4ZhnfJtRwG98hXLOMbxNquI3vEK5ZxrcJNdzGdwjXLOPbhBpu4zuEa5bxbUINt/EdwjXL+Dahhtv4DuGaZXybUB+wzWDhAw6xHsFEsCQyK9+Ma6XyLYnMyjfjWql8SyKz8s24VirfksisfDOulcq3JDIr34xrpfIticzKN+NaqXxLIrPyzbhWKt+SyKx8M653TDVYuOOpDO/JRHAI1yzj24QabuM7hGuW8W1CDbfxHcI1y/g2oYbb+A7hmmV8m1DDbXyHcM0yvk2o4Ta+Q7hmGd8m1HAb3yFcs4xvE2q4je8QrlnGtwn1Adu+fX+GrwP/7QOe5dxH+Pn3Yzz3+T35Zwr86rW05WC9H7YwCiFAgACBNxHw88PWg/Ibh1s5/wjz89kfFv4VAQIECHy+gJ/PPvKMv35O/OafWPjIo/VQBAgQIECAAAECBAgQeE7Abxw+56eaAAECBAgQIPDJAi8dLHz/jZfvf1n3Onxyg3q2cwW8J/a8J87tIE9OgAABAicK+Plhz88Pf3b883Dhz1//3l+uZ94n/tn0zAQIECBwroCfF2Y/L1y53aGjXjpYqB9Krb/9/kP4Loc7NJJ7ILBbYNefj9Nzdp+LPAIECBAgcGeB0/++7/n3/vuslOed/wy5NwIECBAgsFsg9ffT03N3n9Mk7/eRyddB+C8zn+jdpcZ/R+ddTsJ97BTw38G3R9P7YY+jFAIECBB4DwE/P2w9p++/KeffKm4l/d8wP58FUEUSIECAwG0F/Hx226N55sa+fk70v7HwDKBaAgQIECBAgAABAgQIfKpA/Sbgpz6f5yJAgAABAgQIEJgL/GNeqvL2Ar/+8/a3+E43+O3bL//3G1v/eqfbvv+9/vzL/e/xE+/Q+2HrqXo/bOX8IYzvDyRbv8B3K+cPYXx/INnzBT8/7HG8SPFPLFwA7f7Yz2dbRb1/t3L+EMb3B5KtX+C7lfOHML4/kOz5gp/P9ji+UcpL/zcW3sjFrRL4QcBvbP1A4gsECPyfgPdDthX48s0KZNP1b9ZXelZA/2Z9pWcF9C/frEA2Xf/yzQpIJ7BHwGBhj6OUAwT8xtYBh+wRCQwFvB+GcM0yvk2o4Ta+Q7hmGd8mlG23FNC/tzwWN9UU0L9NqOE2vkO4ZhnfJtRwG98hnDICi4DBwgLiksAjAb8x8EjG1wkQ8H7I9gBfvlmBbLr+zfpKzwro36yv9KyA/uWbFcim61++WQHpBPYIGCzscZRygICJ9gGH7BEJDAW8H4ZwzTK+TajhNr5DuGYZ3yaUbbcU0L+3PBY31RTQv02o4Ta+Q7hmGd8m1HAb3yGcMgKLgMHCAuKSwCMBvzHwSMbXCRDwfsj2AF++WYFsuv7N+krPCujfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxlHKAgIn2AYfsEQkMBbwfhnDNMr5NqOE2vkO4ZhnfJpRttxTQv7c8FjfVFNC/TajhNr5DuGYZ3ybUcBvfIZwyAouAwcIC4pLAIwG/MfBIxtcJEPB+yPYAX75ZgWy6/s36Ss8K6N+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HGUcoCAifYBh+wRCQwFvB+GcM0yvk2o4Ta+Q7hmGd8mlG23FNC/tzwWN9UU0L9NqOE2vkO4ZhnfJtRwG98hnDICi4DBwgLiksAjAb8x8EjG1wkQ8H7I9gBfvlmBbLr+zfpKzwro36yv9KyA/uWbFcim61++WQHpBPYIGCzscZRygICJ9gGH7BEJDAW8H4ZwzTK+TajhNr5DuGYZ3yaUbbcU0L+3PBY31RTQv02o4Ta+Q7hmGd8m1HAb3yGcMgKLgMHCAuKSwCMBvzHwSMbXCRDwfsj2AF++WYFsuv7N+krPCujfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxlHKAgIn2AYfsEQkMBbwfhnDNMr5NqOE2vkO4ZhnfJpRttxTQv7c8FjfVFNC/TajhNr5DuGYZ3ybUcBvfIZwyAouAwcIC4pLAIwG/MfBIxtcJEPB+yPYAX75ZgWy6/s36Ss8K6N+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HGUcoCAifYBh+wRCQwFvB+GcM0yvk2o4Ta+Q7hmGd8mlG23FNC/tzwWN9UU0L9NqOE2vkO4ZhnfJtRwG98hnDICi4DBwgLiksAjAb8x8EjG1wkQ8H7I9gBfvlmBbLr+zfpKzwro36yv9KyA/uWbFcim61++WQHpBPYIGCzscZRygICJ9gGH7BEJDAW8H4ZwzTK+TajhNr5DuGYZ3yaUbbcU0L+3PBY31RTQv02o4Ta+Q7hmGd8m1HAb3yGcMgKLgMHCAuKSwCMBvzHwSMbXCRDwfsj2AF++WYFsuv7N+krPCujfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxlHKAgIn2AYfsEQkMBbwfhnDNMr5NqOE2vkO4ZhnfJpRttxTQv7c8FjfVFNC/TajhNr5DuGYZ3ybUcBvfIZwyAouAwcIC4pLAIwG/MfBIxtcJEPB+yPYAX75ZgWy6/s36Ss8K6N+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HGUcoCAifYBh+wRCQwFvB+GcM0yvk2o4Ta+Q7hmGd8mlG23FNC/tzwWN9UU0L9NqOE2vkO4ZhnfJtRwG98hnDICi4DBwgLiksAjAb8x8EjG1wkQ8H7I9gBfvlmBbLr+zfpKzwro36yv9KyA/uWbFcim61++WQHpBPYIGCzscZRygICJ9gGH7BEJDAW8H4ZwzTK+TajhNr5DuGYZ3yaUbbcU0L+3PBY31RTQv02o4Ta+Q7hmGd8m1HAb3yGcMgKLgMHCAuKSwCMBvzHwSMbXCRDwfsj2AF++WYFsuv7N+krPCujfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxlHKAgIn2AYfsEQkMBbwfhnDNMr5NqOE2vkO4ZhnfJpRttxTQv7c8FjfVFNC/TajhNr5DuGYZ3ybUcBvfIZwyAouAwcIC4pLAIwG/MfBIxtcJEPB+yPYAX75ZgWy6/s36Ss8K6N+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HGUcoCAifYBh+wRCQwFvB+GcM0yvk2o4Ta+Q7hmGd8mlG23FNC/tzwWN9UU0L9NqOE2vkO4ZhnfJtRwG98hnDICi4DBwgLiksAjAb8x8EjG1wkQ8H7I9gBfvlmBbLr+zfpKzwro36yv9KyA/uWbFcim61++WQHpBPYIGCzscZRygICJ9gGH7BEJDAW8H4ZwzTK+TajhNr5DuGYZ3yaUbbcU0L+3PBY31RTQv02o4Ta+Q7hmGd8m1HAb3yGcMgKLgMHCAuKSwCMBvzHwSMbXCRDwfsj2AF++WYFsuv7N+krPCujfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxlHKAgIn2AYfsEQkMBbwfhnDNMr5NqOE2vkO4ZhnfJpRttxTQv7c8FjfVFNC/TajhNr5DuGYZ3ybUcBvfIZwyAouAwcIC4pLAIwG/MfBIxtcJEPB+yPYAX75ZgWy6/s36Ss8K6N+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HGUcoCAifYBh+wRCQwFvB+GcM0yvk2o4Ta+Q7hmGd8mlG23FNC/tzwWN9UU0L9NqOE2vkO4ZhnfJtRwG98hnDICi4DBwgLiksAjAb8x8EjG1wkQ8H7I9gBfvlmBbLr+zfpKzwro36yv9KyA/uWbFcim61++WQHpBPYIGCzscZRygICJ9gGH7BEJDAW8H4ZwzTK+TajhNr5DuGYZ3yaUbbcU0L+3PBY31RTQv02o4Ta+Q7hmGd8m1HAb3yGcMgKLgMHCAuKSwCMBvzHwSMbXCRDwfsj2AF++WYFsuv7N+krPCujfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxlHKAgIn2AYfsEQkMBbwfhnDNMr5NqOE2vkO4ZhnfJpRttxTQv7c8FjfVFNC/TajhNr5DuGYZ3ybUcBvfIZwyAouAwcIC4pLAIwG/MfBIxtcJEPB+yPYAX75ZgWy6/s36Ss8K6N+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HGUcoCAifYBh+wRCQwFvB+GcM0yvk2o4Ta+Q7hmGd8mlG23FNC/tzwWN9UU0L9NqOE2vkO4ZhnfJtRwG98hnDICi4DBwgLiksAjAb8x8EjG1wkQ8H7I9gBfvlmBbLr+zfpKzwro36yv9KyA/uWbFcim61++WQHpBPYIGCzscZRygICJ9gGH7BEJDAW8H4ZwzTK+TajhNr5DuGYZ3yaUbbcU0L+3PBY31RTQv02o4Ta+Q7hmGd8m1HAb3yGcMgKLgMHCAuKSwCMBvzHwSMbXCRDwfsj2AF++WYFsuv7N+krPCujfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxlHKAgIn2AYfsEQkMBbwfhnDNMr5NqOE2vkO4ZhnfJpRttxTQv7c8FjfVFNC/TajhNr5DuGYZ3ybUcBvfIZwyAouAwcIC4pLAIwG/MfBIxtcJEPB+yPYAX75ZgWy6/s36Ss8K6N+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HGUcoCAifYBh+wRCQwFvB+GcM0yvk2o4Ta+Q7hmGd8mlG23FNC/tzwWN9UU0L9NqOE2vkO4ZhnfJtRwG98hnDICi4DBwgLiksAjAb8x8EjG1wkQ8H7I9gBfvlmBbLr+zfpKzwro36yv9KyA/uWbFcim61++WQHpBPYIGCzscZRygICJ9gGH7BEJDAW8H4ZwzTK+TajhNr5DuGYZ3yaUbbcU0L+3PBY31RTQv02o4Ta+Q7hmGd8m1HAb3yGcMgKLgMHCAuKSwCMBvzHwSMbXCRDwfsj2AF++WYFsuv7N+krPCujfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxlHKAgIn2AYfsEQkMBbwfhnDNMr5NqOE2vkO4ZhnfJpRttxTQv7c8FjfVFNC/TajhNr5DuGYZ3ybUcBvfIZwyAouAwcIC4pLAIwG/MfBIxtcJEPB+yPYAX75ZgWy6/s36Ss8K6N+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HGUcoCAifYBh+wRCQwFvB+GcM0yvk2o4Ta+Q7hmGd8mlG23FNC/tzwWN9UU0L9NqOE2vkO4ZhnfJtRwG98hnDICi4DBwgLiksAjAb8x8EjG1wkQ8H7I9gBfvlmBbLr+zfpKzwro36yv9KyA/uWbFcim61++WQHpBPYIGCzscZRygICJ9gGH7BEJDAW8H4ZwzTK+TajhNr5DuGYZ3yaUbbcU0L+3PBY31RTQv02o4Ta+Q7hmGd8m1HAb3yGcMgKLgMHCAuKSwCMBvzHwSMbXCRDwfsj2AF++WYFsuv7N+krPCujfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxlHKAgIn2AYfsEQkMBbwfhnDNMr5NqOE2vkO4ZhnfJpRttxTQv7c8FjfVFNC/TajhNr5DuGYZ3ybUcBvfIZwyAouAwcIC4pLAIwG/MfBIxtcJEPB+yPYAX75ZgWy6/s36Ss8K6N+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HGUcoCAifYBh+wRCQwFvB+GcM0yvk2o4Ta+Q7hmGd8mlG23FNC/tzwWN9UU0L9NqOE2vkO4ZhnfJtRwG98hnDICi4DBwgLiksAjAb8x8EjG1wkQ8H7I9gBfvlmBbLr+zfpKzwro36yv9KyA/uWbFcim61++WQHpBPYIGCzscZRygICJ9gGH7BEJDAW8H4ZwzTK+TajhNr5DuGYZ3yaUbbcU0L+3PBY31RTQv02o4Ta+Q7hmGd8m1HAb3yGcMgKLgMHCAuKSwCMBvzHwSMbXCRDwfsj2AF++WYFsuv7N+krPCujfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxlHKAgIn2AYfsEQkMBbwfhnDNMr5NqOE2vkO4ZhnfJpRttxTQv7c8FjfVFNC/TajhNr5DuGYZ3ybUcBvfIZwyAouAwcIC4pLAIwG/MfBIxtcJEPB+yPYAX75ZgWy6/s36Ss8K6N+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HGUcoCAifYBh+wRCQwFvB+GcM0yvk2o4Ta+Q7hmGd8mlG23FNC/tzwWN9UU0L9NqOE2vkO4ZhnfJtRwG98hnDICi4DBwgLiksAjAb8x8EjG1wkQ8H7I9gBfvlmBbLr+zfpKzwro36yv9KyA/uWbFcim61++WQHpBPYIGCzscZRygICJ9gGH7BEJDAW8H4ZwzTK+TajhNr5DuGYZ3yaUbbcU0L+3PBY31RTQv02o4Ta+Q7hmGd8m1HAb3yGcMgKLgMHCAuKSwCMBvzHwSMbXCRDwfsj2AF++WYFsuv7N+krPCujfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxlHKAgIn2AYfsEQkMBbwfhnDNMr5NqOE2vkO4ZhnfJpRttxTQv7c8FjfVFNC/TajhNr5DuGYZ3ybUcBvfIZwyAouAwcIC4pLAIwG/MfBIxtcJEPB+yPYAX75ZgWy6/s36Ss8K6N+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HGUcoCAifYBh+wRCQwFvB+GcM0yvk2o4Ta+Q7hmGd8mlG23FNC/tzwWN9UU0L9NqOE2vkO4ZhnfJtRwG98hnDICi4DBwgLiksAjAb8x8EjG1wkQ8H7I9gBfvlmBbLr+zfpKzwro36yv9KyA/uWbFcim61++WQHpBPYIGCzscZRygICJ9gGH7BEJDAW8H4ZwzTK+TajhNr5DuGYZ3yaUbbcU0L+3PBY31RTQv02o4Ta+Q7hmGd8m1HAb3yGcMgKLgMHCAuKSwCMBvzHwSMbXCRDwfsj2AF++WYFsuv7N+krPCujfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxlHKAgIn2AYfsEQkMBbwfhnDNMr5NqOE2vkO4ZhnfJpRttxTQv7c8FjfVFNC/TajhNr5DuGYZ3ybUcBvfIZwyAouAwcIC4pLAIwG/MfBIxtcJEPB+yPYAX75ZgWy6/s36Ss8K6N+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HGUcoCAifYBh+wRCQwFvB+GcM0yvk2o4Ta+Q7hmGd8mlG23FNC/tzwWN9UU0L9NqOE2vkO4ZhnfJtRwG98hnDICi4DBwgLiksAjAb8x8EjG1wkQ8H7I9gBfvlmBbLr+zfpKzwro36yv9KyA/uWbFcim61++WQHpBDYKfL2wXvLX1y3//n2sex1++6+vvL/5P857nXlmPP+ud79/jfceb757HPUjx+8/wOgDfaAP7vPnwN/f/Hl85z+P+lf/vnP/+nlI/+rf+/w8dLc/j/7+9tr3w/c/i//Jv77673//euVNfH3H37+ddaPD3wwVfv/D/CXNeaMzz0w/6d+Ma/Ur36xvOVs5+/nm60+Bnzv83PXCn7v8/c17953fu/pX/75z//r7vf7Vv37uffQe8Pe3l78ffm/G/9D/+/r3Pj99+/7/vn//76u/3lTg59+P8ceb//WfP37NV8YC37798v3Pylf9v8YZCv9G4Odf/uaLX1/61Wvp72H+za96P/ybYLPt3g8zt24V367UbB/fmVu3im9X6t/c5+eHfxNstt1/B/XM7bLKz2eXRDs2eP/uUHycwfexzY5P+O5QfJzB97HNU5/4+ewpvncr/vo58Zv/jYV3OzX3+x8T+D5U+P5vrvxFgACBVcD7YRXZe813r+eaxncV2XvNd6+ntNcK6N/XevtuewX0717PNY3vKrL3mu9ezzWN7yrimsBMwGBh5qbqQAG/sXXgoXtkAk0B74cm1HAb3yFcs4xvE2q4je8QTtktBPTvLY7BTQwF9O8QrlnGtwk13MZ3CNcs49uEso3AhYDBwgWQjwmUgIl2SVgJEFgFvB9Wkb3XfPd6rml8V5G913z3ekp7rYD+fa2377ZXQP/u9VzT+K4ie6/57vVc0/iuIq4JzAQMFmZuqg4UMNE+8NA9MoGmgPdDE2q4je8QrlnGtwk13MZ3CKfsFgL69xbH4CaGAvp3CNcs49uEGm7jO4RrlvFtQtlG4ELAYOECyMcESsBEuySsBAisAt4Pq8jea757Pdc0vqvI3mu+ez2lvVZA/77W23fbK6B/93quaXxXkb3XfPd6rml8VxHXBGYCBgszN1UHCphoH3joHplAU8D7oQk13MZ3CNcs49uEGm7jO4RTdgsB/XuLY3ATQwH9O4RrlvFtQg238R3CNcv4NqFsI3AhYLBwAeRjAiVgol0SVgIEVgHvh1Vk7zXfvZ5rGt9VZO81372e0l4roH9f6+277RXQv3s91zS+q8jea757Pdc0vquIawIzAYOFmZuqAwVMtA88dI9MoCng/dCEGm7jO4RrlvFtQg238R3CKbuFgP69xTG4iaGA/h3CNcv4NqGG2/gO4ZplfJtQthG4EDBYuADyMYESMNEuCSsBAquA98Mqsvea717PNY3vKrL3mu9eT2mvFdC/r/X23fYK6N+9nmsa31Vk7zXfvZ5rGt9VxDWBmYDBwsxN1YECJtoHHrpHJtAU8H5oQg238R3CNcv4NqGG2/gO4ZTdQkD/3uIY3MRQQP8O4ZplfJtQw218h3DNMr5NKNsIXAgYLFwA+ZhACZhol4SVAIFVwPthFdl7zXev55rGdxXZe813r6e01wro39d6+257BfTvXs81je8qsvea717PNY3vKuKawEzAYGHmpupAARPtAw/dIxNoCng/NKGG2/gO4ZplfJtQw218h3DKbiGgf29xDG5iKKB/h3DNMr5NqOE2vkO4ZhnfJpRtBC4EDBYugHxMoARMtEvCSoDAKuD9sIrsvea713NN47uK7L3mu9dT2msF9O9rvX23vQL6d6/nmsZ3Fdl7zXev55rGdxVxTWAmYLAwc1N1oICJ9oGH7pEJNAW8H5pQw218h3DNMr5NqOE2vkM4ZbcQ0L+3OAY3MRTQv0O4ZhnfJtRwG98hXLOMbxPKNgIXAgYLF0A+JlACJtolYSVAYBXwflhF9l7z3eu5pvFdRfZe893rKe21Avr3td6+214B/bvXc03ju4rsvea713NN47uKuCYwEzBYmLmpOlDARPvAQ/fIBJoC3g9NqOE2vkO4ZhnfJtRwG98hnLJbCOjfWxyDmxgK6N8hXLOMbxNquI3vEK5ZxrcJZRuBCwGDhQsgHxMoARPtkrASILAKeD+sInuv+e71XNP4riJ7r/nu9ZT2WgH9+1pv322vgP7d67mm8V1F9l7z3eu5pvFdRVwTmAkYLMzcVB0oYKJ94KF7ZAJNAe+HJtRwG98hXLOMbxNquI3vEE7ZLQT07y2OwU0MBfTvEK5ZxrcJNdzGdwjXLOPbhLKNwIWAwcIFkI8JlICJdklYCRBYBbwfVpG913z3eq5pfFeRvdd893pKe62A/n2tt++2V0D/7vVc0/iuInuv+e71XNP4riKuCcwEDBZmbqoOFDDRPvDQPTKBpoD3QxNquI3vEK5ZxrcJNdzGdwin7BYC+vcWx+AmhgL6dwjXLOPbhBpu4zuEa5bxbULZRuBCwGDhAsjHBErARLskrAQIrALeD6vI3mu+ez3XNL6ryN5rvns9pb1WQP++1tt32yugf/d6rml8V5G913z3eq5pfFcR1wRmAgYLMzdVBwqYaB946B6ZQFPA+6EJNdzGdwjXLOPbhBpu4zuEU3YLAf17i2NwE0MB/TuEa5bxbUINt/EdwjXL+DahbCNwIWCwcAHkYwIlYKJdElYCBFYB74dVZO81372eaxrfVWTvNd+9ntJeK6B/X+vtu+0V0L97Pdc0vqvI3mu+ez3XNL6riGsCMwGDhZmbqgMFTLQPPHSPTKAp4P3QhBpu4zuEa5bxbUINt/Edwim7hYD+vcUxuImhgP4dwjXL+Dahhtv4DuGaZXybULYRuBAwWLgA8jGBEjDRLgkrAQKrgPfDKrL3mu9ezzWN7yqy95rvXk9prxXQv6/19t32CujfvZ5rGt9VZO81372eaxrfVcQ1gZmAwcLMTdWBAibaBx66RybQFPB+aEINt/EdwjXL+Dahhtv4DuGU3UJA/97iGNzEUED/DuGaZXybUMNtfIdwzTK+TSjbCFwIGCxcAPmYQAmYaJeElQCBVcD7YRXZe813r+eaxncV2XvNd6+ntNcK6N/XevtuewX0717PNY3vKrL3mu9ezzWN7yrimsBMwGBh5qbqQAET7QMP3SMTaAp4PzShhtv4DuGaZXybUMNtfIdwym4hoH9vcQxuYiigf4dwzTK+TajhNr5DuGYZ3yaUbQQuBAwWLoB8TKAETLRLwkqAwCrg/bCK7L3mu9dzTeO7iuy95rvXU9prBfTva719t70C+nev55rGdxXZe813r+eaxncVcU1gJmCwMHNTdaCAifaBh+6RCTQFvB+aUMNtfIdwzTK+TajhNr5DOGW3ENC/tzgGNzEU0L9DuGYZ3ybUcBvfIVyzjG8TyjYCFwIGCxdAPiZQAibaJWElQGAV8H5YRfZe893ruabxXUX2XvPd6ynttQL697XevtteAf2713NN47uK7L3mu9dzTeO7irgmMBMwWJi5qTpQwET7wEP3yASaAt4PTajhNr5DuGYZ3ybUcBvfIZyyWwjo31scg5sYCujfIVyzjG8TariN7xCuWca3CWUbgQsBg4ULIB8TKAET7ZKwEiCwCng/rCJ7r/nu9VzT+K4ie6/57vWU9loB/ftab99tr4D+3eu5pvFdRfZe893ruabxXUVcE5gJGCzM3FQdKGCifeChe2QCTQHvhybUcBvfIVyzjG8TariN7xBO2S0E9O8tjsFNDAX07xCuWca3CTXcxncI1yzj24SyjcCFgMHCBZCPCZSAiXZJWAkQWAW8H1aRvdd893quaXxXkb3XfPd6SnutgP59rbfvtldA/+71XNP4riJ7r/nu9VzT+K4irgnMBAwWZm6qDhQw0T7w0D0ygaaA90MTariN7xCuWca3CTXcxncIp+wWAvr3FsfgJoYC+ncI1yzj24QabuM7hGuW8W1C2UbgQsBg4QLIxwRKwES7JKwECKwC3g+ryN5rvns91zS+q8jea757PaW9VkD/vtbbd9sroH/3eq5pfFeRvdd893quaXxXEdcEZgIGCzM3VQcKmGgfeOgemUBTwPuhCTXcxncI1yzj24QabuM7hFN2CwH9e4tjcBNDAf07hGuW8W1CDbfxHcI1y/g2oWwjcCFgsHAB5GMCJWCiXRJWAgRWAe+HVWTvNd+9nmsa31Vk7zXfvZ7SXiugf1/r7bvtFdC/ez3XNL6ryN5rvns91zS+q4hrAjMBg4WZm6oDBUy0Dzx0j0ygKeD90IQabuM7hGuW8W1CDbfxHcIpu4WA/r3FMbiJoYD+HcI1y/g2oYbb+A7hmmV8m1C2EbgQMFi4APIxgRIw0S4JKwECq4D3wyqy95rvXs81je8qsvea715Paa8V0L+v9fbd9gro372eaxrfVWTvNd+9nmsa31XENYGZgMHCzE3VgQIm2gceukcm0BTwfmhCDbfxHcI1y/g2oYbb+A7hlN1CQP/e4hjcxFBA/w7hmmV8m1DDbXyHcM0yvk0o2whcCBgsXAD5mEAJmGiXhJUAgVXA+2EV2XvNd6/nmsZ3Fdl7zXevp7TXCujf13r7bnsF9O9ezzWN7yqy95rvXs81je8q4prATMBgYeam6kABE+0DD90jE2gKeD80oYbb+A7hmmV8m1DDbXyHcMpuIaB/b3EMbmIooH+HcM0yvk2o4Ta+Q7hmGd8mlG0ELgQMFpWGbcAAAEAASURBVC6AfEygBEy0S8JKgMAq4P2wiuy95rvXc03ju4rsvea711PaawX072u9fbe9Avp3r+eaxncV2XvNd6/nmsZ3FXFNYCZgsDBzU3WggIn2gYfukQk0BbwfmlDDbXyHcM0yvk2o4Ta+QzhltxDQv7c4BjcxFNC/Q7hmGd8m1HAb3yFcs4xvE8o2AhcCBgsXQD4mUAIm2iVhJUBgFfB+WEX2XvPd67mm8V1F9l7z3esp7bUC+ve13r7bXgH9u9dzTeO7iuy95rvXc03ju4q4JjATMFiYuak6UMBE+8BD98gEmgLeD02o4Ta+Q7hmGd8m1HAb3yGcslsI6N9bHIObGAro3yFcs4xvE2q4je8QrlnGtwllG4ELAYOFCyAfEygBE+2SsBIgsAp4P6wie6/57vVc0/iuInuv+e71lPZaAf37Wm/fba+A/t3ruabxXUX2XvPd67mm8V1FXBOYCRgszNxUHShgon3goXtkAk0B74cm1HAb3yFcs4xvE2q4je8QTtktBPTvLY7BTQwF9O8QrlnGtwk13MZ3CNcs49uEso3AhYDBwgWQjwmUgIl2SVgJEFgFvB9Wkb3XfPd6rml8V5G913z3ekp7rYD+fa2377ZXQP/u9VzT+K4ie6/57vVc0/iuIq4JzAQMFmZuqg4UMNE+8NA9MoGmgPdDE2q4je8QrlnGtwk13MZ3CKfsFgL69xbH4CaGAvp3CNcs49uEGm7jO4RrlvFtQtlG4ELAYOECyMcESsBEuySsBAisAt4Pq8jea757Pdc0vqvI3mu+ez2lvVZA/77W23fbK6B/93quaXxXkb3XfPd6rml8VxHXBGYCBgszN1UHCphoH3joHplAU8D7oQk13MZ3CNcs49uEGm7jO4RTdgsB/XuLY3ATQwH9O4RrlvFtQg238R3CNcv4NqFsI3AhYLBwAeRjAiVgol0SVgIEVgHvh1Vk7zXfvZ5rGt9VZO81372e0l4roH9f6+277RXQv3s91zS+q8jea757Pdc0vquIawIzAYOFmZuqAwVMtA88dI9MoCng/dCEGm7jO4RrlvFtQg238R3CKbuFgP69xTG4iaGA/h3CNcv4NqGG2/gO4ZplfJtQthG4EDBYuADyMYESMNEuCSsBAquA98Mqsvea717PNY3vKrL3mu9eT2mvFdC/r/X23fYK6N+9nmsa31Vk7zXfvZ5rGt9VxDWBmYDBwsxN1YECJtoHHrpHJtAU8H5oQg238R3CNcv4NqGG2/gO4ZTdQkD/3uIY3MRQQP8O4ZplfJtQw218h3DNMr5NKNsIXAgYLFwA+ZhACZhol4SVAIFVwPthFdl7zXev55rGdxXZe813r6e01wro39d6+257BfTvXs81je8qsvea717PNY3vKuKawEzAYGHmpupAARPtAw/dIxNoCng/NKGG2/gO4ZplfJtQw218h3DKbiGgf29xDG5iKKB/h3DNMr5NqOE2vkO4ZhnfJpRtBC4EDBYugHxMoARMtEvCSoDAKuD9sIrsvea713NN47uK7L3mu9dT2msF9O9rvX23vQL6d6/nmsZ3Fdl7zXev55rGdxVxTWAmYLAwc1N1oICJ9oGH7pEJNAW8H5pQw218h3DNMr5NqOE2vkM4ZbcQ0L+3OAY3MRTQv0O4ZhnfJtRwG98hXLOMbxPKNgIXAgYLF0A+JlACJtolYSVAYBXwflhF9l7z3eu5pvFdRfZe893rKe21Avr3td6+214B/bvXc03ju4rsvea713NN47uKuCYwEzBYmLmpOlDARPvAQ/fIBJoC3g9NqOE2vkO4ZhnfJtRwG98hnLJbCOjfWxyDmxgK6N8hXLOMbxNquI3vEK5ZxrcJZRuBCwGDhQsgHxMoARPtkrASILAKeD+sInuv+e71XNP4riJ7r/nu9ZT2WgH9+1pv322vgP7d67mm8V1F9l7z3eu5pvFdRVwTmAkYLMzcVB0oYKJ94KF7ZAJNAe+HJtRwG98hXLOMbxNquI3vEE7ZLQT07y2OwU0MBfTvEK5ZxrcJNdzGdwjXLOPbhLKNwIWAwcIFkI8JlICJdklYCRBYBbwfVpG913z3eq5pfFeRvdd893pKe62A/n2tt++2V0D/7vVc0/iuInuv+e71XNP4riKuCcwEDBZmbqoOFDDRPvDQPTKBpoD3QxNquI3vEK5ZxrcJNdzGdwin7BYC+vcWx+AmhgL6dwjXLOPbhBpu4zuEa5bxbULZRuBCwGDhAsjHBErARLskrAQIrALeD6vI3mu+ez3XNL6ryN5rvns9pb1WQP++1tt32yugf/d6rml8V5G913z3eq5pfFcR1wRmAgYLMzdVBwqYaB946B6ZQFPA+6EJNdzGdwjXLOPbhBpu4zuEU3YLAf17i2NwE0MB/TuEa5bxbUINt/EdwjXL+DahbCNwIWCwcAHkYwIlYKJdElYCBFYB74dVZO81372eaxrfVWTvNd+9ntJeK6B/X+vtu+0V0L97Pdc0vqvI3mu+ez3XNL6riGsCMwGDhZmbqgMFTLQPPHSPTKAp4P3QhBpu4zuEa5bxbUINt/Edwim7hYD+vcUxuImhgP4dwjXL+Dahhtv4DuGaZXybULYRuBAwWLgA8jGBEjDRLgkrAQKrgPfDKrL3mu9ezzWN7yqy95rvXk9prxXQv6/19t32CujfvZ5rGt9VZO81372eaxrfVcQ1gZmAwcLMTdWBAibaBx66RybQFPB+aEINt/EdwjXL+Dahhtv4DuGU3UJA/97iGNzEUED/DuGaZXybUMNtfIdwzTK+TSjbCFwIGCxcAPmYQAmYaJeElQCBVcD7YRXZe813r+eaxncV2XvNd6+ntNcK6N/XevtuewX0717PNY3vKrL3mu9ezzWN7yrimsBM4Nv3sq8/UL/NylXdQuDn34/xFrfiJghsE/jVa2mLpffDFkYhBAgQIPAmAn5+2HpQfqNzK+cfYY9+Pvv1n3/s8a+eFvj27Zfv/1nHV86/ns4S8KMA3x9Ndn6F707NH7P4/miy5Ss///L3MX4++3uXN//q18+J3/wTC29+iG6fAAECBAgQIECAAAECCQG/0ZlQlfkqAf2blebLNyuQTde/WV/p5wi89J9YqN94sX77/Tcndjn89Og3Xs7pY0/6gQLf/vv3f5rqp11/Tk7N8X74wD8cHokAAQIEHgr4+WHvv8849een9HM/+vlM/+rf+g87rb/594Hf/Hnw5+D9/hz4+9tr/9w+/IH4RR98/bz02n9iwUsh81J4Ub/4NgReKuB9sed98dJD880IECBAgMB/WMDPD3t+fuCYdXz0x4R71p0v3/TQUP5r/0NV3vfz9ve3175nH3m/8usv/ScWXvlgR30v/8TCUcd9zMP67+Dbc9TeD3scpRAgQIDAewj4+WHrOdV/aLM1VNhPj36j8yf/Gwtbu8N/h/pWzh/C+P5AsvULfLdy/hDG9weSPV/wv7Gwx/FNUr5+TnztP7HwJi5ukwABAgQIECBAgAABAscL1G94Hw8B4C0F9G/22PjyzQpk0/Vv1lf6OQL/OOdRP/hJ/+83s/xGUfaM+fLNCoTSvR9CsH+N9X74q8fuK767Rf+ax/evHruv+O4W/Wse37967L7iu1tU3isF/ujff73y2x7zvfhmj5ov36yAdAJ7BP5rT4yUOwiYuGZPgS/frEA2Xf/yzQpk0/Uv36xANl3/8s0KZNP1b9ZXelZA//LNCmTT9S/frIB0AnsEDBb2ON4i5Y+J9i1u5+Nugm/2SPnyzQpk0/Uv36xANl3/8s0KZNP1L9+sgPR3FvB+yJ4eX75ZgWy6/s36Sj9HwGDhg87aRDt7mHz5ZgWy6fqXb1Ygm65/+WYFsun6l29WIJuuf7O+0rMC+pdvViCbrn/5ZgWkE9gjYLCwx/EWKSau2WPgyzcrkE3Xv3yzAtl0/cs3K5BN1798swLZdP2b9ZWeFdC/fLMC2XT9yzcrIJ3AHgGDhT2Ot0gx0c4eA1++WYFsuv7lmxXIputfvlmBbLr+5ZsVyKbr36yv9KyA/uWbFcim61++WQHpBPYIGCzscbxFiol29hj48s0KZNP1L9+sQDZd//LNCmTT9S/frEA2Xf9mfaVnBfQv36xANl3/8s0KSCewR8BgYY/jLVJMtLPHwJdvViCbrn/5ZgWy6fqXb1Ygm65/+WYFsun6N+srPSugf/lmBbLp+pdvVkA6gT0CBgt7HG+RYqKdPQa+fLMC2XT9yzcrkE3Xv3yzAtl0/cs3K5BN179ZX+lZAf3LNyuQTde/fLMC0gnsETBY2ON4ixQT7ewx8OWbFcim61++WYFsuv7lmxXIputfvlmBbLr+zfpKzwroX75ZgWy6/uWbFZBOYI+AwcIex1ukmGhnj4Ev36xANl3/8s0KZNP1L9+sQDZd//LNCmTT9W/WV3pWQP/yzQpk0/Uv36yAdAJ7BAwW9jjeIsVEO3sMfPlmBbLp+pdvViCbrn/5ZgWy6fqXb1Ygm65/s77SswL6l29WIJuuf/lmBaQT2CNgsLDH8RYpJtrZY+DLNyuQTde/fLMC2XT9yzcrkE3Xv3yzAtl0/Zv1lZ4V0L98swLZdP3LNysgncAeAYOFPY63SDHRzh4DX75ZgWy6/uWbFcim61++WYFsuv7lmxXIpuvfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxvEWKiXb2GPjyzQpk0/Uv36xANl3/8s0KZNP1L9+sQDZd/2Z9pWcF9C/frEA2Xf/yzQpIJ7BHwGBhj+MtUky0s8fAl29WIJuuf/lmBbLp+pdvViCbrn/5ZgWy6fo36ys9K6B/+WYFsun6l29WQDqBPQIGC3scb5Fiop09Br58swLZdP3LNyuQTde/fLMC2XT9yzcrkE3Xv1lf6VkB/cs3K5BN1798swLSCewRMFjY43iLFBPt7DHw5ZsVyKbrX75ZgWy6/uWbFcim61++WYFsuv7N+krPCuhfvlmBbLr+5ZsVkE5gj4DBwh7HW6SYaGePgS/frEA2Xf/yzQpk0/Uv36xANl3/8s0KZNP1b9ZXelZA//LNCmTT9S/frIB0AnsEDBb2ON4ixUQ7ewx8+WYFsun6l29WIJuuf/lmBbLp+pdvViCbrn+zvtKzAvqXb1Ygm65/+WYFpBPYI2CwsMfxFikm2tlj4Ms3K5BN1798swLZdP3LNyuQTde/fLMC2XT9m/WVnhXQv3yzAtl0/cs3KyCdwB4Bg4U9jrdIMdHOHgNfvlmBbLr+5ZsVyKbrX75ZgWy6/uWbFcim69+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HG8RYqJdvYY+PLNCmTT9S/frEA2Xf/yzQpk0/Uv36xANl3/Zn2lZwX0L9+sQDZd//LNCkgnsEfAYGGP4y1STLSzx8CXb1Ygm65/+WYFsun6l29WIJuuf/lmBbLp+jfrKz0roH/5ZgWy6fqXb1ZAOoE9AgYLexxvkWKinT0GvnyzAtl0/cs3K5BN1798swLZdP3LNyuQTde/WV/pWQH9yzcrkE3Xv3yzAtIJ7BEwWNjjeIsUE+3sMfDlmxXIputfvlmBbLr+5ZsVyKbrX75ZgWy6/s36Ss8K6F++WYFsuv7lmxWQTmCPgMHCHsdbpJhoZ4+BL9+sQDZd//LNCmTT9S/frEA2Xf/yzQpk0/Vv1ld6VkD/8s0KZNP1L9+sgHQCewQMFvY43iLFRDt7DHz5ZgWy6fqXb1Ygm65/+WYFsun6l29WIJuuf7O+0rMC+pdvViCbrn/5ZgWkE9gjYLCwx/EWKSba2WPgyzcrkE3Xv3yzAtl0/cs3K5BN1798swLZdP2b9ZWeFdC/fLMC2XT9yzcrIJ3AHgGDhT2Ot0gx0c4eA1++WYFsuv7lmxXIputfvlmBbLr+5ZsVyKbr36yv9KyA/uWbFcim61++WQHpBPYIGCzscbxFiol29hj48s0KZNP1L9+sQDZd//LNCmTT9S/frEA2Xf9mfaVnBfQv36xANl3/8s0KSCewR8BgYY/jLVJMtLPHwJdvViCbrn/5ZgWy6fqXb1Ygm65/+WYFsun6N+srPSugf/lmBbLp+pdvVkA6gT0CBgt7HG+RYqKdPQa+fLMC2XT9yzcrkE3Xv3yzAtl0/cs3K5BN179ZX+lZAf3LNyuQTde/fLMC0gnsETBY2ON4ixQT7ewx8OWbFcim61++WYFsuv7lmxXIputfvlmBbLr+zfpKzwroX75ZgWy6/uWbFZBOYI+AwcIex1ukmGhnj4Ev36xANl3/8s0KZNP1L9+sQDZd//LNCmTT9W/WV3pWQP/yzQpk0/Uv36yAdAJ7BAwW9jjeIsVEO3sMfPlmBbLp+pdvViCbrn/5ZgWy6fqXb1Ygm65/s77SswL6l29WIJuuf/lmBaQT2CNgsLDH8RYpJtrZY+DLNyuQTde/fLMC2XT9yzcrkE3Xv3yzAtl0/Zv1lZ4V0L98swLZdP3LNysgncAeAYOFPY63SDHRzh4DX75ZgWy6/uWbFcim61++WYFsuv7lmxXIpuvfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxvEWKiXb2GPjyzQpk0/Uv36xANl3/8s0KZNP1L9+sQDZd/2Z9pWcF9C/frEA2Xf/yzQpIJ7BHwGBhj+MtUky0s8fAl29WIJuuf/lmBbLp+pdvViCbrn/5ZgWy6fo36ys9K6B/+WYFsun6l29WQDqBPQIGC3scb5Fiop09Br58swLZdP3LNyuQTde/fLMC2XT9yzcrkE3Xv1lf6VkB/cs3K5BN1798swLSCewRMFjY43iLFBPt7DHw5ZsVyKbrX75ZgWy6/uWbFcim61++WYFsuv7N+krPCuhfvlmBbLr+5ZsVkE5gj4DBwh7HW6SYaGePgS/frEA2Xf/yzQpk0/Uv36xANl3/8s0KZNP1b9ZXelZA//LNCmTT9S/frIB0AnsEDBb2ON4ixUQ7ewx8+WYFsun6l29WIJuuf/lmBbLp+pdvViCbrn+zvtKzAvqXb1Ygm65/+WYFpBPYI2CwsMfxFikm2tlj4Ms3K5BN1798swLZdP3LNyuQTde/fLMC2XT9m/WVnhXQv3yzAtl0/cs3KyCdwB4Bg4U9jrdIMdHOHgNfvlmBbLr+5ZsVyKbrX75ZgWy6/uWbFcim69+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HG8RYqJdvYY+PLNCmTT9S/frEA2Xf/yzQpk0/Uv36xANl3/Zn2lZwX0L9+sQDZd//LNCkgnsEfAYGGP4y1STLSzx8CXb1Ygm65/+WYFsun6l29WIJuuf/lmBbLp+jfrKz0roH/5ZgWy6fqXb1ZAOoE9AgYLexxvkWKinT0GvnyzAtl0/cs3K5BN1798swLZdP3LNyuQTde/WV/pWQH9yzcrkE3Xv3yzAtIJ7BEwWNjjeIsUE+3sMfDlmxXIputfvlmBbLr+5ZsVyKbrX75ZgWy6/s36Ss8K6F++WYFsuv7lmxWQTmCPgMHCHsdbpJhoZ4+BL9+sQDZd//LNCmTT9S/frEA2Xf/yzQpk0/Vv1ld6VkD/8s0KZNP1L9+sgHQCewQMFvY43iLFRDt7DHz5ZgWy6fqXb1Ygm65/+WYFsun6l29WIJuuf7O+0rMC+pdvViCbrn/5ZgWkE9gjYLCwx/EWKSba2WPgyzcrkE3Xv3yzAtl0/cs3K5BN1798swLZdP2b9ZWeFdC/fLMC2XT9yzcrIJ3AHgGDhT2Ot0gx0c4eA1++WYFsuv7lmxXIputfvlmBbLr+5ZsVyKbr36yv9KyA/uWbFcim61++WQHpBPYIGCzscbxFiol29hj48s0KZNP1L9+sQDZd//LNCmTT9S/frEA2Xf9mfaVnBfQv36xANl3/8s0KSCewR8BgYY/jLVJMtLPHwJdvViCbrn/5ZgWy6fqXb1Ygm65/+WYFsun6N+srPSugf/lmBbLp+pdvVkA6gT0CBgt7HG+RYqKdPQa+fLMC2XT9yzcrkE3Xv3yzAtl0/cs3K5BN179ZX+lZAf3LNyuQTde/fLMC0gnsETBY2ON4ixQT7ewx8OWbFcim61++WYFsuv7lmxXIputfvlmBbLr+zfpKzwroX75ZgWy6/uWbFZBOYI+AwcIex1ukmGhnj4Ev36xANl3/8s0KZNP1L9+sQDZd//LNCmTT9W/WV3pWQP/yzQpk0/Uv36yAdAJ7BAwW9jjeIsVEO3sMfPlmBbLp+pdvViCbrn/5ZgWy6fqXb1Ygm65/s77SswL6l29WIJuuf/lmBaQT2CNgsLDH8RYpJtrZY+DLNyuQTde/fLMC2XT9yzcrkE3Xv3yzAtl0/Zv1lZ4V0L98swLZdP3LNysgncAeAYOFPY63SDHRzh4DX75ZgWy6/uWbFcim61++WYFsuv7lmxXIpuvfrK/0rID+5ZsVyKbrX75ZAekE9ggYLOxxvEWKiXb2GPjyzQpk0/Uv36xANl3/8s0KZNP1L9+sQDZd/2Z9pWcF9C/frEA2Xf/yzQpIJ7BHwGBhj+MtUky0s8fAl29WIJuuf/lmBbLp+pdvViCbrn/5ZgWy6fo36ys9K6B/+WYFsun6l29WQDqBPQIGC3scb5Fiop09Br58swLZdP3LNyuQTde/fLMC2XT9yzcrkE3Xv1lf6VkB/cs3K5BN1798swLSCewRMFjY43iLFBPt7DHw5ZsVyKbrX75ZgWy6/uWbFcim61++WYFsuv7N+krPCuhfvlmBbLr+5ZsVkE5gj4DBwh7HW6SYaGePgS/frEA2Xf/yzQpk0/Uv36xANl3/8s0KZNP1b9ZXelZA//LNCmTT9S/frIB0AnsEDBb2ON4ixUQ7ewx8+WYFsun6l29WIJuuf/lmBbLp+pdvViCbrn+zvtKzAvqXb1Ygm65/+WYFpBPYI2CwsMfxFikm2tlj4Ms3K5BN1798swLZdP3LNyuQTde/fLMC2XT9m/WVnhXQv3yzAtl0/cs3KyCdwB4Bg4U9jrdIMdHOHgNfvlmBbLr+5ZsVyKbrX75ZgWy6/uWbFcim69+sr/SsgP7lmxXIputfvlkB6QT2CBgs7HG8RYqJdvYY+PLNCmTT9S/frEA2Xf/yzQpk0/Uv36xANl3/Zn2lZwX0L9+sQDZd//LNCkgnsEfAYGGP4y1STLSzx8CXb1Ygm65/+WYFsun6l29WIJuuf/lmBbLp+jfrKz0roH/5ZgWy6fqXb1ZAOoE9AgYLexxvkWKinT0GvnyzAtl0/cs3K5BN1798swLZdP3LNyuQTde/WV/pWQH9yzcrkE3Xv3yzAtIJ7BEwWNjjeIsUE+3sMfDlmxXIputfvlmBbLr+5ZsVyKbrX75ZgWy6/s36Ss8K6F++WYFsuv7lmxWQTmCPwD/2xEj5jwr8/O3/v/1v30dFf7r+/w/8iy0CfLcwPgzh+5Bmywd/8f31ty2Zx4f86X37F9/jYfYD8N1v+udEvn/W2P+v+e43/XMi3z9r7P/Xf/H188N+YIkxgT9+4/tfse9xcjDf7Onz5ZsVkE5gj4B/YmGPoxQCBAgQIECAAAECBAgQIEDgJgJ+4zt7EHz5ZgWy6fo36yv9HIHff9X96w/US351tSau1m8/1Utsx+qfUDjnD6wnJbBL4Nt//7T1PXTqe937d1dHyiFAgACBdxDw88Oefx/36OcHvnt8T/251HPrnx3/+ZI+0kfP9JG/v722f/7TPzt+vS++vfSfWHimOb3cHjfnf7qRfH8CBN5PwPv4t592/H3l/U7eHRMgQIAAgbmAnx+yPz/w3ePLkeOOn/P1kT7SR4//c8hHfz4e/YTxaL+vP/fn7JH3K7/+0n9i4ZUPdtT3+tN/x/dRz+1hCRCYC/jvSJ7b/bnS+/fPGv41AQIECHy6gJ8f9pzwo58ffv3nnnwpvwt8+/bL7/+E7k8/+d9YSLQE34TqH5l8/7BI/Cu+CdWvzJ9/+ftgPz/8vcubf/Vr+Pbaf2Lhzb3cPgECBAgQIECAAAECBAgQIPAGAvWbsG9wq295i3yzx8aXb1ZAOoE9Av/YEyPllgJ+42XrsZhob+X8IYzvDyR7vvDoNwb2pEt5JOD9+0hm9HXvhxFbu4hvm2q0ke+IrV3Et031723088O/52X3LQXqv8bEP7GQOR6+GddK5VsSmZVvxlXqeQIv/d9YOI/XE3+SgN8YyJ4m36yvdALvLOD9kD09vnyzAtl0/Zv1lU7gnQW8H7Knx5dvViCbrn+zvtLPETBYOOesPemTAn9MtJ8MUv63Anz/lsUXCRD4EvB+yLYBX75ZgWy6/s36SifwzgLeD9nT48s3K5BN179ZX+nnCBgsnHPWnvRJARPtJwEvyvleAPmYwMEC3g/Zw+fLNyuQTde/WV/pBN5ZwPshe3p8+WYFsun6N+sr/RwBg4VzztqTPilgov0k4EU53wsgHxM4WMD7IXv4fPlmBbLp+jfrK53AOwt4P2RPjy/frEA2Xf9mfaWfI2CwcM5Ze9InBUy0nwS8KOd7AeRjAgcLeD9kD58v36xANl3/Zn2lE3hnAe+H7Onx5ZsVyKbr36yv9HMEDBbOOWtP+qSAifaTgBflfC+AfEzgYAHvh+zh8+WbFcim69+sr3QC7yzg/ZA9Pb58swLZdP2b9ZV+joDBwjln7UmfFDDRfhLwopzvBZCPCRws4P2QPXy+fLMC2XT9m/WVTuCdBbwfsqfHl29WIJuuf7O+0s8RMFg456w96ZMCJtpPAl6U870A8jGBgwW8H7KHz5dvViCbrn+zvtIJvLOA90P29PjyzQpk0/Vv1lf6OQIGC+ectSd9UsBE+0nAi3K+F0A+JnCwgPdD9vD58s0KZNP1b9ZXOoF3FvB+yJ4eX75ZgWy6/s36Sj9HwGDhnLP2pE8KmGg/CXhRzvcCyMcEDhbwfsgePl++WYFsuv7N+kon8M4C3g/Z0+PLNyuQTde/WV/p5wgYLJxz1p70SQET7ScBL8r5XgD5mMDBAt4P2cPnyzcrkE3Xv1lf6QTeWcD7IXt6fPlmBbLp+jfrK/0cAYOFc87akz4pYKL9JOBFOd8LIB8TOFjA+yF7+Hz5ZgWy6fo36yudwDsLeD9kT48v36xANl3/Zn2lnyNgsHDOWXvSJwVMtJ8EvCjnewHkYwIHC3g/ZA+fL9+sQDZd/2Z9pRN4ZwHvh+zp8eWbFcim69+sr/RzBAwWzjlrT/qkgIn2k4AX5XwvgHxM4GAB74fs4fPlmxXIpuvfrK90Au8s4P2QPT2+fLMC2XT9m/WVfo6AwcI5Z+1JnxQw0X4S8KKc7wWQjwkcLOD9kD18vnyzAtl0/Zv1lU7gnQW8H7Knx5dvViCbrn+zvtLPETBYOOesPemTAibaTwJelPO9APIxgYMFvB+yh8+Xb1Ygm65/s77SCbyzgPdD9vT48s0KZNP1b9ZX+jkCBgvnnLUnfVLARPtJwItyvhdAPiZwsID3Q/bw+fLNCmTT9W/WVzqBdxbwfsieHl++WYFsuv7N+ko/R8Bg4Zyz9qRPCphoPwl4Uc73AsjHBA4W8H7IHj5fvlmBbLr+zfpKJ/DOAt4P2dPjyzcrkE3Xv1lf6ecIGCycc9ae9EkBE+0nAS/K+V4A+ZjAwQLeD9nD58s3K5BN179ZX+kE3lnA+yF7enz5ZgWy6fo36yv9HAGDhXPO2pM+KWCi/STgRTnfCyAfEzhYwPshe/h8+WYFsun6N+srncA7C3g/ZE+PL9+sQDZd/2Z9pZ8jYLBwzll70icFTLSfBLwo53sB5GMCBwt4P2QPny/frEA2Xf9mfaUTeGcB74fs6fHlmxXIpuvfrK/0cwQMFs45a0/6pICJ9pOAF+V8L4B8TOBgAe+H7OHz5ZsVyKbr36yvdALvLOD9kD09vnyzAtl0/Zv1lX6OgMHCOWftSZ8UMNF+EvCinO8FkI8JHCzg/ZA9fL58swLZdP2b9ZVO4J0FvB+yp8eXb1Ygm65/s77SzxEwWDjnrD3pkwIm2k8CXpTzvQDyMYGDBbwfsofPl29WIJuuf7O+0gm8s4D3Q/b0+PLNCmTT9W/WV/o5AgYL55y1J31SwET7ScCLcr4XQD4mcLCA90P28PnyzQpk0/Vv1lc6gXcW8H7Inh5fvlmBbLr+zfpKP0fAYOGcs/akTwqYaD8JeFHO9wLIxwQOFvB+yB4+X75ZgWy6/s36SifwzgLeD9nT48s3K5BN179ZX+nnCBgsnHPWnvRJARPtJwEvyvleAPmYwMEC3g/Zw+fLNyuQTde/WV/pBN5ZwPshe3p8+WYFsun6N+sr/RwBg4VzztqTPilgov0k4EU53wsgHxM4WMD7IXv4fPlmBbLp+jfrK53AOwt4P2RPjy/frEA2Xf9mfaWfI2CwcM5Ze9InBUy0nwS8KOd7AeRjAgcLeD9kD58v36xANl3/Zn2lE3hnAe+H7Onx5ZsVyKbr36yv9HMEDBbOOWtP+qSAifaTgBflfC+AfEzgYAHvh+zh8+WbFcim69+sr3QC7yzg/ZA9Pb58swLZdP2b9ZV+joDBwjln7UmfFDDRfhLwopzvBZCPCRws4P2QPXy+fLMC2XT9m/WVTuCdBbwfsqfHl29WIJuuf7O+0s8RMFg456w96ZMCJtpPAl6U870A8jGBgwW8H7KHz5dvViCbrn+zvtIJvLOA90P29PjyzQpk0/Vv1lf6OQIGC+ectSd9UsBE+0nAi3K+F0A+JnCwgPdD9vD58s0KZNP1b9ZXOoF3FvB+yJ4eX75ZgWy6/s36Sj9HwGDhnLP2pE8KmGg/CXhRzvcCyMcEDhbwfsgePl++WYFsuv7N+kon8M4C3g/Z0+PLNyuQTde/WV/p5wgYLJxz1p70SQET7ScBL8r5XgD5mMDBAt4P2cPnyzcrkE3Xv1lf6QTeWcD7IXt6fPlmBbLp+jfrK/0cAYOFc87akz4pYKL9JOBFOd8LIB8TOFjA+yF7+Hz5ZgWy6fo36yudwDsLeD9kT48v36xANl3/Zn2lnyNgsHDOWXvSJwVMtJ8EvCjnewHkYwIHC3g/ZA+fL9+sQDZd/2Z9pRN4ZwHvh+zp8eWbFcim69+sr/RzBAwWzjlrT/qkgIn2k4AX5XwvgHxM4GAB74fs4fPlmxXIpuvfrK90Au8s4P2QPT2+fLMC2XT9m/WVfo6AwcI5Z+1JnxQw0X4S8KKc7wWQjwkcLOD9kD18vnyzAtl0/Zv1lU7gnQW8H7Knx5dvViCbrn+zvtLPETBYOOesPemTAibaTwJelPO9APIxgYMFvB+yh8+Xb1Ygm65/s77SCbyzgPdD9vT48s0KZNP1b9ZX+jkCBgvnnLUnfVLARPtJwItyvhdAPiZwsID3Q/bw+fLNCmTT9W/WVzqBdxbwfsieHl++WYFsuv7N+ko/R8Bg4Zyz9qRPCphoPwl4Uc73AsjHBA4W8H7IHj5fvlmBbLr+zfpKJ/DOAt4P2dPjyzcrkE3Xv1lf6ecIGCycc9ae9EkBE+0nAS/K+V4A+ZjAwQLeD9nD58s3K5BN179ZX+kE3lnA+yF7enz5ZgWy6fo36yv9HAGDhXPO2pM+KWCi/STgRTnfCyAfEzhYwPshe/h8+WYFsun6N+srncA7C3g/ZE+PL9+sQDZd/2Z9pZ8jYLBwzll70icFTLSfBLwo53sB5GMCBwt4P2QPny/frEA2Xf9mfaUTeGcB74fs6fHlmxXIpuvfrK/0cwQMFs45a0/6pICJ9pOAF+V8L4B8TOBgAe+H7OHz5ZsVyKbr36yvdALvLOD9kD09vnyzAtl0/Zv1lX6OgMHCOWftSZ8UMNF+EvCinO8FkI8JHCzg/ZA9fL58swLZdP2b9ZVO4J0FvB+yp8eXb1Ygm65/s77SzxEwWDjnrD3pkwIm2k8CXpTzvQDyMYGDBbwfsofPl29WIJuuf7O+0gm8s4D3Q/b0+PLNCmTT9W/WV/o5AgYL55y1J31SwET7ScCLcr4XQD4mcLCA90P28PnyzQpk0/Vv1lc6gXcW8H7Inh5fvlmBbLr+zfpKP0fAYOGcs/akTwqYaD8JeFHO9wLIxwQOFvB+yB4+X75ZgWy6/s36SifwzgLeD9nT48s3K5BN179ZX+nnCBgsnHPWnvRJARPtJwEvyvleAPmYwMEC3g/Zw+fLNyuQTde/WV/pBN5ZwPshe3p8+WYFsun6N+sr/RwBg4VzztqTPilgov0k4EU53wsgHxM4WMD7IXv4fPlmBbLp+jfrK53AOwt4P2RPjy/frEA2Xf9mfaWfI2CwcM5Ze9InBUy0nwS8KOd7AeRjAgcLeD9kD58v36xANl3/Zn2lE3hnAe+H7Onx5ZsVyKbr36yv9HMEDBbOOWtP+qSAifaTgBflfC+AfEzgYAHvh+zh8+WbFcim69+sr3QC7yzg/ZA9Pb58swLZdP2b9ZV+joDBwjln7UmfFDDRfhLwopzvBZCPCRws4P2QPXy+fLMC2XT9m/WVTuCdBbwfsqfHl29WIJuuf7O+0s8RMFg456w96ZMCJtpPAl6U870A8jGBgwW8H7KHz5dvViCbrn+zvtIJvLOA90P29PjyzQpk0/Vv1lf6OQIGC+ectSd9UsBE+0nAi3K+F0A+JnCwgPdD9vD58s0KZNP1b9ZXOoF3FvB+yJ4eX75ZgWy6/s36Sj9HwGDhnLP2pE8KmGg/CXhRzvcCyMcEDhbwfsgePl++WYFsuv7N+kon8M4C3g/Z0+PLNyuQTde/WV/p5wgYLJxz1p70SQET7ScBL8r5XgD5mMDBAt4P2cPnyzcrkE3Xv1lf6QTeWcD7IXt6fPlmBbLp+jfrK/0cAYOFc87akz4pYKL9JOBFOd8LIB8TOFjA+yF7+Hz5ZgWy6fo36yudwDsLeD9kT48v36xANl3/Zn2lnyPwP+zdAdZlxXGlUdHyPDT/YdnzUKuBNpZsKAci7lf6342ttbqxK8lD5Y7DpaQAy2Lhzqy9dClgo70EHK7zHYAcEzgs4PvQDp8v31agTdff1lc6gU8W8H1op8eXbyvQputv6yv9joDFwp1Ze+lSwEZ7CThc5zsAOSZwWMD3oR0+X76tQJuuv62vdAKfLOD70E6PL99WoE3X39ZX+h0Bi4U7s/bSpYCN9hJwuM53AHJM4LCA70M7fL58W4E2XX9bX+kEPlnA96GdHl++rUCbrr+tr/Q7AhYLd2btpUsBG+0l4HCd7wDkmMBhAd+Hdvh8+bYCbbr+tr7SCXyygO9DOz2+fFuBNl1/W1/pdwQsFu7M2kuXAjbaS8DhOt8ByDGBwwK+D+3w+fJtBdp0/W19pRP4ZAHfh3Z6fPm2Am26/ra+0u8IWCzcmbWXLgVstJeAw3W+A5BjAocFfB/a4fPl2wq06frb+kon8MkCvg/t9PjybQXadP1tfaXfEbBYuDNrL10K2GgvAYfrfAcgxwQOC/g+tMPny7cVaNP1t/WVTuCTBXwf2unx5dsKtOn62/pKvyNgsXBn1l66FLDRXgIO1/kOQI4JHBbwfWiHz5dvK9Cm62/rK53AJwv4PrTT48u3FWjT9bf1lX5HwGLhzqy9dClgo70EHK7zHYAcEzgs4PvQDp8v31agTdff1lc6gU8W8H1op8eXbyvQputv6yv9joDFwp1Ze+lSwEZ7CThc5zsAOSZwWMD3oR0+X76tQJuuv62vdAKfLOD70E6PL99WoE3X39ZX+h0Bi4U7s/bSpYCN9hJwuM53AHJM4LCA70M7fL58W4E2XX9bX+kEPlnA96GdHl++rUCbrr+tr/Q7AhYLd2btpUsBG+0l4HCd7wDkmMBhAd+Hdvh8+bYCbbr+tr7SCXyygO9DOz2+fFuBNl1/W1/pdwQsFu7M2kuXAjbaS8DhOt8ByDGBwwK+D+3w+fJtBdp0/W19pRP4ZAHfh3Z6fPm2Am26/ra+0u8IWCzcmbWXLgVstJeAw3W+A5BjAocFfB/a4fPl2wq06frb+kon8MkCvg/t9PjybQXadP1tfaXfEbBYuDNrL10K2GgvAYfrfAcgxwQOC/g+tMPny7cVaNP1t/WVTuCTBXwf2unx5dsKtOn62/pKPybw459Q3+VfP7L+/Mfx22cd/vZ/fsz7jf/H+Vlnnjx/+oB9Wg9+69vw04992ju+6s+Xr+/CJ34XvuqfT35e/nzy59PX+XWGv761fz7ybX399YSvv558nb+e+PPx1p+P/vr2fef907fuX/mvH//8/v//+p4/iR//iD//4fz2QYffWCr8/Cfzj9KcH3TmqU+f+P3yfWh7y7f19d3l+4nfXb3V2zf01l/f2h7zbX19h/m+4Tusx3r8iT3217fv3tsfPxX/sn/9tFX44af/76efwU+/9a8PFfjzz2P89U/+r//+6x/zI39Y4Icf/vLTnys/3v+PP5zh4rcF+H7bZnXy57/89vW/+uz/Nsw/+aO+v/8k2B/73X0f/pjb773F9/dK/bHfj+8fc/u9t/j+Xql/8vfz64d/Euyf/N39+uGfBPtjv7vvwx9z+723+P5eqT/2+/H9Y26/9xbf3yv1T/5+fv3wT4J99u/+439XyQ/+OxY+e4Z+9t9R4Kelwk//BT/+1QjwbVylEniDgO9DO0W+fFuBNl1/W1/pBD5ZwPehnR5fvq1Am66/ra/0OwIWC3dm7aVLgZ+WCj/9xce/GgG+jatUAm8Q8H1op8iXbyvQputv6yudwCcL+D600+PLtxVo0/W39ZV+R8Bi4c6svXQpYKO9BByu8x2AHBM4LOD70A6fL99WoE3X39ZXOoFPFvB9aKfHl28r0Kbrb+sr/Y6AxcKdWXvpUsBGewk4XOc7ADkmcFjA96EdPl++rUCbrr+tr3QCnyzg+9BOjy/fVqBN19/WV/odAYuFO7P20qWAjfYScLjOdwByTOCwgO9DO3y+fFuBNl1/W1/pBD5ZwPehnR5fvq1Am66/ra/0OwIWC3dm7aVLARvtJeBwne8A5JjAYQHfh3b4fPm2Am26/ra+0gl8soDvQzs9vnxbgTZdf1tf6XcELBbuzNpLlwI22kvA4TrfAcgxgcMCvg/t8PnybQXadP1tfaUT+GQB34d2enz5tgJtuv62vtLvCFgs3Jm1ly4FbLSXgMN1vgOQYwKHBXwf2uHz5dsKtOn62/pKJ/DJAr4P7fT48m0F2nT9bX2l3xGwWLgzay9dCthoLwGH63wHIMcEDgv4PrTD58u3FWjT9bf1lU7gkwV8H9rp8eXbCrTp+tv6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkCOCRwW8H1oh8+XbyvQputv6yudwCcL+D600+PLtxVo0/W39ZV+R8Bi4c6svXQpYKO9BByu8x2AHBM4LOD70A6fL99WoE3X39ZXOoFPFvB9aKfHl28r0Kbrb+sr/Y6AxcKdWXvpUsBGewk4XOc7ADkmcFjA96EdPl++rUCbrr+tr3QCnyzg+9BOjy/fVqBN19/WV/odAYuFO7P20qWAjfYScLjOdwByTOCwgO9DO3y+fFuBNl1/W1/pBD5ZwPehnR5fvq1Am66/ra/0OwIWC3dm7aVLARvtJeBwne8A5JjAYQHfh3b4fPm2Am26/ra+0gl8soDvQzs9vnxbgTZdf1tf6XcELBbuzNpLlwI22kvA4TrfAcgxgcMCvg/t8PnybQXadP1tfaUT+GQB34d2enz5tgJtuv62vtLvCFgs3Jm1ly4FbLSXgMN1vgOQYwKHBXwf2uHz5dsKtOn62/pKJ/DJAr4P7fT48m0F2nT9bX2l3xGwWLgzay9dCthoLwGH63wHIMcEDgv4PrTD58u3FWjT9bf1lU7gkwV8H9rp8eXbCrTp+tv6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkCOCRwW8H1oh8+XbyvQputv6yudwCcL+D600+PLtxVo0/W39ZV+R8Bi4c6svXQpYKO9BByu8x2AHBM4LOD70A6fL99WoE3X39ZXOoFPFvB9aKfHl28r0Kbrb+sr/Y6AxcKdWXvpUsBGewk4XOc7ADkmcFjA96EdPl++rUCbrr+tr3QCnyzg+9BOjy/fVqBN19/WV/odAYuFO7P20qWAjfYScLjOdwByTOCwgO9DO3y+fFuBNl1/W1/pBD5ZwPehnR5fvq1Am66/ra/0OwIWC3dm7aVLARvtJeBwne8A5JjAYQHfh3b4fPm2Am26/ra+0gl8soDvQzs9vnxbgTZdf1tf6XcELBbuzNpLlwI22kvA4TrfAcgxgcMCvg/t8PnybQXadP1tfaUT+GQB34d2enz5tgJtuv62vtLvCFgs3Jm1ly4FbLSXgMN1vgOQYwKHBXwf2uHz5dsKtOn62/pKJ/DJAr4P7fT48m0F2nT9bX2l3xGwWLgzay9dCthoLwGH63wHIMcEDgv4PrTD58u3FWjT9bf1lU7gkwV8H9rp8eXbCrTp+tv6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkCOCRwW8H1oh8+XbyvQputv6yudwCcL+D600+PLtxVo0/W39ZV+R8Bi4c6svXQpYKO9BByu8x2AHBM4LOD70A6fL99WoE3X39ZXOoFPFvB9aKfHl28r0Kbrb+sr/Y6AxcKdWXvpUsBGewk4XOc7ADkmcFjA96EdPl++rUCbrr+tr3QCnyzg+9BOjy/fVqBN19/WV/odAYuFO7P20qWAjfYScLjOdwByTOCwgO9DO3y+fFuBNl1/W1/pBD5ZwPehnR5fvq1Am66/ra/0OwIWC3dm7aVLARvtJeBwne8A5JjAYQHfh3b4fPm2Am26/ra+0gl8soDvQzs9vnxbgTZdf1tf6XcELBbuzNpLlwI22kvA4TrfAcgxgcMCvg/t8PnybQXadP1tfaUT+GQB34d2enz5tgJtuv62vtLvCFgs3Jm1ly4FbLSXgMN1vgOQYwKHBXwf2uHz5dsKtOn62/pKJ/DJAr4P7fT48m0F2nT9bX2l3xGwWLgzay9dCthoLwGH63wHIMcEDgv4PrTD58u3FWjT9bf1lU7gkwV8H9rp8eXbCrTp+tv6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkCOCRwW8H1oh8+XbyvQputv6yudwCcL+D600+PLtxVo0/W39ZV+R8Bi4c6svXQpYKO9BByu8x2AHBM4LOD70A6fL99WoE3X39ZXOoFPFvB9aKfHl28r0Kbrb+sr/Y6AxcKdWXvpUsBGewk4XOc7ADkmcFjA96EdPl++rUCbrr+tr3QCnyzg+9BOjy/fVqBN19/WV/odAYuFO7P20qWAjfYScLjOdwByTOCwgO9DO3y+fFuBNl1/W1/pBD5ZwPehnR5fvq1Am66/ra/0OwIWC3dm7aVLARvtJeBwne8A5JjAYQHfh3b4fPm2Am26/ra+0gl8soDvQzs9vnxbgTZdf1tf6XcELBbuzNpLlwI22kvA4TrfAcgxgcMCvg/t8PnybQXadP1tfaUT+GQB34d2enz5tgJtuv62vtLvCFgs3Jm1ly4FbLSXgMN1vgOQYwKHBXwf2uHz5dsKtOn62/pKJ/DJAr4P7fT48m0F2nT9bX2l3xGwWLgzay9dCthoLwGH63wHIMcEDgv4PrTD58u3FWjT9bf1lU7gkwV8H9rp8eXbCrTp+tv6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkCOCRwW8H1oh8+XbyvQputv6yudwCcL+D600+PLtxVo0/W39ZV+R8Bi4c6svXQpYKO9BByu8x2AHBM4LOD70A6fL99WoE3X39ZXOoFPFvB9aKfHl28r0Kbrb+sr/Y6AxcKdWXvpUsBGewk4XOc7ADkmcFjA96EdPl++rUCbrr+tr3QCnyzg+9BOjy/fVqBN19/WV/odAYuFO7P20qWAjfYScLjOdwByTOCwgO9DO3y+fFuBNl1/W1/pBD5ZwPehnR5fvq1Am66/ra/0OwIWC3dm7aVLARvtJeBwne8A5JjAYQHfh3b4fPm2Am26/ra+0gl8soDvQzs9vnxbgTZdf1tf6XcELBbuzNpLlwI22kvA4TrfAcgxgcMCvg/t8PnybQXadP1tfaUT+GQB34d2enz5tgJtuv62vtLvCFgs3Jm1ly4FbLSXgMN1vgOQYwKHBXwf2uHz5dsKtOn62/pKJ/DJAr4P7fT48m0F2nT9bX2l3xGwWLgzay9dCthoLwGH63wHIMcEDgv4PrTD58u3FWjT9bf1lU7gkwV8H9rp8eXbCrTp+tv6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkCOCRwW8H1oh8+XbyvQputv6yudwCcL+D600+PLtxVo0/W39ZV+R8Bi4c6svXQpYKO9BByu8x2AHBM4LOD70A6fL99WoE3X39ZXOoFPFvB9aKfHl28r0Kbrb+sr/Y6AxcKdWXvpUsBGewk4XOc7ADkmcFjA96EdPl++rUCbrr+tr3QCnyzg+9BOjy/fVqBN19/WV/odAYuFO7P20qWAjfYScLjOdwByTOCwgO9DO3y+fFuBNl1/W1/pBD5ZwPehnR5fvq1Am66/ra/0OwIWC3dm7aVLARvtJeBwne8A5JjAYQHfh3b4fPm2Am26/ra+0gl8soDvQzs9vnxbgTZdf1tf6XcELBbuzNpLlwI22kvA4TrfAcgxgcMCvg/t8PnybQXadP1tfaUT+GQB34d2enz5tgJtuv62vtLvCFgs3Jm1ly4FbLSXgMN1vgOQYwKHBXwf2uHz5dsKtOn62/pKJ/DJAr4P7fT48m0F2nT9bX2l3xGwWLgzay9dCthoLwGH63wHIMcEDgv4PrTD58u3FWjT9bf1lU7gkwV8H9rp8eXbCrTp+tv6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkCOCRwW8H1oh8+XbyvQputv6yudwCcL+D600+PLtxVo0/W39ZV+R8Bi4c6svXQpYKO9BByu8x2AHBM4LOD70A6fL99WoE3X39ZXOoFPFvB9aKfHl28r0Kbrb+sr/Y6AxcKdWXvpUsBGewk4XOc7ADkmcFjA96EdPl++rUCbrr+tr3QCnyzg+9BOjy/fVqBN19/WV/odAYuFO7P20qWAjfYScLjOdwByTOCwgO9DO3y+fFuBNl1/W1/pBD5ZwPehnR5fvq1Am66/ra/0OwIWC3dm7aVLARvtJeBwne8A5JjAYQHfh3b4fPm2Am26/ra+0gl8soDvQzs9vnxbgTZdf1tf6XcELBbuzNpLlwI22kvA4TrfAcgxgcMCvg/t8PnybQXadP1tfaUT+GQB34d2enz5tgJtuv62vtLvCFgs3Jm1ly4FbLSXgMN1vgOQYwKHBXwf2uHz5dsKtOn62/pKJ/DJAr4P7fT48m0F2nT9bX2l3xGwWLgzay9dCthoLwGH63wHIMcEDgv4PrTD58u3FWjT9bf1lU7gkwV8H9rp8eXbCrTp+tv6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkCOCRwW8H1oh8+XbyvQputv6yudwCcL+D600+PLtxVo0/W39ZV+R8Bi4c6svXQpYKO9BByu8x2AHBM4LOD70A6fL99WoE3X39ZXOoFPFvB9aKfHl28r0Kbrb+sr/Y6AxcKdWXvpUsBGewk4XOc7ADkmcFjA96EdPl++rUCbrr+tr3QCnyzg+9BOjy/fVqBN19/WV/odAYuFO7P20qWAjfYScLjOdwByTOCwgO9DO3y+fFuBNl1/W1/pBD5ZwPehnR5fvq1Am66/ra/0OwIWC3dm7aVLARvtJeBwne8A5JjAYQHfh3b4fPm2Am26/ra+0gl8soDvQzs9vnxbgTZdf1tf6XcELBbuzNpLlwI22kvA4TrfAcgxgcMCvg/t8PnybQXadP1tfaUT+GQB34d2enz5tgJtuv62vtLvCFgs3Jm1ly4FbLSXgMN1vgOQYwKHBXwf2uHz5dsKtOn62/pKJ/DJAr4P7fT48m0F2nT9bX2l3xGwWLgzay9dCthoLwGH63wHIMcEDgv4PrTD58u3FWjT9bf1lU7gkwV8H9rp8eXbCrTp+tv6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkAxhnkYAABAAElEQVSOCRwW8H1oh8+XbyvQputv6yudwCcL+D600+PLtxVo0/W39ZV+R8Bi4c6svXQpYKO9BByu8x2AHBM4LOD70A6fL99WoE3X39ZXOoFPFvB9aKfHl28r0Kbrb+sr/Y7Av915qpcS2An8faP9H7sgt39TgO9vsvhBAgR+FPB9aGvAl28r0Kbrb+sr/TsL/Pkv3/kP+P4/3N9++lspuWaD5pvR/hzMl28rIJ3AXsA/sbA3lHBEwEa7HTTf1lc6gU8W8H1op8eXbyvQputv6yudAAECBAgQIECAwLcEfvjp4MdfkP/tW7/Dkz/+y99R5Lc//GT+X38H5tbjT3/+eYy/GtUP//fn2T72x9n+PN1/du48ef6e74jvQ9sTvq2v7xzf3/Od0xM90ZPn/n3FL38++etb++fVt3x/9W/o/AABAgQIEHiBgP98svl1xb+6Gj/+uvGH7/pPLPhF//O/6P/pF//f+hfvxpsr11/+Tfcn/Nb3oe0r39bX95bvJ3xn9VRP39hTf31re/0tXz9OgAABAgTeKODXy82vK75CV77rP7HwFR78yp/DN/6JhT/99d9f+dx/1aN++OEvP/+TJn/6k/+OhWIGfAvVHzO/9X9T9q/f5R9Uix71hWJ9f7/LMHwfWma+fFuBNl1/I1+/fohg/zP2W79+aP+o0gkQIECAwL9GwH/+8K9xj/+oP/7NNd/3n1iI3yOeQCrwy4Y1/YMcDud7ePieTmAQ8H0YgJbHfJeAw3W+A9DymO8S0HUCBAgQIECAAAECf1Dg3/7gPdcInBP45R9z908sNKPn27hKJfAGAd+Hdop8+bYCbbr+tr7SI4H//Ds3/97f6I9zPJZvWwC+fFuBNl1/+bYCd9K/63/Hwh1WL32jgL8jrp0q39ZXOoFPFvB9aKfHl28r0Kbrb+srvRXQX76tQJuuv3xbgTZdf/m2AnfSLRbuzNpLlwI22kvA4TrfAcgxgcMCvg/t8PnybQXadP1tfaW3AvrLtxVo0/WXbyvQpusv31bgTrrFwp1Ze+lSwEZ7CThc5zsAOSZwWMD3oR0+X76tQJuuv62v9FZAf/m2Am26/vJtBdp0/eXbCtxJt1i4M2svXQrYaC8Bh+t8ByDHBA4L+D60w+fLtxVo0/W39ZXeCugv31agTddfvq1Am66/fFuBO+kWC3dm7aVLARvtJeBwne8A5JjAYQHfh3b4fPm2Am26/ra+0lsB/eXbCrTp+su3FWjT9ZdvK3An3WLhzqy9dClgo70EHK7zHYAcEzgs4PvQDp8v31agTdff1ld6K6C/fFuBNl1/+bYCbbr+8m0F7qRbLNyZtZcuBWy0l4DDdb4DkGMChwV8H9rh8+XbCrTp+tv6Sm8F9JdvK9Cm6y/fVqBN11++rcCddIuFO7P20qWAjfYScLjOdwByTOCwgO9DO3y+fFuBNl1/W1/prYD+8m0F2nT95dsKtOn6y7cVuJNusXBn1l66FLDRXgIO1/kOQI4JHBbwfWiHz5dvK9Cm62/rK70V0F++rUCbrr98W4E2XX/5tgJ30i0W7szaS5cCNtpLwOE63wHIMYHDAr4P7fD58m0F2nT9bX2ltwL6y7cVaNP1l28r0KbrL99W4E66xcKdWXvpUsBGewk4XOc7ADkmcFjA96EdPl++rUCbrr+tr/RWQH/5tgJtuv7ybQXadP3l2wrcSbdYuDNrL10K2GgvAYfrfAcgxwQOC/g+tMPny7cVaNP1t/WV3groL99WoE3XX76tQJuuv3xbgTvpFgt3Zu2lSwEb7SXgcJ3vAOSYwGEB34d2+Hz5tgJtuv62vtJbAf3l2wq06frLtxVo0/WXbytwJ91i4c6svXQpYKO9BByu8x2AHBM4LOD70A6fL99WoE3X39ZXeiugv3xbgTZdf/m2Am26/vJtBe6kWyzcmbWXLgVstJeAw3W+A5BjAocFfB/a4fPl2wq06frb+kpvBfSXbyvQpusv31agTddfvq3AnXSLhTuz9tKlgI32EnC4zncAckzgsIDvQzt8vnxbgTZdf1tf6a2A/vJtBdp0/eXbCrTp+su3FbiTbrFwZ9ZeuhSw0V4CDtf5DkCOCRwW8H1oh8+XbyvQputv6yu9FdBfvq1Am66/fFuBNl1/+bYCd9ItFu7M2kuXAjbaS8DhOt8ByDGBwwK+D+3w+fJtBdp0/W19pbcC+su3FWjT9ZdvK9Cm6y/fVuBOusXCnVl76VLARnsJOFznOwA5JnBYwPehHT5fvq1Am66/ra/0VkB/+bYCbbr+8m0F2nT95dsK3Em3WLgzay9dCthoLwGH63wHIMcEDgv4PrTD58u3FWjT9bf1ld4K6C/fVqBN11++rUCbrr98W4E76RYLd2btpUsBG+0l4HCd7wDkmMBhAd+Hdvh8+bYCbbr+tr7SWwH95dsKtOn6y7cVaNP1l28rcCfdYuHOrL10KWCjvQQcrvMdgBwTOCzg+9AOny/fVqBN19/WV3oroL98W4E2XX/5tgJtuv7ybQXupFss3Jm1ly4FbLSXgMN1vgOQYwKHBXwf2uHz5dsKtOn62/pKbwX0l28r0KbrL99WoE3XX76twJ10i4U7s/bSpYCN9hJwuM53AHJM4LCA70M7fL58W4E2XX9bX+mtgP7ybQXadP3l2wq06frLtxW4k26xcGfWXroUsNFeAg7X+Q5AjgkcFvB9aIfPl28r0Kbrb+srvRXQX76tQJuuv3xbgTZdf/m2AnfSLRbuzNpLlwI22kvA4TrfAcgxgcMCvg/t8PnybQXadP1tfaW3AvrLtxVo0/WXbyvQpusv31bgTrrFwp1Ze+lSwEZ7CThc5zsAOSZwWMD3oR0+X76tQJuuv62v9FZAf/m2Am26/vJtBdp0/eXbCtxJt1i4M2svXQrYaC8Bh+t8ByDHBA4L+D60w+fLtxVo0/W39ZXeCugv31agTddfvq1Am66/fFuBO+kWC3dm7aVLARvtJeBwne8A5JjAYQHfh3b4fPm2Am26/ra+0lsB/eXbCrTp+su3FWjT9ZdvK3An3WLhzqy9dClgo70EHK7zHYAcEzgs4PvQDp8v31agTdff1ld6K6C/fFuBNl1/+bYCbbr+8m0F7qRbLNyZtZcuBWy0l4DDdb4DkGMChwV8H9rh8+XbCrTp+tv6Sm8F9JdvK9Cm6y/fVqBN11++rcCddIuFO7P20qWAjfYScLjOdwByTOCwgO9DO3y+fFuBNl1/W1/prYD+8m0F2nT95dsKtOn6y7cVuJNusXBn1l66FLDRXgIO1/kOQI4JHBbwfWiHz5dvK9Cm62/rK70V0F++rUCbrr98W4E2XX/5tgJ30i0W7szaS5cCNtpLwOE63wHIMYHDAr4P7fD58m0F2nT9bX2ltwL6y7cVaNP1l28r0KbrL99W4E66xcKdWXvpUsBGewk4XOc7ADkmcFjA96EdPl++rUCbrr+tr/RWQH/5tgJtuv7ybQXadP3l2wrcSbdYuDNrL10K2GgvAYfrfAcgxwQOC/g+tMPny7cVaNP1t/WV3groL99WoE3XX76tQJuuv3xbgTvpFgt3Zu2lSwEb7SXgcJ3vAOSYwGEB34d2+Hz5tgJtuv62vtJbAf3l2wq06frLtxVo0/WXbytwJ91i4c6svXQpYKO9BByu8x2AHBM4LOD70A6fL99WoE3X39ZXeiugv3xbgTZdf/m2Am26/vJtBe6kWyzcmbWXLgVstJeAw3W+A5BjAocFfB/a4fPl2wq06frb+kpvBfSXbyvQpusv31agTddfvq3AnXSLhTuz9tKlgI32EnC4zncAckzgsIDvQzt8vnxbgTZdf1tf6a2A/vJtBdp0/eXbCrTp+su3FbiTbrFwZ9ZeuhSw0V4CDtf5DkCOCRwW8H1oh8+XbyvQputv6yu9FdBfvq1Am66/fFuBNl1/+bYCd9ItFu7M2kuXAjbaS8DhOt8ByDGBwwK+D+3w+fJtBdp0/W19pbcC+su3FWjT9ZdvK9Cm6y/fVuBOusXCnVl76VLARnsJOFznOwA5JnBYwPehHT5fvq1Am66/ra/0VkB/+bYCbbr+8m0F2nT95dsK3Em3WLgzay9dCthoLwGH63wHIMcEDgv4PrTD58u3FWjT9bf1ld4K6C/fVqBN11++rUCbrr98W4E76RYLd2btpUsBG+0l4HCd7wDkmMBhAd+Hdvh8+bYCbbr+tr7SWwH95dsKtOn6y7cVaNP1l28rcCfdYuHOrL10KWCjvQQcrvMdgBwTOCzg+9AOny/fVqBN19/WV3oroL98W4E2XX/5tgJtuv7ybQXupFss3Jm1ly4FbLSXgMN1vgOQYwKHBXwf2uHz5dsKtOn62/pKbwX0l28r0KbrL99WoE3XX76twJ10i4U7s/bSpYCN9hJwuM53AHJM4LCA70M7fL58W4E2XX9bX+mtgP7ybQXadP3l2wq06frLtxW4k26xcGfWXroUsNFeAg7X+Q5AjgkcFvB9aIfPl28r0Kbrb+srvRXQX76tQJuuv3xbgTZdf/m2AnfSLRbuzNpLlwI22kvA4TrfAcgxgcMCvg/t8PnybQXadP1tfaW3AvrLtxVo0/WXbyvQpusv31bgTrrFwp1Ze+lSwEZ7CThc5zsAOSZwWMD3oR0+X76tQJuuv62v9FZAf/m2Am26/vJtBdp0/eXbCtxJt1i4M2svXQrYaC8Bh+t8ByDHBA4L+D60w+fLtxVo0/W39ZXeCugv31agTddfvq1Am66/fFuBO+kWC3dm7aVLARvtJeBwne8A5JjAYQHfh3b4fPm2Am26/ra+0lsB/eXbCrTp+su3FWjT9ZdvK3An3WLhzqy9dClgo70EHK7zHYAcEzgs4PvQDp8v31agTdff1ld6K6C/fFuBNl1/+bYCbbr+8m0F7qRbLNyZtZcuBWy0l4DDdb4DkGMChwV8H9rh8+XbCrTp+tv6Sm8F9JdvK9Cm6y/fVqBN11++rcCddIuFO7P20qWAjfYScLjOdwByTOCwgO9DO3y+fFuBNl1/W1/prYD+8m0F2nT95dsKtOn6y7cVuJNusXBn1l66FLDRXgIO1/kOQI4JHBbwfWiHz5dvK9Cm62/rK70V0F++rUCbrr98W4E2XX/5tgJ30i0W7szaS5cCNtpLwOE63wHIMYHDAr4P7fD58m0F2nT9bX2ltwL6y7cVaNP1l28r0KbrL99W4E66xcKdWXvpUsBGewk4XOc7ADkmcFjA96EdPl++rUCbrr+tr/RWQH/5tgJtuv7ybQXadP3l2wrcSbdYuDNrL10K2GgvAYfrfAcgxwQOC/g+tMPny7cVaNP1t/WV3groL99WoE3XX76tQJuuv3xbgTvpFgt3Zu2lSwEb7SXgcJ3vAOSYwGEB34d2+Hz5tgJtuv62vtJbAf3l2wq06frLtxVo0/WXbytwJ91i4c6svXQpYKO9BByu8x2AHBM4LOD70A6fL99WoE3X39ZXeiugv3xbgTZdf/m2Am26/vJtBe6kWyzcmbWXLgVstJeAw3W+A5BjAocFfB/a4fPl2wq06frb+kpvBfSXbyvQpusv31agTddfvq3AnXSLhTuz9tKlgI32EnC4zncAckzgsIDvQzt8vnxbgTZdf1tf6a2A/vJtBdp0/eXbCrTp+su3FbiTbrFwZ9ZeuhSw0V4CDtf5DkCOCRwW8H1oh8+XbyvQputv6yu9FdBfvq1Am66/fFuBNl1/+bYCd9ItFu7M2kuXAjbaS8DhOt8ByDGBwwK+D+3w+fJtBdp0/W19pbcC+su3FWjT9ZdvK9Cm6y/fVuBOusXCnVl76VLARnsJOFznOwA5JnBYwPehHT5fvq1Am66/ra/0VkB/+bYCbbr+8m0F2nT95dsK3Em3WLgzay9dCthoLwGH63wHIMcEDgv4PrTD58u3FWjT9bf1ld4K6C/fVqBN11++rUCbrr98W4E76RYLd2btpUsBG+0l4HCd7wDkmMBhAd+Hdvh8+bYCbbr+tr7SWwH95dsKtOn6y7cVaNP1l28rcCfdYuHOrL10KWCjvQQcrvMdgBwTOCzg+9AOny/fVqBN19/WV3oroL98W4E2XX/5tgJtuv7ybQXupFss3Jm1ly4FbLSXgMN1vgOQYwKHBXwf2uHz5dsKtOn62/pKbwX0l28r0KbrL99WoE3XX76twJ10i4U7s/bSpYCN9hJwuM53AHJM4LCA70M7fL58W4E2XX9bX+mtgP7ybQXadP3l2wq06frLtxW4k26xcGfWXroUsNFeAg7X+Q5AjgkcFvB9aIfPl28r0Kbrb+srvRXQX76tQJuuv3xbgTZdf/m2AnfSf/jpqT/+CfW3O09+4Uv//PMYX/gwTyJAIBP4q8/+I7a+v48wCiFAgACBDxHw64dHB+XvmH2U81dhfH9F8swP+PXvM45SCFwS8OuHV077x7/O/uCfWHjlaD2KAAECBAgQIECAAAECBL6ygL9jtp0O39ZXOgECBAgQ+K6LhZ/+joGf/uW3zzqoMQECBP5ZAd/hZ77D/6y7358AAQIECHyygF8/PPPrh390/Mf/8Psff/ynnvjf9958n+/RJ3/D/NwJEPjXCPjr2f6vZz9N7n86/mum+d//qN91sfDLX9T99m8/l+Eph/8+Uv8bAQIEZoGnvj/Xc2ZpvwcBAgQIEHiPwPW/7nv/s/8+ludner7ni+YlBAh8LwHf++Z7/73m97/9cX5emfw4YP/Htv83pa9+5v/G4VefkJ8fga8n4P/G4TMz8f19xlEKAQIECHyGgF8/PDqnn/7OQ/9W/FHS/xbG979xPPe/+PXvc5aSCFwR8OuHV076x7/O+u9YeOVkPYoAAQIECBAgQIAAAQIEvrTAL38H55f+SX7wT47vBw/PT50AAQIEPkLg3z7iZ+kn+b8L/Ofmz9+R8b8zbU/5bgX/9/t8/3ef7SnfreA37vv+fgPm2R/W32c9/2ca3/8p8uz/zvdZz/+Zxvd/ijz7v/N91vN/pvH9nyLP/u98n/Uc0/767+Pv4nf4/QI//PCX//wnmv7j91/ye/5uAb6/m+qf+x3//Jd/7vf3e3+8wHf971j4eK0v/gB/R0Y7IL58W4E2XX/5tgJtuv7ybQXadP3l2wq06frLtxVo0/W39ZXeCugv31ZAOoFnBCwWnnH8Ein+jox2DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwIWC884fokUG+12DHz5tgJtuv7ybQXadP3l2wq06frLtxVo0/WXbyvQputv6yu9FdBfvq2AdALPCFgsPOP4JVJstNsx8OXbCrTp+su3FWjT9ZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH/5tgLSCTwjYLHwjOOXSLHRbsfAl28r0KbrL99WoE3XX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/eXbCkgn8IyAxcIzjl8ixUa7HQNfvq1Am66/fFuBNl1/+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0l28rIJ3AMwL/9kyMlH+pwJ9/+K8//N9+WhX9w//+Xwf+h0cE+D7C+M0Qvt+keeSA7yOM3wzh+02aRw74PsL4zRC+36R55OC/+f71b49kng/5h1/v/jff8zDPA/B93vQfE/+br+/DP9Ks/2d/x/eaUMC/UODv/f2Pf+HP4r1/aL7vna2XfV8B/8TC9/X2RyNAgAABAgQIECBAgAABAgRiAX/HdwwsPhXQ35T3T3xbX+l3BH7+W91//BPqu/ytU79sBP32h//6iP3yMdv81j+hcOdPWC8lQIAAAQIEPlvgh//7p0d/HXj119V+/fvZfx742f+2gO/Ds/8++er3sX73t76/+qu/m/9cq+6t/O/TT9+H7+P8S59/+1cT3+9Hf/x5/PBd/4kFH5m//emX4T/52+9XGX8kAgQIECBAgACBjYBfDz/z6+HNDNwl8FUFfB+e+T5wbB2/9ecP99adL98n/3PEqk++D9+3p9/y/p4//l3/iYXv+bBTf6x/+L8xe+rdHkuAAAECBAgQ+DQB/zfUn5mYX/8+4yjlawn4Pjw6j1/+Q7hHQ4V9+7/T8a//TudBgR9++MvP/4Tjn/7kv2PhQdb/iuL7XxTP/g9//stv5/nr22+7fPiP/vjX2e/7Tyx8uJefPgECBAgQIECAAAECBAgQIPABAr/8Hbkf8FP1UyTwKwH9/RXJoz/A91FOYYcF/u3w29//dH/HwKMzttF+lPNXYXx/RfLoD/B9lPNXYXx/RfLoD/B9lPNXYXx/RfLMD3zr79h6Jl3KtwT8+vdbMn/ox30f/hDbfMn3YTZ64PfwTyw8gCjiXybw9/76JxaKIfAtVGVeFPiu/x0LF4G9+T0CNtrtLPnybQXadP3l2wq06frb+kon8MkCvg+fPD0/d/3VgU8W0N92enxbX+l3BCwW7szaS5cCf99oL4Nc/00Bvr/J8tgP8n2M8jeD+P4my2M/yPcxyt8M4vubLH6QAIEfBXwf1OCTBfT3k6fn566/bQf4tr7S7whYLNyZtZcuBWy0l4DDdb4D0PKY7xJwuM53AFoe810CDtf5DkCOCRwW8H04PPwXPF1/XzDEw0/Q33b4fFtf6XcELBbuzNpLlwI22kvA4TrfAWh5zHcJOFznOwAtj/kuAYfrfAcgxwQOC/g+HB7+C56uvy8Y4uEn6G87fL6tr/Q7AhYLd2btpUsBG+0l4HCd7wC0POa7BByu8x2Alsd8l4DDdb4DkGMChwV8Hw4P/wVP198XDPHwE/S3HT7f1lf6HQGLhTuz9tKlgI32EnC4zncAWh7zXQIO1/kOQMtjvkvA4TrfAcgxgcMCvg+Hh/+Cp+vvC4Z4+An62w6fb+sr/Y6AxcKdWXvpUsBGewk4XOc7AC2P+S4Bh+t8B6DlMd8l4HCd7wDkmMBhAd+Hw8N/wdP19wVDPPwE/W2Hz7f1lX5HwGLhzqy9dClgo70EHK7zHYCWx3yXgMN1vgPQ8pjvEnC4zncAckzgsIDvw+Hhv+Dp+vuCIR5+gv62w+fb+kq/I2CxcGfWXroUsNFeAg7X+Q5Ay2O+S8DhOt8BaHnMdwk4XOc7ADkmcFjA9+Hw8F/wdP19wRAPP0F/2+HzbX2l3xGwWLgzay9dCthoLwGH63wHoOUx3yXgcJ3vALQ85rsEHK7zHYAcEzgs4PtwePgveLr+vmCIh5+gv+3w+ba+0u8IWCzcmbWXLgVstJeAw3W+A9DymO8ScLjOdwBaHvNdAg7X+Q5AjgkcFvB9ODz8Fzxdf18wxMNP0N92+HxbX+l3BCwW7szaS5cCNtpLwOE63wFoecx3CThc5zsALY/5LgGH63wHIMcEDgv4Phwe/guerr8vGOLhJ+hvO3y+ra/0OwIWC3dm7aVLARvtJeBwne8AtDzmuwQcrvMdgJbHfJeAw3W+A5BjAocFfB8OD/8FT9ffFwzx8BP0tx0+39ZX+h0Bi4U7s/bSpYCN9hJwuM53AFoe810CDtf5DkDLY75LwOE63wHIMYHDAr4Ph4f/gqfr7wuGePgJ+tsOn2/rK/2OgMXCnVl76VLARnsJOFznOwAtj/kuAYfrfAeg5THfJeBwne8A5JjAYQHfh8PDf8HT9fcFQzz8BP1th8+39ZV+R8Bi4c6svXQpYKO9BByu8x2Alsd8l4DDdb4D0PKY7xJwuM53AHJM4LCA78Ph4b/g6fr7giEefoL+tsPn2/pKvyNgsXBn1l66FLDRXgIO1/kOQMtjvkvA4TrfAWh5zHcJOFznOwA5JnBYwPfh8PBf8HT9fcEQDz9Bf9vh8219pd8RsFi4M2svXQrYaC8Bh+t8B6DlMd8l4HCd7wC0POa7BByu8x2AHBM4LOD7cHj4L3i6/r5giIefoL/t8Pm2vtLvCFgs3Jm1ly4FbLSXgMN1vgPQ8pjvEnC4zncAWh7zXQIO1/kOQI4JHBbwfTg8/Bc8XX9fMMTDT9Dfdvh8W1/pdwQsFu7M2kuXAjbaS8DhOt8BaHnMdwk4XOc7AC2P+S4Bh+t8ByDHBA4L+D4cHv4Lnq6/Lxji4Sfobzt8vq2v9DsCFgt3Zu2lSwEb7SXgcJ3vALQ85rsEHK7zHYCWx3yXgMN1vgOQYwKHBXwfDg//BU/X3xcM8fAT9LcdPt/WV/odAYuFO7P20qWAjfYScLjOdwBaHvNdAg7X+Q5Ay2O+S8DhOt8ByDGBwwK+D4eH/4Kn6+8Lhnj4CfrbDp9v6yv9joDFwp1Ze+lSwEZ7CThc5zsALY/5LgGH63wHoOUx3yXgcJ3vAOSYwGEB34fDw3/B0/X3BUM8/AT9bYfPt/WVfkfAYuHOrL10KWCjvQQcrvMdgJbHfJeAw3W+A9DymO8ScLjOdwByTOCwgO/D4eG/4On6+4IhHn6C/rbD59v6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkDLY75LwOE63wFoecx3CThc5zsAOSZwWMD34fDwX/B0/X3BEA8/QX/b4fNtfaXfEbBYuDNrL10K2GgvAYfrfAeg5THfJeBwne8AtDzmuwQcrvMdgBwTOCzg+3B4+C94uv6+YIiHn6C/7fD5tr7S7whYLNyZtZcuBWy0l4DDdb4D0PKY7xJwuM53AFoe810CDtf5DkCOCRwW8H04PPwXPF1/XzDEw0/Q33b4fFtf6XcELBbuzNpLlwI22kvA4TrfAWh5zHcJOFznOwAtj/kuAYfrfAcgxwQOC/g+HB7+C56uvy8Y4uEn6G87fL6tr/Q7AhYLd2btpUsBG+0l4HCd7wC0POa7BByu8x2Alsd8l4DDdb4DkGMChwV8Hw4P/wVP198XDPHwE/S3HT7f1lf6HQGLhTuz9tKlgI32EnC4zncAWh7zXQIO1/kOQMtjvkvA4TrfAcgxgcMCvg+Hh/+Cp+vvC4Z4+An62w6fb+sr/Y6AxcKdWXvpUsBGewk4XOc7AC2P+S4Bh+t8B6DlMd8l4HCd7wDkmMBhAd+Hw8N/wdP19wVDPPwE/W2Hz7f1lX5HwGLhzqy9dClgo70EHK7zHYCWx3yXgMN1vgPQ8pjvEnC4zncAckzgsIDvw+Hhv+Dp+vuCIR5+gv62w+fb+kq/I2CxcGfWXroUsNFeAg7X+Q5Ay2O+S8DhOt8BaHnMdwk4XOc7ADkmcFjA9+Hw8F/wdP19wRAPP0F/2+HzbX2l3xGwWLgzay9dCthoLwGH63wHoOUx3yXgcJ3vALQ85rsEHK7zHYAcEzgs4PtwePgveLr+vmCIh5+gv+3w+ba+0u8IWCzcmbWXLgVstJeAw3W+A9DymO8ScLjOdwBaHvNdAg7X+Q5AjgkcFvB9ODz8Fzxdf18wxMNP0N92+HxbX+l3BCwW7szaS5cCNtpLwOE63wFoecx3CThc5zsALY/5LgGH63wHIMcEDgv4Phwe/guerr8vGOLhJ+hvO3y+ra/0OwIWC3dm7aVLARvtJeBwne8AtDzmuwQcrvMdgJbHfJeAw3W+A5BjAocFfB8OD/8FT9ffFwzx8BP0tx0+39ZX+h0Bi4U7s/bSpYCN9hJwuM53AFoe810CDtf5DkDLY75LwOE63wHIMYHDAr4Ph4f/gqfr7wuGePgJ+tsOn2/rK/2OgMXCnVl76VLARnsJOFznOwAtj/kuAYfrfAeg5THfJeBwne8A5JjAYQHfh8PDf8HT9fcFQzz8BP1th8+39ZV+R8Bi4c6svXQpYKO9BByu8x2Alsd8l4DDdb4D0PKY7xJwuM53AHJM4LCA78Ph4b/g6fr7giEefoL+tsPn2/pKvyNgsXBn1l66FLDRXgIO1/kOQMtjvkvA4TrfAWh5zHcJOFznOwA5JnBYwPfh8PBf8HT9fcEQDz9Bf9vh8219pd8RsFi4M2svXQrYaC8Bh+t8B6DlMd8l4HCd7wC0POa7BByu8x2AHBM4LOD7cHj4L3i6/r5giIefoL/t8Pm2vtLvCFgs3Jm1ly4FbLSXgMN1vgPQ8pjvEnC4zncAWh7zXQIO1/kOQI4JHBbwfTg8/Bc8XX9fMMTDT9Dfdvh8W1/pdwQsFu7M2kuXAjbaS8DhOt8BaHnMdwk4XOc7AC2P+S4Bh+t8ByDHBA4L+D4cHv4Lnq6/Lxji4Sfobzt8vq2v9DsCFgt3Zu2lSwEb7SXgcJ3vALQ85rsEHK7zHYCWx3yXgMN1vgOQYwKHBXwfDg//BU/X3xcM8fAT9LcdPt/WV/odAYuFO7P20qWAjfYScLjOdwBaHvNdAg7X+Q5Ay2O+S8DhOt8ByDGBwwK+D4eH/4Kn6+8Lhnj4CfrbDp9v6yv9joDFwp1Ze+lSwEZ7CThc5zsALY/5LgGH63wHoOUx3yXgcJ3vAOSYwGEB34fDw3/B0/X3BUM8/AT9bYfPt/WVfkfAYuHOrL10KWCjvQQcrvMdgJbHfJeAw3W+A9DymO8ScLjOdwByTOCwgO/D4eG/4On6+4IhHn6C/rbD59v6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkDLY75LwOE63wFoecx3CThc5zsAOSZwWMD34fDwX/B0/X3BEA8/QX/b4fNtfaXfEbBYuDNrL10K2GgvAYfrfAeg5THfJeBwne8AtDzmuwQcrvMdgBwTOCzg+3B4+C94uv6+YIiHn6C/7fD5tr7S7whYLNyZtZcuBWy0l4DDdb4D0PKY7xJwuM53AFoe810CDtf5DkCOCRwW8H04PPwXPF1/XzDEw0/Q33b4fFtf6XcELBbuzNpLlwI22kvA4TrfAWh5zHcJOFznOwAtj/kuAYfrfAcgxwQOC/g+HB7+C56uvy8Y4uEn6G87fL6tr/Q7AhYLd2btpUsBG+0l4HCd7wC0POa7BByu8x2Alsd8l4DDdb4DkGMChwV8Hw4P/wVP198XDPHwE/S3HT7f1lf6HQGLhTuz9tKlgI32EnC4zncAWh7zXQIO1/kOQMtjvkvA4TrfAcgxgcMCvg+Hh/+Cp+vvC4Z4+An62w6fb+sr/Y6AxcKdWXvpUsBGewk4XOc7AC2P+S4Bh+t8B6DlMd8l4HCd7wDkmMBhAd+Hw8N/wdP19wVDPPwE/W2Hz7f1lX5HwGLhzqy9dClgo70EHK7zHYCWx3yXgMN1vgPQ8pjvEnC4zncAckzgsIDvw+Hhv+Dp+vuCIR5+gv62w+fb+kq/I2CxcGfWXroUsNFeAg7X+Q5Ay2O+S8DhOt8BaHnMdwk4XOc7ADkmcFjA9+Hw8F/wdP19wRAPP0F/2+HzbX2l3xGwWLgzay9dCthoLwGH63wHoOUx3yXgcJ3vALQ85rsEHK7zHYAcEzgs4PtwePgveLr+vmCIh5+gv+3w+ba+0u8IWCzcmbWXLgVstJeAw3W+A9DymO8ScLjOdwBaHvNdAg7X+Q5AjgkcFvB9ODz8Fzxdf18wxMNP0N92+HxbX+l3BCwW7szaS5cCNtpLwOE63wFoecx3CThc5zsALY/5LgGH63wHIMcEDgv4Phwe/guerr8vGOLhJ+hvO3y+ra/0OwIWC3dm7aVLARvtJeBwne8AtDzmuwQcrvMdgJbHfJeAw3W+A5BjAocFfB8OD/8FT9ffFwzx8BP0tx0+39ZX+h0Bi4U7s/bSpYCN9hJwuM53AFoe810CDtf5DkDLY75LwOE63wHIMYHDAr4Ph4f/gqfr7wuGePgJ+tsOn2/rK/2OgMXCnVl76VLARnsJOFznOwAtj/kuAYfrfAeg5THfJeBwne8A5JjAYQHfh8PDf8HT9fcFQzz8BP1th8+39ZV+R8Bi4c6svXQpYKO9BByu8x2Alsd8l4DDdb4D0PKY7xJwuM53AHJM4LCA78Ph4b/g6fr7giEefoL+tsPn2/pKvyNgsXBn1l66FLDRXgIO1/kOQMtjvkvA4TrfAWh5zHcJOFznOwA5JnBYwPfh8PBf8HT9fcEQDz9Bf9vh8219pd8RsFi4M2svXQrYaC8Bh+t8B6DlMd8l4HCd7wC0POa7BByu8x2AHBM4LOD7cHj4L3i6/r5giIefoL/t8Pm2vtLvCFgs3Jm1ly4FbLSXgMN1vgPQ8pjvEnC4zncAWh7zXQIO1/kOQI4JHBbwfTg8/Bc8XX9fMMTDT9Dfdvh8W1/pdwQsFu7M2kuXAjbaS8DhOt8BaHnMdwk4XOc7AC2P+S4Bh+t8ByDHBA4L+D4cHv4Lnq6/Lxji4Sfobzt8vq2v9DsCFgt3Zu2lSwEb7SXgcJ3vALQ85rsEHK7zHYCWx3yXgMN1vgOQYwKHBXwfDg//BU/X3xcM8fAT9LcdPt/WV/odAYuFO7P20qWAjfYScLjOdwBaHvNdAg7X+Q5Ay2O+S8DhOt8ByDGBwwK+D4eH/4Kn6+8Lhnj4CfrbDp9v6yv9joDFwp1Ze+lSwEZ7CThc5zsALY/5LgGH63wHoOUx3yXgcJ3vAOSYwGEB34fDw3/B0/X3BUM8/AT9bYfPt/WVfkfAYuHOrL10KWCjvQQcrvMdgJbHfJeAw3W+A9DymO8ScLjOdwByTOCwgO/D4eG/4On6+4IhHn6C/rbD59v6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkDLY75LwOE63wFoecx3CThc5zsAOSZwWMD34fDwX/B0/X3BEA8/QX/b4fNtfaXfEbBYuDNrL10K2GgvAYfrfAeg5THfJeBwne8AtDzmuwQcrvMdgBwTOCzg+3B4+C94uv6+YIiHn6C/7fD5tr7S7whYLNyZtZcuBWy0l4DDdb4D0PKY7xJwuM53AFoe810CDtf5DkCOCRwW8H04PPwXPF1/XzDEw0/Q33b4fFtf6ccEfvwT6rv860fWn/84fvusw9/+z495v/H/OD/rzJPnTx8wPdADPfDnge+A78Dv+Q781q/Nfvox/XmmP3yfcdTHf42j/v5r3PX9GXf9fcZRHzn+nl9PflpPfB++b69/6tC/8l8/9vP//+t7/iR+/CP+/Ifz2wcdfmOp8POfzD9Kc37Qmac++X75fvsO+A74DvgO/N7vgF+ftd8Lvq3v7+253++PzUF//5ibvn0NN/39GnPw54M5fMV/X+L78N17+eOn4F/2r5+2Cj/89P/99DP46bf+9aECf/55jL/+yf/133/9Y37kDwv88MNffvpz5cf7//GHM1z8tgDfb9s8ccL3CcVvZ/D9ts0TJ3yfUPx2Bt9v26xO/vyX377+V7/s/m2Yf/JH/fr3nwT7Y7+778Mfcxtv+T6MRE/8Dv5vqD+h+BsZvr+/gfL8D/n+Pm/6j4l8/1Hjwf/ZX98exPz6UT/+dfYH/x0LX39OfoZfROCnpcJPvzj1r0aAb+P6SyrfXySa3/JtXH9J5fuLRPNbvo2rVAJvEPB9eMMU775Bf+/O/g0v1992inxbX+l3BCwW7szaS5cC/o6XJeBwne8AtDzmuwQcrvMdgJbHfJeAw3W+A5BjAocFfB8OD/8FT9ffFwzx8BP0tx0+39ZX+h0Bi4U7s/bSpYCN9hJwuM53AFoe810CDtf5DkDLY75LwOE63wHIMYHDAr4Ph4f/gqfr7wuGePgJ+tsOn2/rK/2OgMXCnVl76VLARnsJOFznOwAtj/kuAYfrfAeg5THfJeBwne8A5JjAYQHfh8PDf8HT9fcFQzz8BP1th8+39ZV+R8Bi4c6svXQpYKO9BByu8x2Alsd8l4DDdb4D0PKY7xJwuM53AHJM4LCA78Ph4b/g6fr7giEefoL+tsPn2/pKvyNgsXBn1l66FLDRXgIO1/kOQMtjvkvA4TrfAWh5zHcJOFznOwA5JnBYwPfh8PBf8HT9fcEQDz9Bf9vh8219pd8RsFi4M2svXQrYaC8Bh+t8B6DlMd8l4HCd7wC0POa7BByu8x2AHBM4LOD7cHj4L3i6/r5giIefoL/t8Pm2vtLvCFgs3Jm1ly4FbLSXgMN1vgPQ8pjvEnC4zncAWh7zXQIO1/kOQI4JHBbwfTg8/Bc8XX9fMMTDT9Dfdvh8W1/pdwQsFu7M2kuXAjbaS8DhOt8BaHnMdwk4XOc7AC2P+S4Bh+t8ByDHBA4L+D4cHv4Lnq6/Lxji4Sfobzt8vq2v9DsCFgt3Zu2lSwEb7SXgcJ3vALQ85rsEHK7zHYCWx3yXgMN1vgOQYwKHBXwfDg//BU/X3xcM8fAT9LcdPt/WV/odAYuFO7P20qWAjfYScLjOdwBaHvNdAg7X+Q5Ay2O+S8DhOt8ByDGBwwK+D4eH/4Kn6+8Lhnj4CfrbDp9v6yv9joDFwp1Ze+lSwEZ7CThc5zsALY/5LgGH63wHoOUx3yXgcJ3vAOSYwGEB34fDw3/B0/X3BUM8/AT9bYfPt/WVfkfAYuHOrL10KWCjvQQcrvMdgJbHfJeAw3W+A9DymO8ScLjOdwByTOCwgO/D4eG/4On6+4IhHn6C/rbD59v6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkDLY75LwOE63wFoecx3CThc5zsAOSZwWMD34fDwX/B0/X3BEA8/QX/b4fNtfaXfEbBYuDNrL10K2GgvAYfrfAeg5THfJeBwne8AtDzmuwQcrvMdgBwTOCzg+3B4+C94uv6+YIiHn6C/7fD5tr7S7whYLNyZtZcuBWy0l4DDdb4D0PKY7xJwuM53AFoe810CDtf5DkCOCRwW8H04PPwXPF1/XzDEw0/Q33b4fFtf6XcELBbuzNpLlwI22kvA4TrfAWh5zHcJOFznOwAtj/kuAYfrfAcgxwQOC/g+HB7+C56uvy8Y4uEn6G87fL6tr/Q7AhYLd2btpUsBG+0l4HCd7wC0POa7BByu8x2Alsd8l4DDdb4DkGMChwV8Hw4P/wVP198XDPHwE/S3HT7f1lf6HQGLhTuz9tKlgI32EnC4zncAWh7zXQIO1/kOQMtjvkvA4TrfAcgxgcMCvg+Hh/+Cp+vvC4Z4+An62w6fb+sr/Y6AxcKdWXvpUsBGp5sf6QAAQABJREFUewk4XOc7AC2P+S4Bh+t8B6DlMd8l4HCd7wDkmMBhAd+Hw8N/wdP19wVDPPwE/W2Hz7f1lX5HwGLhzqy9dClgo70EHK7zHYCWx3yXgMN1vgPQ8pjvEnC4zncAckzgsIDvw+Hhv+Dp+vuCIR5+gv62w+fb+kq/I2CxcGfWXroUsNFeAg7X+Q5Ay2O+S8DhOt8BaHnMdwk4XOc7ADkmcFjA9+Hw8F/wdP19wRAPP0F/2+HzbX2l3xGwWLgzay9dCthoLwGH63wHoOUx3yXgcJ3vALQ85rsEHK7zHYAcEzgs4PtwePgveLr+vmCIh5+gv+3w+ba+0u8IWCzcmbWXLgVstJeAw3W+A9DymO8ScLjOdwBaHvNdAg7X+Q5AjgkcFvB9ODz8Fzxdf18wxMNP0N92+HxbX+l3BCwW7szaS5cCNtpLwOE63wFoecx3CThc5zsALY/5LgGH63wHIMcEDgv4Phwe/guerr8vGOLhJ+hvO3y+ra/0OwIWC3dm7aVLARvtJeBwne8AtDzmuwQcrvMdgJbHfJeAw3W+A5BjAocFfB8OD/8FT9ffFwzx8BP0tx0+39ZX+h0Bi4U7s/bSpYCN9hJwuM53AFoe810CDtf5DkDLY75LwOE63wHIMYHDAr4Ph4f/gqfr7wuGePgJ+tsOn2/rK/2OgMXCnVl76VLARnsJOFznOwAtj/kuAYfrfAeg5THfJeBwne8A5JjAYQHfh8PDf8HT9fcFQzz8BP1th8+39ZV+R8Bi4c6svXQpYKO9BByu8x2Alsd8l4DDdb4D0PKY7xJwuM53AHJM4LCA78Ph4b/g6fr7giEefoL+tsPn2/pKvyNgsXBn1l66FLDRXgIO1/kOQMtjvkvA4TrfAWh5zHcJOFznOwA5JnBYwPfh8PBf8HT9fcEQDz9Bf9vh8219pd8RsFi4M2svXQrYaC8Bh+t8B6DlMd8l4HCd7wC0POa7BByu8x2AHBM4LOD7cHj4L3i6/r5giIefoL/t8Pm2vtLvCFgs3Jm1ly4FbLSXgMN1vgPQ8pjvEnC4zncAWh7zXQIO1/kOQI4JHBbwfTg8/Bc8XX9fMMTDT9Dfdvh8W1/pdwQsFu7M2kuXAjbaS8DhOt8BaHnMdwk4XOc7AC2P+S4Bh+t8ByDHBA4L+D4cHv4Lnq6/Lxji4Sfobzt8vq2v9DsCFgt3Zu2lSwEb7SXgcJ3vALQ85rsEHK7zHYCWx3yXgMN1vgOQYwKHBXwfDg//BU/X3xcM8fAT9LcdPt/WV/odAYuFO7P20qWAjfYScLjOdwBaHvNdAg7X+Q5Ay2O+S8DhOt8ByDGBwwK+D4eH/4Kn6+8Lhnj4CfrbDp9v6yv9joDFwp1Ze+lSwEZ7CThc5zsALY/5LgGH63wHoOUx3yXgcJ3vAOSYwGEB34fDw3/B0/X3BUM8/AT9bYfPt/WVfkfAYuHOrL10KWCjvQQcrvMdgJbHfJeAw3W+A9DymO8ScLjOdwByTOCwgO/D4eG/4On6+4IhHn6C/rbD59v6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkDLY75LwOE63wFoecx3CThc5zsAOSZwWMD34fDwX/B0/X3BEA8/QX/b4fNtfaXfEbBYuDNrL10K2GgvAYfrfAeg5THfJeBwne8AtDzmuwQcrvMdgBwTOCzg+3B4+C94uv6+YIiHn6C/7fD5tr7S7whYLNyZtZcuBWy0l4DDdb4D0PKY7xJwuM53AFoe810CDtf5DkCOCRwW8H04PPwXPF1/XzDEw0/Q33b4fFtf6XcELBbuzNpLlwI22kvA4TrfAWh5zHcJOFznOwAtj/kuAYfrfAcgxwQOC/g+HB7+C56uvy8Y4uEn6G87fL6tr/Q7AhYLd2btpUsBG+0l4HCd7wC0POa7BByu8x2Alsd8l4DDdb4DkGMChwV8Hw4P/wVP198XDPHwE/S3HT7f1lf6HQGLhTuz9tKlgI32EnC4zncAWh7zXQIO1/kOQMtjvkvA4TrfAcgxgcMCvg+Hh/+Cp+vvC4Z4+An62w6fb+sr/Y6AxcKdWXvpUsBGewk4XOc7AC2P+S4Bh+t8B6DlMd8l4HCd7wDkmMBhAd+Hw8N/wdP19wVDPPwE/W2Hz7f1lX5HwGLhzqy9dClgo70EHK7zHYCWx3yXgMN1vgPQ8pjvEnC4zncAckzgsIDvw+Hhv+Dp+vuCIR5+gv62w+fb+kq/I2CxcGfWXroUsNFeAg7X+Q5Ay2O+S8DhOt8BaHnMdwk4XOc7ADkmcFjA9+Hw8F/wdP19wRAPP0F/2+HzbX2l3xGwWLgzay9dCthoLwGH63wHoOUx3yXgcJ3vALQ85rsEHK7zHYAcEzgs4PtwePgveLr+vmCIh5+gv+3w+ba+0u8IWCzcmbWXLgVstJeAw3W+A9DymO8ScLjOdwBaHvNdAg7X+Q5AjgkcFvB9ODz8Fzxdf18wxMNP0N92+HxbX+l3BCwW7szaS5cCNtpLwOE63wFoecx3CThc5zsALY/5LgGH63wHIMcEDgv4Phwe/guerr8vGOLhJ+hvO3y+ra/0OwIWC3dm7aVLARvtJeBwne8AtDzmuwQcrvMdgJbHfJeAw3W+A5BjAocFfB8OD/8FT9ffFwzx8BP0tx0+39ZX+h0Bi4U7s/bSpYCN9hJwuM53AFoe810CDtf5DkDLY75LwOE63wHIMYHDAr4Ph4f/gqfr7wuGePgJ+tsOn2/rK/2OgMXCnVl76VLARnsJOFznOwAtj/kuAYfrfAeg5THfJeBwne8A5JjAYQHfh8PDf8HT9fcFQzz8BP1th8+39ZV+R8Bi4c6svXQpYKO9BByu8x2Alsd8l4DDdb4D0PKY7xJwuM53AHJM4LCA78Ph4b/g6fr7giEefoL+tsPn2/pKvyNgsXBn1l66FLDRXgIO1/kOQMtjvkvA4TrfAWh5zHcJOFznOwA5JnBYwPfh8PBf8HT9fcEQDz9Bf9vh8219pd8RsFi4M2svXQrYaC8Bh+t8B6DlMd8l4HCd7wC0POa7BByu8x2AHBM4LOD7cHj4L3i6/r5giIefoL/t8Pm2vtLvCFgs3Jm1ly4FbLSXgMN1vgPQ8pjvEnC4zncAWh7zXQIO1/kOQI4JHBbwfTg8/Bc8XX9fMMTDT9Dfdvh8W1/pdwQsFu7M2kuXAjbaS8DhOt8BaHnMdwk4XOc7AC2P+S4Bh+t8ByDHBA4L+D4cHv4Lnq6/Lxji4Sfobzt8vq2v9DsCFgt3Zu2lSwEb7SXgcJ3vALQ85rsEHK7zHYCWx3yXgMN1vgOQYwKHBXwfDg//BU/X3xcM8fAT9LcdPt/WV/odAYuFO7P20qWAjfYScLjOdwBaHvNdAg7X+Q5Ay2O+S8DhOt8ByDGBwwK+D4eH/4Kn6+8Lhnj4CfrbDp9v6yv9joDFwp1Ze+lSwEZ7CThc5zsALY/5LgGH63wHoOUx3yXgcJ3vAOSYwGEB34fDw3/B0/X3BUM8/AT9bYfPt/WVfkfAYuHOrL10KWCjvQQcrvMdgJbHfJeAw3W+A9DymO8ScLjOdwByTOCwgO/D4eG/4On6+4IhHn6C/rbD59v6Sr8jYLFwZ9ZeuhSw0V4CDtf5DkDLY75LwOE63wFoecx3CThc5zsAOSZwWMD34fDwX/B0/X3BEA8/QX/b4fNtfaXfEbBYuDNrL10K2GgvAYfrfAeg5THfJeBwne8AtDzmuwQcrvMdgBwTOCzg+3B4+C94uv6+YIiHn6C/7fD5tr7S7whYLNyZtZcuBWy0l4DDdb4D0PKY7xJwuM53AFoe810CDtf5DkCOCRwW8H04PPwXPF1/XzDEw0/Q33b4fFtf6XcELBbuzNpLlwI22kvA4TrfAWh5zHcJOFznOwAtj/kuAYfrfAcgxwQOC/g+HB7+C56uvy8Y4uEn6G87fL6tr/Q7AhYLd2btpUsBG+0l4HCd7wC0POa7BByu8x2Alsd8l4DDdb4DkGMChwV8Hw4P/wVP198XDPHwE/S3HT7f1lf6HQGLhTuz9tKlgI32EnC4zncAWh7zXQIO1/kOQMtjvkvA4TrfAcgxgcMCvg+Hh/+Cp+vvC4Z4+An62w6fb+sr/Y6AxcKdWXvpUsBGewk4XOc7AC2P+S4Bh+t8B6DlMd8l4HCd7wDkmMBhAd+Hw8N/wdP19wVDPPwE/W2Hz7f1lX5HwGLhzqy9dClgo70EHK7zHYCWx3yXgMN1vgPQ8pjvEnC4zncAckzgsIDvw+Hhv+Dp+vuCIR5+gv62w+fb+kq/I2CxcGfWXroUsNFeAg7X+Q5Ay2O+S8DhOt8BaHnMdwk4XOc7ADkmcFjA9+Hw8F/wdP19wRAPP0F/2+HzbX2l3xGwWLgzay9dCthoLwGH63wHoOUx3yXgcJ3vALQ85rsEHK7zHYAcEzgs4PtwePgveLr+vmCIh5+gv+3w+ba+0u8IWCzcmbWXLgVstJeAw3W+A9DymO8ScLjOdwBaHvNdAg7X+Q5AjgkcFvB9ODz8Fzxdf18wxMNP0N92+HxbX+l3BCwW7szaS5cCNtpLwOE63wFoecx3CThc5zsALY/5LgGH63wHIMcEDgv4Phwe/guerr8vGOLhJ+hvO3y+ra/0OwIWC3dm7aVLARvtJeBwne8AtDzmuwQcrvMdgJbHfJeAw3W+A5BjAocFfB8OD/8FT9ffFwzx8BP0tx0+39ZX+h0Bi4U7s/bSpYCN9hJwuM53AFoe810CDtf5DkDLY75LwOE63wHIMYHDAr4Ph4f/gqfr7wuGePgJ+tsOn2/rK/2OwL/deerBl/75Lwcf3T75bz+t4rhmyHwz2p+D+fJtBdp0/eXbCkgnQOC3BP7+d3T+x28d+zECX1rg7/390j9NPzkCvynw9/76/v4m0PIH+S4BXSfwnwL+iQVVIECAAAECBAgQIECAAIFfCfg7On9F4gc+SEB/P2hYfqq/EtDfX5E8+gN8H+UUdljgh5/e/uOfUH/7Hga/bAT99oefzP/0lMOf/vzzGL/HCP0xCBAgQIAAAQIEFgI//N+ff+392K8Dn/r15KflfOvXv3yf/fcZn9aLT/n56q+ePvmfB3zv3uuv/n5yf7/3ny/X/ni+D9/3+7D4tySPXP2x3z98139iwcfnuWXCP36cHmmDEAIECBAgQIAAgVzAr4ef+fXwtwbF9xlfjq2j/ra++tv66m/rq798//E/7/u0Pvg+fN/+fsv7e/74d/0nFr7nw079sfwTC6fG7bEECBAgQIDABwv89bv8g8IfDPQ7f+rf+vXvX//9dwb43X6PwA8//OXnf9L6T3/yf+P793j97t/nW/+dbb4Pv5vw9/yOv/yHc7/n9/X7/BMCvr//BNYf/119f/+43e+5yff3KP2B38df3/4A2ude+fGvs9/3n1j4XCo/cwIECBAgQIAAAQIECNwS+OXvlLz1aq99i4D+vmWSN9+hv+3c+ba+0u8I/Nudp774pf/5d7b4OzLaGfPl2wq06frLtxVo0/WXbyvQputv6yu9Ffh7f/0TC6209ELg7/0t0mUSaAX+3l/f30Kab6Eq86LAd/3vWLgI/D3fbOPaavPl2wq06frLtxVo0/WXbyvQputv6yu9FdDf1ld6K6C/ra/0VkB/+bYC0gk8I2Cx8Izjl0j5+8b1S/x0XveT4NuOlC/fVqBN11++rUCbrr98WwHpnyzg+/DJ0/Nz118d+GQB/W2nx7f1lX5HwGLhRbO20W6HyZdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH9bX+mtgP62vtJbAf3l2wpIJ/CMgMXCM45fIsXGtR0DX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/W19pbcC+tv6Sm8F9JdvKyCdwDMCFgvPOH6JFBvtdgx8+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0t/WV3grob+srvRXQX76tgHQCzwhYLDzj+CVSbLTbMfDl2wq06frLtxVo0/WXbyvQputv6yu9FdDf1ld6K6C/ra/0VkB/+bYC0gk8I2Cx8Izjl0ix0W7HwJdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH9bX+mtgP62vtJbAf3l2wpIJ/CMgMXCM45fIsVGux0DX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/W19pbcC+tv6Sm8F9JdvKyCdwDMCFgvPOH6JFBvtdgx8+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0t/WV3grob+srvRXQX76tgHQCzwhYLDzj+CVSbLTbMfDl2wq06frLtxVo0/WXbyvQputv6yu9FdDf1ld6K6C/ra/0VkB/+bYC0gk8I2Cx8Izjl0ix0W7HwJdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH9bX+mtgP62vtJbAf3l2wpIJ/CMgMXCM45fIsVGux0DX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/W19pbcC+tv6Sm8F9JdvKyCdwDMCFgvPOH6JFBvtdgx8+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0t/WV3grob+srvRXQX76tgHQCzwhYLDzj+CVSbLTbMfDl2wq06frLtxVo0/WXbyvQputv6yu9FdDf1ld6K6C/ra/0VkB/+bYC0gk8I2Cx8Izjl0ix0W7HwJdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH9bX+mtgP62vtJbAf3l2wpIJ/CMgMXCM45fIsVGux0DX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/W19pbcC+tv6Sm8F9JdvKyCdwDMCFgvPOH6JFBvtdgx8+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0t/WV3grob+srvRXQX76tgHQCzwhYLDzj+CVSbLTbMfDl2wq06frLtxVo0/WXbyvQputv6yu9FdDf1ld6K6C/ra/0VkB/+bYC0gk8I2Cx8Izjl0ix0W7HwJdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH9bX+mtgP62vtJbAf3l2wpIJ/CMgMXCM45fIsVGux0DX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/W19pbcC+tv6Sm8F9JdvKyCdwDMCFgvPOH6JFBvtdgx8+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0t/WV3grob+srvRXQX76tgHQCzwhYLDzj+CVSbLTbMfDl2wq06frLtxVo0/WXbyvQputv6yu9FdDf1ld6K6C/ra/0VkB/+bYC0gk8I2Cx8Izjl0ix0W7HwJdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH9bX+mtgP62vtJbAf3l2wpIJ/CMgMXCM45fIsVGux0DX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/W19pbcC+tv6Sm8F9JdvKyCdwDMCFgvPOH6JFBvtdgx8+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0t/WV3grob+srvRXQX76tgHQCzwhYLDzj+CVSbLTbMfDl2wq06frLtxVo0/WXbyvQputv6yu9FdDf1ld6K6C/ra/0VkB/+bYC0gk8I2Cx8Izjl0ix0W7HwJdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH9bX+mtgP62vtJbAf3l2wpIJ/CMgMXCM45fIsVGux0DX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/W19pbcC+tv6Sm8F9JdvKyCdwDMCFgvPOH6JFBvtdgx8+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0t/WV3grob+srvRXQX76tgHQCzwhYLDzj+CVSbLTbMfDl2wq06frLtxVo0/WXbyvQputv6yu9FdDf1ld6K6C/ra/0VkB/+bYC0gk8I2Cx8Izjl0ix0W7HwJdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH9bX+mtgP62vtJbAf3l2wpIJ/CMgMXCM45fIsVGux0DX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/W19pbcC+tv6Sm8F9JdvKyCdwDMCFgvPOH6JFBvtdgx8+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0t/WV3grob+srvRXQX76tgHQCzwhYLDzj+CVSbLTbMfDl2wq06frLtxVo0/WXbyvQputv6yu9FdDf1ld6K6C/ra/0VkB/+bYC0gk8I2Cx8Izjl0ix0W7HwJdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH9bX+mtgP62vtJbAf3l2wpIJ/CMgMXCM45fIsVGux0DX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/W19pbcC+tv6Sm8F9JdvKyCdwDMCFgvPOH6JFBvtdgx8+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0t/WV3grob+srvRXQX76tgHQCzwhYLDzj+CVSbLTbMfDl2wq06frLtxVo0/WXbyvQputv6yu9FdDf1ld6K6C/ra/0VkB/+bYC0gk8I2Cx8Izjl0ix0W7HwJdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH9bX+mtgP62vtJbAf3l2wpIJ/CMgMXCM45fIsVGux0DX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/W19pbcC+tv6Sm8F9JdvKyCdwDMCFgvPOH6JFBvtdgx8+bYCbbr+8m0F2nT95dsKtOn62/pKbwX0t/WV3grob+srvRXQX76tgHQCzwhYLDzj+CVSbLTbMfDl2wq06frLtxVo0/WXbyvQputv6yu9FdDf1ld6K6C/ra/0VkB/+bYC0gk8I2Cx8Izjl0ix0W7HwJdvK9Cm6y/fVqBN11++rUCbrr+tr/RWQH9bX+mtgP62vtJbAf3l2wpIJ/CMgMXCM45fIsVGux0DX76tQJuuv3xbgTZdf/m2Am26/ra+0lsB/W19pbcC+tv6Sm8F9Jfv/2vvDrCsupYjgULrz+PPf1j2PGQ10C5/t6FWGMWJ4vLO1lpt3JXKoO7O5GJIFWwFpBM4I+CwcMbxESku2tsx8OW7Fdim21++W4Ftuv3luxXYptvfra/0rYD93fpK3wrY362v9K2A/eW7FZBO4IyAw8IZx0ekuGhvx8CX71Zgm25/+W4Ftun2l+9WYJtuf7e+0rcC9nfrK30rYH+3vtK3AvaX71ZAOoEzAg4LZxwfkeKivR0DX75bgW26/eW7Fdim21++W4Ftuv3d+krfCtjfra/0rYD93fpK3wrYX75bAekEzgg4LJxxfESKi/Z2DHz5bgW26faX71Zgm25/+W4Ftun2d+srfStgf7e+0rcC9nfrK30rYH/5bgWkEzgj4LBwxvERKS7a2zHw5bsV2KbbX75bgW26/eW7Fdim29+tr/StgP3d+krfCtjfra/0rYD95bsVkE7gjIDDwhnHR6S4aG/HwJfvVmCbbn/5bgW26faX71Zgm25/t77StwL2d+srfStgf7e+0rcC9pfvVkA6gTMCDgtnHB+R4qK9HQNfvluBbbr95bsV2KbbX75bgW26/d36St8K2N+tr/StgP3d+krfCthfvlsB6QTOCDgsnHF8RIqL9nYMfPluBbbp9pfvVmCbbn/5bgW26fZ36yt9K2B/t77StwL2d+srfStgf/luBaQTOCPgsHDG8REpLtrbMfDluxXYpttfvluBbbr95bsV2Kbb362v9K2A/d36St8K2N+tr/StgP3luxWQTuCMgMPCGcdHpLhob8fAl+9WYJtuf/luBbbp9pfvVmCbbn+3vtK3AvZ36yt9K2B/t77StwL2l+9WQDqBMwIOC2ccH5Hior0dA1++W4Ftuv3luxXYpttfvluBbbr93fpK3wrY362v9K2A/d36St8K2F++WwHpBM4IOCyccXxEiov2dgx8+W4Ftun2l+9WYJtuf/luBbbp9nfrK30rYH+3vtK3AvZ36yt9K2B/+W4FpBM4I+CwcMbxESku2tsx8OW7Fdim21++W4Ftuv3luxXYptvfra/0rYD93fpK3wrY362v9K2A/eW7FZBO4IyAw8IZx0ekuGhvx8CX71Zgm25/+W4Ftun2l+9WYJtuf7e+0rcC9nfrK30rYH+3vtK3AvaX71ZAOoEzAg4LZxwfkeKivR0DX75bgW26/eW7Fdim21++W4Ftuv3d+krfCtjfra/0rYD93fpK3wrYX75bAekEzgg4LJxxfESKi/Z2DHz5bgW26faX71Zgm25/+W4Ftun2d+srfStgf7e+0rcC9nfrK30rYH/5bgWkEzgj4LBwxvERKS7a2zHw5bsV2KbbX75bgW26/eW7Fdim29+tr/StgP3d+krfCtjfra/0rYD95bsVkE7gjIDDwhnHR6S4aG/HwJfvVmCbbn/5bgW26faX71Zgm25/t77StwL2d+srfStgf7e+0rcC9pfvVkA6gTMCDgtnHB+R4qK9HQNfvluBbbr95bsV2KbbX75bgW26/d36St8K2N+tr/StgP3d+krfCthfvlsB6QTOCDgsnHF8RIqL9nYMfPluBbbp9pfvVmCbbn/5bgW26fZ36yt9K2B/t77StwL2d+srfStgf/luBaQTOCPgsHDG8REpLtrbMfDluxXYpttfvluBbbr95bsV2Kbb362v9K2A/d36St8K2N+tr/StgP3luxWQTuCMgMPCGcdHpLhob8fAl+9WYJtuf/luBbbp9pfvVmCbbn+3vtK3AvZ36yt9K2B/t77StwL2l+9WQDqBMwIOC2ccH5Hior0dA1++W4Ftuv3luxXYpttfvluBbbr93fpK3wrY362v9K2A/d36St8K2F++WwHpBM4IOCyccXxEiov2dgx8+W4Ftun2l+9WYJtuf/luBbbp9nfrK30rYH+3vtK3AvZ36yt9K2B/+W4FpBM4I+CwcMbxESku2tsx8OW7Fdim21++W4Ftuv3luxXYptvfra/0rYD93fpK3wrY362v9K2A/eW7FZBO4IyAw8IZx0ekuGhvx8CX71Zgm25/+W4Ftun2l+9WYJtuf7e+0rcC9nfrK30rYH+3vtK3AvaX71ZAOoEzAg4LZxwfkeKivR0DX75bgW26/eW7Fdim21++W4Ftuv3d+krfCtjfra/0rYD93fpK3wrYX75bAekEzgg4LJxxfESKi/Z2DHz5bgW26faX71Zgm25/+W4Ftun2d+srfStgf7e+0rcC9nfrK30rYH/5bgWkEzgj4LBwxvERKS7a2zHw5bsV2KbbX75bgW26/eW7Fdim29+tr/StgP3d+krfCtjfra/0rYD95bsVkE7gjMA/zsRIeYKAi/Z2Cnz5bgW26faX71Zgm25/+W4Ftun2d+v7Xfof//zuQz7QCfz19T9F49oh6v4lAt6/v4Tdd3pI4F/7+++HEsX8dwG+/13D/07g7wv4ioW/b/e4Thft7Uj48t0KbNPtL9+twDbd/vLdCmzT7e/WVzoBAgTeE/D+fU/Gx38HAfu7nRLfra/0ewQ+f33ULz+g/vqIR367CPr281fzTxw42AM/DrwHvAe8B7wHvAe8B7wHfv498OmPb7+M+Yhfwvg+CHyYwOf/+PZrc79O/OznhSf/vPDe+9f+2tsn763/e/tj9tP74WOc3/b5w/4PlHe+oy+fx+cP/YoFL5mf/0XT27L49mN/cPLm7X3lfeU94D3gPeA94D3w3PfAO7++8WECv7WAn3f8vPM7/Lzz3g8y+2t/f4f9tafbPfV+2Pr+z/19z/sjP/6hX7HwkQ924/f19hK/8dk/4pn5bpX58t0KbNPtL9+twDbd/vLdCozSfcXCCFbsLxX480P+IIFf+ogf+Z37+W2k/d77989/G32Hd8Z+/vzPb3/SxadP/o6FxQbwXah+yXzv72Ty89sI/NfGfvl59mO/YuHXPu7rf+9vl6vXf9Jf84R8t+58+W4Ftun2l+9WYJtuf/luBaQTIEDg1wj4+e3XuPtezwjY3zOO76XwfU/Gxwn8nMA/fu5f928/WcB/kbGdDl++W4Ftuv3luxXYpttfvluBbbr9Hfn+53/5xnfk+5+xfPluBbbp9nfrK30r8K/99RULC2m+C1WZNwp86N+xcCPwRz6zi+tWmy/frcA23f7y3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/m59pW8F7C/frYB0AmcEHBbOOD4i5V8X10d8Oi/3SfDdjpQv363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7S/frYD031nA+2E7Pb5bX+n3CDgsvNCsXbS3w+TLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+8t3K7BNt79bX+lbAfvLdysgncAZAYeFM46PSHFx3Y6BL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+bn2lbwXsL9+tgHQCZwQcFs44PiLFRXs7Br58twLbdPvLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+7v1lb4VsL98twLSCZwRcFg44/iIFBft7Rj48t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+3v1lf6VsD+8t0KSCdwRsBh4YzjI1JctLdj4Mt3K7BNt798twLbdPvLdyuwTbe/fLcC23T7y3crsE23v1tf6VsB+8t3KyCdwBkBh4Uzjo9IcdHejoEv363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f5ufaVvBewv362AdAJnBBwWzjg+IsVFezsGvny3Att0+8t3K7BNt798twLbdPvLdyuwTbe/fLcC23T7u/WVvhWwv3y3AtIJnBFwWDjj+IgUF+3tGPjy3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7e/WV/pWwP7y3QpIJ3BGwGHhjOMjUly0t2Pgy3crsE23v3y3Att0+8t3K7BNt798twLbdPvLdyuwTbe/W1/pWwH7y3crIJ3AGQGHhTOOj0hx0d6OgS/frcA23f7y3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/m59pW8F7C/frYB0AmcEHBbOOD4ixUV7Owa+fLcC23T7y3crsE23v3y3Att0+8t3K7BNt798twLbdPu79ZW+FbC/fLcC0gmcEXBYOOP4iBQX7e0Y+PLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+8t0KbNPt79ZX+lbA/vLdCkgncEbAYeGM4yNSXLS3Y+DLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+8t3K7BNt79bX+lbAfvLdysgncAZAYeFM46PSHHR3o6BL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+bn2lbwXsL9+tgHQCZwQcFs44PiLFRXs7Br58twLbdPvLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+7v1lb4VsL98twLSCZwRcFg44/iIFBft7Rj48t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+3v1lf6VsD+8t0KSCdwRsBh4YzjI1JctLdj4Mt3K7BNt798twLbdPvLdyuwTbe/fLcC23T7y3crsE23v1tf6VsB+8t3KyCdwBkBh4Uzjo9IcdHejoEv363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f5ufaVvBewv362AdAJnBBwWzjg+IsVFezsGvny3Att0+8t3K7BNt798twLbdPvLdyuwTbe/fLcC23T7u/WVvhWwv3y3AtIJnBFwWDjj+IgUF+3tGPjy3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7e/WV/pWwP7y3QpIJ3BGwGHhjOMjUly0t2Pgy3crsE23v3y3Att0+8t3K7BNt798twLbdPvLdyuwTbe/W1/pWwH7y3crIJ3AGQGHhTOOj0hx0d6OgS/frcA23f7y3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/m59pW8F7C/frYB0AmcEHBbOOD4ixUV7Owa+fLcC23T7y3crsE23v3y3Att0+8t3K7BNt798twLbdPu79ZW+FbC/fLcC0gmcEXBYOOP4iBQX7e0Y+PLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+8t0KbNPt79ZX+lbA/vLdCkgncEbAYeGM4yNSXLS3Y+DLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+8t3K7BNt79bX+lbAfvLdysgncAZAYeFM46PSHHR3o6BL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+bn2lbwXsL9+tgHQCZwQcFs44PiLFRXs7Br58twLbdPvLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+7v1lb4VsL98twLSCZwRcFg44/iIFBft7Rj48t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+3v1lf6VsD+8t0KSCdwRsBh4YzjI1JctLdj4Mt3K7BNt798twLbdPvLdyuwTbe/fLcC23T7y3crsE23v1tf6VsB+8t3KyCdwBkBh4Uzjo9IcdHejoEv363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f5ufaVvBewv362AdAJnBBwWzjg+IsVFezsGvny3Att0+8t3K7BNt798twLbdPvLdyuwTbe/fLcC23T7u/WVvhWwv3y3AtIJnBFwWDjj+IgUF+3tGPjy3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7e/WV/pWwP7y3QpIJ3BGwGHhjOMjUly0t2Pgy3crsE23v3y3Att0+8t3K7BNt798twLbdPvLdyuwTbe/W1/pWwH7y3crIJ3AGQGHhTOOj0hx0d6OgS/frcA23f7y3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/m59pW8F7C/frYB0AmcEHBbOOD4ixUV7Owa+fLcC23T7y3crsE23v3y3Att0+8t3K7BNt798twLbdPu79ZW+FbC/fLcC0gmcEXBYOOP4iBQX7e0Y+PLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+8t0KbNPt79ZX+lbA/vLdCkgncEbAYeGM4yNSXLS3Y+DLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+8t3K7BNt79bX+lbAfvLdysgncAZAYeFM46PSHHR3o6BL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+bn2lbwXsL9+tgHQCZwQcFs44PiLFRXs7Br58twLbdPvLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+7v1lb4VsL98twLSCZwRcFg44/iIFBft7Rj48t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+3v1lf6VsD+8t0KSCdwRsBh4YzjI1JctLdj4Mt3K7BNt798twLbdPvLdyuwTbe/fLcC23T7y3crsE23v1tf6VsB+8t3KyCdwBkBh4Uzjo9IcdHejoEv363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f5ufaVvBewv362AdAJnBBwWzjg+IsVFezsGvny3Att0+8t3K7BNt798twLbdPvLdyuwTbe/fLcC23T7u/WVvhWwv3y3AtIJnBFwWDjj+IgUF+3tGPjy3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7e/WV/pWwP7y3QpIJ3BGwGHhjOMjUly0t2Pgy3crsE23v3y3Att0+8t3K7BNt798twLbdPvLdyuwTbe/W1/pWwH7y3crIJ3AGQGHhTOOj0hx0d6OgS/frcA23f7y3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/m59pW8F7C/frYB0AmcEHBbOOD4ixUV7Owa+fLcC23T7y3crsE23v3y3Att0+8t3K7BNt798twLbdPu79ZW+FbC/fLcC0gmcEXBYOOP4iBQX7e0Y+PLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+8t0KbNPt79ZX+lbA/vLdCkgncEbAYeGM4yNSXLS3Y+DLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+8t3K7BNt79bX+lbAfvLdysgncAZAYeFM46PSHHR3o6BL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+bn2lbwXsL9+tgHQCZwQcFs44PiLFRXs7Br58twLbdPvLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+7v1lb4VsL98twLSCZwRcFg44/iIFBft7Rj48t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+3v1lf6VsD+8t0KSCdwRsBh4YzjI1JctLdj4Mt3K7BNt798twLbdPvLdyuwTbe/fLcC23T7y3crsE23v1tf6VsB+8t3KyCdwBkBh4Uzjo9IcdHejoEv363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f5ufaVvBewv362AdAJnBBwWzjg+IsVFezsGvny3Att0+8t3K7BNt798twLbdPvLdyuwTbe/fLcC23T7u/WVvhWwv3y3AtIJnBFwWDjj+IgUF+3tGPjy3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7e/WV/pWwP7y3QpIJ3BGwGHhjOMjUly0t2Pgy3crsE23v3y3Att0+8t3K7BNt798twLbdPvLdyuwTbe/W1/pWwH7y3crIJ3AGQGHhTOOj0hx0d6OgS/frcA23f7y3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/m59pW8F7C/frYB0AmcEHBbOOD4ixUV7Owa+fLcC23T7y3crsE23v3y3Att0+8t3K7BNt798twLbdPu79ZW+FbC/fLcC0gmcEXBYOOP4iBQX7e0Y+PLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+8t0KbNPt79ZX+lbA/vLdCkgncEbAYeGM4yNSXLS3Y+DLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+8t3K7BNt79bX+lbAfvLdysgncAZAYeFM46PSHHR3o6BL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+bn2lbwXsL9+tgHQCZwQcFs44PiLFRXs7Br58twLbdPvLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+7v1lb4VsL98twLSCZwRcFg44/iIFBft7Rj48t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+3v1lf6VsD+8t0KSCdwRsBh4YzjI1JctLdj4Mt3K7BNt798twLbdPvLdyuwTbe/fLcC23T7y3crsE23v1tf6VsB+8t3KyCdwBkBh4Uzjo9IcdHejoEv363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f5ufaVvBewv362AdAJnBBwWzjg+IsVFezsGvny3Att0+8t3K7BNt798twLbdPvLdyuwTbe/fLcC23T7u/WVvhWwv3y3AtIJnBFwWDjj+IgUF+3tGPjy3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7e/WV/pWwP7y3QpIJ3BGwGHhjOMjUly0t2Pgy3crsE23v3y3Att0+8t3K7BNt798twLbdPvLdyuwTbe/W1/pWwH7y3crIJ3AGQGHhTOOj0hx0d6OgS/frcA23f7y3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/m59pW8F7C/frYB0AmcEHBbOOD4ixUV7Owa+fLcC23T7y3crsE23v3y3Att0+8t3K7BNt798twLbdPu79ZW+FbC/fLcC0gmcEfjHmRgpv1Tgj8//9d3/9fVU9N/+//9V8L8cEeB7hPHdEL7v0hwp8D3C+G4I33dpjhT4HmF8N4TvuzRHCnyPML4bwvddmiMFvkcY3w3h+y7NkcL/5/vnX0cyhRD4CIF/fcXCv3/Ed3fd98H3upF74JGAr1gYwYolQIAAAQIECBAgQIAAAQIECBAg8LMCvmLhZ8V+7t/n+3Ne/m0C7wl8+0/dv/yA+pDT/dtF0LefP729xE586ysU3ltvHydAgAABAgQIECBAgAABAp8+ff6PT0d/HX7r72u89/sPfM/+Ps+t++W5f+898n742Pn96p/bv/x4/fyhX7Fw4jfRvWS+X9JfvUi+fwIECBAgQIAAAQIECBAg8GQBvx/x16cTv5/y3oz5nvHlyPHEj9NftUfeDx+7v+95f+THP/QrFj7ywa76vvydCleN28MSIECAAAECBAgQIECAwE8K+DsWfhLsnX/9vd9/+PPf3mnw4b8j8PnzP799hc2nT/6Ohb/jl3r4JqG/Wf/jnz9u9P79sctv/tEvR7CP/YqF39zLp0+AAAECBAgQIECAAAECBAgQIEBgKvD2X5xPv5OLw/lePHyPflTgH0fThD1LwH8xcHQeLtpHOb8L4/sdydEP8D3K+V0Y3+9Ijn6A71HO78L4fkdy9AN8j3J+F8b3O5KjH+B7lPO7ML7fkZz5wHv/xeyZdCkEPkTg7Y/D8RULG26+G1ep9wl86N+xcB+vJ34lARft7TT58t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f5ufaUT+J0FvB+20+O79ZV+j4DDwj2z9qSlwL8u2mWQ9h8K8P0hy7EP8j1G+cMgvj9kOfZBvscofxjE94csxz7I9xjlD4P4/pDl2Af5HqP8YRDfH7L4IAECXwS8H7ZrwHfrK/0eAYeFe2btSUsBF+0SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAKRM4GIB74ft8PlufaXfI+CwcM+sPWkp4KJdAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4CUCVws4P2wHT7fra/0ewQcFu6ZtSctBVy0S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfAOQMoGLBbwftsPnu/WVfo+Aw8I9s/akpYCLdgkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AUiZwsYD3w3b4fLe+0u8RcFi4Z9aetBRw0S4BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQMoELhbwftgOn+/WV/o9Ag4L98zak5YCLtolYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+AUiZwMUC3g/b4fPd+kq/R8Bh4Z5Ze9JSwEW7BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwApE7hYwPthO3y+W1/p9wg4LNwza09aCrhol4ChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+QYgZQIXC3g/bIfPd+sr/R4Bh4V7Zu1JSwEX7RIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98ApEzgYgHvh+3w+W59pd8j4LBwz6w9aSngol0Chna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgJQJXCzg/bAdPt+tr/R7BBwW7pm1Jy0FXLRLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A5AygYsFvB+2w+e79ZV+j4DDwj2z9qSlgIt2CRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwBSJnCxgPfDdvh8t77S7xFwWLhn1p60FHDRLgFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AygQuFvB+2A6f79ZX+j0CDgv3zNqTlgIu2iVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BSJnAxQLeD9vh8936Sr9HwGHhnll70lLARbsEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43ACkTuFjA+2E7fL5bX+n3CDgs3DNrT1oKuGiXgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BiBlAhcLeD9sh8936yv9HgGHhXtm7UlLARftEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wCkTOBiAe+H7fD5bn2l3yPgsHDPrD1pKeCiXQKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAlAlcLOD9sB0+362v9HsEHBbumbUnLQVctEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDkDKBiwW8H7bD57v1lX6PgMPCPbP2pKWAi3YJGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vAFImcLGA98N2+Hy3vtLvEXBYuGfWnrQUcNEuAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUDKBC4W8H7YDp/v1lf6PQIOC/fM2pOWAi7aJWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgFImcDFAt4P2+Hz3fpKv0fAYeGeWXvSUsBFuwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAKRO4WMD7YTt8vltf6fcIOCzcM2tPWgq4aJeAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGIGUCFwt4P2yHz3frK/0eAYeFe2btSUsBF+0SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAKRM4GIB74ft8PlufaXfI+CwcM+sPWkp4KJdAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4CUCVws4P2wHT7fra/0ewQcFu6ZtSctBVy0S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfAOQMoGLBbwftsPnu/WVfo+Aw8I9s/akpYCLdgkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AUiZwsYD3w3b4fLe+0u8RcFi4Z9aetBRw0S4BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQMoELhbwftgOn+/WV/o9Ag4L98zak5YCLtolYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+AUiZwMUC3g/b4fPd+kq/R8Bh4Z5Ze9JSwEW7BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwApE7hYwPthO3y+W1/p9wg4LNwza09aCrhol4ChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+QYgZQIXC3g/bIfPd+sr/R4Bh4V7Zu1JSwEX7RIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98ApEzgYgHvh+3w+W59pd8j4LBwz6w9aSngol0Chna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgJQJXCzg/bAdPt+tr/R7BBwW7pm1Jy0FXLRLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A5AygYsFvB+2w+e79ZV+j4DDwj2z9qSlgIt2CRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwBSJnCxgPfDdvh8t77S7xFwWLhn1p60FHDRLgFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AygQuFvB+2A6f79ZX+j0CDgv3zNqTlgIu2iVgaOcbgMoy3xIwtPMNQGWZbzmdCE0AADLzSURBVAkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BSJnAxQLeD9vh8936Sr9HwGHhnll70lLARbsEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43ACkTuFjA+2E7fL5bX+n3CDgs3DNrT1oKuGiXgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BiBlAhcLeD9sh8936yv9HgGHhXtm7UlLARftEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wCkTOBiAe+H7fD5bn2l3yPgsHDPrD1pKeCiXQKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAlAlcLOD9sB0+362v9HsEHBbumbUnLQVctEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDkDKBiwW8H7bD57v1lX6PgMPCPbP2pKWAi3YJGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vAFImcLGA98N2+Hy3vtLvEXBYuGfWnrQUcNEuAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUDKBC4W8H7YDp/v1lf6PQIOC/fM2pOWAi7aJWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgFImcDFAt4P2+Hz3fpKv0fAYeGeWXvSUsBFuwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAKRO4WMD7YTt8vltf6fcIOCzcM2tPWgq4aJeAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGIGUCFwt4P2yHz3frK/0eAYeFe2btSUsBF+0SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAKRM4GIB74ft8PlufaXfI+CwcM+sPWkp4KJdAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4CUCVws4P2wHT7fra/0ewQcFu6ZtSctBVy0S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfAOQMoGLBbwftsPnu/WVfo+Aw8I9s/akpYCLdgkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AUiZwsYD3w3b4fLe+0u8RcFi4Z9aetBRw0S4BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQMoELhbwftgOn+/WV/o9Ag4L98zak5YCLtolYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+AUiZwMUC3g/b4fPd+kq/R8Bh4Z5Ze9JSwEW7BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwApE7hYwPthO3y+W1/p9wg4LNwza09aCrhol4ChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+QYgZQIXC3g/bIfPd+sr/R4Bh4V7Zu1JSwEX7RIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98ApEzgYgHvh+3w+W59pd8j4LBwz6w9aSngol0Chna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgJQJXCzg/bAdPt+tr/R7BBwW7pm1Jy0FXLRLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A5AygYsFvB+2w+e79ZV+j4DDwj2z9qSlgIt2CRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwBSJnCxgPfDdvh8t77S7xFwWLhn1p60FHDRLgFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AygQuFvB+2A6f79ZX+j0CDgv3zNqTlgIu2iVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BSJnAxQLeD9vh8936Sr9HwGHhnll70lLARbsEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43ACkTuFjA+2E7fL5bX+n3CDgs3DNrT1oKuGiXgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BiBlAhcLeD9sh8936yv9HgGHhXtm7UlLARftEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wCkTOBiAe+H7fD5bn2l3yPgsHDPrD1pKeCiXQKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAlAlcLOD9sB0+362v9HsEHBbumbUnLQVctEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDkDKBiwW8H7bD57v1lX6ZwJcfUB/yzxfWb9+Pb886/PV/vuT94P9xPuvMk+fXF5g9sAf2wI8D7wHvAe8B7wHvAe8B74Hnvgd+9Gvjrx/z4/bMj1u+ZxztI8dX/HnE++Fj9/rrDv3Kf768x/7fPx/5SXz5Hr99d7496PCDo8K3H8xfpDkfdOZpn7y/vL+9B7wHvAe8B7wHvAe8B7wHvAee/R7w6+PtfPhufb1f+P7O/3eG98OH7++3/6PsF/2Pr1eFz1//x9fv/+u3/vlNBf74NsbvP/k//+37j/nI3xb4/PmfX3+sfOn/97+dofF9Ab7v25yo8D2h+H4G3/dtTlT4nlB8P4Pv+zYnKnxPKL6fwfd9mxMVvicU38/g+75NVfnjnz9u/9Nve/wY5ic/6vcffhLs7/3r3g9/z+1/28X3fyv1k/+e9+9Pgv3e//qXv6vks79j4feeoc/+AwW+HhW+/gU//tkI8N24vqXyfZPYfMt34/qWyvdNYvMt343rWyrfN4nNt3w3rm+pfN8kNt/y3bhKJfAKAt4P2yny3fpKv0fAYeGeWXvSUuDrUeHrTz7+2Qjw3bi+pfJ9k9h8y3fj+pbK901i8y3fjetbKt83ic23fDeub6l83yQ23/LduEol8AoC3g/bKfLd+kq/R8Bh4Z5Ze9JSwEW7BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwApE7hYwPthO3y+W1/p9wg4LNwza09aCrhol4ChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+QYgZQIXC3g/bIfPd+sr/R4Bh4V7Zu1JSwEX7RIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98ApEzgYgHvh+3w+W59pd8j4LBwz6w9aSngol0Chna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgJQJXCzg/bAdPt+tr/R7BBwW7pm1Jy0FXLRLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A5AygYsFvB+2w+e79ZV+j4DDwj2z9qSlgIt2CRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwBSJnCxgPfDdvh8t77S7xFwWLhn1p60FHDRLgFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AygQuFvB+2A6f79ZX+j0CDgv3zNqTlgIu2iVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BSJnAxQLeD9vh8936Sr9HwGHhnll70lLARbsEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43ACkTuFjA+2E7fL5bX+n3CDgs3DNrT1oKuGiXgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BiBlAhcLeD9sh8936yv9HgGHhXtm7UlLARftEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wCkTOBiAe+H7fD5bn2l3yPgsHDPrD1pKeCiXQKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAlAlcLOD9sB0+362v9HsEHBbumbUnLQVctEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDkDKBiwW8H7bD57v1lX6PgMPCPbP2pKWAi3YJGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vAFImcLGA98N2+Hy3vtLvEXBYuGfWnrQUcNEuAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUDKBC4W8H7YDp/v1lf6PQIOC/fM2pOWAi7aJWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgFImcDFAt4P2+Hz3fpKv0fAYeGeWXvSUsBFuwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAKRO4WMD7YTt8vltf6fcIOCzcM2tPWgq4aJeAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGIGUCFwt4P2yHz3frK/0eAYeFe2btSUsBF+0SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAKRM4GIB74ft8PlufaXfI+CwcM+sPWkp4KJdAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4CUCVws4P2wHT7fra/0ewQcFu6ZtSctBVy0S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfAOQMoGLBbwftsPnu/WVfo+Aw8I9s/akpYCLdgkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AUiZwsYD3w3b4fLe+0u8RcFi4Z9aetBRw0S4BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQMoELhbwftgOn+/WV/o9Ag4L98zak5YCLtolYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+AUiZwMUC3g/b4fPd+kq/R8Bh4Z5Ze9JSwEW7BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwApE7hYwPthO3y+W1/p9wg4LNwza09aCrhol4ChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+QYgZQIXC3g/bIfPd+sr/R4Bh4V7Zu1JSwEX7RIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98ApEzgYgHvh+3w+W59pd8j4LBwz6w9aSngol0Chna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgJQJXCzg/bAdPt+tr/R7BBwW7pm1Jy0FXLRLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A5AygYsFvB+2w+e79ZV+j4DDwj2z9qSlgIt2CRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwBSJnCxgPfDdvh8t77S7xFwWLhn1p60FHDRLgFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AygQuFvB+2A6f79ZX+j0CDgv3zNqTlgIu2iVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BSJnAxQLeD9vh8936Sr9HwGHhnll70lLARbsEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43ACkTuFjA+2E7fL5bX+n3CDgs3DNrT1oKuGiXgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BiBlAhcLeD9sh8936yv9HgGHhXtm7UlLARftEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wCkTOBiAe+H7fD5bn2l3yPgsHDPrD1pKeCiXQKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAlAlcLOD9sB0+362v9HsEHBbumbUnLQVctEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDkDKBiwW8H7bD57v1lX6PgMPCPbP2pKWAi3YJGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vAFImcLGA98N2+Hy3vtLvEXBYuGfWnrQUcNEuAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUDKBC4W8H7YDp/v1lf6PQIOC/fM2pOWAi7aJWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgFImcDFAt4P2+Hz3fpKv0fAYeGeWXvSUsBFuwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAKRO4WMD7YTt8vltf6fcIOCzcM2tPWgq4aJeAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGIGUCFwt4P2yHz3frK/0eAYeFe2btSUsBF+0SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAKRM4GIB74ft8PlufaXfI+CwcM+sPWkp4KJdAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4CUCVws4P2wHT7fra/0ewQcFu6ZtSctBVy0S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfAOQMoGLBbwftsPnu/WVfo+Aw8I9s/akpYCLdgkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AUiZwsYD3w3b4fLe+0u8RcFi4Z9aetBRw0S4BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQMoELhbwftgOn+/WV/o9Ag4L98zak5YCLtolYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+AUiZwMUC3g/b4fPd+kq/R8Bh4Z5Ze9JSwEW7BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwApE7hYwPthO3y+W1/p9wg4LNwza09aCrhol4ChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+QYgZQIXC3g/bIfPd+sr/R4Bh4V7Zu1JSwEX7RIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98ApEzgYgHvh+3w+W59pd8j4LBwz6w9aSngol0Chna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgJQJXCzg/bAdPt+tr/R7BBwW7pm1Jy0FXLRLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A5AygYsFvB+2w+e79ZV+j4DDwj2z9qSlgIt2CRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwBSJnCxgPfDdvh8t77S7xFwWLhn1p60FHDRLgFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AygQuFvB+2A6f79ZX+j0CDgv3zNqTlgIu2iVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BSJnAxQLeD9vh8936Sr9HwGHhnll70lLARbsEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43ACkTuFjA+2E7fL5bX+n3CDgs3DNrT1oKuGiXgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BiBlAhcLeD9sh8936yv9HgGHhXtm7UlLARftEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wCkTOBiAe+H7fD5bn2l3yPgsHDPrD1pKeCiXQKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAlAlcLOD9sB0+362v9HsEHBbumbUnLQVctEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDkDKBiwW8H7bD57v1lX6PgMPCPbP2pKWAi3YJGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vAFImcLGA98N2+Hy3vtLvEXBYuGfWnrQUcNEuAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUDKBC4W8H7YDp/v1lf6PQIOC/fM2pOWAi7aJWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgFImcDFAt4P2+Hz3fpKv0fAYeGeWXvSUsBFuwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAKRO4WMD7YTt8vltf6fcIOCzcM2tPWgq4aJeAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGIGUCFwt4P2yHz3frK/0eAYeFe2btSUsBF+0SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAKRM4GIB74ft8PlufaXfI/D566N++QH11z2P/IJP+se3Mb7gg3kkAgQIECBAgAABAgQIECBwQOBPv+1xQPHTJ7//cIRRCIGrBLx/X3LcX77y57OvWHjJ0XooAgQIECBAgAABAgQIECBAgAABAgQIECCwEfjQw8LXP8Ps6z++PeuwWQ2pBAgQIECAAAECBAgQIEDgNQT8PsSZ34d4jW3wFAQIfKSA9++Z9+//dPzIGb73fX3oYeHtzzDz7V/fjiunHN4bro8TIECAAAECBAgQIECAAAEC3/4I6KO/Dj/16/nfLccuESBA4GcFfrf33O/y+f7sHBb//reTyRcwf9jgQvejMv0Zhx8l7fshQIAAAQIECBAgQIAAgd9RwJ/xfWZqfv/hjKMUAjcJeP++5LS/fAWFv2PhJSfroQgQIECAAAECBAgQIECAAAECBAgQIECAwEjAVyyMYH9F7Nc/a8sXn+zk+e5svybz5bsV2KbbX75bgW26/eW7Fdim21++W4Ftuv3luxXYpttfvluBbbr95bsVuCP9y48jX7HwSqN++zPAXumZnvQsfLfT4Mt3K7BNt798twLbdPvLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+8t3K3BP+of+5c33sP6aJ3Vx3brz5bsV2KbbX75bgW26/eW7Fdim21++W4Ftuv3luxXYpttfvluBbbr95bsV2Kbb363vk9IdFp40jfJzcXEtAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+AeiFyg4LLzRMF8HtMPny3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+3v1vdJ6Q4LT5pG+bm4CJaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98A9EJlh4UXGqaL4HaYfPluBbbp9pfvVmCbbn/5bgW26faX71Zgm25/+W4Ftun2l+9WYJtuf/luBbbp9nfr+6R0h4UnTaP8XFwES8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwB6obLDwgsN00VwO0y+fLcC23T7y3crsE23v3y3Att0+8t3K7BNt798twLbdPvLdyuwTbe/fLcC23T7u/V9UrrDwpOmUX4uLoIlYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AL1Q2WHhhYbpIrgdJl++W4Ftuv3luxXYpttfvluBbbr95bsV2KbbX75bgW26/eW7Fdim21++W4Ftuv3d+j4p3WHhSdMoPxcXwRIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAXqjssPBCw3QR3A6TL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/m59n5TusPCkaZSfi4tgCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUAvVHZYeKFhughuh8mX71Zgm25/+W4Ftun2l+9WYJtuf/luBbbp9pfvVmCbbn/5bgW26faX71Zgm25/t75PSndYeNI0ys/FRbAEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoBcqOyy80DBdBLfD5Mt3K7BNt798twLbdPvLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+8t3K7BNt79b3yelOyw8aRrl5+IiWAKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfAPQC5UdFl5omC6C22Hy5bsV2KbbX75bgW26/eW7Fdim21++W4Ftuv3luxXYpttfvluBbbr95bsV2Kbb363vk9IdFp40jfJzcREsAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+AeiFyg4LLzRMF8HtMPny3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+3v1vdJ6Q4LT5pG+bm4CJaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98A9EJlh4UXGqaL4HaYfPluBbbp9pfvVmCbbn/5bgW26faX71Zgm25/+W4Ftun2l+9WYJtuf/luBbbp9nfr+6R0h4UnTaP8XFwES8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwB6obLDwgsN00VwO0y+fLcC23T7y3crsE23v3y3Att0+8t3K7BNt798twLbdPvLdyuwTbe/fLcC23T7u/V9UrrDwpOmUX4uLoIlYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AL1Q2WHhhYbpIrgdJl++W4Ftuv3luxXYpttfvluBbbr95bsV2KbbX75bgW26/eW7Fdim21++W4Ftuv3d+j4p3WHhSdMoPxcXwRIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAXqjssPBCw3QR3A6TL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/m59n5TusPCkaZSfi4tgCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUAvVHZYeKFhughuh8mX71Zgm25/+W4Ftun2l+9WYJtuf/luBbbp9pfvVmCbbn/5bgW26faX71Zgm25/t75PSndYeNI0ys/FRbAEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoBcqOyy80DBdBLfD5Mt3K7BNt798twLbdPvLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+8t3K7BNt79b3yelOyw8aRrl5+IiWAKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfAPQC5UdFl5omC6C22Hy5bsV2KbbX75bgW26/eW7Fdim21++W4Ftuv3luxXYpttfvluBbbr95bsV2Kbb363vk9IdFp40jfJzcREsAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+AeiFyg4LLzRMF8HtMPny3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+3v1vdJ6Q4LT5pG+bm4CJaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98A9EJlh4UXGqaL4HaYfPluBbbp9pfvVmCbbn/5bgW26faX71Zgm25/+W4Ftun2l+9WYJtuf/luBbbp9nfr+6R0h4UnTaP8XFwES8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwB6obLDwgsN00VwO0y+fLcC23T7y3crsE23v3y3Att0+8t3K7BNt798twLbdPvLdyuwTbe/fLcC23T7u/V9UrrDwpOmUX4uLoIlYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AL1Q2WHhhYbpIrgdJl++W4Ftuv3luxXYpttfvluBbbr95bsV2KbbX75bgW26/eW7Fdim21++W4Ftuv3d+j4p3WHhSdMoPxcXwRIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAXqjssPBCw3QR3A6TL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/m59n5TusPCkaZSfi4tgCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUAvVHZYeKFhughuh8mX71Zgm25/+W4Ftun2l+9WYJtuf/luBbbp9pfvVmCbbn/5bgW26faX71Zgm25/t75PSndYeNI0ys/FRbAEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoBcqOyy80DBdBLfD5Mt3K7BNt798twLbdPvLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+8t3K7BNt79b3yelOyw8aRrl5+IiWAKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfAPQC5UdFl5omC6C22Hy5bsV2KbbX75bgW26/eW7Fdim21++W4Ftuv3luxXYpttfvluBbbr95bsV2Kbb363vk9IdFp40jfJzcREsAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+AeiFyg4LLzRMF8HtMPny3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+3v1vdJ6Q4LT5pG+bm4CJaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98A9EJlh4UXGqaL4HaYfPluBbbp9pfvVmCbbn/5bgW26faX71Zgm25/+W4Ftun2l+9WYJtuf/luBbbp9nfr+6R0h4UnTaP8XFwES8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwB6obLDwgsN00VwO0y+fLcC23T7y3crsE23v3y3Att0+8t3K7BNt798twLbdPvLdyuwTbe/fLcC23T7u/V9UrrDwpOmUX4uLoIlYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AL1Q2WHhhYbpIrgdJl++W4Ftuv3luxXYpttfvluBbbr95bsV2KbbX75bgW26/eW7Fdim21++W4Ftuv3d+j4p3WHhSdMoPxcXwRIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAXqjssPBCw3QR3A6TL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/m59n5TusPCkaZSfi4tgCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUAvVHZYeKFhughuh8mX71Zgm25/+W4Ftun2l+9WYJtuf/luBbbp9pfvVmCbbn/5bgW26faX71Zgm25/t75PSndYeNI0ys/FRbAEDO18A1BZ5lsChna+Aags8y0BQzvfAFSW+ZaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoBcqOyy80DBdBLfD5Mt3K7BNt798twLbdPvLdyuwTbe/fLcC23T7y3crsE23v3y3Att0+8t3K7BNt79b3yelOyw8aRrl5+IiWAKGdr4BqCzzLQFDO98AVJb5loChnW8AKst8S8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfAPQC5UdFl5omC6C22Hy5bsV2KbbX75bgW26/eW7Fdim21++W4Ftuv3luxXYpttfvluBbbr95bsV2Kbb363vk9IdFp40jfJzcREsAUM73wBUlvmWgKGdbwAqy3xLwNDONwCVZb4lYGjnG4DKMt8SMLTzDUBlmW8JGNr5BqCyzLcEDO18A1BZ5lsChna+AeiFyg4LLzRMF8HtMPny3Qps0+0v363ANt3+8t0KbNPtL9+twDbd/vLdCmzT7S/frcA23f7y3Qps0+3v1vdJ6Q4LT5pG+bm4CJaAoZ1vACrLfEvA0M43AJVlviVgaOcbgMoy3xIwtPMNQGWZbwkY2vkGoLLMtwQM7XwDUFnmWwKGdr4BqCzzLQFDO98A9EJlh4UXGqaL4HaYfPluBbbp9pfvVmCbbn/5bgW26faX71Zgm25/+W4Ftun2l+9WYJtuf/luBbbp9nfr+6R0h4UnTaP8XFwES8DQzjcAlWW+JWBo5xuAyjLfEjC08w1AZZlvCRja+Qagssy3BAztfANQWeZbAoZ2vgGoLPMtAUM73wBUlvmWgKGdbwB6ofLnr8/yZeB/vdAzeRQCBAgQIECAAAECBAgQIECAAAECBAgQIEBgIPDlK1M++4qFAaxIAgQIECBAgAABAgQIECBAgAABAgQIECDwqgIOC686Wc9FgAABAgQIECBAgAABAgQIECBAgAABAgQGAg4LA1SRBAgQIECAAAECBAgQIECAAAECBAgQIEDgVQUcFl51sp6LAAECBAgQIECAAAECBAgQIECAAAECBAgMBBwWBqgiCRAgQIAAAQIECBAgQIAAAQIECBAgQIDAqwo4LLzqZD0XAQIECBAgQIAAAQIECBAgQIAAAQIECBAYCDgsDFBFEiBAgAABAgQIECBAgAABAgQIECBAgACBVxVwWHjVyXouAgQIECBAgAABAgQIECBAgAABAgQIECAwEHBYGKCKJECAAAECBAgQIECAAAECBAgQIECAAAECryrgsPCqk/VcBAgQIECAAAECBAgQIECAAAECBAgQIEBgIOCwMEAVSYAAAQIECBAgQIAAAQIECBAgQIAAAQIEXlXAYeFVJ+u5CBAgQIAAAQIECBAgQIAAAQIECBAgQIDAQMBhYYAqkgABAgQIECBAgAABAgQIECBAgAABAgQIvKqAw8KrTtZzESBAgAABAgQIECBAgAABAgQIECBAgACBgYDDwgBVJAECBAgQIECAAAECBAgQIECAAAECBAgQeFUBh4VXnaznIkCAAAECBAgQIECAAAECBAgQIECAAAECAwGHhQGqSAIECBAgQIAAAQIECBAgQIAAAQIECBAg8KoCDguvOlnPRYAAAQIECBAgQIAAAQIECBAgQIAAAQIEBgIOCwNUkQQIECBAgAABAgQIECBAgAABAgQIECBA4FUFHBZedbKeiwABAgQIECBAgAABAgQIECBAgAABAgQIDAQcFgaoIgkQIECAAAECBAgQIECAAAECBAgQIECAwKsKOCy86mQ9FwECBAgQIECAAAECBAgQIECAAAECBAgQGAg4LAxQRRIgQIAAAQIECBAgQIAAAQIECBAgQIAAgVcV+L+fxeLZ8iQwpAAAAABJRU5ErkJggg==\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; text-decoration: underline; text-decoration-line: underline; \"\u003earea limit\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e 'n', find the length\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e (i.e. the longer side if sides are unequal) \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eof the prime-sided rectangle, with the largest area less than or equal to 'n'. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIn the figure above the rectangle with the maximum area is the 5x5 square. Therefore for n = 25 the output should be 5. For n = 100, the output should be 19, since 19 x 5 = 95 \u0026lt; 100. No other combination of prime sides will produce an area greater than 95 for area \u0026lt;= 100.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function length = maxPrimeRec(n)\r\n    l \u003e= w; % l is the larger side\r\n    isprime(l) == 1; isprime(w) == 1; % both sides are primes\r\n    l*w \u003c= n; % area should be less than or equal to n\r\n    length = 'l such that l*w is the largest area possible';\r\nend","test_suite":"%%\r\nn = 25;\r\nl_correct = 5;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = 100;\r\nl_correct = 19;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nns = 1000:10000;\r\nls = arrayfun(@(n) maxPrimeRec(n),ns);\r\nys = [sum(ls) ls(7500:7529)];\r\nys_correct = [10870381 2833 2833 2833 2833 773 773 773 4253 181 181 127 127 2837 2837 ... \r\n    2837 2837 2837 2837 2837 4259 1217 1217 1217 4261 4261 4261 4261 4261 4261 4261];\r\nassert(isequal(ys,ys_correct))\r\n%%\r\nn = 1000000;\r\nl_correct = 1321;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = 100000000;\r\nl_correct = 77101;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax);\r\nl_correct = 715827881;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax)*109 - 1000000009;\r\nl_correct = 7574033;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax)*109 + 1000000009;\r\nl_correct = 2156657959;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nn = double(intmax-1)*1111;\r\nl_correct = 9920021;\r\nassert(isequal(maxPrimeRec(n),l_correct))\r\n%%\r\nfiletext = fileread('maxPrimeRec.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2021-09-15T07:53:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-14T21:01:26.000Z","updated_at":"2026-04-22T11:19:13.000Z","published_at":"2021-09-15T07:53:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA prime-sided rectangle is a rectangle having sides represented by prime numbers. The figure below shows all the possible prime-sided rectangles whose areas are less than or equal to 25:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"312\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"390\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003earea limit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e 'n', find the length\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e. the longer side if sides are unequal) \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eof the prime-sided rectangle, with the largest area less than or equal to 'n'. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the figure above the rectangle with the maximum area is the 5x5 square. Therefore for n = 25 the output should be 5. For n = 100, the output should be 19, since 19 x 5 = 95 \u0026lt; 100. No other combination of prime sides will produce an area greater than 95 for area \u0026lt;= 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44779,"title":"Don't be mean.  Be nice!","description":"For this problem, you will be given a range of single digits R, and a separate number K.  You job is to calculate the mean of all K digit numbers that contain only distinct digits from the range R.\r\n\r\nFor example, if R=1:4 and K=2, you should calculate the mean of 12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, and 43, as these are all of the two digit numbers that contain two distinct numbers from the range 1:4.  The numbers 11, 22, 33 and 44 are not included, as they contain multiple copies of the same digit.\r\n\r\nIf 0 is included in R, it should not be a leading digit for any of the numbers, so an R of 0:2 and K=3 would include:\r\n\r\n* 120\r\n* 210\r\n* 201\r\n* 102\r\n\r\nbut not 012 or 021 for the purposes of this calculation.\r\n\r\nYou can assume that R will always have at least K digits, and there will be no repeating digits in R.","description_html":"\u003cp\u003eFor this problem, you will be given a range of single digits R, and a separate number K.  You job is to calculate the mean of all K digit numbers that contain only distinct digits from the range R.\u003c/p\u003e\u003cp\u003eFor example, if R=1:4 and K=2, you should calculate the mean of 12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, and 43, as these are all of the two digit numbers that contain two distinct numbers from the range 1:4.  The numbers 11, 22, 33 and 44 are not included, as they contain multiple copies of the same digit.\u003c/p\u003e\u003cp\u003eIf 0 is included in R, it should not be a leading digit for any of the numbers, so an R of 0:2 and K=3 would include:\u003c/p\u003e\u003cul\u003e\u003cli\u003e120\u003c/li\u003e\u003cli\u003e210\u003c/li\u003e\u003cli\u003e201\u003c/li\u003e\u003cli\u003e102\u003c/li\u003e\u003c/ul\u003e\u003cp\u003ebut not 012 or 021 for the purposes of this calculation.\u003c/p\u003e\u003cp\u003eYou can assume that R will always have at least K digits, and there will be no repeating digits in R.\u003c/p\u003e","function_template":"function y = dont_be_mean(R,k)\r\n  y = k.^R;\r\nend","test_suite":"%%\r\nR=1:4;k=2;y_correct = 27.5;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=0:8;k=3;y_correct = 493.3125;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=[1 2 4 6 8];k=4;y_correct = 4666.2;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=[2 8 6 7 4 5];k=1;y_correct = 5.33333333333333;\r\na=dont_be_mean(R,k)\r\nassert(abs(a-y_correct)\u003c1e-10)\r\n%%\r\nR=0:9;\r\ny=0;\r\nfor k=1:8\r\n    y=y+dont_be_mean(R,k);\r\nend\r\ny_correct=61042519.44444444;\r\nassert(abs(y-y_correct)\u003c1e-3)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":68,"created_at":"2018-11-07T18:32:08.000Z","updated_at":"2026-04-28T00:31:30.000Z","published_at":"2018-11-07T18:32:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, you will be given a range of single digits R, and a separate number K. You job is to calculate the mean of all K digit numbers that contain only distinct digits from the range R.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if R=1:4 and K=2, you should calculate the mean of 12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, and 43, as these are all of the two digit numbers that contain two distinct numbers from the range 1:4. The numbers 11, 22, 33 and 44 are not included, as they contain multiple copies of the same digit.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf 0 is included in R, it should not be a leading digit for any of the numbers, so an R of 0:2 and K=3 would include:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e210\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e201\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e102\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebut not 012 or 021 for the purposes of this calculation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can assume that R will always have at least K digits, and there will be no repeating digits in R.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1238,"title":"PACMAT - Ghosts Random; 3 Lives","description":"The Classic PACMAN game brought to Cody.\r\n\r\nPACMAT Ghosts Random requires clearing the board of Yellow Dots while not bumping into the randomly moving ghosts in 3 lives. Adjacent Ghosts will capture PACMAT.  Ghosts do not use the tunnel. On Ghost capture everyone gets reset.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_300.jpg\u003e\u003e\r\n\r\nTo aid in development of your routine, a PACMAT_Ghosts.m file that creates a video has been posted at \u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_Ghosts_001.m PACMAT_Ghosts_001.m\u003e. (Right click, 'save link as'). Using patches (not sprites).\r\n\r\n\r\n\u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_G001_SNC365_20_video.mp4 Alfonso PACMAT Random Ghost Video\u003e  (MP4: Left click and Windows Media Player)\r\n\r\n\u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_G001_video_ANC.mp4 Alfonso's Enhanced Ghost Avoider\u003e (MP4)\r\n\r\n\r\nThe reference solution uses Alfonso's Local Optimum Algorithm with a Catch.\r\n\r\n*Inputs:* Map   Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u003e2=Ghost\r\n\r\n*Output:* Direction  Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\r\n\r\n*Scoring:* Total # of Moves to Clear the Yellow Dots +(LivesRemaining-3)*100\r\n\r\n\r\n*Near Future:* Ghosts will get brighter.\r\n\r\n*Future:* Player will be Team Ghosts versus PACMAT_BOT","description_html":"\u003cp\u003eThe Classic PACMAN game brought to Cody.\u003c/p\u003e\u003cp\u003ePACMAT Ghosts Random requires clearing the board of Yellow Dots while not bumping into the randomly moving ghosts in 3 lives. Adjacent Ghosts will capture PACMAT.  Ghosts do not use the tunnel. On Ghost capture everyone gets reset.\u003c/p\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_300.jpg\"\u003e\u003cp\u003eTo aid in development of your routine, a PACMAT_Ghosts.m file that creates a video has been posted at \u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Ghosts_001.m\"\u003ePACMAT_Ghosts_001.m\u003c/a\u003e. (Right click, 'save link as'). Using patches (not sprites).\u003c/p\u003e\u003cp\u003e\u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_G001_SNC365_20_video.mp4\"\u003eAlfonso PACMAT Random Ghost Video\u003c/a\u003e  (MP4: Left click and Windows Media Player)\u003c/p\u003e\u003cp\u003e\u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_G001_video_ANC.mp4\"\u003eAlfonso's Enhanced Ghost Avoider\u003c/a\u003e (MP4)\u003c/p\u003e\u003cp\u003eThe reference solution uses Alfonso's Local Optimum Algorithm with a Catch.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e Map   Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u003e2=Ghost\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Direction  Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Total # of Moves to Clear the Yellow Dots +(LivesRemaining-3)*100\u003c/p\u003e\u003cp\u003e\u003cb\u003eNear Future:\u003c/b\u003e Ghosts will get brighter.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFuture:\u003c/b\u003e Player will be Team Ghosts versus PACMAT_BOT\u003c/p\u003e","function_template":"function  [newdir]=pacmat(map)\r\n newdir=randi(4);\r\nend","test_suite":"%%\r\nfeval(@assignin,'caller','score',2000);\r\n%%\r\nmax_moves=2000; % Fixed path expect to succeed by 600 moves\r\n\r\nmap=[...\r\n      repmat('a',1,28);\r\n      'accccccccccccaacccccccccccca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acccccccccccccccccccccccccca';\r\n      'acaaaacaacaaaaaaaacaacaaaaca';\r\n      'acaaaacaacaaaaaaaacaacaaaaca';\r\n      'accccccaaccccaaccccaacccccca';\r\n      'aaaaaacaaaaabaabaaaaacaaaaaa';\r\n      'aaaaaacaaaaabaabaaaaacaaaaaa';\r\n      'aaaaaacaabbbbbbbbbbaacaaaaaa';\r\n      'aaaaaacaabaaabbaaabaacaaaaaa';\r\n      'aaaaaacaabalbbbblabaacaaaaaa';\r\n      'bbbbbbcbbbabbbbbbabbbcbbbbbb';\r\n      'aaaaaacaabalbbbblabaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'aaaaaacaabbbbbbbbbbaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'accccccccccccaacccccccccccca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acccaacccccccbdcccccccaaccca';\r\n      'aaacaacaacaaaaaaaacaacaacaaa';\r\n      'aaacaacaacaaaaaaaacaacaacaaa';\r\n      'accccccaaccccaaccccaacccccca';\r\n      'acaaaaaaaaaacaacaaaaaaaaaaca';\r\n      'acaaaaaaaaaacaacaaaaaaaaaaca';\r\n      'acccccccccccccccccccccccccca';\r\n      repmat('a',1,28);];\r\n  \r\n  map=map-'b';\r\n  [nr, nc]=size(map);\r\n\r\n  gmap=map; % Map used by ghosts to simplify PAC Capture\r\n  gmap(15,6)=-1; %No tunnel ghosts\r\n  gmap(15,26)=-1;\r\n\r\n\r\n  mapdelta=[-1 nr 1 -nr]; % Valid as long as not on an edge\r\n  gmovxy=[0 -1;1 0;0 1;-1 0];\r\n\r\n  tunnel=find(map(:,1)==0); % tunnelptr\r\n  tunnel=[tunnel tunnel+nr*(nc-1)]; % Entrance/Exit Tunnel\r\n\r\n  [pmr, pmc]=find(map==2); % pi 24 row  pj 15 column of map\r\n   ptrpac=find(map==2);\r\n\r\n  ptrpac=find(map==2);\r\n  ptrpac_start=ptrpac;\r\n  ptrg_start=find(map\u003e2);\r\n  map(ptrg_start)=[10 20 30 40];% use deal?\r\n  [gstartx, gstarty]=find(map\u003e2);\r\n  \r\n  lives=3; % Lives\r\n  movepac=0;\r\n\r\nwhile lives \u0026\u0026 any(mod(map(:),10)==1) \u0026\u0026 movepac\u003cmax_moves\r\n movepac=movepac+1;\r\n\r\n [curdir]=pacmat(map);\r\n %if curdir==0,continue;end % bug 020213\r\n [pmr, pmc]=find(map==2);\r\nif curdir\u003e0 % bug fix 020213\r\n if map(ptrpac+mapdelta(curdir))==-1\r\n  % Do nothing - Ran into a Wall\r\n elseif map(ptrpac+mapdelta(curdir))\u003e2 % ran into ghost\r\n  map(ptrpac)=0; % remove PAC from the board\r\n  lives=lives-1;\r\n  if lives==0,break;end\r\n  % reset the board\r\n  [ptrgx, ptrgy]=find(map\u003e2);\r\n  ptrg=find(map\u003e2);\r\n  map(ptrg)=mod(map(ptrg),10);\r\n  map(ptrpac_start)=2;\r\n  map(ptrg_start)=[10 20 30 40];\r\n  ptrpac=find(map==2);\r\n  continue;\r\n else % legal move\r\n  map(ptrpac)=0; % Eat Dot and clear PAC\r\n  ptrpac=ptrpac+mapdelta(curdir);\r\n  if ptrpac==tunnel(1),ptrpac=tunnel(2)-nr;end\r\n  if ptrpac==tunnel(2),ptrpac=tunnel(1)+nr;end\r\n  map(ptrpac)=2;\r\n end\r\nend % curdir\u003e0 bug fix 020213\r\n\r\n% Ghosts\r\n for i=1:4\r\n\r\n  gmap=map;\r\n  gmap(15,6)=-1; %No tunnel ghosts\r\n  gmap(15,26)=-1;\r\n  dot=false;\r\n  [gptrx, gptry]=find(map==10*i);\r\n  gidx=find(map==10*i);\r\n  if isempty(gidx)\r\n   [gptrx, gptry]=find(map==10*i+1); % ghost must be on a dot\r\n   gidx=find(map==10*i+1);\r\n   dot=true;\r\n  end\r\n\r\n% Find valid ghost moves using gmap\r\n% mapdelta=[-1 nr 1 -nr]; \r\n  gmov=find(map(gidx+mapdelta)==2); % adjacent to PACMAT\r\n  if ~isempty(gmov) % PAC adjacent\r\n   lives=lives-1;\r\n   if lives==0,break;end\r\n   % reset the board\r\n   [pmr, pmc]=find(map==2); % PACMAT erase coords\r\n   map(map==2)=0;\r\n      \r\n   [ptrgx, ptrgy]=find(map\u003e2);\r\n   ptrg=find(map\u003e2);\r\n   map(ptrg)=mod(map(ptrg),10);\r\n   map(ptrpac_start)=2;\r\n   map(ptrg_start)=[10 20 30 40];\r\n   ptrpac=find(map==2);     \r\n   break; % Ghost move loop\r\n      \r\n  else % Random Ghost move  gmap avoids tunnel \r\n   gmov=intersect(find(gmap(gidx+mapdelta)\u003c10),find(gmap(gidx+mapdelta)\u003e-1)); \r\n   if ~isempty(gmov) % valid g move : ghost may not stand on ghost\r\n    gmov=gmov(randi(length(gmov)));\r\n    map(gptrx,gptry)=mod(map(gptrx,gptry),10);\r\n    map(gidx+mapdelta(gmov))=map(gidx+mapdelta(gmov))+10*i;     \r\n   end\r\n  end\r\n  \r\n end % i ghost moves\r\nend % while alive\r\n\r\nfprintf('moves %i\\n',movepac)\r\n\r\nassert(lives\u003e0,sprintf('Three Captures\\n'))\r\nassert(~isempty(any(mod(map(:),10)==1)),sprintf('Moves\\n',movepac)) % Test Move Timeout\r\n\r\n\r\nfeval( @assignin,'caller','score',floor(min( 2000,300-100*lives+movepac )) );\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2013-02-02T18:27:37.000Z","rescore_all_solutions":false,"group_id":33,"created_at":"2013-02-01T04:44:13.000Z","updated_at":"2026-04-23T17:56:11.000Z","published_at":"2013-02-01T06:15:30.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Classic PACMAN game brought to Cody.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT Ghosts Random requires clearing the board of Yellow Dots while not bumping into the randomly moving ghosts in 3 lives. Adjacent Ghosts will capture PACMAT. Ghosts do not use the tunnel. On Ghost capture everyone gets reset.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo aid in development of your routine, a PACMAT_Ghosts.m file that creates a video has been posted at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Ghosts_001.m\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT_Ghosts_001.m\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. (Right click, 'save link as'). Using patches (not sprites).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_G001_SNC365_20_video.mp4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAlfonso PACMAT Random Ghost Video\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MP4: Left click and Windows Media Player)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_G001_video_ANC.mp4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAlfonso's Enhanced Ghost Avoider\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MP4)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe reference solution uses Alfonso's Local Optimum Algorithm with a Catch.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Map Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u0026gt;2=Ghost\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Direction Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Total # of Moves to Clear the Yellow Dots +(LivesRemaining-3)*100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNear Future:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Ghosts will get brighter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFuture:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Player will be Team Ghosts versus 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\"}]}"},{"id":58807,"title":"Array size along k-th dimension","description":"Given an n-dimensional array M, find the size of M along the k-th dimension (1 \u003c= k \u003c= n), without using size(), height() or width(). You may ignore trailing singleton dimensions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven an \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-dimensional array \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eM\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find the size of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eM\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e along the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-th dimension (1 \u0026lt;= \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u0026lt;= \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e), without using \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003esize()\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eheight()\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ewidth()\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. You may ignore trailing singleton dimensions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = dimlen(M, k)\r\n    \r\nend","test_suite":"while true\r\n    d = 5 + randi(10)\r\n    s = randi(100);\r\n    s1 = 1 + randi(4, 1, d);\r\n    s2 = 1 + randi(4, 1, d);\r\n    s3 = 1 + randi(4, 1, d);\r\n    if prod(s1) \u003e 1e6 || prod(s2) \u003e 1e6 | prod(s3) \u003e 1e6\r\n        continue\r\n    end\r\n    M1 = ones(s1);\r\n    M2 = NaN(s2);\r\n    M3 = zeros(s3);\r\n    M4 = eye(s, 1);\r\n    M5 = eye(1, s);\r\n    break\r\nend\r\n\r\n%%\r\nfiletext = fileread('dimlen.m');\r\nassert(~contains(filetext, \"size\"),   \"size is forbidden.\"  );\r\nassert(~contains(filetext, \"height\"), \"height is forbidden.\");\r\nassert(~contains(filetext, \"width\"),  \"width is forbidden.\" );\r\n\r\n%%\r\nfor k = 1:d\r\n    assert(isequal(dimlen(M1, k), size(M1, k)))\r\n    assert(isequal(dimlen(M2, k), size(M2, k)))\r\n    assert(isequal(dimlen(M3, k), size(M3, k)))\r\nend\r\n\r\n%%\r\nassert(isequal(dimlen(M4, 1), size(M4, 1)))\r\nassert(isequal(dimlen(M5, 2), size(M5, 2)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":332395,"edited_by":332395,"edited_at":"2023-08-04T20:37:25.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2023-08-04T20:37:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-04T20:20:03.000Z","updated_at":"2026-04-24T14:25:49.000Z","published_at":"2023-08-04T20:37:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eGiven an \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e-dimensional array \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, find the size of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e along the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e-th dimension (1 \u0026lt;= \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e \u0026lt;= \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e), without using \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esize()\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eheight()\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewidth()\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e. You may ignore trailing singleton dimensions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58409,"title":"Calculate the volume of the intersection of two balls","description":"Consider two balls (solid spheres) in , with radius  and  respectively. Suppose that the distance between the centers of the two balls is . Please find the volume of the intersection of the two balls.\r\nIllustration:\r\n\r\n[X, Y, Z] = sphere(36);\r\nr1 = 1;\r\nr2 = 0.8;\r\nc2 = [0.6 -0.8 0];\r\nsurf(X * r1, Y * r1, Z * r1)\r\nhold on\r\nsurf(X * r2 + c2(1), Y * r2 + c2(2), Z * r2 + c2(3))\r\nhold off\r\naxis equal\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 328.438px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 164.219px; transform-origin: 407.5px 164.219px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21.4167px; text-align: left; transform-origin: 384.5px 21.4167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider two balls (solid spheres) in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAmCAYAAACoPemuAAAAAXNSR0IArs4c6QAAAvdJREFUWEft1kuIXEUUBuCvLkEYXAhBERwEESEIPnBjEF8LRXAVJCuNQURlUAPiOyQmGoIQfGQgBkREXIjobIy6UDcushAVE9wpoiAiIiIigm/klpzu6uTOndudvm10IV2r7rqnqv76z3/+U8nasaCyLFuSy8fEsd8xdfz/Z/gCH+ItfIy6Y8+YWoed+B0v4/TE7sy1uAHvNtfFEe2xQLVM/QP241y8gIfwUSv4bNyV2JSTBckhtUfwdce+l+JCvNgAH3Ov41nsnQKYZXxTgjeQVsh3472OA3dhEQcT+zJ/Ygnft2LPwXf4rTG/ASt4plz+2KdOxiqW61XABosnAKsWqe9FHP5K10Fj0nt9YikPLxKgJwOjzdiJgA0YC2DB1t6K02ruL3oag8kFpKfIkfoj7aAxGusJrLKoHgCLNG0hbSVvQei0Pc7C7bgH60lfke/DoWaJnexUFmC2DgF2AhvV9Zm4RbJT9gluxJejW3QzFnZRHxd/YiVP0FjFYj1MZVjBoypnqE+YymIh1R7yDvImvHlSgZWqDGDrEy/loU+FxUwzrpIclt1c/G2wZjqNJSvy+KosjIVtPFZArqmyCQgvx9u4Dh9MZqy7Krd3GGy4eVTVJfipuPs2fD4NVSUmLnFN8b4fZwF28ZjDvsXPeBjvtAy0uWQzbi3peg1/EJZhD3Yg2ts/8rGr8TwexBuI6noO7+Np/DXmAlfiSWzE0dJXI3XRktbYynQaG7aNkfPHmvCh2woDn2IENjQWzj9q/z0yujp0FmCxw6l4omwVzf3X4kMB7KYuJ++LcFZgcc755aUQDB3AKXgc5xUhr+p9/yWwOCtK/CDuwOGG3uJlEkz+0hfQLFXZ9boIu4hmfVmDpTaTM+ltUirbD8U7x7zHRlUZfW5fqcroew8MeuGQyd5jErAwvua4YgywiLkIrxbdNdfEkzu8Kyq31+gC1muDfyt4Dqwvs3PG5oz1ZaBv/Fxjc8b6MtA3fq6xOWN9GegbP9fY/4axvwF9AOQn9gJZ3AAAAABJRU5ErkJggg==\" width=\"19\" height=\"19\" style=\"width: 19px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, with radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"20\" style=\"width: 40px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"40\" height=\"20\" style=\"width: 40px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e respectively. Suppose that the distance between the centers of the two balls is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEsAAAAkCAYAAADB7MdlAAAAAXNSR0IArs4c6QAABKlJREFUaEPt2FeIXHUUx/HPnQgaIQ8WbEEiopgnFTQiibGgMYq9YIsi1hVEsWGMolGCRGyLSgJJFE21YiwPalRQUBFBMfqggmBB7EZ0Y0FwrpyZO5vr7Mzu/Gc2RGEuBHaz59++/1N+55/p7Zua8UTONjgdH3Q43T54CGvxCH7qcFyvZmdhqYq1qq7Ar6UJJ8uslNsWF+Cj5sWyHlc/Ec/iRZyHHzucb3c8LHMkNsgNYgl+6HB8N2Z7YBXZDPLT8HTTJMHiatxDZQnV+PmPsk0vsCZUWFDNzJNbiJvxd8IptsZRMvPl2bQaNHlAC4/7JmGeTk0vwoNk68nPxCctBs4geyGTb8w5Ge+MF6wdsVLmGLmT8Fynu26yq0NjPqZlbMgrlqlajC+7nLN52KQKi6p1738KF+OXFnNPkVkjz6aTx+Xfjrxh14tnHYDn8T3a3VTKWQto2VzMJB9SsVw1wsLnKRO1h2C6isWqrsWfLex2kFktz2aTr8TlGEqBFUD3xYXYCd9iAr4mW9hq0h4P1vC0GrSMoZzl1PLaZ+WbTljnYKzDJNyCBW3GTqQymKkO5LyFc/BFp7C2x/U4HtfhpWLgZVgcFHOuKQ6SsPeOTGvQMubmm6BFCN2FjxOhHYrXi1VHh1UxqGoA65sjZrQwnIxF2B/nlxaLNWdlrMtlQ+TH4s2Ojt+dUaMQzM1yMyOBVFhR5Y4EaHMyVuVq1zsmrKxqIK97wiHls7WDtXNRyiNxX4X7m25yjswqudcwpx6Sm+2rYHp4WOHh4c2hz8LD3u7Qw2oSp4iEMcLQoMyAvFaRT8C7o4XhVrgNNxYV7pIiiZfH3FTEfeSRG/DXZkBVg6QECY/ibryPasKaM/BGR2FYz40dh2HE92PYFa3EWyTJCM8ow+didcKmOzFthhTVqNtc1VgvClTMsffYCX4YVnhUKP5P23lW5Ic7cSVtQ+wgPIONiS3OWKAC0mGFJ80uSnavkBprTsGawlNDv7WTDtvVtCPHtdJjzTkrerbHsV9R4ZpDrByio4m7scCU/94KUq9SoXn9icV5IrxGF6WboIa8iHQ03JU0wyqX2JAH0a+VvwOLxeKmYqL4N6xwUwjVi9q/PGkDloUkGUflXt5S0e6M1E8lo4Yei/86Ba+WJ2iGFZVtVWHQnI/KFTJMGi3O4fi9uY8aA9xueACn1nvCWp7YXD1hYyshhSLEjsDReLnFHqN5vhdPFkn+59FgzSqUbthEXMchwnNCnIYXRZ6K0PwQZxSKPsrrrfgtwbO27BNNPdSaXxUaMPcs5NAI7djsWVEBVxSNbcj8+4qbv7TwhMhZcTtRoeKJI0AGvO8SQIVpVNT4hvuuxPHdmsf+QwpFkxydSUALCRI5LX4/u9CV0amMSC+tRGmU13lFmMVhXilAxcPeXgWsXQqQSxM9qttDjue4OPPU4uUhUstXCG96T70Hbfs81Murw3ge4H8x15aCVZYo3YKKSj3iNbPbyToZ14fVCaXCZkvBStjif8e0DyvhLvqw+rASCCSY9j2rDyuBQIJp37P6sBIIJJj2PasPK4FAgmnfs/qwEggkmPY9qw8rgUCCad+zEmD9Ayi9MTS3ql3GAAAAAElFTkSuQmCC\" width=\"37.5\" height=\"18\" style=\"width: 37.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. Please find the volume of the intersection of the two balls.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIllustration:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 183.938px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404.5px 91.9688px; transform-origin: 404.5px 91.9688px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e[X, Y, Z] = sphere(36);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003er1 = 1;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003er2 = 0.8;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ec2 = [0.6 -0.8 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003esurf(X * r1, Y * r1, Z * r1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ehold \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eon\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003esurf(X * r2 + c2(1), Y * r2 + c2(2), Z * r2 + c2(3))\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003ehold \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eoff\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.666667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.666667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.666667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.666667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404.5px 10.2188px; transform-origin: 404.5px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eaxis \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration: none; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eequal\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function V = Vlens(r1, r2, d)\r\n    \r\nend","test_suite":"%%\r\nassert(abs(Vlens(sqrt(3), sqrt(3), 12*cos(pi/9)*sin(pi/9) - sqrt(12)*(1 - 2*sin(pi/9)^2)) - sqrt(12)*pi) \u003c 1e-13)\r\n\r\n%%\r\nassert(abs(Vlens(1, 2, 0) - 4*pi/3) \u003c 1e-13)\r\nassert(abs(Vlens(1, 2, 0.5) - 4*pi/3) \u003c 1e-13)\r\nassert(abs(Vlens(1, 2, 1) - 4*pi/3) \u003c 1e-13)\r\nassert(abs(Vlens(1, 2, 1.5) - 3.239767424014474) \u003c 1e-13)\r\nassert(abs(Vlens(1, 2, 2) - 1.701696020694471) \u003c 1e-13)\r\nassert(abs(Vlens(1, 2, 2.5) - 0.477783882733448) \u003c 1e-13)\r\nassert(isequal(Vlens(1, 2, 3), 0))\r\n\r\n%% \r\nassert(abs(Vlens(3, 4, 5) - 19.268434942017397) \u003c 1e-13)\r\nassert(abs(Vlens(1, 0.8, 1) - 0.750631204697721) \u003c 1e-13)\r\nassert(isequal(Vlens(10, 0, 2), 0))\r\nassert(isequal(Vlens(0, 5, 0), 0))\r\nassert(abs(Vlens((1 + sqrt(5))/2, exp(1), pi) - 3.982801259482478) \u003c 1e-13)\r\nassert(abs(Vlens(17, 89, 105) - 44.214176608022065) \u003c 1e-13)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":332395,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-06-09T15:45:44.000Z","updated_at":"2026-04-24T14:37:56.000Z","published_at":"2023-06-09T15:45:44.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider two balls (solid spheres) in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\mathbb{R}^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, with radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_1 \\\\ge 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_2 \\\\ge 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e respectively. Suppose that the distance between the centers of the two balls is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ed \\\\ge 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Please find the volume of the intersection of the two balls.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIllustration:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[X, Y, Z] = sphere(36);\\nr1 = 1;\\nr2 = 0.8;\\nc2 = [0.6 -0.8 0];\\nsurf(X * r1, Y * r1, Z * r1)\\nhold on\\nsurf(X * r2 + c2(1), Y * r2 + c2(2), Z * r2 + c2(3))\\nhold off\\naxis equal]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61174,"title":"[Master Regular Expression] String To Integer","description":"Implement the myAtoi(string s) function, which converts a string to a 32-bit signed integer.\r\nThe algorithm for myAtoi(string s) is as follows:\r\n \r\nWhitespace: Ignore any leading whitespace (\" \").\r\n \r\nSignedness: Determine the sign by checking if the next character is '-' or '+', assuming positivity if neither present.\r\n \r\nConversion: Read the integer by skipping leading zeros until a non-digit character is encountered or the end of the string is reached. If no digits were read, then the result is 0.\r\n \r\nRounding: If the integer is out of the 32-bit signed integer range [-231, 231 - 1], then round the integer to remain in the range. Specifically, integers less than -231 should be rounded to -231, and integers greater than 231     - 1 should be rounded to 231 - 1.\r\nReturn the integer as the final result.\r\n \r\nExample 1:\r\nInput: s = \"42\"\r\nOutput: 42\r\nExplanation:\r\nThe underlined characters are what is read in and the caret is the current reader position.\r\nStep 1: \"42\" (no characters read because there is no leading whitespace)\r\n         ^\r\nStep 2: \"42\" (no characters read because there is neither a '-' nor '+')\r\n         ^\r\nStep 3: \"42\" (\"42\" is read in)\r\n           ^\r\nExample 2:\r\nInput: s = \" -042\"\r\nOutput: -42\r\nExplanation:\r\nStep 1: \"   -042\" (leading whitespace is read and ignored)\r\n            ^\r\nStep 2: \"   -042\" ('-' is read, so the result should be negative)\r\n             ^\r\nStep 3: \"   -042\" (\"042\" is read in, leading zeros ignored in the result)\r\n               ^\r\nExample 3:\r\nInput: s = \"1337c0d3\"\r\nOutput: 1337\r\nExplanation:\r\nStep 1: \"1337c0d3\" (no characters read because there is no leading whitespace)\r\n         ^\r\nStep 2: \"1337c0d3\" (no characters read because there is neither a '-' nor '+')\r\n         ^\r\nStep 3: \"1337c0d3\" (\"1337\" is read in; reading stops because the next character is a non-digit)\r\n             ^\r\nExample 4:\r\nInput: s = \"0-1\"\r\nOutput: 0\r\nExplanation:\r\nStep 1: \"0-1\" (no characters read because there is no leading whitespace)\r\n         ^\r\nStep 2: \"0-1\" (no characters read because there is neither a '-' nor '+')\r\n         ^\r\nStep 3: \"0-1\" (\"0\" is read in; reading stops because the next character is a non-digit)\r\n          ^\r\nExample 5:\r\nInput: s = \"words and 987\"\r\nOutput: 0\r\nExplanation:\r\nReading stops at the first non-digit character 'w'.\r\n \r\nConstraints:\r\n \r\n0 \u003c= s.length \u003c= 200\r\n \r\ns consists of English letters (lower-case and upper-case), digits (0-9), ' ', '+', '-', and '.'.\r\n ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 2070.94px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 1035.46px; transform-origin: 408px 1035.47px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eImplement the myAtoi(string s) function, which converts a string to a 32-bit signed integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe algorithm for myAtoi(string s) is as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWhitespace\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Ignore any leading whitespace (\" \").\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSignedness\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Determine the sign by checking if the next character is '-' or '+', assuming positivity if neither present.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConversion\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Read the integer by skipping leading zeros until a non-digit character is encountered or the end of the string is reached. If no digits were read, then the result is 0.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 61.3125px; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.6562px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 30.65px; text-align: left; transform-origin: 363px 30.6562px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRounding\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: If the integer is out of the 32-bit signed integer range [-2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e31\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, 2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e31\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - 1], then round the integer to remain in the range. Specifically, integers less than -2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e31\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e should be rounded to -2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e31\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and integers greater than 2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e31\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e     - 1 should be rounded to 2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e31\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e - 1.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn the integer as the final result.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 1:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e s = \"42\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 42\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe underlined characters are what is read in and the caret is the current reader position.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: \"42\" (no characters read because there is no leading whitespace)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: \"42\" (no characters read because there is neither a '-' nor '+')\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 3: \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e42\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\" (\"42\" is read in)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e           \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e s = \" -042\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e -42\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-042\" (leading whitespace is read and ignored)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e-\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e042\" ('-' is read, so the result should be negative)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e             \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 3: \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e042\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\" (\"042\" is read in, leading zeros ignored in the result)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e               \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 3:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e s = \"1337c0d3\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 1337\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: \"1337c0d3\" (no characters read because there is no leading whitespace)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: \"1337c0d3\" (no characters read because there is neither a '-' nor '+')\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 3: \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e1337\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ec0d3\" (\"1337\" is read in; reading stops because the next character is a non-digit)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e             \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 4:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e s = \"0-1\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 1: \"0-1\" (no characters read because there is no leading whitespace)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 2: \"0-1\" (no characters read because there is neither a '-' nor '+')\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e         \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eStep 3: \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-1\" (\"0\" is read in; reading stops because the next character is a non-digit)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e          \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e^\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 5:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e s = \"words and 987\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReading stops at the first non-digit character 'w'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraints:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e0 \u0026lt;= s.length \u0026lt;= 200\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003es consists of English letters (lower-case and upper-case), digits (0-9), ' ', '+', '-', and '.'.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = solution(s)\r\n\r\nend","test_suite":"%%\r\ns = '42';\r\nresult = 42;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '   -042';\r\nresult = -42;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '1337c0d3';\r\nresult = 1337;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '0-1';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = 'words and 987';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '5467824652315';\r\nresult = 2147483647;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '     -535262335433103';\r\nresult = -2147483648;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = ' +-3242asfjkahw asu   ';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '      -.a0e3';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '+0003247er12349';\r\nresult = 3247;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = 'F6m28 d54L 1 3oC52m543196j861396J07929B321 04Vl4 2 BI58 b7641726M8L1Y15p.7525251xV3c0  002C4989577X06q+5J15G  82RG7x56r1R0507qL9';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '9j0845U3839Z2S23 21 0X96cR6 .n-6A3rZ4c 78RSg60996F  51435A228.2 zo453754O66-13f93z798317079 0c2- n0B6659565  YQ53M49M1479I3U7p857eLH22H 08I64336+4 s1f 8O1+309z9y';\r\nresult = 9;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = ' 240bRjk9444T393726quJ9vc0234234R5565k62 ';\r\nresult = 240;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '61D71J4  3T 9D908th90e7 ks0o9142991Y4550846RM2-6e848Bf326C  21E787843IK';\r\nresult = 61;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '6+ I197 931015o5 Y 93hHC+ L74 5 0Z3 5e01N15849o8O274+0151260c 21673D+0I701ZD 05719579105894Lw7W93t74S28V  79K63747 96E568';\r\nresult = 6;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111';\r\nresult = 2147483647;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '7C4w5Q4S89Yn500u768H6.1524643 r3Ii9U93BC55y80o7456r0fE4 3 1U 60B.A80M6g2uKok6b995b20999aNQJ.N1509h3715o9m H127hH027l8k2  0hY263d3X0';\r\nresult = 7;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = 'sC9k893';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '005 H  ar 85O48h4z9K5PN9164430H795YXT f584eo133 fx037651l6 905UO6 9xS1G933b+9U91212  626r6k5 G381211 ';\r\nresult = 5;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = ' BlVoPh4e nj58n9S2Kj4 729U7-13204362Z86466N8 09o 8wT5r40155027m d7MYO7J6.9z4 . 553';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '469Y0cJD2S7ED6 C0162';\r\nresult = 469;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = 'o5u2 E';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '366451770 12 90462176w9u70026e24 4526IG6 4R 3194120 ot4I 059 7t2Vx5 518wlR562599216x382Cm968GJ88K9n 73.33C2 7 h50y6 I4Zxq 96v+oXqA8E5380w4 q  48P434n5.3';\r\nresult = 366451770;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '53KP0-078y 4Jm9I6';\r\nresult = 53;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = ' 163te Lv9018RzOV65p3TO65 ds-190k +3df50zm8cq5L944H62Q W3w8-09 8180';\r\nresult = 163;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '+   S38z8l3 L2703 E50J8K5 0855Sj5 79T 2yf125784wq4 1 5 5 663fvN83.36B7N6a-17N06436N8s57R21cO1 2  0rX75039.4 1P15 896m4 M5up227   02lziQM38p8 9g18359i78234744H9P 4197 l69';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = 'Q843R c o98F644JbB6 0M78m5 55 714Va 50904';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '7m 5412e1M719x5oc-667738090EC5VSY20453';\r\nresult = 7;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '3745J026y3OU6X2l9 832 s 8Q-3 5jZ4Oa14O8Go0n D9 13075483OP-0J 1Z5t7989292797xZVi3039 6 H4428v5p79X U1I02 65r5 74x9142938fSl1PV S5J08252- 500010Vgj014HVY';\r\nresult = 3745;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '43ie370 oCp750v104Q 6B  7Tv02894762R6y0715QB295J1p2e333W6 03E707wE54x';\r\nresult = 43;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '832KY6wSHy 24704W59 J6 31  595t6a T3+19z05cC8Z748224k Un974j11g695d6eZ171fL189 5.3 a727';\r\nresult = 832;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '5x24P jt07f2 4yy76T068 12 32028Dm21 8855K7j3139 P02751t6 90 547 s90q4v .61Z 314J38K37 + 47rO757542281N22e 6106q71s 798 ';\r\nresult = 5;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '3s36440N87855Y8i r44d3x2Se2BO967b40RZoY827i Ek 45y61D720 667858025i9bsA2 kb.035 31W3X 48d41935V5Q6052Y794G1w7M8E56+K206+M49o5170 ';\r\nresult = 3;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = '39 6 zb694f515502C B4I';\r\nresult = 39;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n%%\r\ns = 'T73v68jx614qP9P+Xl38 D.Z248233 5q93 09Y69';\r\nresult = 0;\r\ncorrect_answer = solution(s)\r\nassert(isequal(correct_answer, result))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":4945898,"edited_by":4945898,"edited_at":"2026-02-01T12:51:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2026-02-01T12:51:22.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-31T09:59:26.000Z","updated_at":"2026-04-28T18:34:27.000Z","published_at":"2026-01-31T09:59:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eImplement the myAtoi(string s) function, which converts a string to a 32-bit signed integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe algorithm for myAtoi(string s) is as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWhitespace\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Ignore any leading whitespace (\\\" \\\").\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSignedness\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Determine the sign by checking if the next character is '-' or '+', assuming positivity if neither present.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConversion\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Read the integer by skipping leading zeros until a non-digit character is encountered or the end of the string is reached. If no digits were read, then the result is 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRounding\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: If the integer is out of the 32-bit signed integer range [-2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e31\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e31\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e - 1], then round the integer to remain in the range. Specifically, integers less than -2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e31\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e should be rounded to -2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e31\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and integers greater than 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e31\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e     - 1 should be rounded to 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e31\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e - 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the integer as the final result.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e s = \\\"42\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe underlined characters are what is read in and the caret is the current reader position.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: \\\"42\\\" (no characters read because there is no leading whitespace)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: \\\"42\\\" (no characters read because there is neither a '-' nor '+')\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 3: \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e42\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" (\\\"42\\\" is read in)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e           \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e s = \\\" -042\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e -42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-042\\\" (leading whitespace is read and ignored)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e042\\\" ('-' is read, so the result should be negative)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e             \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 3: \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e042\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" (\\\"042\\\" is read in, leading zeros ignored in the result)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e               \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 3:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e s = \\\"1337c0d3\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 1337\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: \\\"1337c0d3\\\" (no characters read because there is no leading whitespace)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: \\\"1337c0d3\\\" (no characters read because there is neither a '-' nor '+')\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 3: \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1337\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ec0d3\\\" (\\\"1337\\\" is read in; reading stops because the next character is a non-digit)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e             \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 4:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e s = \\\"0-1\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 1: \\\"0-1\\\" (no characters read because there is no leading whitespace)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 2: \\\"0-1\\\" (no characters read because there is neither a '-' nor '+')\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e         \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStep 3: \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-1\\\" (\\\"0\\\" is read in; reading stops because the next character is a non-digit)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e          \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 5:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e s = \\\"words and 987\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReading stops at the first non-digit character 'w'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e0 \u0026lt;= s.length \u0026lt;= 200\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003es consists of English letters (lower-case and upper-case), digits (0-9), ' ', '+', '-', and '.'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61177,"title":"[Master Regular Expression] Unique Email Addresses","description":"Every valid email consists of a local name and a domain name, separated by the '@' sign. Besides lowercase letters, the email may contain one or more '.' or '+'.\r\nFor example, in \"alice@leetcode.com\", \"alice\" is the local name, and \"leetcode.com\" is the domain name.\r\nIf you add periods '.' between some characters in the local name part of an email address, mail sent there will be forwarded to the same address without dots in the local name. Note that this rule does not apply to domain names.\r\nFor example, \"alice.z@leetcode.com\" and \"alicez@leetcode.com\" forward to the same email address.\r\nIf you add a plus '+' in the local name, everything after the first plus sign will be ignored. This allows certain emails to be filtered. Note that this rule does not apply to domain names.\r\nFor example, \"m.y+name@email.com\" will be forwarded to \"my@email.com\".\r\nIt is possible to use both of these rules at the same time.\r\nGiven an array of strings emails where we send one email to each emails[i], return the number of different addresses that actually receive mails.\r\n \r\nExample 1:\r\nInput: emails = [\"test.email+alex@leetcode.com\",\"test.e.mail+bob.cathy@leetcode.com\",\"testemail+david@lee.tcode.com\"] Output: 2 \r\nExplanation: \"testemail@leetcode.com\" and \"testemail@lee.tcode.com\" actually receive mails. \r\n\r\nExample 2:\r\nInput: emails = [\"a@leetcode.com\",\"b@leetcode.com\",\"c@leetcode.com\"] \r\nOutput: 3 \r\n \r\nConstraints:\r\n1 \u003c= emails.length \u003c= 100\r\n1 \u003c= emails[i].length \u003c= 100\r\nemails[i] consist of lowercase English letters, '+', '.' and '@'.\r\nEach emails[i] contains exactly one '@' character.\r\nAll local and domain names are non-empty.\r\nLocal names do not start with a '+' character.\r\nDomain names end with the \".com\" suffix.\r\nDomain names must contain at least one character before \".com\" suffix.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 843.812px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 421.9px; transform-origin: 408px 421.906px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEvery\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003evalid email\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003econsists of a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003elocal name\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edomain name\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, separated by the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'@'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esign. Besides lowercase letters, the email may contain one or more\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'.'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eor\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'+'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, in\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"alice@leetcode.com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"alice\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003elocal name\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"leetcode.com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edomain name\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf you add periods\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'.'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ebetween some characters in the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003elocal name\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003epart of an email address, mail sent there will be forwarded to the same address without dots in the local name. Note that this rule\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edoes not apply\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eto\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edomain names\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"alice.z@leetcode.com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"alicez@leetcode.com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eforward to the same email address.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf you add a plus\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'+'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003elocal name\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, everything after the first plus sign\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ewill be ignored\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. This allows certain emails to be filtered. Note that this rule\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edoes not apply\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eto\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003edomain names\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"m.y+name@email.com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewill be forwarded to\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\"my@email.com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt is possible to use both of these rules at the same time.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an array of strings\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eemails\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere we send one email to each\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eemails[i]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, return\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ethe number of different addresses that actually receive mails\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 1:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e emails = [\"test.email+alex@leetcode.com\",\"test.e.mail+bob.cathy@leetcode.com\",\"testemail+david@lee.tcode.com\"] \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 2 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExplanation:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"testemail@leetcode.com\" and \"testemail@lee.tcode.com\" actually receive mails. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e emails = [\"a@leetcode.com\",\"b@leetcode.com\",\"c@leetcode.com\"] \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 3 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraints:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 163.5px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 81.75px; transform-origin: 391px 81.75px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1 \u0026lt;= emails.length \u0026lt;= 100\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1 \u0026lt;= emails[i].length \u0026lt;= 100\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eemails[i]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003econsist of lowercase English letters,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'+'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'.'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'@'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eemails[i]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003econtains exactly one\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'@'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003echaracter.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAll local and domain names are non-empty.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLocal names do not start with a\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e'+'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003echaracter.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDomain names end with the\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\".com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esuffix.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDomain names must contain at least one character before\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\".com\"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esuffix.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = solution(emails)\r\n\r\nend","test_suite":"%%\r\nemails = [\"test.email+alex@leetcode.com\" \"test.e.mail+bob.cathy@leetcode.com\" \"testemail+david@lee.tcode.com\"];\r\ncorrect_answer = 2;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"a@leetcode.com\" \"b@leetcode.com\" \"c@leetcode.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"wjhlbrie@t..j.mrg.com\" \"hwbrvpohlgr+ed@rn.uafx.ix.fmut.com\" \"v.tejo@x+oprw.com\" \"gerpzqhpheaur@pfngovbsx+a...com\" \"phgn+d@eategig.com\" \"ejoaqlqtcyc@d+rj+mhzraz.com\" \"yaqli@pn.bk.com\"];\r\ncorrect_answer = 7;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"gdksgnj@.zcm.c..com\" \"ia+rirqhpz+.bh@+nir.mna+.narn.com\" \"tdmafwenkjn+@v+eawfkimygd.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"htbv+v+xhaq+@shs+qknwhfev.com\" \"buayr.eqllgo@vn.nmootopsw.com\" \"xp+tqxmaz.@.sghdcvgxj.com\" \".t.sbvxhm+kbxf@.pv..lssiliniy.com\" \"lmogy@+.o+f.com\" \"nfjjsnl+.+r@maard+jybz..com\" \"pieizze@i.qfzj..com\" \"ocdz.oobbf@k+rbhwh+k..com\" \"shfewmgunty..j@gbzyd+ycvyjsdcg.com\"];\r\ncorrect_answer = 9;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"lutiy.imybcj.r@fcqze.ldj.dwmi.com\" \"jhn.cj@.isopja.com\" \"spogtwhtrq@c+cca+qsaqp.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"w+.jqzvv+u@ok.kkgc+j..com\" \"ngoikkt@iblhmfx.com\" \"kj.qby@tdipvy.com\" \".lbtymy@gj.rwwa.com\" \"ugigzcfwgbfn@vnjoabkxsrvp.com\" \"exudwkules@xrqfp+qqfi..com\" \"fhwhmh@olgc+p.com\" \"mhpmqixa@u.+xtqic.com\" \".ligb.fvvgu@wkhghvyxeka.com\"];\r\ncorrect_answer = 9;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"a.uyfnngdr@rwxpkk.ujz.com\" \".sjpzarzekgp@ya+kridafidw.com\"];\r\ncorrect_answer = 2;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\".ccrxzyiud@ti+mrviezj.com\" \"qelcesbdgqqmlj@+yxfafndxvccan.com\" \"wtyo+l@olhjyj.com\" \"ah.mphqmt@trvfb+.wyz.com\" \"um+xu.mona+x+p@zteq++m+rk+nil.com\" \"dlvvupcrlxwbrjm@fgohf+uwo+uofum.com\" \"uq.hrr@cuarwk.com\" \"ydbghox+kl+noe@boexhfj.ctecwq.com\" \"dlrshw+k.c.w@msuzwzocmhsz.com\"];\r\ncorrect_answer = 9;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"xmdykvtahgyp@lterrniu+.ur.com\" \"qld+wq.ek@oi.mw.hy+.com\" \"tsg+ut@mz++ox.com\" \".trwkzce@lcxmomue.com\" \"t.b+bfpeh.v@lb+uny.gr+i.com\" \"qsy.lno@mzknpk+u.com\" \"hct+uqr@vdcs.et.com\" \"qmiussebdmpfn@wmzn.c.sjgoc..com\"];\r\ncorrect_answer = 8;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"cqqh.avzp@robtj+htf.com\" \"qjdwzhvn@pjlpq++y.com\" \"bmlr+q@htqwupm.com\" \"wpddmnz.txfuvw@xudvlgxnv+zj++.com\" \"xnqtqbhtfz@m+ssz.qyn+.com\"];\r\ncorrect_answer = 5;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\".zmjgh@+sbvhe.com\" \"nh+onxodyfnp@ps.a+fk+of++.com\"];\r\ncorrect_answer = 2;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"emqg+nociysj@ell+.gcndyeg.com\" \"xudupb..dmsl@hx+qxejgvzou.com\" \"gi+yj+vzd@go.shnerp.com\" \"exegawmmybuhj@oynjvqdwmwetc.com\"];\r\ncorrect_answer = 4;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"ivyvy@.koud.com\" \"zlya+d@v+zlxo.com\" \"hfepaczs@lvaqpc+a.com\" \"mkhiihjwgpsh@.coaqlfhrbgz.com\" \"wjvgijfibmzk@.uqfo+u.+mxr.com\" \"bknkbmznylqm@wxt++n+zbm+y.com\" \"gflhomxq@tdmmhksp.com\" \"hknwtdctuun+sa@abxrmyyn+q+jzp.com\"];\r\ncorrect_answer = 8;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"mzo+sjve@gejsbgth.com\" \"hhwdnr@zzvzee.com\" \"hezr+ov@bb.aloi.com\" \"ngzazovqa.nvb+@x+lraofkkqx.ar.com\" \"blup+@+ymca.com\" \"szkznwyoqh@.ot.kkwdql.com\" \"nfkyat+iu@cxasim+z+.com\" \"lqdhzf+.@vms+n+zo.com\" \"fosq.wjbkw+xikw@g.axsoacnrmvusm.com\" \"a+egj.de@byyk+iox.com\"];\r\ncorrect_answer = 10;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"wosbgfbq+iohjs@w+a.wf+h+khs.t.com\" \"yoryltsqgprg+jg@hy.t.qrwdkodwqd.com\" \"dcknj@e.r+i.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"nrzlyiewbu@sb.+peednq.com\" \"zj.pre.agf+soq@udki.emvlyzujz.com\" \"h+aeeap.iiocu.@.+z.oglfkpxsbu.com\" \"h+yhm@fvzki.com\"];\r\ncorrect_answer = 4;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"koguyqhghscjiob@xi+.r+hlx+tcxqw.com\" \"fdqgr.tqgjlyyra@mtbvrcqenvkibqg.com\" \"bpaxe.lo.hrydqy@tru+b.irfstinxy.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"ncsyteko@qfxr+++dm.com\" \".qdh.hz@gvecrk+.com\" \".j+hb@.sol+.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"vgqkvatdx@qrdsolaz..com\" \"xei+++osalaqm@xxeeqqjgsnsao.com\"];\r\ncorrect_answer = 2;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"onutdg@eqbhng.com\" \"rsptijxxsnadwn@v+hdlhhpliptgn.com\" \"kuofap@lq+qdg.com\" \"btfpitlmblpnr@+cb.uzrxk.drv.com\" \"vxolxcm+rwlq@..nbwpgxjy+..com\"];\r\ncorrect_answer = 5;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"h.npduspt+xt@.gm+trja+gvy.com\" \"eekvae++kjs@pr.txifzbdi.com\" \"n.+syybgkgg@jivviajknfl.com\" \"j++zrdfoc..uj@ishji..po.sed.com\"];\r\ncorrect_answer = 4;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"oslxuvd+j+ppdtj@+++akbe.kjoukhz.com\" \".fgnbscrtpc.j+@.+hgpqbbwourp+.com\" \"y+sh.bf.n@xh+sm+krf.com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"rkfqxlo.y.+@ibeduayh.i+.com\" \"xcuiy.au@vmfwel...com\" \"kkx..lwnuw@eueutajdrs.com\" \"v+oqoufiqmdzo@lgroppjdjbehe.com\" \"d.znfhymi..ybu@zhcsbqguazgwhc.com\" \"r+ulbtcjs@m++o+cfa..com\" \"aajyp+dyuyxnw.@eyjiyhgxjlarpa.com\"];\r\ncorrect_answer = 7;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"dp.+vp+k@kaagwxkb.com\" \"r.lhe.o@kjvljpa.com\" \"vxhjyeu+llbdd@wz+cfo+pgbtmg.com\" \"nrv+p@lwmsz.com\" \"pylevc@wv.zjd.com\"];\r\ncorrect_answer = 5;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"pniur@pb.iu.com\" \"jadg.@uk+bp.com\" \"vrdq.hlhmu.f.@uvlysycaayckm.com\" \"glffs+ezwlhxjl@+nobjdaejgtlwfy.com\" \"rjeay@vx+ji.com\" \"movemhf+rjdu+b@v.w++fvrlpyg+t.com\" \"nrj.kjwhdrd@pqhrhiqnzbf.com\" \"qbkn.@ugotg.com\"];\r\ncorrect_answer = 8;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"d+mhas.tsgqorpw@srjrbeqzfngvhcc.com\" \".wd.nycikhwpio@uluma+y.zptdvxo.com\" \"ewfu+c.cpkgxqi@cpkwcquwmhfjlk.com\" \"rtojs..@yxpal.a.com\" \"ftogpu@wy.zpf.com\" \".qjrog++yxy@te.i+nttbbi.com\" \"skqac@wbpfw.com\" \".yus+rotyed@+yvfccxjtxs.com\" \"znfa.tlseed@+sjidvzaufr.com\" \"eocdtookevafe@.vejunakxmwmu.com\"];\r\ncorrect_answer = 10;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"nnazmvkxsqseu@owlov+y++sh++.com\" \"mcd+.zaoqvjt@mshwokdsnbpa.com\" \"rvgxh@uepgp.com\" \"pyxs.tccxm@hwqtesq+ac.com\" \"nkohjc.rdoom@lnwnahosijdx.com\" \"squpelgagh@fysvplojt..com\" \"svr.thd.akqo@pnvu++nc.g+..com\" \"atx+qtgps@krecrkgco.com\" \"hfbngnwgsjdy@csxah+ujrhbf.com\" \".gblz+gv+@+ccoudafz.com\"];\r\ncorrect_answer = 10;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"lumrfllp@ycgw..+y.com\" \"e+meeqfiv+sgdb@kfatozbkmjqnwu.com\" \"oopl.tztedjk@vwnwy+sbdwj..com\"];\r\ncorrect_answer = 3;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\".hy.flt@oduitys.com\" \"r+kyc@q+pkp.com\" \".htrhfbptj@febgrmels+.com\" \"cgiy+aoodkoyuad@tmczkzjutq.rmp..com\" \"nrcbiwxcjg@atvxzuuya..com\" \"yy.ica+vy@evulrlsul.com\" \"kxdu.xgqr@qkehuqjzl.com\" \"cdiyt++@mpb.jos.com\" \"jvx+opucdmj@zpsgwhusqw..com\"];\r\ncorrect_answer = 9;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"vvtjpnbwceyz@gdcgjaxiiiqo.com\" \"dxb+pfbibxfm@cxk.fqegt+w+s.com\" \"xlxiq.sdffx@iczdyroddo..com\" \"udvnp.@bzldti.com\" \"myvdwpwk+@pxahvnofh.com\" \".i+.t@srhjn.com\" \"q.nt+cmrxj@jfefhhvqyn.com\" \"g.bjes.m@+m+ncvfw.com\" \"dcumhljkpg+@bkinkypk.o+.com\" \".rmsmixyyiyn@mw+vozgvkev..com\"];\r\ncorrect_answer = 10;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"kbzkwnexjd+j+f@i+.ttkuphkfuf..com\" \"vzz+.mgo@nofllmhs.com\" \".iodt@recpp.com\" \"wfjixhqgtx+xk@tbcu.mfcc.mmq.com\" \"olk.ivns.tt++@tvgfits.ighr+.com\" \"eehxp+cj+onn+ku@lxbdwjocmfjlxnu.com\" \"doycs.zkeqwiywn@pe+c.dwo+mgtyzi.com\" \"n+voq@ietp+.com\" \".zkwm.gredn@umj+uhugnza.com\"];\r\ncorrect_answer = 9;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"iyexebhw.iau+hl@wlkxwcizawtsgxk.com\" \"fqdruepre.swxnb@jaqjnp.dvfiveug.com\" \"i+vwklzdm@xpeejkmlp..com\" \"qpla+@.vmbz.com\" \"pg+etmaqi+wae@rrxhpqk.frevh.com\" \"bdfqqoejbcb@qprhwxqzgmd.com\" \".en+qpx.dtkg@aapkhyixcvzm.com\"];\r\ncorrect_answer = 7;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"luffyuctpfb@lcrcudc+oas.com\" \"liedcyn@skgq.ny.com\" \"vdiuwqvnbbt@zomxloeqbu+.com\" \"dei.yrqq+tjb@+nrvays+bj+x.com\" \"wd..bxdxxamf@rtphghmicffc.com\" \"g+emmrm.au+t@rpl.sv+gvfnk.com\" \"uenakj.jtvg@ldduvmakrpg+.com\" \"nt+zofb@rhmc.oq.com\" \"yosrqs@exesju.com\" \"kehogbp.nol@+bxlsqqj.fg.com\"];\r\ncorrect_answer = 10;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n%%\r\nemails = [\"xamepf@m+ie...com\" \"blwpot@evqzxa.com\" \"ibyuogiqh@hwhangzte.com\" \"rdri.la.emkpa@guupavcgqsnq..com\" \"fxtes@cxxir.com\" \"krwy..x++i.exba@jhniby.cxy+f..v.com\" \"abgobuyol@rsexxbwlm.com\" \"jnalpyhai@bccsuj.af.com\"];\r\ncorrect_answer = 8;\r\nyour_answer = solution(emails)\r\nassert(isequal(correct_answer, your_answer))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4945898,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-31T14:56:56.000Z","updated_at":"2026-04-28T18:28:47.000Z","published_at":"2026-01-31T14:56:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEvery\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003evalid email\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003econsists of a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elocal name\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edomain name\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, separated by the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'@'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esign. Besides lowercase letters, the email may contain one or more\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'.'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eor\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'+'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"alice@leetcode.com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"alice\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eis the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elocal name\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"leetcode.com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eis the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edomain name\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you add periods\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'.'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ebetween some characters in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elocal name\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003epart of an email address, mail sent there will be forwarded to the same address without dots in the local name. Note that this rule\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edoes not apply\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eto\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edomain names\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"alice.z@leetcode.com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"alicez@leetcode.com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eforward to the same email address.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you add a plus\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'+'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ein the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003elocal name\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, everything after the first plus sign\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewill be ignored\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. This allows certain emails to be filtered. Note that this rule\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edoes not apply\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eto\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edomain names\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"m.y+name@email.com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewill be forwarded to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"my@email.com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is possible to use both of these rules at the same time.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an array of strings\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eemails\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ewhere we send one email to each\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eemails[i]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe number of different addresses that actually receive mails\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e emails = [\\\"test.email+alex@leetcode.com\\\",\\\"test.e.mail+bob.cathy@leetcode.com\\\",\\\"testemail+david@lee.tcode.com\\\"] \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 2 \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExplanation:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"testemail@leetcode.com\\\" and \\\"testemail@lee.tcode.com\\\" actually receive mails. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e emails = [\\\"a@leetcode.com\\\",\\\"b@leetcode.com\\\",\\\"c@leetcode.com\\\"] \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 3 \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 \u0026lt;= emails.length \u0026lt;= 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 \u0026lt;= emails[i].length \u0026lt;= 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eemails[i]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003econsist of lowercase English letters,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'+'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'.'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eand\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'@'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eemails[i]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003econtains exactly one\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'@'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003echaracter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll local and domain names are non-empty.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLocal names do not start with a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e'+'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 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before\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e\\\".com\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003esuffix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":364,"title":"Matrix spiral","description":"Make a spiral in a (n*n) matrix. The spiral has to start in the top left, and has to rotate clockwise to the center. The spiral has to have a padding of zeros between itself.\r\n\r\nThe (n*n) matrix is filled with zeros except for the spiral, that has to be made of 11 (elevens, for visual reference).\r\nThe final matrix has to have the same or more zeros than elevens.\r\n\r\nExample:\r\nn=8\r\n\r\nA =\r\n\r\n    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11     0    11\r\n     0     0    11     0     0    11     0    11\r\n     0     0    11     0    11    11     0    11\r\n     0     0    11     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0","description_html":"\u003cp\u003eMake a spiral in a (n*n) matrix. The spiral has to start in the top left, and has to rotate clockwise to the center. The spiral has to have a padding of zeros between itself.\u003c/p\u003e\u003cp\u003eThe (n*n) matrix is filled with zeros except for the spiral, that has to be made of 11 (elevens, for visual reference).\r\nThe final matrix has to have the same or more zeros than elevens.\u003c/p\u003e\u003cp\u003eExample:\r\nn=8\u003c/p\u003e\u003cp\u003eA =\u003c/p\u003e\u003cpre\u003e    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11     0    11\r\n     0     0    11     0     0    11     0    11\r\n     0     0    11     0    11    11     0    11\r\n     0     0    11     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0\u003c/pre\u003e","function_template":"function A = Matrix_Spiral(n)\r\n  A = n;\r\nend","test_suite":"%%\r\nn = 1;\r\ny_correct =[0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 2;\r\ny_correct =[11    11\r\n     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 3;\r\ny_correct =[11    11    11\r\n     0     0    11\r\n     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 4;\r\ny_correct =[11    11    11    11\r\n     0     0     0    11\r\n     0     0    11    11\r\n     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n\r\n%%\r\nn = 5;\r\ny_correct =[11    11    11    11    11\r\n     0     0     0     0    11\r\n     0     0    11     0    11\r\n     0     0    11    11    11\r\n     0     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n%%\r\nn = 10;\r\ny_correct =[11    11    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0    11     0    11\r\n     0     0    11     0    11    11     0    11     0    11\r\n     0     0    11     0    11     0     0    11     0    11\r\n     0     0    11     0    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))\r\n\r\n\r\n%%\r\nn = 17;\r\ny_correct =[11    11    11    11    11    11    11    11    11    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11    11    11    11    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0     0     0     0     0     0     0     0    11     0    11\r\n     0     0    11     0    11    11    11    11    11    11    11    11    11     0    11     0    11\r\n     0     0    11     0    11     0     0     0     0     0     0     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11    11    11    11    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0     0     0    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0    11     0    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0    11    11    11     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11     0     0     0     0     0    11     0    11     0    11\r\n     0     0    11     0    11     0    11    11    11    11    11    11    11     0    11     0    11\r\n     0     0    11     0    11     0     0     0     0     0     0     0     0     0    11     0    11\r\n     0     0    11     0    11    11    11    11    11    11    11    11    11    11    11     0    11\r\n     0     0    11     0     0     0     0     0     0     0     0     0     0     0     0     0    11\r\n     0     0    11    11    11    11    11    11    11    11    11    11    11    11    11    11    11\r\n     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0];\r\nassert(isequal(Matrix_Spiral(n),y_correct))","published":true,"deleted":false,"likes_count":5,"comments_count":3,"created_by":872,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":98,"test_suite_updated_at":"2012-02-20T12:29:13.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-02-20T12:17:08.000Z","updated_at":"2026-04-28T18:06:26.000Z","published_at":"2012-02-20T12:29:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a spiral in a (n*n) matrix. The spiral has to start in the top left, and has to rotate clockwise to the center. The spiral has to have a padding of zeros between itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe (n*n) matrix is filled with zeros except for the spiral, that has to be made of 11 (elevens, for visual reference). The final matrix has to have the same or more zeros than elevens.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: n=8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA =\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    11    11    11    11    11    11    11    11\\n     0     0     0     0     0     0     0    11\\n     0     0    11    11    11    11     0    11\\n     0     0    11     0     0    11     0    11\\n     0     0    11     0    11    11     0    11\\n     0     0    11     0     0     0     0    11\\n     0     0    11    11    11    11    11    11\\n     0     0     0     0     0     0     0     0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44345,"title":"MATLAB Counter","description":"Write a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b. \r\n\r\nE.g.,\r\n\r\n  \u003e\u003e f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\r\n  \u003e\u003e f()\r\n  ans =\r\n       0\r\n  \u003e\u003e f()\r\n  ans =\r\n       1\r\n  \u003e\u003e f()\r\n  ans =\r\n       2\r\n\r\n\r\n","description_html":"\u003cp\u003eWrite a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b.\u003c/p\u003e\u003cp\u003eE.g.,\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e\u0026gt;\u0026gt; f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     0\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     1\r\n\u0026gt;\u0026gt; f()\r\nans =\r\n     2\r\n\u003c/pre\u003e","function_template":"function y = counter(x,b)\r\n  y = x;\r\nend","test_suite":"%%\r\nassessFunctionAbsence({'regexp','regexpi','regexprep','str2num'},'FileName','counter.m')\r\n\r\n%%\r\nf = counter(0,1);\r\nassert(isequal(f(),0))\r\nassert(isequal(f(),1))\r\nassert(isequal(2,f()))\r\nassert(isequal(3,f()))\r\n\r\n%%\r\nf = counter(1,0);\r\nassert(isequal(f(),1))\r\nassert(isequal(f(),1))\r\nassert(isequal(1,f()))\r\nassert(isequal(1,f()))\r\n\r\n%%\r\nf = counter(10,2);\r\nassert(isequal(f(),10))\r\nassert(isequal(f(),12))\r\nassert(isequal(14,f()))\r\nassert(isequal(16,f()))\r\n\r\n%%\r\nf = counter(0,5);\r\ny_correct = [0, 5, 10, 15, 20, 55];\r\nassert(isequal([f() f() f() f() f() f()+f()],y_correct))\r\n\r\n%%\r\nx0 = randi(10);\r\nb = randi(10);\r\nf = counter(x0,b);\r\ny_correct = x0 + (0:1000)*b;\r\nassert(isequal(arrayfun(@(n)f(),0:1000),y_correct))","published":true,"deleted":false,"likes_count":23,"comments_count":9,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":302,"test_suite_updated_at":"2017-10-17T00:19:49.000Z","rescore_all_solutions":false,"group_id":34,"created_at":"2017-09-24T01:58:21.000Z","updated_at":"2026-04-22T09:04:29.000Z","published_at":"2017-10-16T01:45:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function f = counter(x0,b) to construct a counter handle f that counts with an initial value x0 and a step size b.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE.g.,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e f = counter(0,1)  % Initialize a counter f() with initial_count = 0 and step_size = 1\\n\u003e\u003e f()\\nans =\\n     0\\n\u003e\u003e f()\\nans =\\n     1\\n\u003e\u003e f()\\nans =\\n     2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42503,"title":"Generating random matrix with given probability mass function","description":"Inspired by \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2356-simulating-the-selection-of-a-state-with-given-probabilities Problem 2356. Simulating the selection of a state with given probabilities\u003e, let's consider a similar yet more useful problem. Write a function\r\n\r\n                             x = rndsampling(m,n,prob)\r\n\r\nto generate an m-by-n matrix x, whose entries are drawn independently from integer symbols 1:numel(prob) according to the given probability mass function prob. Specifically, symbol k occurs with probability prob(k), k = 1, 2, ..., numel(prob), where all(prob\u003e0) == 1 and sum(prob) == 1.","description_html":"\u003cp\u003eInspired by \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2356-simulating-the-selection-of-a-state-with-given-probabilities\"\u003eProblem 2356. Simulating the selection of a state with given probabilities\u003c/a\u003e, let's consider a similar yet more useful problem. Write a function\u003c/p\u003e\u003cpre\u003e                             x = rndsampling(m,n,prob)\u003c/pre\u003e\u003cp\u003eto generate an m-by-n matrix x, whose entries are drawn independently from integer symbols 1:numel(prob) according to the given probability mass function prob. Specifically, symbol k occurs with probability prob(k), k = 1, 2, ..., numel(prob), where all(prob\u0026gt;0) == 1 and sum(prob) == 1.\u003c/p\u003e","function_template":"function x = rndsampling(m,n,prob);\r\n  x = rand(m,n)\r\nend","test_suite":"%%\r\nrnd = sort(rand(randi([10,20]),1));\r\nprob = vertcat(rnd(1,:),diff(rnd,1,1),1-rnd(end,:));\r\nsz = [1 1e5;1e5 1;1e3 1e2;randi([100 200], 100, 2)];\r\nsz = sz(randi(size(sz,1)),:);\r\nx = rndsampling(sz(1),sz(2),prob);\r\nprob_est = histcounts(x,1:numel(prob)+1,'Normalization','probability').';\r\nerr = mean(abs(prob_est - prob))\r\nassert(err \u003c 0.005 \u0026\u0026 isequal(size(x),sz) \u0026\u0026 all(~isnan(x(:))));\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":117,"test_suite_updated_at":"2015-08-13T18:44:59.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2015-08-11T19:26:49.000Z","updated_at":"2026-04-30T03:11:57.000Z","published_at":"2015-08-11T19:26:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2356-simulating-the-selection-of-a-state-with-given-probabilities\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 2356. Simulating the selection of a state with given probabilities\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, let's consider a similar yet more useful problem. Write a function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[                             x = rndsampling(m,n,prob)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eto generate an m-by-n matrix x, whose entries are drawn independently from integer symbols 1:numel(prob) according to the given probability mass function prob. Specifically, symbol k occurs with probability prob(k), k = 1, 2, ..., numel(prob), where all(prob\u0026gt;0) == 1 and sum(prob) == 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1092,"title":"Decimation","description":"When dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn.  The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\r\n\r\nThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences.  Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others.  Instead of killing every tenth prisoner, he chooses a number (kill_every).  If kill_every=3, he kills every third prisoner.  If kill_every=5, he kills every fifth prisoner.  He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left.  For example, if there are 10 prisoners, and kill_every=3\r\n\r\nFirst iteration: 1 2 3 4 5 6 7 8 9 10\r\n\r\n1-2-3 4-5-6 7-8-9 10\r\n\r\nPrisoners 3, 6 and 9 will be killed.\r\n\r\nSecond iteration: 1 2 4 5 7 8 10\r\n\r\nBecause Prisoner 10 was counted during the first iteration, the executions\r\nwill proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\r\n\r\nThird iteration: 1 4 5 8 10\r\n8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\r\n\r\nFourth Iteration:  10-4-5 10\r\nPrisoner 5 is executed.\r\n\r\nFifth iteration:  10-4 10\r\nPrisoner 10 is executed\r\n\r\nSince the sole survivor is prisoner 4, he is released.\r\n\r\nYou are an unlucky prisoner caught by Carnage Maximum.  Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day.  Your job is to figure out which prisoner you need to be in order to survive.  Write a MATLAB script that takes the values of num_prisoners and kill_every.  The output will be survivor, which is the position of the person who survives.  If you write your script quickly enough, that person will be you.\r\n\r\nGood luck!","description_html":"\u003cp\u003eWhen dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn.  The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\u003c/p\u003e\u003cp\u003eThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences.  Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others.  Instead of killing every tenth prisoner, he chooses a number (kill_every).  If kill_every=3, he kills every third prisoner.  If kill_every=5, he kills every fifth prisoner.  He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left.  For example, if there are 10 prisoners, and kill_every=3\u003c/p\u003e\u003cp\u003eFirst iteration: 1 2 3 4 5 6 7 8 9 10\u003c/p\u003e\u003cp\u003e1-2-3 4-5-6 7-8-9 10\u003c/p\u003e\u003cp\u003ePrisoners 3, 6 and 9 will be killed.\u003c/p\u003e\u003cp\u003eSecond iteration: 1 2 4 5 7 8 10\u003c/p\u003e\u003cp\u003eBecause Prisoner 10 was counted during the first iteration, the executions\r\nwill proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\u003c/p\u003e\u003cp\u003eThird iteration: 1 4 5 8 10\r\n8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\u003c/p\u003e\u003cp\u003eFourth Iteration:  10-4-5 10\r\nPrisoner 5 is executed.\u003c/p\u003e\u003cp\u003eFifth iteration:  10-4 10\r\nPrisoner 10 is executed\u003c/p\u003e\u003cp\u003eSince the sole survivor is prisoner 4, he is released.\u003c/p\u003e\u003cp\u003eYou are an unlucky prisoner caught by Carnage Maximum.  Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day.  Your job is to figure out which prisoner you need to be in order to survive.  Write a MATLAB script that takes the values of num_prisoners and kill_every.  The output will be survivor, which is the position of the person who survives.  If you write your script quickly enough, that person will be you.\u003c/p\u003e\u003cp\u003eGood luck!\u003c/p\u003e","function_template":"function survivor=decimate(num_prisoners,kill_every)\r\nsurvivor=4;\r\nend","test_suite":"%%\r\nassert(isequal(decimate(10,3),4))\r\n%%\r\nassert(isequal(decimate(1024,3),676))\r\n%%\r\nassert(isequal(decimate(2012,50),543))\r\n%%\r\nassert(isequal(decimate(30,5),3))\r\n%%\r\nassert(isequal(decimate(10,10),8))\r\n%%\r\nassert(isequal(decimate(2048,2),1))","published":true,"deleted":false,"likes_count":20,"comments_count":12,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":315,"test_suite_updated_at":"2012-12-04T21:28:04.000Z","rescore_all_solutions":false,"group_id":13,"created_at":"2012-12-04T19:47:49.000Z","updated_at":"2026-04-20T18:16:53.000Z","published_at":"2012-12-04T19:53:55.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen dealing to the Roman Army, the term decimate meant that the entire unit would be broken up into groups of ten soldiers, and lots would be drawn. The person who was unlucky enough to draw the short straw would be executed by the other nine members of his group.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe bloodthirsty Roman Centurion Carnage Maximus decided to apply this to his prisoners, with a few gruesome differences. Rather than kill every tenth prisoner and allow the rest to live, he is going to leave only one prisoner alive and kill all of the others. Instead of killing every tenth prisoner, he chooses a number (kill_every). If kill_every=3, he kills every third prisoner. If kill_every=5, he kills every fifth prisoner. He always chooses a number between 2 and the number of prisoners he has, and this process will be repeated until there is only one prisoner left. For example, if there are 10 prisoners, and kill_every=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst iteration: 1 2 3 4 5 6 7 8 9 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1-2-3 4-5-6 7-8-9 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePrisoners 3, 6 and 9 will be killed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSecond iteration: 1 2 4 5 7 8 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBecause Prisoner 10 was counted during the first iteration, the executions will proceed as such: 10-1-2 4-5-7 8-10, so prisoners 2 and 7 will be killed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThird iteration: 1 4 5 8 10 8-10-1 4-5-8 10, so prisoners 1 and 8 executed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFourth Iteration: 10-4-5 10 Prisoner 5 is executed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFifth iteration: 10-4 10 Prisoner 10 is executed\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince the sole survivor is prisoner 4, he is released.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are an unlucky prisoner caught by Carnage Maximum. Prior to lining up the prisoners, he reveals the number of prisoners he has and his value of kill_every for the day. Your job is to figure out which prisoner you need to be in order to survive. Write a MATLAB script that takes the values of num_prisoners and kill_every. The output will be survivor, which is the position of the person who survives. If you write your script quickly enough, that person will be you.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":59516,"title":"Determine aquifer properties: slug test","description":"An important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems 59152, 49473,  and 59147, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity  of the aquifer are determined. \r\nInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement  of water in the well is given as a function of time  by\r\n\r\nwhere  is the initial displacement,  is the radius of the well casing,  is the radius of the well screen,  is the length of the well screen, and  is the effective distance over which the water table returns to its undisturbed level. If the distance  from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness , then \r\n\r\nIf ,\r\n\r\nBouwer and Rice provided the coefficients , , and  in a figure, and Yang and Yeh (2004) fit the curves as functions of :\r\n\r\n\r\n\r\nWrite a function that computes the distance  and determines the hydraulic conductivity  by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1075.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 537.75px; transform-origin: 407px 537.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382.358px 8px; transform-origin: 382.358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59152\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e59152\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/49743\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e49473\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,  and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/59147-determine-aquifer-properties-steady-pump-test-in-a-leaky-confined-aquifer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e59147\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.4667px 8px; transform-origin: 89.4667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.56667px 8px; transform-origin: 9.56667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer are determined. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.933px 8px; transform-origin: 383.933px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.075px 8px; transform-origin: 152.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of water in the well is given as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 8px; transform-origin: 9.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-20px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"181\" height=\"42\" alt=\"H = H0 exp(-2KLet/(rc^2 ln(Re/R)))\" style=\"width: 181px; height: 42px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.5px; text-align: left; transform-origin: 384px 32.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" alt=\"H0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.6333px 8px; transform-origin: 83.6333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the initial displacement, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"13.5\" height=\"20\" alt=\"rc\" style=\"width: 13.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.1833px 8px; transform-origin: 99.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of the well casing, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.9583px 8px; transform-origin: 99.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the radius of the well screen, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16\" height=\"20\" alt=\"Le\" style=\"width: 16px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 49.3917px 8px; transform-origin: 49.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the length of the well screen, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"20\" alt=\"Re\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302.475px 8px; transform-origin: 302.475px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the effective distance over which the water table returns to its undisturbed level. If the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"18\" height=\"20\" alt=\"Lw\" style=\"width: 18px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.0416667px 8px; transform-origin: 0.0416667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.4417px 8px; transform-origin: 19.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"305.5\" height=\"44\" alt=\"ln(Re/R) = [1.1/ln(Lw/R) + [A+Bln((h-Lw)/R)]/(Le/R)]^{-1}\" style=\"width: 305.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.825px 8px; transform-origin: 5.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"20\" alt=\"Lw = h\" style=\"width: 44px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.9px; text-align: left; transform-origin: 384px 21.9px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"203\" height=\"44\" alt=\"ln(Re/R) = [1.1/ln(Lw/R) + C/(Le/R)]^{-1}\" style=\"width: 203px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.525px 8px; transform-origin: 132.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBouwer and Rice provided the coefficients \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.15px 8px; transform-origin: 206.15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in a figure, and Yang and Yeh (2004) fit the curves as functions of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"101\" height=\"20\" alt=\"x = log10(Le/R)\" style=\"width: 101px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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Es7MspDHqndWYQvTaLL8aEyiBsqflU2dGCl2XHNBSjh0Xw4jEiFVu8CWZd5aLuOI+FKHJ6cYHX2EgJQjjA/OR+kk6mvUmLeixTVM9+i8x6KW2zgaQ//7TKS9rHcv8RVBIa/uiDxFj3FExlbYjUiaQ4ljufKzJ/I9GvtzrfIdoTOjvvnf/WakqIzTZtJORpuHZdtId8JXQ4L1FUe1IUp+I6tQM/1u3bvC/kfSGmd8WtRP+j6VaSZwOfJiSRnimEH24PDJ+tYHrPQ8dp4VQ1bS32OFdusqye8eLtAaD88bIpPyoQy0cve8wi95UdGSPcS3DH3POIH7dZrEcCAaN9w24lsjO5GlFuCZWRYq4VSkOUpEVxg+2hB9H/ci12zy0CYO/oahIjf2Q1aIrnJFlyORnd4u5gjx5X2M2SutaNOg8rd/zf72utO4+A+PRJ34TOrKHp2XLHjHsVUfo6SgVv9e4kv7uWYm+rP99BOdUV/3Et8taQ7qj099efJsJyfuvzTiO6MzE938KhnVp4xH40690UmYVpx4ppygbEmnLNNcjkpdWGH/I8R3ZjyjKYG1cWdiA3HVxJ9V/M9YwT99yorPmffPS8/KiUlvD1iU+G4NfEQnSV35jxDfIyK+EBESpKOb28pOiMhEhMs/u2dz24whuaZ79zow+uoNRfRkBo2djzZEn42SP42Dxn2GiPbGcHWqw0hevJOIKv4Wpx2J9Kmt3lmW6VBRkjeTurJV50fYnuv3KCa19mhz4pGkl/d6ZzQiQHvtxpY0B2GjZ2fkdfU4r0x1oG1R+ZjRmZk+q97RuCsKyIR8FHTSOLXs9Uy6E33xhGvUzpm+3897dXrWSJblw3pfN53th8ezDHDqt1a6mn/Wj+8eLtBqv/c1S3x4i/j62cUROb57CGgZBY0eiQaovJew/ZYowRYiUQ7kLFGfFeQt9+91YLwz+sEDrxRStOhXyTxBHuWEljhI3lYZy3MSX4/tzCR0i7yOjK/H1ZOPcqODSOqoPrVxZGP26PwWnTjimSixKd99LtLLez2ZG21o3mM3FOnaciRbGY27X/s1VhPf1TozK8PI50hfZ0gv7xepa5EVH/Ec+Uafi0zd0S+YzeJw7vv9PonRl25bkdmtbZbM1TYaql29cVFE2MvNHi7Q6ofnozM+sIlLizR6ksHD0VMQEE5yQEabDWQ0o/WqA8orerP9gcI1Y/hQ7tlood69hUiUwI+Ue6sA73lujwPz740sP/qIkievUsAeAfJEayavT8a1t9FqFr9zEt8jZvr0N5rqUMPGk4+aPkWWJL3T6+nkXp2fHduj7t9CfCOkFxxXLflKPyN2ao/dULRo1omJ/JBXymkOXPeLAK0mvit1ZlaGNe49PYySXi+PkvlelE72bSRz3MdGdqWCzcrOLCbnut9HTlureZ5Mrko99fpbCyRFxqXlQ/ZwgRJ33sGYs1dFG3Bngp3VcWxVsGV2JcUgcb13IDUNUZQvumzLM2oTO0g5vuLLFcMHYW+9W++cjRaeSwHu13tmHVjryLjIMpRXFB9R8s+2JkOKHswqvt65ZInkNEjnIr4er94mEh3j9IkJIdpKfL1twPnUlt8jS1OePLcmr3t1fgKOw2+dJb7oBGdl8nnpFrHVh3t8yhiY6Win2U5pl37rqCJf36zd8M8qmjSrkzhjltg5xUfO1RMgMIO8rZoI9PBbTXxX6Axtah3t1OsLuD7FSu90BmTj0VZ0DGWtPvwvx4zplCWNUc9mi2CNPrLAx4kIqOHfHzq9XPyFfrNha8b+zerGkfcr8NOaeCgQ2VohGR3jWra9tvJa3qOJWC8YJRtQTkL2cAHfDtp5zwonSuhcbn6Xv0Bn+DuyOXX1mLNfgqbSHmGkowguUdgR6VUDGeyPWqntONc9dJydhAg15/V6Ul0aPjrPrKB1tBmDRB9GS3hTAN6Cm2ccmL+3nLT4o1Fas3cpeM3hyQDWjKTPN/JEANnhXD+WgGpGw+8o3ppPXhvicxDfKOmNGLFeH0bLm/5Z8NSO7Bbp1f0iN636FcEvZWWlzl+Ses4QX8k7evLJRic4WQOb60mqn5SUDos6b042EjtYkkO9MxpBnbEbvgs+zWF0LB/yxgWhkXNT232EFD9G+19oZbTauEomVhNf2rVVZ3jWrwz5FTFvR2r+OTLufkKEL65dnBLA2Ph3q+6WDWilvEBoKNgG6vAfn/CrhhAg2oNNuuajzbwNr5232/ObPZ9cGyfvM3sTksiGx9bmt61cQJN2Jm+8n/N6b05y4FcIsVFvsQIn3HS02ShkjOHh5TqyCGOKkGGMmdk9wwpfwdlyttqIiPp0CxSHA7C9wfaGT1+CqRl0DX6EaNdV+nb/1efPjCLw/t4e0YSIlkolotNSNq0YPMme9e0QeSXiW36Ewc8sGSV9VpEv/WCIkU0OMB9twpgd4SOJLwr/m1YwhujbK6z0Ihne8M2kc8xGfDW5Bat3BzD141kjYSxVl+R5tc7PjutR93vHNspnLmW616byQwz+PeUmGJ9LqK+0cVoIF5E+TgAZfT7Wt2XGbvjn1L8RDuXZ1XyZ05MbT4B0vuc5yc8RxHeLzghbn4rng1Syu7oP3N9kBcLIUYlE0zim8B0NQSuf78ljLeCh53mv/6IqfcWnE2kuV7P8hi/JJ3VzlSchcO+NFf3ea98l/9bSi5HfHPlk9Rnc3nDCWkdTtsZcz/iJSzlJFf9q+XN/RGeUC5Q2qpyo+ePs6MOMvXrY2I+IrweATwESLS2PxPhj+9sHrcwuL/l8rdoAlDMTnKJ/BwSBiDGkHGDL331HlSc4kxt6yUqyt21gR2QcZ6dJjeqE0HLESS1yr4kQE50WIZOC6YxAzm/k4hmOwOoZKP+snmEzIsubELXaF/kUEYAw64JQEf3/VStHLH8dQXyRURwRqQNgds/KyDDRXzmQJ9i/ew7MwfPVf0aIL3LyPCs6sxd9IwrZ+8xo+R5FGrEbjIuuWv9W6nzZjvvx/4pCMrb+wmi/y8r7rHj59GQu0t6a08EhvdxKOTlBd3/Zim8LZITTdT5gJZIisNVu+L7IuY0iy96+Izc/XpE7Of3W7xEMt95zBPFVW2Z0xj8Dph+34qPesqn+s/H+M+LIS0uffXApglMrcAJWHH34oBX5A+rDRtfsicYVPbmxUvoM2a7W75G2XuI9wumpJ73E90k/W75g5JP5/SVWFKAkEES0NMrX0EMIKBMkfDiFa9afc17wiAuMVifkH3j/THbBI8Y6SnyPEhJ15Oj0A2YKDHj0C29H9TfrvR0IyDGx2WJFNBlDD7knUs0kcoZYHoUofWSyi3MiMnjtEZWjcMp67yYCyq+m9yvTqO4mmtnrIxBg4sL1pZMNPyIIdES7D6/zfhNfOqjcrV6u7x4gmEWwKzCN0x4U89lEIBFIBBKBRCARSASuHIFLIL5ASMTrnpXI0u4M5CwdvN2Kzy2aeT7vTQQSgUQgEUgEEoFEIBG4JQhcCvEFTiK/H1lIfrUUVTtu6ZYMX3YjEUgEEoFEIBFIBBKBRCCKwCURX9pMusP0mWyNzq6sK4pn3pcIJAKJQCKQCCQCiUAicKEIXBrxvVCYslmJQCKQCCQCiUAikAgkAteOQBLfax/BbH8ikAgkAolAIpAIJAKJQAiBJL4hmPKmRCARSAQSgUQgEUgEEoFrRyCJ77WPYLY/EUgEEoFEIBFIBBKBRCCEQBLfEEx5UyKQCCQCiUAikAgkAonAtSPwf/RFCqAs9MSiAAAAAElFTkSuQmCC\" width=\"351\" height=\"19.5\" alt=\"C(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\" style=\"width: 351px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 136px 8px; transform-origin: 136px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that computes the distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16.5\" height=\"20\" alt=\"Re\" style=\"width: 16.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.258px 8px; transform-origin: 132.258px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and determines the hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.625px 8px; transform-origin: 83.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 412.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 206.35px; text-align: left; transform-origin: 384px 206.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"455\" height=\"407\" style=\"vertical-align: baseline;width: 455px;height: 407px\" 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\" alt=\"Schematic of the Bouwer-Rice slug test\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h)\r\n%  t = measurement time\r\n%  H = displacement\r\n%  rc = casing radius\r\n%  R = screen radius\r\n%  Le = screen length\r\n%  Lw = distance from undisturbed water table to bottom of well\r\n%  h = initial saturated thickness\r\n  Re = ln(Re/R) = [1.1/ln(Lw/R) + [A+B*ln((h-Lw)/R)]/(Le/R)]^{-1}\r\n  K = rc^2*log(Re/R)*log(H(1)/H)/(2*Le*t);\r\nend","test_suite":"%%\r\nt = 0:2:16;             %  Measurement times (sec)                                                 \r\nrc = 0.05;              %  Casing radius (m)\r\nR = 0.1;                %  Screen radius (m)\r\nLe = 3;                 %  Screen length (m)\r\nLw = 5;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.5 0.645 0.372 0.195 0.13 0.067 0.044 0.023 0.015];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 2.82e-4;\r\nRe_correct = 1.11;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:2:16;             %  Measurement times (sec)\r\nrc = 0.03;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 4;                 %  Screen length (m)\r\nLw = 6;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.0 0.498 0.248 0.123 6.14e-2 3.06e-2 1.52e-2 7.57e-3 3.77e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 8.10e-5;\r\nRe_correct = 1.576;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:2:16;             %  Measurement times (sec)\r\nrc = 0.03;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 4;                 %  Screen length (m)\r\nLw = 6;                 %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [1.0 0.498 0.248 0.123 6.14e-2 3.06e-2 1.52e-2 7.57e-3 3.77e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 8.10e-5;\r\nRe_correct = 1.576;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:5:40;             %  Measurement times (sec)\r\nrc = 0.04;              %  Casing radius (m)\r\nR = 0.2;                %  Screen radius (m)\r\nLe = 3.5;               %  Screen length (m)\r\nLw = 15;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 15;                 %  Undisturbed saturated thickness (m)\r\nH = [0.8 0.404 0.204 0.103 5.21e-2 2.63e-2 1.33e-2 6.72e-3 3.4e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 9.4e-5;\r\nRe_correct = 4.065;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:50:400;           %  Measurement times (sec)\r\nrc = 0.035;             %  Casing radius (m)\r\nR = 0.08;               %  Screen radius (m)\r\nLe = 7;                 %  Screen length (m)\r\nLw = 14;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 28;                 %  Undisturbed saturated thickness (m)\r\nH = [1.7 0.978 0.562 0.323 0.186 0.107 6.15e-2 3.53e-2 2.03e-2];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 3.2e-6;\r\nRe_correct = 2.179;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:50:400;           %  Measurement times (sec)\r\nrc = 0.035;             %  Casing radius (m)\r\nR = 0.08;               %  Screen radius (m)\r\nLe = 7;                 %  Screen length (m)\r\nLw = 28;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 28;                 %  Undisturbed saturated thickness (m)\r\nH = [1.7 1.11 0.719 0.467 0.304 0.197 0.128 8.35e-2 5.43e-2];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 3.2e-6;\r\nRe_correct = 5.592;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nt = 0:60:480;           %  Measurement times (sec)\r\nrc = 0.04;              %  Casing radius (m)\r\nR = 0.1;                %  Screen radius (m)\r\nLe = 5;                 %  Screen length (m)\r\nLw = 30;                %  Distance from undisturbed water table to bottom of well screen (m)\r\nh = 30;                 %  Undisturbed saturated thickness (m)\r\nH = [1.3 0.651 0.326 0.163 8.16e-2 4.09e-2 2.05e-2 1.02e-2 5.13e-3];   %  Displacements (m)\r\n[K,Re] = BouwerRice(t,H,rc,R,Le,Lw,h);\r\nK_correct = 7.43e-6;\r\nRe_correct = 5.608;\r\nassert(abs((K-K_correct)/K_correct) \u003c 5e-3)\r\nassert(abs((Re-Re_correct)/Re_correct) \u003c 5e-3)\r\n\r\n%%\r\nfiletext = fileread('BouwerRice.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2023-12-30T14:18:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-12-30T13:54:14.000Z","updated_at":"2026-02-12T15:36:49.000Z","published_at":"2023-12-30T14:04:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn important task in characterizing the flow of groundwater is to determine the properties of the aquifer, or the underground water-bearing formation. One approach is to disturb the aquifer, observe its response, and fit a theoretical formula to the observations. This approach is demonstrated in Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59152\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e59152\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/49743\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e49473\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e,  and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/59147-determine-aquifer-properties-steady-pump-test-in-a-leaky-confined-aquifer\\\"\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e59147\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, which involve steady pump tests in confined or unconfined aquifers, an unsteady pump test in a confined aquifer, and a steady pump test in a leaky confined aquifer. In these cases, a well is pumped at a constant rate, and properties such as the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer are determined. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInstead of pumping a well, one can displace the water in the well—by pouring water into the well, bailing it out of the well, or inserting a “slug” and removing it quickly—and observing how the water level recovers. In the Bouwer-Rice model of a slug test, the displacement \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of water in the well is given as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H = H0 exp(-2KLet/(rc^2 ln(Re/R)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH = H_0 \\\\exp\\\\left(-\\\\frac{2 K L_e t}{r_c^2 \\\\ln(R_e/R)}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the initial displacement, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"rc\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er_c\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of the well casing, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the radius of the well screen, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Le\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the length of the well screen, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the effective distance over which the water table returns to its undisturbed level. If the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Lw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the undisturbed water table to the bottom of the well is smaller than the initial saturated thickness \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ln(Re/R) = [1.1/ln(Lw/R) + [A+Bln((h-Lw)/R)]/(Le/R)]^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ln\\\\left(\\\\frac{R_e}{R}\\\\right) = \\\\left[\\\\frac{1.1}{\\\\ln(L_w/R)} + \\\\frac{A+B\\\\ln((h-L_w)/R)}{L_e/R}\\\\right]^{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Lw = h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL_w = h\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ln(Re/R) = [1.1/ln(Lw/R) + C/(Le/R)]^{-1}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\ln\\\\left(\\\\frac{R_e}{R}\\\\right) = \\\\left[\\\\frac{1.1}{\\\\ln(L_w/R)} + \\\\frac{C}{L_e/R}\\\\right]^{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBouwer and Rice provided the coefficients \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in a figure, and Yang and Yeh (2004) fit the curves as functions of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = log10(Le/R)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = \\\\log_{10}(L_e/R)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA(x) = 1.353+2.157x-4.027x^2+2.777x^3-0.460x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB(x) = -0.401+2.619x-3.267x^2+1.548x^3-0.210x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC(x) = -1.605+9.496x-12.317x^2+6.528x^3-0.986x^4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that computes the distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Re\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR_e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and determines the hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e by fitting the Bouwer-Rice formula to measurements of displacement as a function of time. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"407\\\"/\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59217,"title":"List lunar triangular numbers without duplication","description":"Triangular numbers—which are the subject of Cody Problems 5, 291, 44289, 44732, 45833, 55680, 55695, and 55705—are the sums of consecutive integers. For example, the 10th triangular number is the sum of the numbers 1 to 10, or 55. \r\nLunar addition, which is the subject of Cody Problem 44785, involves taking the largest digit in the sum. For example, 1+3 = 3, 3+6 = 6, 13+51 = 53, and 428+620 = 628.\r\nWrite a function to compute the th lunar triangular number without duplicating any terms. For example, the 10th lunar triangular number is 1+2+3+4+5+6+7+8+9+10 = 19. The 11th lunar triangular number is also 19, but because it is a duplicate, it would not be listed in this sequence. Express the answer as a character string.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.5px; transform-origin: 407px 82.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.683px 8px; transform-origin: 192.683px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTriangular numbers—which are the subject of Cody Problems \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/5\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e5\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/291\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e291\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44289\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44289\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44732\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e44732\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45833\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e45833\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55680\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55680\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55695\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55695\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 8px; transform-origin: 17.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55705\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003e55705\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.2px 8px; transform-origin: 18.2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—are the sums of consecutive integers. For example, the 10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 186.3px 8px; transform-origin: 186.3px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e triangular number is the sum of the numbers 1 to 10, or 55. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 118.642px 8px; transform-origin: 118.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLunar addition, which is the subject of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44785\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 44785\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 199.608px 8px; transform-origin: 199.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, involves taking the largest digit in the sum. For example, 1+3 = 3, 3+6 = 6, 13+51 = 53, and 428+620 = 628.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 98.6583px 8px; transform-origin: 98.6583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 238.45px 8px; transform-origin: 238.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth lunar triangular number without duplicating any terms. For example, the 10\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.45px 8px; transform-origin: 19.45px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e lunar triangular number is 1+2+3+4+5+6+7+8+9+10 = 19. The 11\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eth\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.042px 8px; transform-origin: 168.042px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e lunar triangular number is also 19, but because it is a duplicate, it would not be listed in this sequence. Express the answer as a character string.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = lunarTriNum(n)\r\n  y = num2str(n);\r\nend","test_suite":"%%\r\ns = char(48:57);\r\nfor n = 0:9\r\n    assert(strcmp(lunarTriNum(n),s(n+1)));\r\nend\r\n\r\n%%\r\nassert(strcmp(lunarTriNum(10),'19'))\r\n\r\n%%\r\nfor k = 1:1000\r\n    n = randi(10000);\r\n    assert(isequal(sum(lunarTriNum(n)-'0'),n))\r\nend\r\n\r\n%%\r\nn = 77;\r\np_correct = 215233605;\r\nassert(isequal(prod(lunarTriNum(n)-'0'),p_correct))\r\n\r\n%%\r\nn = 134;\r\np_correct = 183014339639688;\r\nassert(isequal(prod(lunarTriNum(n)-'0'),p_correct))\r\n\r\n%%\r\nn = 6259;\r\nlen_correct = 696;\r\nassert(isequal(length(lunarTriNum(n)),len_correct))\r\n\r\n%%\r\nn = 5*(10.^(1:7));\r\np = primes(1e8);\r\nx_correct = [267 4103 256889 33082235 4266286911 523279276675 61893416706717];\r\nfor k = 1:length(n)\r\n    a = str2num(reshape(lunarTriNum(n(k)),[],2));\r\n    x(k) = sum(a+p(1:size(a,1))');\r\nend\r\nassert(isequal(x,x_correct))\r\n\r\n%%\r\nfiletext = fileread('lunarTriNum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-11-25T14:58:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-11-25T14:57:46.000Z","updated_at":"2023-11-25T14:58:06.000Z","published_at":"2023-11-25T14:58:06.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTriangular numbers—which are the subject of Cody Problems \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/5\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/291\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e291\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44289\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44289\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44732\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e44732\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45833\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e45833\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55680\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55680\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55695\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55695\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55705\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e55705\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—are the sums of consecutive integers. For example, the 10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e triangular number is the sum of the numbers 1 to 10, or 55. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLunar addition, which is the subject of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44785\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 44785\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, involves taking the largest digit in the sum. For example, 1+3 = 3, 3+6 = 6, 13+51 = 53, and 428+620 = 628.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eth lunar triangular number without duplicating any terms. For example, the 10\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e lunar triangular number is 1+2+3+4+5+6+7+8+9+10 = 19. The 11\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eth\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e lunar triangular number is also 19, but because it is a duplicate, it would not be listed in this sequence. Express the answer as a character string.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56423,"title":"French Conundrum","description":"The French army is trapped, sorrounded in backwards direction (South and West directions) by enemy traps and ambushes. You are now constrained to move forward only (North, East and North-East).\r\nThe battle-ground is in a form of a 2-D rectangular lattice spanning from (0,0) to (m,n). In order to make a formidable strategy and safely retreat, it is necessary to visualize the field. Now to visualize the field, the first required is the number of all possible paths from your initial position (although relative, consider it to be 0,0) to the end point (m,n).\r\nHowever, to be cautious, you must only take a single step at a time to check from any traps and ambushes in the next step. If you take more than 1 step at a time, the enemy will know your location and the mission will fail.\r\n\r\nThey turn to you, The Army officer and an avid mathematics aficionado to solve the problem.\r\n\r\nGiven two whole numbers, m and n, find the number of paths with the mentioned restriction, to prepare a strategy.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 285px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 142.5px; transform-origin: 407px 142.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 357px 8px; transform-origin: 357px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe French army is trapped, sorrounded in backwards direction (South and West directions) by enemy traps and ambushes. You are now constrained to move forward only (North, East and North-East).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 228.5px 8px; transform-origin: 228.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe battle-ground is in a form of a 2-D rectangular lattice spanning from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15px 8px; transform-origin: 15px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(0,0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.5px 8px; transform-origin: 21.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(m,n). \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94.5px 8px; transform-origin: 94.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn order to make a formidable strategy and safely retreat, it is necessary to visualize the field. Now to visualize the field, the first required is the number of all possible paths from your initial position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(although relative, consider it to be 0,0)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.5px 8px; transform-origin: 53.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the end point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.5px 8px; transform-origin: 19.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e(m,n).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370px 8px; transform-origin: 370px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHowever, to be cautious, you must only take a single step at a time to check from any traps and ambushes in the next step. If you take more than 1 step at a time, the enemy will know your location and the mission will fail.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 291px 8px; transform-origin: 291px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThey turn to you, The Army officer and an avid mathematics aficionado to solve the problem.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 357px 8px; transform-origin: 357px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven two whole numbers, m and n, find the number of paths with the mentioned restriction, to prepare a strategy.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = henridnum(m,n)\r\n  y = f(m,n);\r\nend","test_suite":"%%\r\nfiletext = fileread('henridnum.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || ...\r\n          contains(filetext, 'switch'); \r\nassert(~illegal)\r\n\r\n%%\r\nassert(isequal(henridnum(1,1),3))\r\n\r\n%%\r\nassert(isequal(henridnum(1,3),7))\r\n\r\n%%\r\nassert(isequal(henridnum(3,2),(3+2)^2))\r\n\r\n%%\r\nassert(isequal(henridnum(2,8),145))\r\n\r\n%%\r\nassert(isequal(henridnum(5,5),1683))\r\n\r\n%%\r\nfor i=0:9\r\n    assert(isequal(henridnum(i,1),2*i+1))\r\nend\r\n\r\n%%\r\nassert(isequal(henridnum(6,4),1289))\r\n\r\n%%\r\nassert(isequal(henridnum(7,6),19825))\r\n\r\n%%\r\nassert(isequal(henridnum(3,3),(3+3+1)*3*3))\r\n\r\n%%\r\nassert(isequal(henridnum(8,6),40081))\r\n\r\n%%\r\nassert(isequal(henridnum(10,10),8097453))\r\n\r\n%%\r\nassert(isequal(henridnum(5,3),(5*3)^2+3+3))\r\n\r\n%%\r\nassert(isequal(henridnum(3,7),575))\r\n\r\n%%\r\nassert(isequal(henridnum(11,9),7059735))\r\n\r\n%%\r\nassert(isequal(henridnum(4,2),4*2*5+1))\r\n\r\n%%\r\nassert(isequal(henridnum(8,7),108545))\r\n\r\n%%\r\nassert(isequal(henridnum(11,13),224298231))\r\n\r\n%%\r\nassert(isequal(henridnum(12,12),251595969))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2022-10-27T11:34:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-26T17:38:03.000Z","updated_at":"2025-09-19T20:55:15.000Z","published_at":"2022-10-27T11:34:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe French army is trapped, sorrounded in backwards direction (South and West directions) by enemy traps and ambushes. You are now constrained to move forward only (North, East and North-East).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe battle-ground is in a form of a 2-D rectangular lattice spanning from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(0,0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(m,n). \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eIn order to make a formidable strategy and safely retreat, it is necessary to visualize the field. Now to visualize the field, the first required is the number of all possible paths from your initial position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(although relative, consider it to be 0,0)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e to the end point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(m,n).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003eHowever, to be cautious, you must only take a single step at a time to check from any traps and ambushes in the next step. If you take more than 1 step at a time, the enemy will know your location and the mission will fail.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThey turn to you, The Army officer and an avid mathematics aficionado to solve the problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven two whole numbers, m and n, find the number of paths with the mentioned restriction, to prepare a strategy.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60406,"title":"Alert a city about a spill","description":"Problem statement\r\nCody Problem 54750 involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s maximum contaminant level (MCL). As in CP 54750, the spill of mass  will be assumed instantaneous at position  and time  and mixed over the cross section (with area ). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with  \r\n\r\nwhere  is the mean velocity of the river,  is the discharge or volumetric flow rate, and  is a dispersion coefficient, which describes spreading by several mechanisms. \r\nWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position  downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return 'The MCL is not exceeded.' Please note that the MCL is given in mg/L, whereas other variables are given in SI units. \r\nDetails\r\nMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of Seo and Cheong (1998):\r\n\r\nwhere  is the width of the channel (assumed rectangular here),  is the water depth, and  is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\r\n\r\nwhere  is the gravitational acceleration,  is the longitudinal slope of the channel,  is the hydraulic radius, and  is the wetted perimeter. For a rectangular channel, . \r\nIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city.  ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 690.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 345.017px; transform-origin: 407px 345.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 7.79167px; transform-origin: 63.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/54750\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 54750\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 307.167px 7.79167px; transform-origin: 307.167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003emaximum contaminant level\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 129.9px 7.79167px; transform-origin: 129.9px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (MCL). As in CP 54750, the spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23.3417px 7.79167px; transform-origin: 23.3417px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e will be assumed instantaneous at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.725px 7.79167px; transform-origin: 30.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"33.5\" height=\"18\" alt=\"t = 0\" style=\"width: 33.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34.2333px 7.79167px; transform-origin: 34.2333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and mixed\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.625px 7.79167px; transform-origin: 104.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 62.6083px 7.79167px; transform-origin: 62.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20px; text-align: left; transform-origin: 384px 20px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"204.5\" height=\"40\" alt=\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\" style=\"width: 204.5px; height: 40px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61.5\" height=\"18.5\" alt=\"U = Q/A\" style=\"width: 61.5px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.892px 7.79167px; transform-origin: 101.892px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.858px 7.79167px; transform-origin: 138.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the discharge or volumetric flow rate, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.625px 7.79167px; transform-origin: 48.625px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84.45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.225px; text-align: left; transform-origin: 384px 42.225px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.758px 7.79167px; transform-origin: 376.758px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 218.967px 7.79167px; transform-origin: 218.967px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.95px 7.79167px; transform-origin: 103.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 103.95px 8.25px; transform-origin: 103.95px 8.25px; \"\u003e'The MCL is not exceeded.' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.242px 7.79167px; transform-origin: 132.242px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.95px 7.79167px; transform-origin: 22.95px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eDetails\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 322.725px 7.79167px; transform-origin: 322.725px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eSeo and Cheong (1998)\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44.1333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.0667px; text-align: left; transform-origin: 384px 22.0667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"190.5\" height=\"44\" alt=\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\" style=\"width: 190.5px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.9083px; text-align: left; transform-origin: 384px 31.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eB\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 174.65px 7.79167px; transform-origin: 174.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the channel (assumed rectangular here), \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eH\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 74.675px 7.79167px; transform-origin: 74.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the water depth, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"u*\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 86.6083px 7.79167px; transform-origin: 86.6083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.9083px; text-align: left; transform-origin: 384px 10.9083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"90\" height=\"21\" alt=\"u* = sqrt(gRS0)\" style=\"width: 90px; height: 21px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.8167px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.4083px; text-align: left; transform-origin: 384px 21.4083px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.79167px; transform-origin: 21.0083px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK8AAAAnCAYAAAB5cRjAAAAH80lEQVR4Xu2cx6stRRDG3/sDzK5ciQEUFMUIhoUuzIigYkQExcxbiFk3LowYQDCi8BaKGTdmQRcGMKKgKBgWKq6M+Afo93tMSZ0+nWbunXPPeHrg4947M91dXf11dVV1z928qV1NAxPVwOaJyt3EbhrY1MjbSDBZDTTyTnbomuCNvI0Dy6iBXSTUvp1g76UEbORdxqFbXZkg7VPC8U4F3+v3LcKroVoaeVeXKGP0/DtVerrwxcDKP1a554UnhB2Ea4TLhT+EY8J6G3kHarkVm9PASbrzpLC38NsA/VD+AuHsoCyEPkS4XrjbP1tV8h4gJWzXKSLpUw0YAIoc5coNrRv5hlqvgWKvudhDXQ1XDKwJ0n4k/BCUv05/3yXcLty8yuS9VJ2/VnhW+Es4VjhMeFi4TxhiMYywt+gXfDaWPa6DhLM6pdfWDfGpB5l2HkiCjShGv78VzhfmfNM1CmTkPUf1PLOq5KXjkOlAwVs1CP2IgF/F8hTO/JLusRhPdySdsQy6Z8/e0O/nCanJgaXFuliggixTIi/9xPKOIbON266h/lbFbbhNHb9JgEQnRNj4ekec1PMUgffQA6LhHPFN+XOWo6uUyUNw8qWAz7hTV98YRChNxKHP6SN6CCfv0PqsnFn0O3Vjxt/lhVUgrxGM/l4mPBrRqFlIHp0s1C593mqnyGbLHq5KGIyEotgkmpLlhWC/CuGKtlbiUh7dnSkcGqtsFchrBKP/KQV7gvexvkZM6p5b1jqF2zv41aVgZorktThir/Vgq6sDV+pF4XAh6m6tAnlt2c6Rl2f/dIrrY/VI77zSlUuR01I9NRZ9PcgbZioss/K35IxlMJi4uwmp5yVO0r/HhdiK5staO9z7OkXIroC5C9kYpA95/ZbdL2qkb2BTUsJYz40QJfKSYN+zE6LPEujLhekcH7DFfO2wz0PIy7hgnU4RaO/N7icW8Q4BH9ouXJcrO+Iw8R5wfeadUmAZymsrFnpL8cEs6Cd65zMB/57AGSOBnxy6UvQHPVwshJNtZmLWkJdO3iowCxgcLnY9yMm93f1NsFHjJ/oJECqiz999Jo8nb8761ZI8lBOFviMYSRgkBucMgQxCys+O9XcIeRn8/QUCUi4IyPVnJ9dX+nluN2bcZwyRFeJtFX4Wrupktue1gReB8MFCamKaBbUJZX3m/ocCuvLkNeLeq/szaTH9zWQkvfnf/RJ5SX9AVGaI9z0sekcYlIUSwsZMUP+TPOa7sQc97/UhhPdL5xLdrt2h5KWKkMDcQ2fHCX1WqCHktS54+WOZDb9CxFwcc2+Qu9Z/pU7y0qmxt5UnNl48Oy0gL30gx41h9BekxrrPBMU58voI/GgV9LtFNYFKjI+Wz+zJ1bnXWe5qLL0R6/OuhnAS+oqHug1WR4zATGyCtFoCrwd5Uz67Nzgxt6jvmJohSgWq6MXqxMJincPAC9Kb5eXnhRlivKRnM351jry5mWgWmbZywq+VpOtV3gdtMevrJ+qQzQosw4MCrhVLJKuVXX3qG5O8npwl8tb4/DXbwT6g7TuRi2OfI69F37HBNivVZ4kpCjPiC+FRO+R+rGvvEv00P5Vbfftkfhp+pJ2owiptFSwAhMA1B1amRN7f1aea7WDvzqBf+FS7XZ6lRI68CMeAhOT1fmsf33NEblZXjSU4UiDI4CLg/EDYXrCUV84vjjVkgxPqwkiNNeYaO89bIv56Wl5Wqtrt4NgZXSYz7lRNnJQc3Bx5zTUId4bMnajZMQob3ohsQw2zhwZr+Ln40ynXwKJqLHCN9S0RMNeXUtn1JO+Q7WAjvE/d9TUUM/3PkdfPGKzKT4JPmdWmU3yDG5FtKJHXy1RjHX19RojcxkbNDp/VWSLgMpC3z3Yw6TjSWxaoUfYi4QbBSJw681Eat+LZBgaHhjgYwfWj8JYTpthA8MJGZBtyMnrLmMtEpOqoIa+fHKVAaArk7bMdjH5iewA+MzNkBd82HjnLa6mVvtaoL6E38n3LQkDc3OcrLHnsDL0QTFxzG+hDapfJIu6aQHAK5LVPdeZOeUUGEvLuLsTOdKyZXzXZBmSCwC8L3wi1OcuNJGWpbe8SkWmIbUVaHT6NFju0Y4RLTXKbIDXB7bKTt2Y72OveVqbYxLaYqubMR3Q8c+T1Dr4vzCDdM2ES+z39mrSN91kheng8z08ErxvuXy2wbTv3/VVkNMJ4INwYyk1I24Y1PzJGFh+UxiZS6TntZ48oJiwvW+TEBKcKttFlOh0lYENI8p9sb+4j2KEPUw7CzH3NWTJ3G/gcYhzR9QkxyPHiAtSuIrb8scOT+raMNk4ULA3H2QIOopTaoRxnD7Bq4fWpbrwv5HYTbZt1x6Cw7Uil6qfu5wS+5eNsQ1ie52E+trQdHMpP26QhuXyKkrpfE4Z+47etwtDy+oR7eI7SIkVmEtdgRzsySGPfgnzkc/sc6BlbpqnVb/790uyohuQ1VyGXvvD71dET7lMblSZvlQZsU8LOIlQVGvOlkLzm9+ScaPPN/s9ZiDF1PtW6a7eDF9a/kLyWvsg50hY95w4gL6wDraGFaMD+ochSfRSa8nntP5SQGrIABZ/nRoFnuZzoQrTZGlmoBjBYWN7SN3gLFSqVKmOm7SfwTzns4hBL7RcTC+1Ea2xUDfTZDh5VkLDy0pcUCxWmNbaUGiDGuV9YuuC8kXcp+dKEqtFAI2+Nlto7S6mBRt6lHJYmVI0G/gU0VRtGYpEBlwAAAABJRU5ErkJggg==\" width=\"87.5\" height=\"19.5\" alt=\"g = 9.81 m/s^2\" style=\"width: 87.5px; height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 7.79167px; transform-origin: 101.917px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gravitational acceleration, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"S0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 124.483px 7.79167px; transform-origin: 124.483px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the longitudinal slope of the channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"59\" height=\"18.5\" alt=\"R = A/P\" style=\"width: 59px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5667px 7.79167px; transform-origin: 50.5667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the hydraulic radius, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 159.858px 7.79167px; transform-origin: 159.858px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the wetted perimeter. For a rectangular channel, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"78\" height=\"18\" alt=\"P = B + 2H\" style=\"width: 78px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 7.79167px; transform-origin: 384px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.00833px 7.79167px; transform-origin: 1.00833px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = spillAlert(x,t0,M,Q,B,H,S0,MCL)\r\n% See the tests for the definitions of the variables and note that the MCL is given in mg/L.\r\n  t = datetime(x*B*H/Q);\r\nend","test_suite":"%% Benzene\r\nx = 80000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 26000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.005;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 08 05; 2018 05 28 05 06 05])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Chlorobenzene\r\nx = 79500;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2018,5,26,10,0,0);    %  Datetime for spill\r\nM = 34000;                          %  Mass of spill (kg)\r\nQ = 5.1;                            %  Discharge (m3/s)\r\nB = 10;                             %  Width of channel (m)\r\nH = 0.8;                            %  Depth of channel (m)\r\nS0 = 1.5e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.1;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2018 05 27 14 43 39; 2018 05 28 03 41 07])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Atrazine\r\nx = 14300;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2020,7,3,16,35,0);    %  Datetime for spill\r\nM = 5600;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 32;                             %  Width of channel (m)\r\nH = 0.4;                            %  Depth of channel (m)\r\nS0 = 6e-4;                          %  Longitudinal slope of channel\r\nMCL = 0.003;                        %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2020 07 04 00 51 03; 2020 07 04 14 00 39])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Dalapon\r\nx = 4200;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2019,6,13,14,23,0);   %  Datetime for spill\r\nM = 3000;                           %  Mass of spill (kg)\r\nQ = 3.8;                            %  Discharge (m3/s)\r\nB = 15;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.2;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2019 06 13 15 47 17; 2019 06 13 19 39 06])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 1\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2015 5 11 22 49 08; 2015 5 12 0 43 38])';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 2\r\nx = 9400;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 80;                             %  Mass of spill (kg)\r\nQ = 23;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Glyphosate 3\r\nx = 94000;                          %  Distance from spill to water intake (m)\r\nt0 = datetime(2015,5,11,20,12,00);  %  Datetime for spill\r\nM = 300;                            %  Mass of spill (kg)\r\nQ = 37;                             %  Discharge (m3/s)\r\nB = 28;                             %  Width of channel (m)\r\nH = 1.1;                            %  Depth of channel (m)\r\nS0 = 3.2e-4;                        %  Longitudinal slope of channel\r\nMCL = 0.7;                          %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = 'The MCL is not exceeded.';\r\nassert(isequal(t,t_correct))\r\n\r\n%% Nitrate \r\nx = 1600;                           %  Distance from spill to water intake (m)\r\nt0 = datetime(2024,4,30,15,20,00);  %  Datetime for spill\r\nM = 140;                            %  Mass of spill (kg)\r\nQ = 14;                             %  Discharge (m3/s)\r\nB = 14;                             %  Width of channel (m)\r\nH = 0.6;                            %  Depth of channel (m)\r\nS0 = 5e-4;                          %  Longitudinal slope of channel\r\nMCL = 10;                           %  Maximum contaminant level (mg/L) \r\nt = spillAlert(x,t0,M,Q,B,H,S0,MCL);\r\nt_correct = datetime([2024 4 30 15 32 22; 2024 4 30 15 38 03])';\r\nassert(isequal(t,t_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2024-05-28T15:13:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-27T17:17:23.000Z","updated_at":"2026-01-25T17:02:57.000Z","published_at":"2024-05-27T17:22:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/54750\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 54750\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved determining the length of a stream affected by a spill of a contaminant. Any municipalities within that reach would want to know when water from the river would be safe to drink—for example, below the U.S. Environmental Protection Agency’s \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.epa.gov/ground-water-and-drinking-water/national-primary-drinking-water-regulations\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emaximum contaminant level\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MCL). As in CP 54750, the spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will be assumed instantaneous at position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and mixed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e). Then if the flow is steady and the geometry of the flow does not change downstream, the concentration can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t)) exp(-(x-Ut)^2/(4Kt))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U = Q/A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU = Q/A\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the discharge or volumetric flow rate, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that returns the dates and times (given as datetimes) between which the water is unsafe to drink (i.e., the concentration exceeds the MCL) at position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e downstream of the spill. Round the times to the nearest second. If the concentration does not exceed the MCL, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'The MCL is not exceeded.' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ePlease note that the MCL is given in mg/L, whereas other variables are given in SI units. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDetails\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMany empirical formulas are available for the dispersion coefficient. For this problem, use the formula of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9429%281998%29124%3A1%2825%29\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSeo and Cheong (1998)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = 5.915u*H(B/H)^0.62(U/u*)^1.428\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = 5.915u_*H\\\\left(\\\\frac{B}{H}\\\\right)^{\\\\!\\\\!0.62}\\\\left(\\\\frac{U}{u_*}\\\\right)^{\\\\!\\\\!1.428}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"B\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the channel (assumed rectangular here), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eH\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the water depth, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u*\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the shear velocity, which is related to the shear stress on the wetted perimeter of the channel. In steady uniform flow, the component of the fluid’s weight down the slope will balance the friction on the channel bed, and the shear velocity can be computed as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u* = sqrt(gRS0)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu_* = (g R S_0)^{1/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"g = 9.81 m/s^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\,\\\\rm{m/s^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gravitational acceleration, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"S0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the longitudinal slope of the channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"R = A/P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR = A/P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the hydraulic radius, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the wetted perimeter. For a rectangular channel, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"P = B + 2H\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = B + 2H\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn addition to assuming steady uniform flow and an unchanging channel, ignore any reaction, decay, or loss of the chemical; this assumption provides a conservative estimate of the time range. In practice, one would include a factor of safety that accounts for uncertainty in the parameters. Nevertheless, the calculations here would form a basis for the advice to the city. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":46636,"title":"Montgomery Multiplication","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eMultiply all elements of an input matrix (A) modulo N, given all elements are less than R (2^number of bits). Where gcd(R,N)=1 and N\u0026lt;R. Output the final result, P (in normal form) and all intermediate products (p) in Montgomery form \u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 1px; border-bottom-style: solid; border-bottom-width: 1px; \"\u003e(\u003c/span\u003e\u003cspan style=\"\"\u003efirst product is just first element of matrix (A)*R modulo N\u003c/span\u003e\u003cspan style=\"border-block-end-style: solid; border-block-end-width: 1px; border-bottom-style: solid; border-bottom-width: 1px; \"\u003e)\u003c/span\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [P,p] = montgomeryMult(a,R,N)\r\n  P=N-1;\r\n  p=mod(a,N);\r\nend","test_suite":"%%\r\nR=2^16;\r\nN=3329;\r\nY=2050;\r\ny =[    1263         470        2922         960         982         369        2562        2142        1318         744];\r\na =[    1112       36822       19271       42840       48879       33433       48232       54170        3299       62565\r\n        7920       12071       15556       62713       53288       59399       52080       25560       14987       28219\r\n       56538       39138       34791       61324       25120       41217       35710       32630       54669       63016\r\n       31738       19656        5996       30008       40454        6654       44972       45534        1025       49965\r\n       55368        8789       26562       15759       37715       25615       58565       54681       56604         481\r\n       13723       13933        6871       50062       34737        3579        3590       39952        5116       44567\r\n       36194       58650        7358       49763       18026       32852       19900       37665       43846       46265\r\n       41280        4682       51408       48539       16294       28293        3027       21367       32781       42279\r\n        2096       15891       19108       48738       29598       65376       12810       29912       14286       36196\r\n       40285        3522       39553        6941       14923       53189       47196       46779       37461       14293\r\n       23750       28948       63204       44666       52720       31827       47300       57960        8007       50617\r\n        3246         870       28343       30360       64625       58618       57527       47241       43985       14944\r\n       32084       58798       45531       13904        1965        9014       38170        1219       39294       24304\r\n       12616       12888       49682        6456       35105       25559        4632       44222        3668       58387\r\n        8066        6119       28353       53973        5706       60775       60472       28738        3692       56123\r\n       13467       20143       42958       11469       52565       60128       52453       28692        9994       26373\r\n        9602       29888        7192       10719       64824       46764       18739        7670        1285       20841\r\n       12391        6663       61194       43646        4387       40523       35629       53390       28519       39887\r\n        2795       65233       12285       58614       61564       22497       64538       21289       54540       59650\r\n       41628       21764       17444       33853        1191       61343       46902       16136       40461       59578\r\n       18472       19486       52286       46052       44816        8177       54982       22460       34087       38770\r\n       35297        4066       31955       10065       51362       47879       28394       24621       56614       21795\r\n       45558       19545       50394       62485       35005       42367       30842       35818        6402       55906\r\n       32710        3037       25952       35447       58022       54601       36746       36825       59510       28992\r\n       35114       33123       17887       44547       58917       26101       17635       25940        7078       59267\r\n       29175       49900        2440        2396       41021       49140       49087       26091       33881        2174\r\n        8122       41357       44125       53031        9035       54737       33022       33775        9381       34893\r\n       32136        5891       28151       49061       14273       21132       42389       43091       36658       46956\r\n       55902        5299       29605        7876       11936       36193       20168       62319         300       11750\r\n       57273       50937       39967       34409        2740       64168        9091       47339       50245       22055\r\n       17714       59318        3893       21353        7008       35999       31167       26219       55621       12301\r\n       13661       34981       20697       35812       40399       21654       23754       54517       60084       21097\r\n       37026        7153       50641       26141       61581       40597       51649        8803       64681       26467\r\n       41963       54120       45641       27203       23229       23634       51137        3962       33104       35950\r\n       27330       22157        8213       11844       26910       49578       43811        5521       17787        3194\r\n       13498       19265        8529       16737       64510       27125        8749       10741        6602       36223\r\n       62123       48910        6052        1345       61969       32266        1412       21248       33282       18010\r\n        5378         677         512       60534       44344       45530       36689       19773       38378       15827\r\n        6927        3175       27728       42840       64769       63749       19714         765       49996       15934\r\n        9308       43772       42963       61119       50255       21479       61565       35383        5437       10102\r\n       10909       39548       47377       10715       22065       54906       64284        6250       43358       62679\r\n       40695       34478       34813       60365       43409       48435       18783        9601       33880       61319\r\n       37598       47822        7131       52078       16001       62532       52482       41362       11209       53655\r\n        3412       46350       41403       37840       19366        2092       58727       56316       61509       47727\r\n       61027       51208        8290       28838       44576       23387       39159       63846       38697       11521\r\n       47753       18872        8801       16882       34592       43427       57934       37410       28877       23617\r\n       48355       45385        6461       49279       26974       18448       61848       65329       61729       12372\r\n        4155       36481        9307       14986       39494       15098       35989       36276       42985          78\r\n       56389       25986       11026        4206       49186       46604       47735       33781       29618       20736\r\n       61237        4036       12861       50287       38242       40932       37798       21671       55030       45850\r\n       64513       51129       20806       43987       36162       38706        1694       28180       34906       40976\r\n       56291       22123       20737       46872       38244       43282       29263       32231       36299       35590\r\n       51482       39837       14258       42078       33542        3116       42356        4655       44568       28772\r\n       33644       48578       16452       27462        5412       22857       34157       58178       24064       18836\r\n       11639        6869       58518       25608       47157       29579       24399        4235       15682       32876\r\n       26121        8381       46086       53486       65284       15787       61416       28585       37940       49908\r\n        8777       36014       36420       20802       23234       46861       54364       54173       56812       49965\r\n        2024       31799       12087       53381       63652       56110       55645       25856       26658       37752\r\n       61547       58358       13895       51712       22704       18448       24414       40204        7380       48998\r\n       19746       52360        5069       55853       58100       47910       38874       53650       29087       42305\r\n       19368       48125       59886       33137       29798        9028       57183       58080       19672        8075\r\n       21819        3364       46315       41658       27094       54835       61177       61021       26305       33056\r\n       30609        4776       36555       62317       14269        9083       43808       12503       54615       22758\r\n       42480        5801       20540       29095        8234       38548       13551       16946       26452        6038\r\n        1653       52320       10892        3933       20245       23996       42850       58842       25570        9689\r\n       55194       61800       40795       56803       47585       52871        4721       38886       23622       12987\r\n       36636       44807       64745       41365       51306       33015       26655       33019        9191       44057\r\n       55974        8656       11169       23270       45468       32086       43708       40161       17047       28279\r\n       22798       47364       16894       65339         642       57478       61192       53701        5689       45508\r\n       29230        7232       26004       14691       55260       23143       53146       34857       28140       16828\r\n        3554        7700        4849       42759       60445       29454       31755       13243       16861         639\r\n       11606       41990       44832       39648       50525       63145       49594       29746       19500       34883\r\n       43437       21549       26370       25378        2795        2772       27331       28043       27843       18310\r\n       21681       42848       64411        9318       24784       63763       63686       63311        7812       62012\r\n       58883       49095       26357        1647       46159       12399       64747       40635       32444       59404\r\n        7743       38219       40676       27598       47809       43720       56632       45573       46295       25734\r\n       64776       48498       10116       12065       14698       38432       25485       47196       15962        1628\r\n       35388       15389       24991       47564       17632       44244       29801       22734       51450       44003\r\n       46328       48166       10560       24272       44107       23659       16166       33881        4855       54864\r\n       65502       63609       49683       55152       31292       40650       51407       36483       25813       63668\r\n       18864       56815       57089       48118       40875       53159       57857       10256         222        3731\r\n       27166        5651       22988       37422       15495        1262       59881       36834       14462       29512\r\n       30463       24014       44927       11590       11607        5496       36587       45534          85       38172\r\n       50066       24195       19277       62743       54371       63884       39247       27948       12398       44999\r\n       53621       44894       34775       17388       50260       42686        9756       54805        9337       47148\r\n        6568       39186       54553       60593       61241       15154       58963       47932       17568       42601\r\n       11673       51731       39157       14665        7070       26443       29516       23594       11461       47639\r\n       23569       24094       21974       24481       11942        7996       13478       29767        9086       24500\r\n        3716       13502       19610        5734        6494       17592       58959       25322       39248       38114\r\n       34202        5679       29661       41950       32097       16898       49976       50826       59051        7609\r\n       22010       50589       27698       11836       12664       21736       57834       48121       61563        3778\r\n       11512       13479       23567        2952       58713        9976       18674       28198       14495       64209\r\n       13693       25445       36590       47393        6493       22807       44120       45465       31632       18666\r\n       59320       36161       48663       22769        2894        7973       43534       61945       24642       38992\r\n       44262       15004       27809       43294       36522       57943        8048       51395       34326       63056\r\n       30701       42070       28138       25157       50626        6178       26694       46240       17358       12175\r\n       59777       31750        8183       41113       20443       60951       18041        7165        4479       12651\r\n        6816        9951        1601        1418       11729       26150       46967       25554       28595       22389\r\n       48860       51244       19017       59675       22213        3106       18571       38725       11393       61138\r\n       48252        6593       20809       52465       13772       22437       58733       30105        1710       25602];\r\n[P,p]=montgomeryMult(a,R,N);\r\nassert(isequal(P,Y))\r\nassert(isequal(y,p(10:100:end)))\r\n%%\r\nN=3347;\r\nR=2^16;\r\na =[    1112       36822       19271       42840       48879       33433       48232       54170        3299       62565\r\n        7920       12071       15556       62713       53288       59399       52080       25560       14987       28219\r\n       56538       39138       34791       61324       25120       41217       35710       32630       54669       63016\r\n       31738       19656        5996       30008       40454        6654       44972       45534        1025       49965\r\n       55368        8789       26562       15759       37715       25615       58565       54681       56604         481\r\n       13723       13933        6871       50062       34737        3579        3590       39952        5116       44567\r\n       36194       58650        7358       49763       18026       32852       19900       37665       43846       46265\r\n       41280        4682       51408       48539       16294       28293        3027       21367       32781       42279\r\n        2096       15891       19108       48738       29598       65376       12810       29912       14286       36196\r\n       40285        3522       39553        6941       14923       53189       47196       46779       37461       14293\r\n       23750       28948       63204       44666       52720       31827       47300       57960        8007       50617\r\n        3246         870       28343       30360       64625       58618       57527       47241       43985       14944\r\n       32084       58798       45531       13904        1965        9014       38170        1219       39294       24304\r\n       12616       12888       49682        6456       35105       25559        4632       44222        3668       58387\r\n        8066        6119       28353       53973        5706       60775       60472       28738        3692       56123\r\n       13467       20143       42958       11469       52565       60128       52453       28692        9994       26373\r\n        9602       29888        7192       10719       64824       46764       18739        7670        1285       20841\r\n       12391        6663       61194       43646        4387       40523       35629       53390       28519       39887\r\n        2795       65233       12285       58614       61564       22497       64538       21289       54540       59650\r\n       41628       21764       17444       33853        1191       61343       46902       16136       40461       59578\r\n       18472       19486       52286       46052       44816        8177       54982       22460       34087       38770\r\n       35297        4066       31955       10065       51362       47879       28394       24621       56614       21795\r\n       45558       19545       50394       62485       35005       42367       30842       35818        6402       55906\r\n       32710        3037       25952       35447       58022       54601       36746       36825       59510       28992\r\n       35114       33123       17887       44547       58917       26101       17635       25940        7078       59267\r\n       29175       49900        2440        2396       41021       49140       49087       26091       33881        2174\r\n        8122       41357       44125       53031        9035       54737       33022       33775        9381       34893\r\n       32136        5891       28151       49061       14273       21132       42389       43091       36658       46956\r\n       55902        5299       29605        7876       11936       36193       20168       62319         300       11750\r\n       57273       50937       39967       34409        2740       64168        9091       47339       50245       22055\r\n       17714       59318        3893       21353        7008       35999       31167       26219       55621       12301\r\n       13661       34981       20697       35812       40399       21654       23754       54517       60084       21097\r\n       37026        7153       50641       26141       61581       40597       51649        8803       64681       26467\r\n       41963       54120       45641       27203       23229       23634       51137        3962       33104       35950\r\n       27330       22157        8213       11844       26910       49578       43811        5521       17787        3194\r\n       13498       19265        8529       16737       64510       27125        8749       10741        6602       36223\r\n       62123       48910        6052        1345       61969       32266        1412       21248       33282       18010\r\n        5378         677         512       60534       44344       45530       36689       19773       38378       15827\r\n        6927        3175       27728       42840       64769       63749       19714         765       49996       15934\r\n        9308       43772       42963       61119       50255       21479       61565       35383        5437       10102\r\n       10909       39548       47377       10715       22065       54906       64284        6250       43358       62679\r\n       40695       34478       34813       60365       43409       48435       18783        9601       33880       61319\r\n       37598       47822        7131       52078       16001       62532       52482       41362       11209       53655\r\n        3412       46350       41403       37840       19366        2092       58727       56316       61509       47727\r\n       61027       51208        8290       28838       44596       23387       39159       63846       38697       11521\r\n       47753       18872        8801       16882       34592       43427       57934       37410       28877       23617\r\n       48355       45385        6461       49279       26974       18448       61848       65329       61729       12372\r\n        4155       36481        9307       14986       39494       15098       35989       36276       42985          78\r\n       56389       25986       11026        4206       49186       46604       47735       33781       29618       20736\r\n       61237        4036       12861       50287       38242       40932       37798       21671       55030       45850\r\n       64513       51129       20806       43987       36162       38706        1694       28180       34906       40976\r\n       56291       22123       20737       46872       38244       43282       29263       32231       36299       35590\r\n       51482       39837       14258       42078       33542        3116       42356        4655       44568       28772\r\n       33644       48578       16452       27462        5412       22857       34157       58178       24064       18836\r\n       11639        6869       58518       25608       47157       29579       24399        4235       15682       32876\r\n       26121        8381       46086       53486       65284       15787       61416       28585       37940       49908\r\n        8777       36014       36420       20802       23234       46861       54364       54173       56812       49965\r\n        2024       31799       12087       53381       63652       56110       55645       25856       26658       37752\r\n       61547       58358       13895       51712       22704       18448       24414       40204        7380       48998\r\n       19746       52360        5069       55853       58100       47910       38874       53650       29087       42305\r\n       19368       48125       59886       33137       29798        9028       57183       58080       19672        8075\r\n       21819        3364       46315       41658       27094       54835       61177       61021       26305       33056\r\n       30609        4776       36555       62317       14269        9083       43808       12503       54615       22758\r\n       42480        5801       20540       29095        8234       38548       13551       16946       26452        6038\r\n        1653       52320       10892        3933       20245       23996       42850       58842       25570        9689\r\n       55194       61800       40795       56803       47585       52871        4721       38886       23622       12987\r\n       36636       44807       64745       41365       51306       33015       26655       33019        9191       44057\r\n       55974        8656       11169       23270       45468       32086       43708       40161       17047       28279\r\n       22798       47364       16894       65339         642       57478       61192       53701        5689       45508\r\n       29230        7232       26004       14691       55260       23143       53146       34857       28140       16828\r\n        3554        7700        4849       42759       60445       29454       31755       13243       16861         639\r\n       11606       41990       44832       39648       50525       63145       49594       29746       19500       34883\r\n       43437       21549       26370       25378        2795        2772       27331       28043       27843       18310\r\n       21681       42848       64411        9318       24784       63763       63686       63311        7812       62012\r\n       58883       49095       26357        1647       46159       12399       64747       40635       32444       59404\r\n        7743       38219       40676       27598       47809       43720       56632       45573       46295       25734\r\n       64776       48498       10116       12065       14698       38432       25485       47196       15962        1628\r\n       35388       15389       24991       47564       17632       44244       29801       22734       51450       44003\r\n       46328       48166       10560       24272       44107       23659       16166       33881        4855       54864\r\n       65502       63609       49683       55152       31292       40650       51407       36483       25813       63668\r\n       18864       56815       57089       48118       40875       53159       57857       10256         222        3731\r\n       27166        5651       22988       37422       15495        1262       59881       36834       14462       29512\r\n       30463       24014       44927       11590       11607        5496       36587       45534          85       38172\r\n       50066       24195       19277       62743       54371       63884       39247       27948       12398       44999\r\n       53621       44894       34775       17388       50260       42686        9756       54805        9337       47148\r\n        6568       39186       54553       60593       61241       15154       58963       47932       17568       42601\r\n       11673       51771       39157       14665        7070       26443       29516       23594       11461       47639\r\n       23569       24094       21974       24481       11942        7996       13478       29767        9086       24500\r\n        3716       13502       19610        5734        6494       17592       58959       25322       39248       38114\r\n       34202        5679       29661       41950       32097       16898       49976       50826       59051        7609\r\n       22010       50589       27698       11836       12664       21736       57834       48121       61563        3778\r\n       11512       13479       23567        2952       58713        9976       18674       28198       14495       64209\r\n       13693       25445       36590       47393        6493       22807       44120       45465       31632       18666\r\n       59320       36161       48663       22769        2894        7973       43534       61945       24642       38992\r\n       44262       15004       27809       43294       36522       57943        8048       51395       34326       63056\r\n       30701       42070       28138       25157       50626        6178       26694       46240       17358       12175\r\n       59777       31750        8183       41113       20443       60951       18041        7165        4479       12651\r\n        6816        9951        1601        1418       11729       26150       46967       25554       28595       22389\r\n       48860       51244       19017       59675       22213        3106       18571       38725       11393       61138\r\n       48252        6593       20809       52465       13772       22437       58733       30105        1710       25602];\r\nY=1870;\r\ny=[130,1496,2440,2533,1292,1876,783,751,107,3006];\r\n[P,p]=montgomeryMult(a,R,N);\r\nassert(isequal(P,Y))\r\nassert(isequal(y,p(10:100:end)))\r\n%%\r\nR=2^16;\r\nN=3967;\r\nY=3799;\r\ny=[788,2020,2960,1688,2874,3752,1280,2265,1542,1371];\r\na =[    1112       36822       19271       42840       48879       33433       48232       54170        3299       62565\r\n        7920       12071       15556       62713       53288       59399       52080       25560       14987       28219\r\n       56538       39138       34791       61324       25120       41217       35710       32630       54669       63016\r\n       31738       19656        5996       30008       40454        6654       44972       45534        1025       49965\r\n       55368        8789       26562       15759       37715       25615       58565       54681       56604         481\r\n       13723       13933        6871       50062       34737        3579        3590       39952        5116       44567\r\n       36194       58650        7358       49763       18026       32852       19900       37665       43846       46265\r\n       41280        4682       51408       48539       16294       28293        3027       21367       32781       42279\r\n        2096       15891       19108       48738       29598       65376       12810       29912       14286       36196\r\n       40285        3522       39553        6941       14923       53189       47196       46779       37461       14293\r\n       23750       28948       63204       44666       52720       31827       47300       57960        8007       50617\r\n        3246         870       28343       30360       64625       58618       57527       47241       43985       14944\r\n       32084       58798       45531       13904        1965        9014       38170        1219       39294       24304\r\n       12616       12888       49682        6456       35105       25559        4632       44222        3668       58387\r\n        8066        6119       28353       53973        5706       60775       60472       28738        3692       56123\r\n       13467       20143       42958       11469       52565       60128       52453       28692        9994       26373\r\n        9602       29888        7192       10719       64824       46764       18739        7670        1285       20841\r\n       12391        6663       61194       43646        4387       40523       35629       53390       28519       39887\r\n        2795       65233       12285       58614       61564       22497       64538       21289       54540       59650\r\n       41628       21764       17444       33853        1191       61343       46902       16136       40461       59578\r\n       18472       19486       52286       46052       44816        8177       54982       22460       34087       38770\r\n       35297        4066       31955       10065       51362       47879       28394       24621       56614       21795\r\n       45558       19545       50394       62485       35005       42367       30842       35818        6402       55906\r\n       32710        3037       25952       35447       58022       54601       36746       36825       59510       28992\r\n       35114       33123       17887       44547       58917       26101       17635       25940        7078       59267\r\n       29175       49900        2440        2396       41021       49140       49087       26091       33881        2174\r\n        8122       41357       44125       53031        9035       54737       33022       33775        9381       34893\r\n       32136        5891       28151       49061       14273       21132       42389       43091       36658       46956\r\n       55902        5299       29605        7876       11936       36193       20168       62319         300       11750\r\n       57273       50937       39967       34409        2740       64168        9091       47339       50245       22055\r\n       17714       59318        3893       21353        7008       35999       31167       26219       55621       12301\r\n       13661       34981       20697       35812       40399       21654       23754       54517       60084       21097\r\n       37026        7153       50641       26141       61581       40597       51649        8803       64681       26467\r\n       41963       54120       45641       27203       23229       23634       51137        3962       33104       35950\r\n       27330       22157        8213       11844       26910       49578       43811        5521       17787        3194\r\n       13498       19265        8529       16737       64510       27125        8749       10741        6602       36223\r\n       62123       48910        6052        1345       61969       32266        1412       21248       33282       18010\r\n        5378         677         512       60534       44344       45530       36689       19773       38378       15827\r\n        6927        3175       27728       42840       64769       63749       19714         765       49996       15934\r\n        9308       43772       42963       61119       50255       21479       61565       35383        5437       10102\r\n       10909       39548       47377       10715       22065       54906       64284        6250       43358       62679\r\n       40695       34478       34813       60365       43409       48435       18783        9601       33880       61319\r\n       37598       47822        7131       52078       16001       62532       52482       41362       11209       53655\r\n        3412       46350       41403       37840       19366        2092       58727       56316       61509       47727\r\n       61027       51208        8290       28838       44596       23387       39159       63846       38697       11521\r\n       47753       18872        8801       16882       34592       43427       57934       37410       28877       23617\r\n       48355       45385        6461       49279       26974       18448       61848       65329       61729       12372\r\n        4155       36481        9307       14986       39494       15098       35989       36276       42985          78\r\n       56389       25986       11026        4206       49186       46604       47735       33781       29618       20736\r\n       61237        4036       12861       50287       38242       40932       37798       21671       55030       45850\r\n       64513       51129       20806       43987       36162       38706        1694       28180       34906       40976\r\n       56291       22123       20737       46872       38244       43282       29263       32231       36299       35590\r\n       51482       39837       14258       42078       33542        3116       42356        4655       44568       28772\r\n       33644       48578       16452       27462        5412       22857       34157       58178       24064       18836\r\n       11639        6869       58518       25608       47157       29579       24399        4235       15682       32876\r\n       26121        8381       46086       53486       65284       15787       61416       28585       37940       49908\r\n        8777       36014       36420       20802       23234       46861       54364       54173       56812       49965\r\n        2024       31799       12087       53381       63652       56110       55645       25856       26658       37752\r\n       61547       58358       13895       51712       22704       18448       24414       40204        7380       48998\r\n       19746       52360        5069       55853       58100       47910       38874       53650       29087       42305\r\n       19368       48125       59886       33137       29798        9028       57183       58080       19672        8075\r\n       21819        3364       46315       41658       27094       54835       61177       61021       26305       33056\r\n       30609        4776       36555       62317       14269        9083       43808       12503       54615       22758\r\n       42480        5801       20540       29095        8234       38548       13551       16946       26452        6038\r\n        1653       52320       10892        3933       20245       23996       42850       58842       25570        9689\r\n       55194       61800       40795       56803       47585       52871        4721       38886       23622       12987\r\n       36636       44807       64745       41365       51306       33015       26655       33019        9191       44057\r\n       55974        8656       11169       23270       45468       32086       43708       40161       17047       28279\r\n       22798       47364       16894       65339         642       57478       61192       53701        5689       45508\r\n       29230        7232       26004       14691       55260       23143       53146       34857       28140       16828\r\n        3554        7700        4849       42759       60445       29454       31755       13243       16861         639\r\n       11606       41990       44832       39648       50525       63145       49594       29746       19500       34883\r\n       43437       21549       26370       25378        2795        2772       27331       28043       27843       18310\r\n       21681       42848       64411        9318       24784       63763       63686       63311        7812       62012\r\n       58883       49095       26357        1647       46159       12399       64747       40635       32444       59404\r\n        7743       38219       40676       27598       47809       43720       56632       45573       46295       25734\r\n       64776       48498       10116       12065       14698       38432       25485       47196       15962        1628\r\n       35388       15389       24991       47564       17632       44244       29801       22734       51450       44003\r\n       46328       48166       10560       24272       44107       23659       16166       33881        4855       54864\r\n       65502       63609       49683       55152       31292       40650       51407       36483       25813       63668\r\n       18864       56815       57089       48118       40875       53159       57857       10256         222        3731\r\n       27166        5651       22988       37422       15495        1262       59881       36834       14462       29512\r\n       30463       24014       44927       11590       11607        5496       36587       45534          85       38172\r\n       50066       24195       19277       62743       54371       63884       39247       27948       12398       44999\r\n       53621       44894       34775       17388       50260       42686        9756       54805        9337       47148\r\n        6568       39186       54553       60593       61241       15154       58963       47932       17568       42601\r\n       11673       51771       39157       14665        7070       26443       29516       23594       11461       47639\r\n       23569       24094       21974       24481       11942        7996       13478       29767        9086       24500\r\n        3716       13502       19610        5734        6494       17592       58959       25322       39248       38114\r\n       34202        5679       29661       41950       32097       16898       49976       50826       59051        7609\r\n       22010       50589       27698       11836       12664       21736       57834       48121       61563        3778\r\n       11512       13479       23567        2952       58713        9976       18674       28198       14495       64209\r\n       13693       25445       36590       47393        6493       22807       44120       45465       31632       18666\r\n       59320       36161       48663       22769        2894        7973       43534       61945       24642       38992\r\n       44262       15004       27809       43294       36522       57943        8048       51395       34326       63056\r\n       30701       42070       28138       25157       50626        6178       26694       46240       17358       12175\r\n       59777       31750        8183       41113       20443       60951       18041        7165        4479       12651\r\n        6816        9951        1601        1418       11729       26150       46967       25554       28595       22999\r\n       48860       51244       19017       59675       22213        3106       18571       38725       11393       61138\r\n       48252        6593       20809       52465       13772       22437       58733       30105        1710       25602];\r\n[P,p]=montgomeryMult(a,R,N);\r\nassert(isequal(P,Y))\r\nassert(isequal(y,p(10:100:end)))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-09-30T21:17:47.000Z","updated_at":"2025-10-12T15:14:20.000Z","published_at":"2020-09-30T21:17:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMultiply all elements of an input matrix (A) modulo N, given all elements are less than R (2^number of bits). Where gcd(R,N)=1 and N\u0026lt;R. Output the final result, P (in normal form) and all intermediate products (p) in Montgomery form (first product is just first element of matrix (A)*R modulo N).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":2266,"title":"2048 tile game","description":"The popular 2048 game has been implemented here:\r\n\r\nhttp://gabrielecirulli.github.io/2048/\r\n\r\nGiven the board like this:\r\n\r\n  [2 4 8 0\r\n   4 0 0 0\r\n   2 0 0 0\r\n   2 0 4 0]\r\n\r\nYou give the direction\r\n\r\n1 (left)\r\n2 (up)\r\n3 (right)\r\n4 (down)\r\n\r\nThe system here will keep calling your solver.  Score for each board is the biggest tile achieved.  The Cody score is the maximum board score plus the average score across all 200 boards.","description_html":"\u003cp\u003eThe popular 2048 game has been implemented here:\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://gabrielecirulli.github.io/2048/\"\u003ehttp://gabrielecirulli.github.io/2048/\u003c/a\u003e\u003c/p\u003e\u003cp\u003eGiven the board like this:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e[2 4 8 0\r\n 4 0 0 0\r\n 2 0 0 0\r\n 2 0 4 0]\r\n\u003c/pre\u003e\u003cp\u003eYou give the direction\u003c/p\u003e\u003cp\u003e1 (left)\r\n2 (up)\r\n3 (right)\r\n4 (down)\u003c/p\u003e\u003cp\u003eThe system here will keep calling your solver.  Score for each board is the biggest tile achieved.  The Cody score is the maximum board score plus the average score across all 200 boards.\u003c/p\u003e","function_template":"function direction = getMove(board)\r\n  direction = 1;\r\nend","test_suite":"%%\r\nfh=fopen('main.m','wt');\r\nfprintf(fh, '%s \\n', 'function out = main(n)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'result = 0;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'for i = 1:n    ');\r\nfprintf(fh, '%s \\n', '    board = zeros(4);');\r\nfprintf(fh, '%s \\n', '    board = saltBoard(board);');\r\nfprintf(fh, '%s \\n', '    board = saltBoard(board);');\r\nfprintf(fh, '%s \\n', '    %dispBoard(board)');\r\nfprintf(fh, '%s \\n', '    direction = 1;');\r\nfprintf(fh, '%s \\n', '    while (direction ~= 0)');\r\nfprintf(fh, '%s \\n', '        %pause(0.1)');\r\nfprintf(fh, '%s \\n', '        %clc');\r\nfprintf(fh, '%s \\n', '        direction = getMove(board);');\r\nfprintf(fh, '%s \\n', '        board = updateBoard(board, direction);');\r\nfprintf(fh, '%s \\n', '        %dispBoard(board)');\r\nfprintf(fh, '%s \\n', '    end');\r\nfprintf(fh, '%s \\n', '    %figure(1)');\r\nfprintf(fh, '%s \\n', '    %dispBoard(board)');\r\nfprintf(fh, '%s \\n', '    %figure(2)');\r\nfprintf(fh, '%s \\n', '    %hist(result,[2 4 8 16 32 64 128 256 512 1024,2048])');\r\nfprintf(fh, '%s \\n', '    %drawnow');\r\nfprintf(fh, '%s \\n', '    result(i) = max(board(:));');\r\nfprintf(fh, '%s \\n', '    %disp([i result(i) max(result)])');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = max(result) + mean(result)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = collapse(in)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'in = squish(in);');\r\nfprintf(fh, '%s \\n', 'for i = 1:3');\r\nfprintf(fh, '%s \\n', '    result = miniCollapse(in(i:i+1));');\r\nfprintf(fh, '%s \\n', '    out(i:i+1) = result;');\r\nfprintf(fh, '%s \\n', '     in(i:i+1) = result;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = squish(in);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = squish(in);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = in(in ~= 0);');\r\nfprintf(fh, '%s \\n', 'if numel(out) ~= 4');\r\nfprintf(fh, '%s \\n', '    out(4) = 0;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = miniCollapse(in)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'if in(1) == in(2)');\r\nfprintf(fh, '%s \\n', '    out(1) = in(1) * 2;');\r\nfprintf(fh, '%s \\n', '    out(2)  = 0;');\r\nfprintf(fh, '%s \\n', 'else');\r\nfprintf(fh, '%s \\n', '    out = in;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = saltBoard(in)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'if nnz(in) == 16');\r\nfprintf(fh, '%s \\n', '    out = nan;');\r\nfprintf(fh, '%s \\n', '    return;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'vi = find(in == 0);');\r\nfprintf(fh, '%s \\n', 'selected = randi(numel(vi));');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'thresh = 0.1;');\r\nfprintf(fh, '%s \\n', 'if (rand \u003c thresh)');\r\nfprintf(fh, '%s \\n', '    salt = 4;');\r\nfprintf(fh, '%s \\n', 'else');\r\nfprintf(fh, '%s \\n', '    salt = 2;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = in;');\r\nfprintf(fh, '%s \\n', 'out(vi(selected)) = salt;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function board = updateBoard(board, direction)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'boardOriginal = board;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'board = collapseBoard(board,direction);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'if ~isequal(boardOriginal, board)');\r\nfprintf(fh, '%s \\n', '    board = saltBoard(board);');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function dispBoard(board)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'clf');\r\nfprintf(fh, '%s \\n', 'r = 1;');\r\nfprintf(fh, '%s \\n', 'c = 1;');\r\nfprintf(fh, '%s \\n', 'v = 2;');\r\nfprintf(fh, '%s \\n', 'for r = 1:4');\r\nfprintf(fh, '%s \\n', '    for c = 1:4');\r\nfprintf(fh, '%s \\n', '        v = board(r,c);');\r\nfprintf(fh, '%s \\n', '        dispSquare(r,c,v)');\r\nfprintf(fh, '%s \\n', '    end');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function dispSquare(r,c,v)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'cmap = autumn(12);');\r\nfprintf(fh, '%s \\n', 'absIndex = (r-1)*4 + c;');\r\nfprintf(fh, '%s \\n', 'if v == 0 ');\r\nfprintf(fh, '%s \\n', '    cMapIndex = 1;');\r\nfprintf(fh, '%s \\n', 'else');\r\nfprintf(fh, '%s \\n', '    cMapIndex = log2(v) + 1;');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'h = subplot(4,4,absIndex);');\r\nfprintf(fh, '%s \\n', 'set(h,''xtick'',[])');\r\nfprintf(fh, '%s \\n', 'set(h,''ytick'',[])');\r\nfprintf(fh, '%s \\n', 'set(h,''color'',cmap(cMapIndex,:))');\r\nfprintf(fh, '%s \\n', '%axis off');\r\nfprintf(fh, '%s \\n', 'text(0.5,0.5,num2str(v), ''fontsize'', 20)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function flag = isMoveDirection(board, direction)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'originalBoard = board;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'board = updateBoard(board, direction);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'flag = ~isequal(board, originalBoard);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'function out = collapseBoard(in, direction)');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'rotDirection = direction-1;');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'in = rot90(in,rotDirection);');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'for r = 1:4');\r\nfprintf(fh, '%s \\n', '    out(r,:) = collapse(in(r,:));');\r\nfprintf(fh, '%s \\n', 'end');\r\nfprintf(fh, '%s \\n', '');\r\nfprintf(fh, '%s \\n', 'out = rot90(out,-rotDirection);');\r\n\r\nfclose(fh);\r\n\r\nrehash path\r\n%%\r\nn = 200;\r\nscore = main(n)\r\nscore = 4056 - score;\r\n\r\nassert(score \u003c (4056 - 256))\r\nassignin('caller','score',score)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":240,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2014-04-02T17:36:53.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-04-01T20:01:55.000Z","updated_at":"2026-02-03T10:02:13.000Z","published_at":"2014-04-02T14:29:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe popular 2048 game has been implemented here:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://gabrielecirulli.github.io/2048/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://gabrielecirulli.github.io/2048/\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the board like this:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[[2 4 8 0\\n 4 0 0 0\\n 2 0 0 0\\n 2 0 4 0]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou give the direction\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 (left) 2 (up) 3 (right) 4 (down)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe system here will keep calling your solver. Score for each board is the biggest tile achieved. The Cody score is the maximum board score plus the average score across all 200 boards.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60834,"title":"Bell 202 Decoder","description":"Decode an audio frequency shift key stream at a certain baud-rate and sample rate into a binary stream of data using the Bell 202 standard. \r\nWhere a '1' is represented as 1200 Hz and a  '0' is represnted as 2200 Hz.\r\nDuration of each bit is based on the baud-rate.\r\nDigitized audio stream is produced at the sample rate and is smooth between bits.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 66px; transform-origin: 408px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDecode an audio frequency shift key stream at a certain baud-rate and sample rate into a binary stream of data using the Bell 202 standard. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhere a '1' is represented as 1200 Hz and a  '0' is represnted as 2200 Hz.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDuration of each bit is based on the baud-rate.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDigitized audio stream is produced at the sample rate and is smooth between bits.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function decodedStream = decodeBell202(audioSignal, sampleRate, bitRate)\r\n decodedStream=audioSignal/bitRate;\r\nend","test_suite":"%%\r\nrng(2718);\r\nbS=num2str(randi(2,1,1e4)-1);\r\nbS(bS==' ')=[];\r\nt = 1/1e5:1/1e5:1/9.2e2;\r\naS=[];\r\np=0;\r\nfor i = 1:length(bS)\r\n   if isequal(bS(i),'0')\r\n     aS=[aS, sin(2*pi*2200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*2200*t(end)+p));\r\n   else\r\n     aS=[aS, sin(2*pi*1200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*1200*t(end)+p));\r\n   end\r\nend\r\nassert(isequal(decodeBell202(aS,1e5,920),bS))\r\n%%\r\nrng(2718);\r\nbS=num2str(randi(2,1,1e4)-1);\r\nbS(bS==' ')=[];\r\nt = 1/1e5:1/1e5:1/1e3;\r\naS=[];\r\np=0;\r\nfor i = 1:length(bS)\r\n   if isequal(bS(i),'0')\r\n     aS=[aS, sin(2*pi*2200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*2200*t(end)+p));\r\n   else\r\n     aS=[aS, sin(2*pi*1200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*1200*t(end)+p));\r\n   end\r\nend\r\nassert(isequal(decodeBell202(aS,1e5,1e3),bS))\r\n%%\r\nbS='1011110001100110011001110001110101011010101010111000111000111000111100011100110101011001';\r\nt = 1/1.2e5:1/1.2e5:1/600;\r\naS=[];\r\np=0;\r\nfor i = 1:length(bS)\r\n   if isequal(bS(i),'0')\r\n     aS=[aS, sin(2*pi*2200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*2200*t(end)+p));\r\n   else\r\n     aS=[aS, sin(2*pi*1200*t+p)];\r\n     p=atan2(aS(end),cos(2*pi*1200*t(end)+p));\r\n   end\r\nend\r\nassert(isequal(decodeBell202(aS,1.2e5,600),bS))\r\n%%","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-03-27T15:12:44.000Z","updated_at":"2025-12-07T15:19:32.000Z","published_at":"2025-03-27T15:12:43.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDecode an audio frequency shift key stream at a certain baud-rate and sample rate into a binary stream of data using the Bell 202 standard. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere a '1' is represented as 1200 Hz and a  '0' is represnted as 2200 Hz.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDuration of each bit is based on the baud-rate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDigitized audio stream is produced at the sample rate and is smooth between bits.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60749,"title":"Compute the dispersion coefficient","description":"A contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\r\nG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \r\n\r\nwhere  is the width of the stream,  is the transverse mixing coefficient, and  is the deviation of the velocity profile from the cross-sectional average velocity\r\n\r\nWrite a function that takes a (normalized) velocity profile  specified at several points and computes the quantity \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 375px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 187.5px; transform-origin: 407px 187.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"240\" height=\"44\" alt=\"K = -(1/hD) integral(u' integral(integral(u'(y2),0\u003c=y2\u003c=y1),0\u003c=y1\u003c=y),0\u003c=y\u003c=h)\" style=\"width: 240px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the stream, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eD\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the transverse mixing coefficient, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"64\" height=\"19\" alt=\"u' = u - bar(u)\" style=\"width: 64px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the deviation of the velocity profile from the cross-sectional average velocity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"103\" height=\"44\" alt=\"ubar = (1/h) integral(u(y),0\u003c=y\u003c=h)\" style=\"width: 103px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a (normalized) velocity profile \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"30\" height=\"18\" alt=\"u(y)\" style=\"width: 30px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e specified at several points and computes the quantity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"215\" height=\"44\" alt=\"I = -integral(u' integral(integral(u'(y2),0\u003c=y2\u003c=y1),0\u003c=y1\u003c=y),0\u003c=y\u003c=h)\" style=\"width: 215px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = computeK(y,u)\r\n  I = -integral(u'*integral(integral(u',0,y1),0,y),0,h);\r\nend","test_suite":"%%\r\nny = 1000;\r\ny = linspace(0,1,ny);\r\nu = y.*(1-y);\r\nI = computeK(y,u);\r\nI_correct = 1/7560;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6);\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = 2*y;\r\nu(y\u003e1/2) = 2*(1-y(y\u003e1/2));\r\nI = computeK(y,u);\r\nI_correct = 1/480;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6);\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 2.5; \r\nb = 2.5;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.00788915;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 2.5; \r\nb = 3;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.01168232;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 3.2; \r\nb = 3.2;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.01192484;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-10-16T01:19:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-10-16T01:18:30.000Z","updated_at":"2024-10-27T15:58:26.000Z","published_at":"2024-10-16T01:19:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = -(1/hD) integral(u' integral(integral(u'(y2),0\u0026lt;=y2\u0026lt;=y1),0\u0026lt;=y1\u0026lt;=y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = -\\\\frac{1}{hD}\\\\int_0^h u^\\\\prime \\\\int_0^y \\\\int_0^{y_1} u^\\\\prime(y_2) dy_2 dy_1 dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the stream, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the transverse mixing coefficient, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u' = u - bar(u)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu^\\\\prime = u-{\\\\bar u}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the deviation of the velocity profile from the cross-sectional average velocity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ubar = (1/h) integral(u(y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\bar u} = \\\\frac{1}{h} \\\\int_0^h u(y) dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a (normalized) velocity profile \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u(y)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu(y)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e specified at several points and computes the quantity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = -integral(u' integral(integral(u'(y2),0\u0026lt;=y2\u0026lt;=y1),0\u0026lt;=y1\u0026lt;=y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = -\\\\int_0^h u^\\\\prime \\\\int_0^y \\\\int_0^{y_1} u^\\\\prime(y_2) dy_2 dy_1 dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1949,"title":"Get top 5 Cody Player Emails Automatically","description":"Yes, this is a little scary and also entirely possible to do in MATLAB, so let's do it!\r\n\r\nLooking at the list of the players \u003chttp://www.mathworks.com/matlabcentral/cody/players\u003e automatically sorts them in order according to rank. For times sake, let's say we only want to get the emails from the first 5 people. This is relatively easy to do by hand, just click on the persons name, click on \"View Profile Information\" and you have the email but if you wanted to do say the first 1,000 people instead, that would be not very fun to do by hand. \r\n\r\nFor this program, let's say we want the top 5 profiles that give a \"real\" email address (not a contact form) to be in a cell array. This means that if one of the top 5 people have removed their email address, your returned cell array will have less than 5 emails in it. \r\n\r\nIf you are not sure where to start, check out the urlread command, it allows you to put the web page source code into a string. From there, you are able to parse through that to get the URLs for the top 5 players web profile. From there, look for a \"mailto:\" and if it is there, the email address is immediately following it. If the string \"mailto:\" does not exist, there is no email address on that webpage. Put the emails in a cell array when you find them and you are good to go!\r\n\r\nAs an example, I have poorly written MATLAB code that works in the test case since I want the test case to always be accurate. 98% of the execution time is spent reading the webpages, and at least on my computer, that takes quite a while to do (about 2.5 seconds per profile page).\r\n\r\n*I am definitely not collecting emails for anything, and you should not either! This is designed solely as a learning example and should in no way be used for anything unethical. All information obtained here is easily obtained by anyone in the world who knows how to program.*\r\n\r\n*If this scares you and you want to remove your email address from your profile, it's easy. All you have to do is click \"My Community Profile\" (underneath the search bar at very top of screen) and then edit your preferences to not display your email address.* ","description_html":"\u003cp\u003eYes, this is a little scary and also entirely possible to do in MATLAB, so let's do it!\u003c/p\u003e\u003cp\u003eLooking at the list of the players \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/players\"\u003ehttp://www.mathworks.com/matlabcentral/cody/players\u003c/a\u003e automatically sorts them in order according to rank. For times sake, let's say we only want to get the emails from the first 5 people. This is relatively easy to do by hand, just click on the persons name, click on \"View Profile Information\" and you have the email but if you wanted to do say the first 1,000 people instead, that would be not very fun to do by hand.\u003c/p\u003e\u003cp\u003eFor this program, let's say we want the top 5 profiles that give a \"real\" email address (not a contact form) to be in a cell array. This means that if one of the top 5 people have removed their email address, your returned cell array will have less than 5 emails in it.\u003c/p\u003e\u003cp\u003eIf you are not sure where to start, check out the urlread command, it allows you to put the web page source code into a string. From there, you are able to parse through that to get the URLs for the top 5 players web profile. From there, look for a \"mailto:\" and if it is there, the email address is immediately following it. If the string \"mailto:\" does not exist, there is no email address on that webpage. Put the emails in a cell array when you find them and you are good to go!\u003c/p\u003e\u003cp\u003eAs an example, I have poorly written MATLAB code that works in the test case since I want the test case to always be accurate. 98% of the execution time is spent reading the webpages, and at least on my computer, that takes quite a while to do (about 2.5 seconds per profile page).\u003c/p\u003e\u003cp\u003e\u003cb\u003eI am definitely not collecting emails for anything, and you should not either! This is designed solely as a learning example and should in no way be used for anything unethical. All information obtained here is easily obtained by anyone in the world who knows how to program.\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eIf this scares you and you want to remove your email address from your profile, it's easy. All you have to do is click \"My Community Profile\" (underneath the search bar at very top of screen) and then edit your preferences to not display your email address.\u003c/b\u003e\u003c/p\u003e","function_template":"function emails = getCodyEmails()\r\n  emails = {};\r\nend","test_suite":"%%\r\n% My code is below, it's used to generate the expected result.\r\n\r\n%Read in the player page\r\nplayerPage=urlread('http://www.mathworks.com/matlabcentral/cody/players');\r\n\r\n%Find where the web address for each profile starts\r\nstartIdx=strfind(playerPage,'\u003cdiv class=\"grid_53 push_3\"\u003e')+104; \r\n\r\n%Initialize output array\r\nemails={};\r\n\r\n%Get top 5 only\r\nfor i=1:5\r\n    % Get the profile page link\r\n   tempStr=playerPage(startIdx(i):startIdx(i)+100);\r\n   quoteIdx=strfind(tempStr,'\"')-1;\r\n   profilePageLink=['http://www.mathworks.com' tempStr(1:quoteIdx(1))];\r\n   \r\n   profilePage=urlread(profilePageLink);\r\n   % Try and find mailto link\r\n   tStartIdx=strfind(profilePage,'mailto');\r\n   \r\n   %If you could find it\r\n   if ~isempty(tStartIdx)\r\n       % Get the email\r\n       tEndIdx=strfind(profilePage(tStartIdx:tStartIdx+100),'\"')+tStartIdx;\r\n       \r\n       % Add it to our cell array\r\n       emails{length(emails)+1}=profilePage(tStartIdx+7:tEndIdx-2);\r\n   end\r\n    \r\nend\r\n\r\n\r\ntic\r\nyourResponse=getCodyEmails()\r\ntimeElapsed=toc\r\n\r\n\r\nassert(isequal(yourResponse,emails))\r\nassert(isequal(1,timeElapsed\u003e3))","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":3743,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-10-20T05:40:10.000Z","updated_at":"2025-07-31T17:14:24.000Z","published_at":"2013-10-20T05:40:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYes, this is a little scary and also entirely possible to do in MATLAB, so let's do it!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLooking at the list of the players\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/players\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://www.mathworks.com/matlabcentral/cody/players\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e automatically sorts them in order according to rank. For times sake, let's say we only want to get the emails from the first 5 people. This is relatively easy to do by hand, just click on the persons name, click on \\\"View Profile Information\\\" and you have the email but if you wanted to do say the first 1,000 people instead, that would be not very fun to do by hand.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this program, let's say we want the top 5 profiles that give a \\\"real\\\" email address (not a contact form) to be in a cell array. This means that if one of the top 5 people have removed their email address, your returned cell array will have less than 5 emails in it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf you are not sure where to start, check out the urlread command, it allows you to put the web page source code into a string. From there, you are able to parse through that to get the URLs for the top 5 players web profile. From there, look for a \\\"mailto:\\\" and if it is there, the email address is immediately following it. If the string \\\"mailto:\\\" does not exist, there is no email address on that webpage. Put the emails in a cell array when you find them and you are good to go!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs an example, I have poorly written MATLAB code that works in the test case since I want the test case to always be accurate. 98% of the execution time is spent reading the webpages, and at least on my computer, that takes quite a while to do (about 2.5 seconds per profile page).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eI am definitely not collecting emails for anything, and you should not either! This is designed solely as a learning example and should in no way be used for anything unethical. All information obtained here is easily obtained by anyone in the world who knows how to program.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIf this scares you and you want to remove your email address from your profile, it's easy. All you have to do is click \\\"My Community Profile\\\" (underneath the search bar at very top of screen) and then edit your preferences to not display your email address.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":53990,"title":"Classify product/digit-sum sequences","description":"Cody Problem 53120 involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\r\nWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved Cody Problem 53120, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \r\nWrite a function to classify the product/digit-sum sequences given the first two terms  and . To encourage solvers to find the pattern, loops are banned, and to allow for large inputs,  and  are specified as strings. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 93px; transform-origin: 407.5px 93px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 309.642px 7.66667px; transform-origin: 309.642px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383.883px 7.66667px; transform-origin: 383.883px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/53120\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 53120\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 103.075px 7.66667px; transform-origin: 103.075px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21px; text-align: left; transform-origin: 384.5px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 262.017px 7.66667px; transform-origin: 262.017px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to classify the product/digit-sum sequences given the first two terms \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93.35px 7.66667px; transform-origin: 93.35px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.66667px; transform-origin: 15.5583px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4px 7.66667px; transform-origin: 77.4px 7.66667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are specified as strings. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = PDSseq(a,b)\r\n  c = [1 9 26 62 163];\r\n  y = c(a+b);\r\nend","test_suite":"%%\r\na = '1';\r\nb = '2';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7';\r\nb = '31';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '17';\r\nb = '28';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '51';\r\nb = '77';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '82';\r\nb = '262';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '7021';\r\nb = '8878';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264';\r\nb = '412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8675308';\r\nb = '2941300';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '9142534264';\r\nb = '8424812653';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164';\r\nb = '8424812753';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '1352408463575';\r\nb = '9898989898985';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '534264534264534264534264';\r\nb = '412578412578412578412578';\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '86753088675308867530886753088675308';\r\nb = '28413002941300294130029413002941300';\r\ny_correct = 163;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '914253426491425342649142534264914253463';\r\nb = '842481265384248126538424812653842481265324';\r\ny_correct = 62;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '8031423164842481275380314231648424812753';\r\nb = '84248127538031423164842481275380314231648424812756';\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = '43524084635758031423164842481275380314231648424812753';\r\nb = '98989898989858031423164842481275380614231648424812753';\r\ny_correct = 1;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = num2str(randi(835042)*57);\r\nb = char(randi(9,20,1)+48);\r\ny_correct = 9;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\na = repelem('1',1,23);\r\na(randi(23)) = '4';\r\nb = num2str(10^randi(14));\r\ny_correct = 26;\r\nassert(isequal(PDSseq(a,b),y_correct))\r\n\r\n%%\r\nfiletext = fileread('PDSseq.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'system') || contains(filetext,'regexp') || contains(filetext,'java') || contains(filetext,'for') || contains(filetext,'while') || contains(filetext,'numpy'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":3,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2022-02-05T01:46:00.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-02-04T04:01:11.000Z","updated_at":"2026-01-15T18:05:52.000Z","published_at":"2022-02-04T04:04:20.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involved a sequence in which a term is computed by multiplying the previous two terms and adding the digits of the product. In that problem the first two terms of the sequence were 1 and 2. The next four terms were 2, 4, 8, and 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhat happens if the first two terms are changed? It turns out that these product/digit-sum sequences can be sorted into five groups. For reasons that will likely be apparent to those who solved \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/53120\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 53120\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the sequence there (and others like it) is assigned the number 163. The other four types of sequence are assigned the numbers 1, 9, 26, and 62. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to classify the product/digit-sum sequences given the first two terms \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. To encourage solvers to find the pattern, loops are banned, and to allow for large inputs, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"b\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are specified as strings. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55315,"title":"Chain multiplication - 04","description":"Following up on the problem in 55305, you found the optimal way to multiply a chain of matrices.\r\nHowever, here in this problem, you will be given a chain of matrices as a string with parenthesis placed in certain places along with their dimensions. You have to find out the number of multiplications required if you multiply the matrices that way.\r\nFor example, \r\nd= [1, 2, 3, 2] and s = \"A(BC)\".\r\nhere, the sizes of the matrices are - A(1,2), B(2,3), and C(3,2).\r\nFirst, B and C are to be multiplied (since they are inside parenthesis). The resultant matrix is to be multiplied with A. You need to find out the total number of multiplications required, which is 12+4=16.\r\n\r\nn.b. only valid parenthesization are given in this problem for simplicity.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 273px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 136.5px; transform-origin: 407px 136.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFollowing up on the problem in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55305-chain-multiplication-02\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e55305\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, you found the optimal way to multiply a chain of matrices.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHowever, here in this problem, you will be given a chain of matrices as a string with parenthesis placed in certain places along with their dimensions. You have to find out the number of multiplications required if you multiply the matrices that way.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ed= [1, 2, 3, 2] and s = \"A(BC)\".\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ehere, the sizes of the matrices are - A(1,2), B(2,3), and C(3,2).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFirst, B and C are to be multiplied (since they are inside parenthesis). The resultant matrix is to be multiplied with A. You need to find out the total number of multiplications required, which is 12+4=16.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en.b. only valid parenthesization are given in this problem for simplicity.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = chain_mul_04(s,d)\r\n  y = x;\r\nend","test_suite":"%%\r\nd= [1, 2, 3, 2];\r\ns = \"A(BC)\";\r\ny_correct = 16;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n%%\r\nd= [1, 2, 3, 2];\r\ns = \"(AB)C\";\r\ny_correct = 12;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n%%\r\nd= [40, 20, 30, 10, 30];\r\ns = \"A(B(CD))\";\r\ny_correct = 51000;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n%%\r\nd= [40, 20, 30, 10, 30];\r\ns = \"(AB)(CD)\";\r\ny_correct = 69000;\r\nassert(isequal(chain_mul_04(s,d),y_correct))\r\n\r\n\r\n%%\r\nd= [81,213,78,96,2,1,98,102, 1200,4];\r\ns = \"(((AB)C)(DE))((FG)(HI))\";\r\ny_correct = 2460558;\r\nassert(isequal(chain_mul_04(s,d),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":363598,"edited_by":363598,"edited_at":"2022-08-16T22:04:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-16T21:31:49.000Z","updated_at":"2022-08-16T22:04:11.000Z","published_at":"2022-08-16T22:04:11.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollowing up on the problem in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55305-chain-multiplication-02\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e55305\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, you found the optimal way to multiply a chain of matrices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHowever, here in this problem, you will be given a chain of matrices as a string with parenthesis placed in certain places along with their dimensions. You have to find out the number of multiplications required if you multiply the matrices that way.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ed= [1, 2, 3, 2] and s = \\\"A(BC)\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ehere, the sizes of the matrices are - A(1,2), B(2,3), and C(3,2).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst, B and C are to be multiplied (since they are inside parenthesis). The resultant matrix is to be multiplied with A. You need to find out the total number of multiplications required, which is 12+4=16.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en.b. only valid parenthesization are given in this problem for simplicity.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54720,"title":"Hyperperfect Numbers","description":"A k-hyperperfect number is a natural number n for which the equality n = 1 + k(σ(n)  − n  − 1) holds, where σ(n) is the divisor function (i.e., the sum of all positive divisors of n).\r\n%Example\r\nsigma(6) = 1 + 2 + 3 + 6 = 12\r\n%for k=1\r\n1 + 1*(12-6-1) = 1 + 5 = 6\r\n\r\n%Example\r\nsigma(325) = 1 + 5 + 13 + 25 + 65 + 325 = 434\r\n%for k=3\r\n1 + 3*(434-325-1) = 1 + 3*108 = 324  \r\n\r\nGiven a number x, return the xth Hyperperfect number (serial/order wise) and corresponding k value.\r\n\r\n\r\nP.S - Check the test suite for banned functions. More functions might be added later to prevent hard coded solutions.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 386.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 193.45px; transform-origin: 408px 193.45px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.60833px 8px; transform-origin: 6.60833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Hyperperfect_number\"\u003e\u003cspan style=\"perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"perspective-origin: 72.3417px 8px; transform-origin: 72.3417px 8px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-hyperperfect number\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.7917px 8px; transform-origin: 63.7917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a natural number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69.625px 8px; transform-origin: 69.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for which the equality \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19.8417px 8px; transform-origin: 19.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e = 1 + \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003ek\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.64167px 8px; transform-origin: 4.64167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003eσ\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.25px 8px; transform-origin: 12.25px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e)  − \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.1417px 8px; transform-origin: 16.1417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e  − 1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5667px 8px; transform-origin: 43.5667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e holds, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.225px 8px; transform-origin: 4.225px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eσ\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2.33333px 8px; transform-origin: 2.33333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.9417px 8px; transform-origin: 22.9417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Divisor_function\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003edivisor function\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 120.175px 8px; transform-origin: 120.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (i.e., the sum of all positive divisors of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.89167px 8px; transform-origin: 3.89167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 183.9px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 91.95px; transform-origin: 405px 91.95px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Example\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 111.65px 8.5px; tab-size: 4; transform-origin: 111.65px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003esigma(6) = 1 + 2 + 3 + 6 = 12\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%for k=1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 100.1px 8.5px; tab-size: 4; transform-origin: 100.1px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 + 1*(12-6-1) = 1 + 5 = 6\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%Example\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 173.25px 8.5px; tab-size: 4; transform-origin: 173.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003esigma(325) = 1 + 5 + 13 + 25 + 65 + 325 = 434\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 30.8px 8.5px; tab-size: 4; transform-origin: 30.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"border-block-end-color: rgb(2, 128, 9); border-block-start-color: rgb(2, 128, 9); border-bottom-color: rgb(2, 128, 9); border-inline-end-color: rgb(2, 128, 9); border-inline-start-color: rgb(2, 128, 9); border-left-color: rgb(2, 128, 9); border-right-color: rgb(2, 128, 9); border-top-color: rgb(2, 128, 9); caret-color: rgb(2, 128, 9); color: rgb(2, 128, 9); column-rule-color: rgb(2, 128, 9); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(2, 128, 9); text-decoration-color: rgb(2, 128, 9); text-emphasis-color: rgb(2, 128, 9); \"\u003e%for k=3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 142.45px 8.5px; tab-size: 4; transform-origin: 142.45px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e1 + 3*(434-325-1) = 1 + 3*108 = 324  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.7333px 8px; transform-origin: 51.7333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.8333px 8px; transform-origin: 33.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e return the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.4417px 8px; transform-origin: 12.4417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003exth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185.175px 8px; transform-origin: 185.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHyperperfect number (serial/order wise) and corresponding \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.83333px 8px; transform-origin: 5.83333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ek \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.675px 8px; transform-origin: 18.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003evalue.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 360.442px 8px; transform-origin: 360.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP.S - Check the test suite for banned functions. More functions might be added later to prevent hard coded solutions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = hyper(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('hyper.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'interp1') || contains(filetext, 'find') || ...\r\n          contains(filetext, 'str2num') || contains(filetext, 'switch') || ...\r\n          contains(filetext, '26977') || contains(filetext, '1403221')|| ...\r\n          contains(filetext, '1570153') || contains(filetext, '4304341'); \r\nassert(~illegal)\r\n\r\n\r\n%%\r\nx = 1;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,6)\u0026isequal(k,1))\r\n\r\n%%\r\nx = 2;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,21)\u0026isequal(k,2))\r\n\r\n%%\r\nx = 4;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,6)\u0026isequal(n,301))\r\n\r\n%%\r\nx = 7;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,697)\u0026isequal(k,12))\r\n\r\n%%\r\nx = 11;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,2)\u0026isequal(n,2133))\r\n\r\n%%\r\nx = 17;\r\n[n,k]=hyper(x);\r\nassert(isequal(60,k)\u0026isequal(24601,n))\r\n\r\n%%\r\nx = 18;\r\n[n,k]=hyper(x);\r\nassert(isequal(26977,n)\u0026isequal(48,k))\r\n\r\n%%\r\nx = 20;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,132)\u0026isequal(96361,n))\r\n\r\n%%\r\nx = 21;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,130153)\u0026isequal(k,132))\r\n\r\n%%\r\nx = 25;\r\n[n,k]=hyper(x);\r\nassert(isequal(214273,n)\u0026isequal(k,31))\r\n\r\n%%\r\nx = 31;\r\n[n,k]=hyper(x);\r\nassert(isequal(78,k)\u0026isequal(n,486877))\r\n\r\n%%\r\nx = 37;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,1055833)\u0026isequal(k,348))\r\n\r\n%%\r\nx = 39;\r\n[n,k]=hyper(x);\r\nassert(isequal(1232053,n)\u0026isequal(498,k))\r\n\r\n%%\r\nx = 43;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,12)\u0026isequal(1570153,n))\r\n\r\n%%\r\nx = 45;\r\n[n,k]=hyper(x);\r\nassert(isequal(1787917,n)\u0026isequal(438,k))\r\n\r\n%%\r\nx = 48;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,336)\u0026isequal(2462881,n))\r\n\r\n%%\r\nx = 52;\r\n[n,k]=hyper(x);\r\nassert(isequal(798,k)\u0026isequal(n,2708413))\r\n\r\n%%\r\nx = 53;\r\n[n,k]=hyper(x);\r\nassert(isequal(810,k)\u0026isequal(2768581,n))\r\n\r\n%%\r\nx = 54;\r\n[n,k]=hyper(x);\r\nassert(isequal(n,2856481)\u0026isequal(k,528))\r\n\r\n%%\r\nx = 60;\r\n[n,k]=hyper(x);\r\nassert(isequal(k,162)\u0026isequal(n,4304341))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":223089,"edited_by":223089,"edited_at":"2025-09-13T06:25:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":"2025-09-13T06:25:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-07T10:09:14.000Z","updated_at":"2025-12-15T21:31:12.000Z","published_at":"2022-06-08T17:42:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Hyperperfect_number\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-hyperperfect number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is a natural number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for which the equality \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e = 1 + \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eσ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e)  − \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e  − 1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e holds, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eσ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e) is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Divisor_function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003edivisor function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e., the sum of all positive divisors of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[%Example\\nsigma(6) = 1 + 2 + 3 + 6 = 12\\n%for k=1\\n1 + 1*(12-6-1) = 1 + 5 = 6\\n\\n%Example\\nsigma(325) = 1 + 5 + 13 + 25 + 65 + 325 = 434\\n%for k=3\\n1 + 3*(434-325-1) = 1 + 3*108 = 324  ]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e return the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eHyperperfect number (serial/order wise) and corresponding \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003evalue.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP.S - Check the test suite for banned functions. More functions might be added later to prevent hard coded solutions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54750,"title":"Find the length of stream affected by a spill","description":"When a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration  is often computed as a function of time  and distance  from the spill using the advection-dispersion equation:\r\n\r\nwhere  is the mean velocity of the river and  is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass  mixed over the cross section (with area ) at , the concentration can be shown—using some of the math needed for Cody Problem 51625—to be\r\n\r\nWrite a function to compute the length of stream affected by the spill. In other words, find the position  (say) beyond which the concentration never exceeds a threshold . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 282.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 141.35px; transform-origin: 407px 141.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.317px 8px; transform-origin: 378.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.675px 8px; transform-origin: 123.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is often computed as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.833px 8px; transform-origin: 168.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the spill using the advection-dispersion equation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAP0AAABJCAYAAAD2biCfAAAPb0lEQVR4Xu2d2es+NxXG2z9Ai8tVFREXUFSUoq24ouCORVFxA/lBizuCbVGr9kLcqLig4IreiFoFRRFal4IFFcG6oOBy4UIRvXNB/QP0fNp5ymlIZk4yM+8yk4HD+/2+bzKTPDlPcnJykrn4on51BDoCu0Lg4l3Vtle2I9ARuKiTvitBR2BnCHTS76zBe3U7Ap30XQc6AodF4LH2uCeaXGLyF5OvHvbxF3Xz/tCA9+ftGoFPWe1fYXK7yXMGJH5un1eb/PpQyPSR/lBI9+fsHYG3GQCXDaQHi/uZfNfk8SbfM3nuoQDqpD8U0v05e0fgZwbAy03+7IDA1P/V8P/97fMfhwApSnoKJ3OEctEztZojD7G8jzB5dFLBn9j/Px6+e5193poAdAg8Tv0Zz3e4/XsmRk+x/I8yYW6pizkmpieKSZs/0uTgc85Tb4RM+SL8oO1uyeT93/BdLembeRQhPcrxZpNfDoXDRKHHgvhvN4mSn7nMtSaYM/8y+b675zPtb9+p8KhaEM5QV6qKTEeIct0x5HrZgOWn7fMGk8gogaJcZ0Jb3MeE+STtQAcC+d8wfK+CfcD+eFdVKfeXeC4/ID3t8IQgdLN5FCF9riw8+CaTP5lcMaFwKOo3TB5qAtmvN/ls5qa6Jz/VgBDEapPJcAxB1K8NRB6r5Pvtx3cOCeiw32jiTU1+8vNM/n+BSW502iSYC1Yqyg86jB+ZvL7ACV+kxXjUSnoKI4UbGw08kekgnp1RNF8xnB03BpV4wTY661v90UpPh1oiaEpkrLMPjdSY9H8wwRJ4nEnUkjtrEFcofIQfpGGEnxrlF+XRHNIzR7nZBDI/LANaWtApi4BbYH5yvynFXKGNzvaWGsEx8xm9/ZUSPjKikF9LSw+3vyPThrMFb8WCT/GDkfs2k2dMdKyL82gO6VGovw+gpSOC90pi0l9pIifdFM6MXG8x6WblFFJ3/S7lAuf7JllwwuF/4YpMAZRd88apEShWwn2mGuMHv33Z5H0TvFiFR3NIT1PK8+hNSyr0UxNMTq5aZxAV7SZlnCiaF0J6nKSap+P4+8xwm/S3qbvThjj20jn/VL7++z0RyPGDFHTGjPI535busBqPoqSnAJjnWmbTkp0q5c1GzcspfK2ydaUZR4Dpz+UmDzLRkt2l9jfOIC5ZXH5ezve1HW9vhzoEavjB1IlBLSU8FhuDpaZTq/FoivRU5hoTvL4QmB6KTzzG/M0nlye9HEt8X2NS1sG8r9SQHWVhWROfB7jiaAN/5vJqB5HezwNBqjvk1tGXWn7QhkzBaB9/adnPf78aj8ZIn4YJvtpKqV5I80gVXKSXqanvXzl0DutAvo+7yuEDydMR2y/DeXIT3qm4h5KjdR/orVfLWn5QEk23cqXyXFmVRyXSj1VIBZZp75XNmyR8z7y+zwvbFW+M8NzVK4d35Pm2yXn120vUc4JALT+ebnnYWTd2+WXUVXlUIr1/aMk09IolcvsRhgr2qLp5JBGepSAoT3qN6Oko0efz89ogl7uVH9GSrMqjHOm9E6g0Smg9nUp483HLZiV1fqlJLmQYDD5nktuTgIL4PPKN4MgZW6Xw5C1Nk/zcXW21qmkY1dojpaPuzzNhmVKrRyoK+HgHWtou0mXa8QsmpfiEOfyIwrIqj3Kk94r0VCtlbn3dp/EjyaqFjSJ2gHTeyQLRvb+j9PjS8k0pvSK66CRKQTJKwz20bLpn0gvLks8pxdqno1P4sMnUdHQOP6KquSqPcqT3ypYGe6jQPujDr9F7JSTtVs17P7WJOiu1sYJ905EoN3UsYysg/7R74eDzWHsrjO/3aN57MpemRt5fEo1UBM85/IiSflUe5UivXqa0sd8rVboxZs5SEfdl7TlCiCh4pKM+XLkNJjX3UdrUeRYJVVWemvBidSylPCVri3LOWe7ZQnCUJ01uiirC02leMIlGi0qfWBlp4UdU31bl0RjpSyOMBzQ1/9OgkKiSawdRbQNEQBR5llqr9k6c6IknylNThlzgk6+viJ0z/9PAjkjHpFEst44cwfmU0vhOL7XERKjSTsOpemhQbOHH1L31+6o8ypF+bKebjwUumY2+l0IhpzYUYIp9oqHHjQK4NOk5AYVwV66oWUgezPDIpiPVS8qVe4YPsc3trks32kwt25H+k8OD08CRKM6nki6d3mhlSXXEycdgNOasG6vLXH5EcVqNRznSC7R0LjS1Zuwrk8Z95/bQY/K+24Qdei8xWSvefknS+00U1DcycivPFPFSZVCjpyOKV4ax/e60I3nVQfH3BxOcKdtVJu8woXxbODDD6x7TT3woDzThTAesGKZ5c04DWoIfUeKvwqPSOr03gX5gJXywCaGedAQQNQKaSJ0es0WFfTjp2oq2JOk94SIHiFBXOZWiDj+vEJpKQcg7TLT0Fz1B1ZNaDj/KjflLZ8soWHsCUlRhj5XOO5mxRjkCjEi4KGaRci/Bj8hzSLM4j8bCcLUuzYMB7q8mNQ4PVQrF46w1ncfGvX5vstbInoK5JOmnHES5hpy7N51Gf9Jw49/Y598ascNSe4CJNk1xJiHtsKTjNF0ujCp2mi46bcrd369o0MHRsUH49FDK1rIp31L8iJZjMR5NbbiJFuiU0y1J+jEHUQkD8iAHO+L4iI1xbNJ7n1MKQz/6a0Ckkz7OkFShIjEIyjNn5IqXsKdMV1Z+YZDoXMB+7uKGSJ/GKbeofu7UmfQ+qYMocqqM8kQcfi3l7nnuiYDXBXnodd4fKVv8KpvDeAsj/aFI7+fz0Sg3ysZcLBqFtzkFO2CF0pUVxZCkMQulKNMDFvW4j9oC6acQXGpO79fnI/PD1qW6qfr03/MI+NDbNGDJ+2KiAWObxbmTPt60Pt4+Mp/fo2l/TEeeP1BkLLaBFo+0X1wzzixlSvqxg/qOVTXIM+daaqSvIb0ONWSEiezAS+t3au3wOyvgxwONcEzS+9E85zj108DaQClVnbcKKd4hAMdJJWHL8J1XSnqv2KdS4rmn7yxF+tLOwhxOGnUi04A0/wvti2+fCvhDOX5rn+m7B0+piGnobc5xmnZILc5VHwNwSvWPlIXITFYzdvF++qVI75fsxqLx5DhqHU0iDdjT3BOBaKSkH+2jm6X8k+hcznWkv5PwnfT11MFZ9CXX8HjxvzPchojDq03oUfn+oyZLRrvVl3Y/OaKHTqRnz+1yCa878uqJwXydY7NebOL3FTD68wbYr5i0hCvXl6TnYIS/kLQDqODI+5aJ9oiQ7jEm6Vt5c2k3j+oeSK9DNFiqOVS8/+YVp1fw6AhgdfL6Nw084Y1TeyD90VunF6AjsDACWC7XmnzE5D8mrzHROwtL51reXYS5pKe3eY+J9mzrpNfIAYML47C723Xsd9fkd1eY5cn0te9aXZp8q9Rc0uPN5NIJot7R1bJctd9mrK95x74esy3k0DHf6TkUikic3Fg0l/Q5ELW0NXZ08xbAP8U6dOyP3yo4et9rggmu5T2IiCkeOXymtQaKQ1h9pC8VUKbGWJwzCnovk+7pbm3mfL4I9ss+sd8tRQACSq+xyK4zYeVgchSeAaViFSa3ca8x0lNuxZ2XKqkwVUID/Tu8ZtS5Zx0QmMK+A3UcBNbujNkFynbvyR2da5FepkZun7o/qbUlFPI4TXY+Tx3D/nxqsb2S+ojOpXmnMORJzz2wLv1wNZWPc/bE9o6+6MGS22v+dWtUwn7dp/a7RxBQ7P7STm5iUb5pEtqoNZf0KNirTFg+YGOMluyISvvRgAKk/68J0WrpSwUF1NxNNRHAt5Ymir0CkrCwnmXyNNdePgxVDiidesxpuf1aFoGxdxm0PonNXVzhU6XnkF47yXQs9q324EtM/FnrFMaP9N7E2WXcc2vLJvlasKeTuLcJwRzs4sOzrDcOa8rFYxRz0TvihRrL3Wbq7Ti1T8R5Ryd+g0l4n0cr6XV0FEqTvqgifTMHSqR1fH/OXFeq2ia+K30r9v5p/sAJDpRgiQkrjdGC+SGrKj1kua19cnszcGi/1YR3RhA2my6rMe19sgkWM3xJd2iyUYgXktBRizfad5Ce1yCLjZd6ZK8W0munEkpypUm65ObnlKkjTx5MvXkk3Du14b+5XHOw92D4o6VQQK43mfT2mKcyeicjxIS4zLHpPP1gxxM86elkLzfhvRLqFEgjctPJ0xlwth+kx0LGWrt5eMYdSZFfa/8Tk39LqSq1pPcv1ivtF/ekT/csa2979GDJeU2wrdxzsfdo+EMk6Zi9NbYt1A5Xm6nXvvmTfUr67ztjnH1Mxy6YMJpz8dIY/GO3DR1ArnaTDvJa0qvHKo3yFMLvWfbBOb4zWNp7ebimPd6T5mCfK7UO+lwzYOR4aB32yb5DLkXE+T3/pQAa3xkzYPL/0m/mqV6yU8HHFMWfGuudeN40jb46+bBNd9pPm4N9rmbyDUTO/D9tZI5fOq/bpbc0e9KPrafXnrpcXfvakV7mecm092eVpR2DKtNyTFF1xTaYYQ72KRzpeXGhoI4NYrpUlbT+Phb3rvab2pOSOlkX97O0kr5knvgXQngT3pstuz93vFHTpDS12KePkymKd/em4cfeJo2NYtki09bUcYrnvXT51a9VIlZrSS9nRE7x/CifW5LA28ilUYUOoris0N4Gm83Zin0KCGYmrx9nz0PO+kLpiLlYfITZaMtETPvSYFjqkLU7b5XOuJb0KnxaGB9Pj/merh36YJIr7HfWhX9osuZWw63pWCv2eJW5WDriHlwK5vCmJLoA4V9k0pfv4trjSZ97ZdbYlDfXIXNqrdbrV5kK15KeCjBX59IyD+bNx4b/GeFzCiMnBvMZwnGZA/VRPq5YpGzB3kdAgj3LOd4b7M1OfiPN4t7iumqeXWqZ4yWHqHeY5uJaVGE6j8sG/lxjn3rbrjgKz1iumx00VUt6Cogi3WiiA/noBFCYL5qUAgI0ogDM9SZfN+nmY71+12JPR6E9D4wadLSKjtTT1SGXfq8v5b5y+JE85ZPvEMDeW7bku9SE4DadeacO13fGTIch++eX6pBbSL+vJu217QhMI6BBTUE3THevGgZH7U1Jp7Ly+DMQcnkrIA2eIu2FoYOYLs1Eik762RD2G3QE7kTAx8dD5NtNcJhi1abWFellYdEp5AgtX0Hp92bYO+mboesZOwLniUAn/Xm2Wy91R6AZgU76Zuh6xo7AeSLQSX+e7dZL3RFoRqCTvhm6nrEjcJ4IdNKfZ7v1UncEmhHopG+GrmfsCJwnAp3059luvdQdgWYEOumboesZOwLnicD/AWS5b4YFIT97AAAAAElFTkSuQmCC\" alt=\"dC/dt + U dC/dx = K d^2C/dx^2\" style=\"width: 126.5px; height: 36.5px;\" width=\"126.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.958px 8px; transform-origin: 113.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 202.158px 8px; transform-origin: 202.158px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.242px 8px; transform-origin: 125.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e mixed over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 8px; transform-origin: 12.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.5083px 8px; transform-origin: 59.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the concentration can be shown—using some of the math needed for \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51625\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 51625\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5583px 8px; transform-origin: 22.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—to be\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.05px; text-align: left; transform-origin: 384px 20.05px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\" style=\"width: 204.5px; height: 40px;\" width=\"204.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 313.617px 8px; transform-origin: 313.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = L_a\" style=\"width: 42.5px; height: 20px;\" width=\"42.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3417px 8px; transform-origin: 44.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (say) beyond which the concentration never exceeds a threshold \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = C_t\" style=\"width: 46px; height: 20px;\" width=\"46\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function La = affectedReach(U,K,M,A,Ct)\r\n% La = length of affected reach of stream [L]\r\n% U  = mean velocity [L/T]\r\n% K  = dispersion coefficient [L^2/T]\r\n% M  = mass of contaminant [M]\r\n% A  = cross-sectional area (L^2)\r\n% Ct = threshold concentration (M/L^3)\r\n\r\n  La = M/(Ct*A);\r\nend","test_suite":"%%\r\nM = 100;                    %  Mass (kg)\r\nA = 30;                     %  Cross-sectional area (m2)\r\nU = 0.3;                    %  Mean velocity (m/s)\r\nK = 2;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 50;                     %  Mass (kg)\r\nA = 15;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 8.4;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.001;                 %  Target concentration (kg/m3)\r\nLa_correct = 26332.1;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 0.003;                 %  Target concentration (kg/m3)\r\nLa_correct = 91.59;         %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 3e-4;                  %  Target concentration (kg/m3)\r\nLa_correct = 7256.28;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 70;                     %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.15;                   %  Mean velocity (m/s)\r\nK = 1;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 280;                    %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.54;                   %  Mean velocity (m/s)\r\nK = 3.7;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.007;                 %  Target concentration (kg/m3)\r\nLa_correct = 42140.42;      %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%% Approximately plug flow\r\nM = 5*rand;                 %  Mass (kg)\r\nA = 40;                     %  Cross-sectional area (m2)\r\nU = 0.3*(1+rand);           %  Mean velocity (m/s)\r\nK = rand*1e-3;              %  Dispersion coefficient (m2/s)\r\nCt = 0.02*rand;             %  Target concentration (kg/m3)\r\nLa_approx = (U/(4*pi*K))*(M/(Ct*A))^2;\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_approx)/La_approx\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('affectedReach.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp') || contains(filetext,'if'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2022-06-14T05:04:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2022-06-14T05:04:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-14T04:57:20.000Z","updated_at":"2022-06-14T05:04:44.000Z","published_at":"2022-06-14T04:59:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is often computed as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the spill using the advection-dispersion equation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dC/dt + U dC/dx = K d^2C/dx^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial C}{\\\\partial t} + U \\\\frac{\\\\partial C}{\\\\partial x} = K \\\\frac{\\\\partial^2 C}{\\\\partial x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e mixed over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the concentration can be shown—using some of the math needed for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51625\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 51625\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—to be\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L_a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L_a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (say) beyond which the concentration never exceeds a threshold \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = C_t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = C_t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44374,"title":"Tautology","description":"Check if the given expression is always true. For example, the sentence\r\n\r\n  '~(A \u0026 B) == (~A | ~B)'\r\n\r\nis always true.\r\n\r\nCharacters in the input sequences may include *~ \u0026 | == ( )*, whitespace, 0 for false, 1 for true and letters for variables.","description_html":"\u003cp\u003eCheck if the given expression is always true. For example, the sentence\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e'~(A \u0026 B) == (~A | ~B)'\r\n\u003c/pre\u003e\u003cp\u003eis always true.\u003c/p\u003e\u003cp\u003eCharacters in the input sequences may include \u003cb\u003e~ \u0026 | == ( )\u003c/b\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/p\u003e","function_template":"function y = tautology(x)\r\n  y = true;\r\nend","test_suite":"%%\r\nx = '0';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1\u0026A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A\u0026B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|~A';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '0==0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(A \u0026 B) == (~A | ~B)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(Z \u0026 Y) == (~Y | ~Z)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|~A|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nassert(isequal(tautology('(A|B)|C'),false));\r\n%%\r\nassert(isequal(tautology('(A|B)|(C == C)'),true));\r\n%%\r\nassert(isequal(tautology('(A == B)|(B == C)|(C == A)'),true));\r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(0))))))'),false)); \r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(~0))))))'),true));\r\n% provided by Alfonso:\r\nassert(isequal(tautology('((0\u00261)|~B)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((0\u0026~B)\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)\u0026~A)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((0|~B)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((1\u00260)|B)'),false)); \r\n%%\r\nassert(isequal(tautology('((1\u00261)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('((1|0)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|A)|0)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|~A)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u00261)|~A)|A'),true)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~A)\u0026~B)|~A'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~B)\u00261)|B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|0)\u00261)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|A)\u0026A)|~A'),true)); \r\n%%\r\nassert(isequal(tautology('((B|0)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((B|1)\u0026B)\u0026A'),false)); \r\n%%\r\nassert(isequal(tautology('((B|A)|~A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)\u00260)\u0026B'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|0)'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|~A)|1'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|A)|~B)\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|B)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~B)\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('((~B\u00260)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('(0\u00261)|1\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('(0|~A\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(1|A\u00260)'),true)); \r\n%%\r\nassert(isequal(tautology('(A\u0026A\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('(A\u0026~A|1)'),true)); \r\n%%\r\nassert(isequal(tautology('(A|1)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(A|A)|A|1'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u00261)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u0026~B)\u0026~B\u00260'),false)); \r\n%%\r\nassert(isequal(tautology('(B|~B)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A\u0026B\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|0)|~B\u0026~A'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|1)|1'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|B\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|B)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|~A)|0'),false)); \r\n%%\r\nassert(isequal(tautology('(~B\u00260)\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('1\u0026B|~B|0'),true)); \r\n%%\r\nassert(isequal(tautology('B\u00261\u0026A\u00261'),false)); \r\n%%\r\nassert(isequal(tautology('~A\u00260\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('~B\u00260\u0026~A|B'),false)); \r\n%%\r\nassert(isequal(tautology('~B|1|1|~B'),true)); \r\n%%\r\nassert(isequal(tautology('~B|~B\u00261|1'),true));\r\n%%\r\nassert(isequal(tautology('A==~A'),false));\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":30,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2017-10-31T07:45:16.000Z","rescore_all_solutions":true,"group_id":35,"created_at":"2017-10-10T23:20:08.000Z","updated_at":"2026-04-18T11:07:15.000Z","published_at":"2017-10-16T01:51:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck if the given expression is always true. For example, the sentence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA['~(A \u0026 B) == (~A | ~B)']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis always true.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCharacters in the input sequences may include\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e~ \u0026amp; | == ( )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":53125,"title":"Easy Sequences 54: Product of Products of Proper Divisors","description":"A divisor of a number that is less than the number is called a \"proper divisor\". \r\nFor a given positive integer , we are asked to evaluate the following summation:\r\n             \r\nThis is equivalent to finding the product of the products of proper divisors of all integers from  to .\r\nFor example for , we have:\r\n                            \r\nPlease present your output modulo .","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 413.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 206.75px; transform-origin: 407px 206.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 244.5px 8px; transform-origin: 244.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA divisor of a number that is less than the number is called a \"proper divisor\". \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eF\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95.5px 8px; transform-origin: 95.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eor a given positive integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 162px 8px; transform-origin: 162px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we are asked to evaluate the following summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.75px; text-align: left; transform-origin: 384px 22.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24px 8px; transform-origin: 24px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 110px; height: 45.5px;\" width=\"110\" height=\"45.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88px 8px; transform-origin: 88px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis is equivalent to finding \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233px 8px; transform-origin: 233px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ethe product of the products of proper divisors of all integers from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e2\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11px 8px; transform-origin: 11px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.5px 8px; transform-origin: 51.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 209px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 104.5px; text-align: left; transform-origin: 384px 104.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-99px\"\u003e\u003cimg 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style=\"width: 509px; height: 209px;\" width=\"509\" height=\"209\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.5px 8px; transform-origin: 112.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ePlease present your output modulo \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 55.5px; height: 18px;\" width=\"55.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = pppd(n)\r\n    s = 2 * (n + 2) ^ 2 * n;\r\nend","test_suite":"%%\r\nn = 10;\r\ns_correct = 2880;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 20;\r\ns_correct = 178754;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = 651627;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 200;\r\ns_correct = 471492;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 1000;\r\ns_correct = 132068;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 2000;\r\ns_correct = 192916;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 10000;\r\ns_correct = 700691;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 20000;\r\ns_correct = 135567;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 100000;\r\ns_correct = 919193;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 200000;\r\ns_correct = 581218;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nn = 1000000;\r\ns_correct = 811966;\r\nassert(isequal(pppd(n),s_correct))\r\n%%\r\nns = 2000000:2222222;\r\ns = arrayfun(@(n) pppd(n),ns);\r\nss = mod([sum(s) sum(num2str(s))],1000003);\r\nss_correct = [526924 445038];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('pppd.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-12-04T15:11:17.000Z","updated_at":"2026-03-19T13:19:46.000Z","published_at":"2021-12-06T15:33:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA divisor of a number that is less than the number is called a \\\"proper divisor\\\". \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eor a given positive integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we are asked to evaluate the following summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\prod_{i=2}^{n}\\\\left (\\\\prod_{\\\\ d|i\\\\ \\\\\u0026amp;\\\\  d\u0026lt;i}^{}d\\\\   \\\\right )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is equivalent to finding \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe product of the products of proper divisors of all integers from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\prod_{i=2}^{10}\\\\prod_{d|i\\\\ \\\\\u0026amp;\\\\  d\u0026lt;i}^{}d\\\\ = \\\\prod_{d|2\\\\ \\\\\u0026amp;\\\\  d\u0026lt;2}^{}d \\\\ \\\\times\\\\prod_{d|3\\\\ \\\\\u0026amp;\\\\  d\u0026lt;3}^{}d \\\\ \\\\times\\\\prod_{d|4\\\\ \\\\\u0026amp;\\\\  d\u0026lt;4}^{}d  \\\\ \\\\times\\\\prod_{d|5\\\\ \\\\\u0026amp;\\\\  d\u0026lt;5}^{}d\\\\ \\\\times\\\\prod_{d|6\\\\ \\\\\u0026amp;\\\\  d\u0026lt;6}^{}d \\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\times\\\\prod_{d|7\\\\ \\\\\u0026amp;\\\\  d\u0026lt;7}^{}d \\\\ \\\\times\\\\prod_{d|8\\\\ \\\\\u0026amp;\\\\  d\u0026lt;8}^{}d \\\\ \\\\times\\\\prod_{d|9\\\\ \\\\\u0026amp;\\\\  d\u0026lt;9}^{}d \\\\ \\\\times\\\\prod_{d|10\\\\ \\\\\u0026amp;\\\\  d\u0026lt;10}^{}d \\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ =1\\\\times1\\\\times(1\\\\cdot2)\\\\times1\\\\times(1\\\\cdot2\\\\cdot3)\\\\times1\\\\times(1\\\\cdot2\\\\cdot4)\\\\times(1\\\\cdot3)\\\\times(1\\\\cdot2\\\\cdot5) \\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ =1\\\\times1\\\\times2\\\\times1\\\\times6\\\\times1\\\\times8\\\\times3\\\\times10 \\\\\\\\ \\\\\\\\\\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ =2880\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present your output modulo \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1000003\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60411,"title":"Compute a sequence with the whyphi sieve","description":"A few problems on Cody involve sieving. For example, Cody Problem 45367 involves the famous Sieve of Eratosthenes. CP 50811 uses the sieve of Flavius Josephus, and CP 50913 uses the golden sieve. \r\nThis problem uses a process that I will call the whyphi sieve: \r\nMake a list x of integers 1, 2, 3,… \r\nRemove the first term. That is, delete x(1).\r\nRenumber the terms. \r\nDelete x(2) and x(2+1)\r\nRenumber the terms. \r\nDelete x(3), x(3+2), and x(3+2+1). \r\nContinue renumbering and deleting terms in this way. \r\nWrite a function to compute the nth term of this sequence. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 266.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 133.017px; transform-origin: 407px 133.017px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 170.375px 7.79167px; transform-origin: 170.375px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA few problems on Cody involve sieving. For example, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/45367\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 45367\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.075px 7.79167px; transform-origin: 138.075px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e involves the famous Sieve of Eratosthenes. \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/50811\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCP 50811\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127.967px 7.79167px; transform-origin: 127.967px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e uses the sieve of Flavius Josephus, and \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/50913\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCP 50913\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5167px 7.79167px; transform-origin: 73.5167px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e uses the golden sieve. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 188.65px 7.79167px; transform-origin: 188.65px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem uses a process that I will call the whyphi sieve: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 143.033px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 71.5167px; transform-origin: 391px 71.5167px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.775px 7.79167px; transform-origin: 105.775px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eMake a list x of integers 1, 2, 3,… \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 130.667px 7.79167px; transform-origin: 130.667px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRemove the first term. That is, delete x(1).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 67.675px 7.79167px; transform-origin: 67.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRenumber the terms. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 69.8333px 7.79167px; transform-origin: 69.8333px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDelete x(2) and x(2+1)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 67.675px 7.79167px; transform-origin: 67.675px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRenumber the terms. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 107.567px 7.79167px; transform-origin: 107.567px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDelete x(3), x(3+2), and x(3+2+1). \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 166.758px 7.79167px; transform-origin: 166.758px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eContinue renumbering and deleting terms in this way. \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 181.108px 7.79167px; transform-origin: 181.108px 7.79167px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the nth term of this sequence. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = whyphiSieve(n)\r\n  c = 100*[0.000057513128234 0.093378634167431 -2.856145294974328]\r\n  y = polyval(c,n);\r\nend","test_suite":"%%\r\nassert(isequal(whyphiSieve(1),2))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(5),14))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(19),79))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(54),305))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(89),594))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(135),1032))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(336),3443))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(689),8948))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(1000),14685))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(4509),109040))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(whyphiSieve(428)),116991))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(whyphiSieve(620)),225368))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(10000),315192))\r\n\r\n%%\r\nassert(isequal(whyphiSieve(20000),793960))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-06-04T15:38:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-28T02:46:53.000Z","updated_at":"2026-03-30T07:39:19.000Z","published_at":"2024-05-28T02:47:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA few problems on Cody involve sieving. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/45367\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 45367\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e involves the famous Sieve of Eratosthenes. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/50811\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCP 50811\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e uses the sieve of Flavius Josephus, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/50913\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCP 50913\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e uses the golden sieve. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem uses a process that I will call the whyphi sieve: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a list x of integers 1, 2, 3,… \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemove the first term. That is, delete x(1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRenumber the terms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDelete x(2) and x(2+1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRenumber the terms. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDelete x(3), x(3+2), and x(3+2+1). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eContinue renumbering and deleting terms in this way. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the nth term of this sequence. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1241,"title":"PACMAT  - Ghosts maximize unique locations; 3 Lives","description":"The Classic PACMAN game brought to Cody.\r\n\r\nPACMAT Ghosts Random requires clearing the board of Yellow Dots while not bumping into the wandering ghosts in 3 lives. Adjacent Ghosts will capture PACMAT.  Ghosts do not use the tunnel. On Ghost capture everyone gets reset.\r\n\r\n\u003c\u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_300.jpg\u003e\u003e\r\n\r\nTo aid in development of your routine, a PACMAT_Ghosts_002.m file that creates a video has been posted at \u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_Ghosts_002.m PACMAT_Ghosts_002.m\u003e. (Right click, 'save link as'). Using patches thus enable/figure  disable/video for best results.\r\n\r\n\r\n\u003chttps://sites.google.com/site/razapor/matlab_cody/PACMAT_G002_video_ANC.mp4 Alfonso's Enhanced Ghost Avoider\u003e (MP4) Quite an impressive solution\r\n\r\n\r\nThe reference solution uses Alfonso's Local Optimum Algorithm with a Catch.\r\n\r\n*Inputs:* Map   Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u003e2=Ghost\r\n\r\n*Output:* Direction  Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\r\n\r\n*Scoring:* Total # of Moves to Clear the Yellow Dots +(LivesRemaining-3)*100\r\n\r\n\r\n*Near Future:* Ghosts with LOS Tracking.\r\n\r\n*Future:* Player will be Team Ghosts versus PACMAT_BOT","description_html":"\u003cp\u003eThe Classic PACMAN game brought to Cody.\u003c/p\u003e\u003cp\u003ePACMAT Ghosts Random requires clearing the board of Yellow Dots while not bumping into the wandering ghosts in 3 lives. Adjacent Ghosts will capture PACMAT.  Ghosts do not use the tunnel. On Ghost capture everyone gets reset.\u003c/p\u003e\u003cimg src=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_300.jpg\"\u003e\u003cp\u003eTo aid in development of your routine, a PACMAT_Ghosts_002.m file that creates a video has been posted at \u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Ghosts_002.m\"\u003ePACMAT_Ghosts_002.m\u003c/a\u003e. (Right click, 'save link as'). Using patches thus enable/figure  disable/video for best results.\u003c/p\u003e\u003cp\u003e\u003ca href=\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_G002_video_ANC.mp4\"\u003eAlfonso's Enhanced Ghost Avoider\u003c/a\u003e (MP4) Quite an impressive solution\u003c/p\u003e\u003cp\u003eThe reference solution uses Alfonso's Local Optimum Algorithm with a Catch.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e Map   Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u003e2=Ghost\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Direction  Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Total # of Moves to Clear the Yellow Dots +(LivesRemaining-3)*100\u003c/p\u003e\u003cp\u003e\u003cb\u003eNear Future:\u003c/b\u003e Ghosts with LOS Tracking.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFuture:\u003c/b\u003e Player will be Team Ghosts versus PACMAT_BOT\u003c/p\u003e","function_template":"function  [newdir]=pacmat(map)\r\n% 314 move solver if Ghosts do not move\r\n persistent ptr\r\n if isempty(ptr)\r\n  ptr=['bbbbbbbcccbbbbbcccdddddddddddddddddddddddddaaa'...\r\n      'bbbbbaaaaaaaaaaaaaaaaaaaaaaaaadddddcccccccbbbbddddaaabbbbbbbb'...\r\n      'cccbbbdddaaabbbaaaadddddbbbbbccccbbbbbbbbbbbbbbaaaaddddddddddd'...\r\n      'ccccbbbcccdddbbbaaabbbaaaccccccbbbbbaaccdddddccccccccccccccaabbbbbcccddccc'...\r\n      'dddaaaaaaddddddcccbbbcccdddcccdddaaadddaaaddbbbbbaaadddddddddddcccbbccc'];\r\n  ptr=(ptr-'a')+1;\r\n end\r\n  \r\n newdir=ptr(1);\r\n ptr(1)=[];\r\n\r\n% usage of newdir=randi(4) will barely move\r\nend","test_suite":"%%\r\nfeval(@assignin,'caller','score',2000);\r\n%%\r\nmax_moves=2000; % Fixed path expect to succeed by 600 moves\r\n\r\nmap=[...\r\n      repmat('a',1,28);\r\n      'accccccccccccaacccccccccccca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acccccccccccccccccccccccccca';\r\n      'acaaaacaacaaaaaaaacaacaaaaca';\r\n      'acaaaacaacaaaaaaaacaacaaaaca';\r\n      'accccccaaccccaaccccaacccccca';\r\n      'aaaaaacaaaaabaabaaaaacaaaaaa';\r\n      'aaaaaacaaaaabaabaaaaacaaaaaa';\r\n      'aaaaaacaabbbbbbbbbbaacaaaaaa';\r\n      'aaaaaacaabaaabbaaabaacaaaaaa';\r\n      'aaaaaacaabalbbbblabaacaaaaaa';\r\n      'bbbbbbcbbbabbbbbbabbbcbbbbbb';\r\n      'aaaaaacaabalbbbblabaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'aaaaaacaabbbbbbbbbbaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'aaaaaacaabaaaaaaaabaacaaaaaa';\r\n      'accccccccccccaacccccccccccca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acaaaacaaaaacaacaaaaacaaaaca';\r\n      'acccaacccccccbdcccccccaaccca';\r\n      'aaacaacaacaaaaaaaacaacaacaaa';\r\n      'aaacaacaacaaaaaaaacaacaacaaa';\r\n      'accccccaaccccaaccccaacccccca';\r\n      'acaaaaaaaaaacaacaaaaaaaaaaca';\r\n      'acaaaaaaaaaacaacaaaaaaaaaaca';\r\n      'acccccccccccccccccccccccccca';\r\n      repmat('a',1,28);];\r\n  \r\n  map=map-'b';\r\n  [nr, nc]=size(map);\r\n\r\n  gmap=map; % Map used by ghosts to simplify PAC Capture\r\n  gmap(15,6)=Inf; %No tunnel ghosts\r\n  gmap(15,26)=Inf;\r\n  gmap(map==-1)=Inf; % walls to Inf\r\n  gmap(map\u003e2)=Inf; % Elim start points as viable moves, quicker box exit\r\n\r\n\r\n  mapdelta=[-1 nr 1 -nr]; % Valid as long as not on an edge\r\n  gmovxy=[0 -1;1 0;0 1;-1 0];\r\n\r\n  tunnel=find(map(:,1)==0); % tunnelptr\r\n  tunnel=[tunnel tunnel+nr*(nc-1)]; % Entrance/Exit Tunnel\r\n\r\n  [pmr, pmc]=find(map==2); % pi 24 row  pj 15 column of map\r\n   ptrpac=find(map==2);\r\n\r\n  ptrpac=find(map==2);\r\n  ptrpac_start=ptrpac;\r\n  ptrg_start=find(map\u003e2);\r\n  map(ptrg_start)=[10 20 30 40];% use deal?\r\n  [gstartx, gstarty]=find(map\u003e2);\r\n  \r\n  lives=3; % Lives\r\n  movepac=0;\r\n\r\nwhile lives \u0026\u0026 any(mod(map(:),10)==1) \u0026\u0026 movepac\u003cmax_moves\r\n movepac=movepac+1;\r\n\r\n [curdir]=pacmat(map);\r\n% if curdir==0,continue;end % Inf loop error\r\n [pmr, pmc]=find(map==2);\r\nif curdir\u003e0\r\n if map(ptrpac+mapdelta(curdir))==-1\r\n  % Do nothing - Ran into a Wall\r\n elseif map(ptrpac+mapdelta(curdir))\u003e2 % ran into ghost\r\n  map(ptrpac)=0; % remove PAC from the board\r\n  lives=lives-1;\r\n  if lives==0,break;end\r\n  % reset the board\r\n  [ptrgx, ptrgy]=find(map\u003e2);\r\n  ptrg=find(map\u003e2);\r\n  map(ptrg)=mod(map(ptrg),10);\r\n  map(ptrpac_start)=2;\r\n  map(ptrg_start)=[10 20 30 40];\r\n  ptrpac=find(map==2);\r\n  continue;\r\n else % legal move\r\n  map(ptrpac)=0; % Eat Dot and clear PAC\r\n  ptrpac=ptrpac+mapdelta(curdir);\r\n  if ptrpac==tunnel(1),ptrpac=tunnel(2)-nr;end\r\n  if ptrpac==tunnel(2),ptrpac=tunnel(1)+nr;end\r\n  map(ptrpac)=2;\r\n end\r\nend % curdir \u003e0\r\n\r\n% Ghosts\r\n for i=1:4\r\n\r\n   gmapT=gmap;\r\n   ptrg=find(map\u003e2); % Find all ghosts\r\n   gmapT(ptrg)=Inf; % Rule out moving onto a ghost\r\n\r\n\r\n  dot=false;\r\n  [gptrx, gptry]=find(map==10*i);\r\n  gidx=find(map==10*i);\r\n  if isempty(gidx)\r\n   [gptrx, gptry]=find(map==10*i+1); % ghost must be on a dot\r\n   gidx=find(map==10*i+1);\r\n   dot=true;\r\n  end\r\n\r\n% Find valid ghost moves using gmap\r\n% mapdelta=[-1 nr 1 -nr]; \r\n  gmov=find(map(gidx+mapdelta)==2); % adjacent to PACMAT\r\n  if ~isempty(gmov) % PAC adjacent\r\n   lives=lives-1;\r\n   if lives==0,break;end\r\n   % reset the board\r\n   [pmr, pmc]=find(map==2); % PACMAT erase coords\r\n   map(map==2)=0;\r\n      \r\n   [ptrgx, ptrgy]=find(map\u003e2);\r\n   ptrg=find(map\u003e2);\r\n   map(ptrg)=mod(map(ptrg),10);\r\n   map(ptrpac_start)=2;\r\n   map(ptrg_start)=[10 20 30 40];\r\n   ptrpac=find(map==2);     \r\n   break; % Ghost move loop\r\n      \r\n  else % gmap/gmapT avoids tunnel,other ghosts, Walls\r\n \r\n   gmap(gidx)=gmap(gidx)+1;\r\n   ghost_adj=gmapT(gidx+mapdelta);\r\n   if min(ghost_adj)\u003cInf\r\n    if rand\u003c0.5 % Push ghosts away from each other\r\n     gmov=find(ghost_adj==min(ghost_adj),1,'first');\r\n    else\r\n     gmov=find(ghost_adj==min(ghost_adj),1,'last');\r\n    end\r\n   else\r\n    gmov=[];\r\n   end\r\n \r\n   if ~isempty(gmov) % valid g move : ghost may not stand on ghost\r\n    map(gptrx,gptry)=mod(map(gptrx,gptry),10);\r\n    map(gidx+mapdelta(gmov))=map(gidx+mapdelta(gmov))+10*i;     \r\n   end % ~isempty(gmov) standard move - no capture\r\n\r\n  end % ~isempty(gmov) PACMAT adjacent\r\n  \r\n end % i ghost moves\r\nend % while alive\r\n\r\nfprintf('moves %i\\n',movepac)\r\n\r\nassert(lives\u003e0,sprintf('Three Captures\\n'))\r\nassert(~isempty(any(mod(map(:),10)==1)),sprintf('Moves\\n',movepac)) % Test Move Timeout\r\n\r\n\r\nfeval( @assignin,'caller','score',floor(min( 2000,300-100*lives+movepac )) );\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":"2013-02-02T05:09:50.000Z","rescore_all_solutions":false,"group_id":33,"created_at":"2013-02-02T00:36:11.000Z","updated_at":"2026-04-23T18:03:04.000Z","published_at":"2013-02-02T01:21:05.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe Classic PACMAN game brought to Cody.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT Ghosts Random requires clearing the board of Yellow Dots while not bumping into the wandering ghosts in 3 lives. Adjacent Ghosts will capture PACMAT. Ghosts do not use the tunnel. On Ghost capture everyone gets reset.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo aid in development of your routine, a PACMAT_Ghosts_002.m file that creates a video has been posted at\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_Ghosts_002.m\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePACMAT_Ghosts_002.m\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. (Right click, 'save link as'). Using patches thus enable/figure disable/video for best results.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://sites.google.com/site/razapor/matlab_cody/PACMAT_G002_video_ANC.mp4\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAlfonso's Enhanced Ghost Avoider\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e (MP4) Quite an impressive solution\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe reference solution uses Alfonso's Local Optimum Algorithm with a Catch.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Map Definitions: -1=Wall, 0=Empty, 1=Dot, 2=PACMAT, \u0026gt;2=Ghost\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Direction Definitions: 1-Up, 2-Right, 3-Down, 4-Left, 0-No move\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Total # of Moves to Clear the Yellow Dots +(LivesRemaining-3)*100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNear Future:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Ghosts with LOS Tracking.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFuture:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Player will be Team Ghosts versus PACMAT_BOT\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" 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\"}]}"},{"id":58019,"title":"Factor a number into Fermi-Dirac primes","description":"Cody Problem 58018 asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, . \r\nWrite a function analogous to factor(n) that factors the number  into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 135px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 67.5px; transform-origin: 407px 67.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58018\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 58018\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"122\" height=\"18\" alt=\"2250 = 2x5x9x25\" style=\"width: 122px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function analogous to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003efactor(n)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that factors the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = factorFD(n)\r\n  y = factor(n).^n;\r\nend","test_suite":"%%\r\nassert(isequal(factorFD(1),1))\r\n\r\n%%\r\np = primes(1000);\r\nfor q = p\r\n    assert(isequal(factorFD(q),q))\r\nend\r\n\r\n%%\r\nassert(isequal(factorFD(56),[2 4 7]))\r\n\r\n%%\r\nassert(isequal(factorFD(64),[4 16]))\r\n\r\n%%\r\nassert(isequal(factorFD(644),[4 7 23]))\r\n\r\n%%\r\nassert(isequal(factorFD(2250),[2 5 9 25]))\r\n\r\n%%\r\nassert(isequal(factorFD(6444),[4 9 179]))\r\n\r\n%%\r\nassert(isequal(factorFD(64444),[4 16111]))\r\n\r\n%%\r\nassert(isequal(factorFD(644444),[4 73 2207]))\r\n\r\n%%\r\nassert(isequal(factorFD(3736368),[3 16 81 961]))\r\n\r\n%%\r\nassert(isequal(factorFD(3736368),[3 16 81 961]))\r\n\r\n%%\r\nassert(isequal(factorFD(5784354),[2 9 211 1523]))\r\n\r\n%%\r\nassert(isequal(factorFD(11739420),[4 5 9 11 49 121]))\r\n\r\n%%\r\nassert(isequal(factorFD(28437991),[17 103 109 149]))\r\n\r\n%%\r\nassert(isequal(factorFD(1106427169),[841 961 1369]))\r\n\r\n%%\r\nassert(isequal(factorFD(753345263125),[13 73 529 625 2401]))\r\n\r\n%%\r\nassert(isequal(factorFD(159360553668481),[14641 83521 130321]))\r\n\r\n%%\r\nassert(isequal(factorFD(2760834326158300),[4 7 25 49 10201 7890481]))\r\n\r\n%%\r\nfiletext = fileread('factorFD.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2024-12-28T23:50:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-25T01:29:47.000Z","updated_at":"2026-04-27T10:19:43.000Z","published_at":"2023-04-25T01:29:53.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58018\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 58018\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asked you to list the Fermi-Dirac primes, which are prime powers with exponents that are powers of 2. As noted there, the name comes from an analogy with particle physics because every number can be written as the product of a unique subset of the Fermi-Dirac primes, in which the Fermi-Dirac primes appear at most once. For example, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2250 = 2x5x9x25\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2250 = 2 \\\\cdot5\\\\cdot9\\\\cdot25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function analogous to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efactor(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that factors the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e into Fermi-Dirac primes. List the Fermi-Dirac primes in ascending order. Take the factorization of 1 to be 1. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59701,"title":"Express numbers as the sum of a prime, a square, and a cube","description":"While traveling on an interstate highway, I noticed a sign that gave distances to three places. The distances were 3, 8, and 9 miles, or a prime, a perfect cube, and a perfect square. I then wondered whether it was possible to express integers (above a certain value) as the sum of a prime, a square, and a cube. For example, 11 can be expressed as , and 17 can be expressed as  or . \r\nWrite a function to list ways to express numbers as the sum of a prime, a square, and a cube. All three must be positive. The function should return a matrix the primes in the first column, the squares in the second, and the cubs in the third, and the rows should be sorted by the first column and then the second. Given an input of 11, the function should return [2 1 8], and given an input of 17, the function should return [5 4 8; 7 9 1]. If the input cannot be expressed in this way, return the empty vector [].\r\nOptional: Prove that all integers greater than 6 can be expressed as the sum of a prime, a square, and a cube.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 228.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 114.25px; transform-origin: 408px 114.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 42px; text-align: left; transform-origin: 385px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 385px 8px; transform-origin: 385px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhile traveling on an interstate highway, I noticed a sign that gave distances to three places. The distances were 3, 8, and 9 miles, or a prime, a perfect cube, and a perfect square. I then wondered whether it was possible to express integers (above a certain value) as the sum of a prime, a square, and a cube. For example, 11 can be expressed as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"144.5\" height=\"19\" alt=\"2+1+8 = 2+1^2+2^3\" style=\"width: 144.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.74167px 8px; transform-origin: 3.74167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and 17 can be expressed as \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"144.5\" height=\"19\" alt=\"5+4+8 = 5 + 2^2+2^3\" style=\"width: 144.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 8px; transform-origin: 10.1083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASEAAAAmCAYAAACLby0XAAAHSklEQVR4Xu1dS8h2UxT+/zm5jRhQ/ANKUXJJGZBLiZSB+0DIrSSJ+Af6M/gVycDAJUmKUExIkQxIuaSEYoBiwIiIOc9TZ2l/+93nnL3PXnuffc5Zp1bv+72dy17Pes6z1157n/Pt32ebIWAIGAIzIrB/xmvbpQ0BQ8AQ2GciZCQwBAyBWREwEZoVfru4IWAImAgZBwwBQ2BWBEyEZoXfLr4xBB6Hv1fCTu38fgOfd8H+WCEO18KnQ46v7+P79SFfTYRWGH1zqUkEXkerjoa9CDsGdm93g/6Dz5NWJkQUoKdgj8J+gt0PuxT2Gew8PzomQk3y1Rq1MgTOhj9Pwy53xOZYfP8WdjzsIOyxFfn8KXy5Efaj49Ovna/H+YJrIrSiyJsrzSLAYdiXMGZD7vYc/rgd9jzsjmZbn9YwiuspsC+8wyhMJ8JOjxWh77CjjFvHmsBxLdOvVreH0bCrusYdhU/a2zD+vrSxOAP8EOwm2AmtAj7QrrXwinGgaJBX53b+ft/x6sGEuFCcHoAtJROayj8e93Pn67M+PqFMiKnj5wlAXod9fYVPOLzYrlTjd7qzX4FPSQ05Nn2z+/22RtvugyLBZxHzCBjrCEcWQ67MidfCK8biExg7adY4uIkQ8TvF6LRICHnfXAM7B+ZnDpGnqLJbDv947DNdK4PJSkiECMwFMCkq9Xn5XncztFhUc4kSEklmQYc7xw7g0x27VolqwkUYuKthf8KYunNbogitgVfEntncL7C7Hd7IjUZB4cbOYqfHD8ScdZKPYS2PJHL4x/vsHhjrXtyCoyZfhCRtuggHDCkzG/Za30kDYMf8xDEjN7+gFXOsv4+kuUMzD3/jIGYVnDq8bMpFvGOk+PiX0vnk9MzoRCSJEXvdpYnQXLzSjsmdwP7CAdFI4RTP9QiMHb5GJ6jtqxb/JIvisJMb7zXec/9vvgjRkYthY5V6SSM1h2L/dq3SSE2lEh+cEuyuw0yOQzNuGtkQzyXZYamh0lJFaC5eaceEvB9a1yPxGauTyszYzf4N6d6cid+1fQ1dPod/Mvp4AifeUzebOjtGxed2JkxDxXkuLRFi5vBD176hLEeyJe6qURhsnQSJnJ5ld21e1YiJC5QU3sc6Z+53CKZZS63ha44IyT2+MxM4RYRkKDaUZUxhsJYISTDYhiERcutCYz1XjD9LIEGMH3PtU4JXNWIieEnnN3ZfUHi+go2NNlLjUMNXDRHaqZdNESEZisUW32LBLCFCQ4SIFavY9i+BBLG+zLFfCV7ViAmxkomQr/F9aLhGHznB4K8JYjvPyhSmGr7miJDMSu+MnqaIkHbKLITXEiES4nfnLurzccsi5A5FcwRHo34n1y/Bqxo3Jq/xEowzQL/B7oOFhllcmHgD7FUYJy9k47o1Pk+WW6Cu4WuMCLH+9yHsXUeQRaRfDgltqgiVSJm1RYjncxfF9Y3PxRfurzFD1goJYkSlNREqxauSMZHZLZl+dnH36x7cV9bKhOKzJv5xWPoKTNZOsdTB7O8FWHDGPVWESqTMJUTIFRj2TqHVxe7smNWEYqSr3D6leFVShAQN9vKXwJgBuYsWx4rT2mjW8DUmE0r2K1WEclJmcSC5kc4BKetjhNg8nEIkiy9Pxnc+wcw0WHqx2NkxGTLm+JDT6xUhQY4zSsfm8GrumLgQyLNg/C0nzn2wzu1rEf6liFBuylxbhBhItvkW2PkwLkykGH0DexImrxegsI0tzhRSrJIESkIy9TS5vJo7Jr7fskYtpcOMxW5uX2cXoVIps3+DaxY7+4LrriVKedZniCyLTYdj74BC+5XkVY2Y+LBINlRChFbJv9hMSGacCKzmAkUXVK3ZsZh7RYhPf7QeYq1BeK2eqJXCdGle1YiJzzfBdmy9UAxPU/ap4asW//b4FStCUt0vCWwtEXKn5jUK0gLokkjQigiV5lWNmPRlQrF1xhSh2XQmJDNJJYGtIULyICXrQxRU9013uWSoQfgiPVGu4xnHl+ZVjZiEakL8LXfdTyqsNXwtwr+YTMhNmWMLuKkAcv/SIsRFVFwsJe+B0RQgtn+xJJgSLIVjavBKOyas95wB+wgWenkZh/nkldYQPwVmbV9D155NhCRl1irg9gFbUoToA5/e5cYVqyVepVmaBG4WRz923tWbwtgG9q3BK+2YyKs6CJ+77IMvrucsLF9fyuUfe15VUQlrbV/9ZhfjX0wmJCnzziP4yuBqixBnwLiITNYE8eVRHE5qPfXvu1+KBDzvrV0Py2GkbCyqU1C5RF7zaWzlsPaergavtGPi/xsbOsdhPV9d+tbMcdD2VQJXnH8xIlSLlPJSM76JLfdVl/LyKZLjg0o9k7xUinjt/FuTWiDadfYgsKWYLNbXlkTI7h9DwBDYIAImQhsMurlsCLSEgIlQS9GwthgCG0TARGiDQTeXDYGWEDARaika1hZDYIMImAhtMOjmsiHQEgImQi1Fw9piCGwQAROhDQbdXDYEWkLgP1z7G0XU12krAAAAAElFTkSuQmCC\" width=\"144.5\" height=\"19\" alt=\"7+9+1 = 7+3^2+1^3\" style=\"width: 144.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 52.75px; text-align: left; transform-origin: 385px 52.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 385px 8px; transform-origin: 385px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to list ways to express numbers as the sum of a prime, a square, and a cube. All three must be positive. The function should return a matrix the primes in the first column, the squares in the second, and the cubs in the third, and the rows should be sorted by the first column and then the second. Given an input of 11, the function should return [2 1 8], and given an input of 17, the function should return [5 4 8; 7 9 1]. If the input cannot be expressed in this way, return the empty vector \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.85px 8px; transform-origin: 3.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 3.85px 8.5px; transform-origin: 3.85px 8.5px; \"\u003e[\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 341.117px 8px; transform-origin: 341.117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eOptional: Prove that all integers greater than 6 can be expressed as the sum of a prime, a square, and a cube.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function v = primeSquareCube(n)\r\n  v = [primes(n) n^2 n^3];\r\nend","test_suite":"%%\r\nn = 11;\r\nv = primeSquareCube(n);\r\nv_correct = [2 1 8];\r\nassert(isequal(v,v_correct))\r\n\r\n%%\r\nn = 17;\r\nv = primeSquareCube(n);\r\nv_correct = [5 4 8; 7 9 1];\r\nassert(isequal(v,v_correct))\r\n\r\n%%\r\nn = 58;\r\nv = primeSquareCube(n);\r\nv_correct = [41 9 8; 41 16 1; 53 4 1];\r\nassert(isequal(v,v_correct))\r\n\r\n%%\r\nn = 82;\r\nv = primeSquareCube(n);\r\nv_correct = [2 16 64; 17 1 64; 17 64 1; 19 36 27; 73 1 8];\r\nassert(isequal(v,v_correct))\r\n\r\n%%\r\nn = 56342;\r\nv = primeSquareCube(n);\r\nsum_correct = [24203820 13786001 8886723];\r\nN_correct = 832;\r\nmax_correct = 56333;\r\nassert(isequal(sum(v),sum_correct))\r\nassert(isequal(size(v,1),N_correct))\r\nassert(isequal(max(v,[],'all'),max_correct))\r\n\r\n%%\r\nn = 4938523;\r\nv = primeSquareCube(n);\r\nsum_correct = [53237782818 28599306108 19254476884];\r\nN_correct = 20470;\r\nmax_correct = 4938473;\r\nassert(isequal(sum(v),sum_correct))\r\nassert(isequal(size(v,1),N_correct))\r\nassert(isequal(max(v,[],'all'),max_correct))\r\n\r\n%%\r\na = NaN(1,10000);\r\nfor n = 1:10000\r\n    v = primeSquareCube(n);\r\n    a(n) = size(v,1);\r\n    if a(n)\u003e0\r\n        assert(all(sum(v,2)==n))\r\n        p = v(:,1); s = v(:,2); c = v(:,3);\r\n        assert(all(isprime(p)))\r\n        assert(all(sqrt(s)==floor(sqrt(s))))\r\n        assert(all(nthroot(c,3)==floor(nthroot(c,3))))\r\n    end\r\nend\r\nu = unique(a);\r\nh = groupcounts(a')';\r\na100_correct = [0 0 0 1 1 0 2 1 1 1 1 3 2 2 3 2 2 1 4 3 2 4 2 3 2 2 2 5 4 3 5 1 5 4 4 5 2 4 6 5 5 3 5 3 4 7 5 6 5 5 3 4 5 6 8 4 6 3 5 6 4 5 6 5 6 4 7 7 6 9 6 5 7 7 7 10 4 9 7 7 8 5 8 10 9 5 8 7 7 6 10 7 8 9 8 10 7 5 9 7];\r\nsum_correct = 1232200;\r\nu_correct = [0:255 258:261 264 273 276];\r\nh_correct = [4 8 11 9 14 19 11 17 16 18 24 25 23 14 28 18 28 29 22 26 25 26 36 26 25 24 31 27 32 37 27 31 31 43 38 32 29 27 31 39 38 23 34 34 47 50 42 38 34 34 37 37 32 38 45 53 39 34 43 45 23 47 32 40 38 54 41 44 38 47 34 49 50 32 53 54 39 43 53 51 45 26 43 52 62 50 59 48 41 45 55 48 41 48 36 48 41 59 57 48 51 48 50 36 53 61 52 55 49 49 46 48 50 52 50 71 55 47 58 53 60 48 52 70 47 51 61 47 67 53 62 63 50 52 52 59 47 55 62 58 59 56 44 49 65 58 54 61 60 58 70 61 58 49 63 55 53 59 54 48 66 53 47 53 56 64 69 51 70 52 65 64 75 53 55 59 56 63 61 53 58 69 61 63 52 48 54 46 49 59 50 61 34 53 38 45 46 33 44 26 31 35 47 40 39 42 31 30 34 27 32 35 35 30 30 23 24 29 21 12 19 26 15 23 20 15 17 12 15 12 8 13 15 9 10 9 13 10 6 6 8 4 5 3 4 3 5 6 7 2 1 4 3 1 2 4 2 1 1 1 1 1 1];\r\nassert(isequal(a(1:100),a100_correct))\r\nassert(isequal(sum(a),sum_correct))\r\nassert(isequal(u,u_correct))\r\nassert(isequal(h,h_correct))\r\n\r\n%%\r\nfiletext = fileread('primeSquareCube.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":46909,"edited_by":46909,"edited_at":"2025-07-16T16:58:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-03-16T13:48:17.000Z","updated_at":"2026-04-24T11:37:32.000Z","published_at":"2024-03-16T13:51:57.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhile traveling on an interstate highway, I noticed a sign that gave distances to three places. The distances were 3, 8, and 9 miles, or a prime, a perfect cube, and a perfect square. I then wondered whether it was possible to express integers (above a certain value) as the sum of a prime, a square, and a cube. For example, 11 can be expressed as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"2+1+8 = 2+1^2+2^3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e2+1+8 = 2+1^2+2^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and 17 can be expressed as \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"5+4+8 = 5 + 2^2+2^3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5+4+8 = 5 + 2^2+2^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"7+9+1 = 7+3^2+1^3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7+9+1 = 7+3^2+1^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to list ways to express numbers as the sum of a prime, a square, and a cube. All three must be positive. The function should return a matrix the primes in the first column, the squares in the second, and the cubs in the third, and the rows should be sorted by the first column and then the second. Given an input of 11, the function should return [2 1 8], and given an input of 17, the function should return [5 4 8; 7 9 1]. If the input cannot be expressed in this way, return the empty vector \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOptional: Prove that all integers greater than 6 can be expressed as the sum of a prime, a square, and a cube.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1288,"title":"Balanced Ternary Numbers: Easy as |, |-, |o","description":"This problem concerns the so-called \u003chttp://en.wikipedia.org/wiki/Balanced_ternary balanced ternary\u003e system for representing numbers. It is a Base 3 system in which the digits can be 1, 0, or -1. \r\n\r\nIn balanced ternary, the number 8 would be represented as 9 (or 3^2) minus 1 (or 3^0). Typographically we will use \"|\" for one, \"o\" for zero (that's a lower-case O), and \"-\" for negative one. So if the decimal input d is the number 8, the balanced ternary output is the string \"|o-\". Thus\r\n \r\n dec 8  =\u003e bt \"|o-\"\r\n\r\nHere are some more examples.\r\n\r\n dec 3  =\u003e bt \"|o\"\r\n dec 15 =\u003e bt \"|--o\"\r\n dec 52 =\u003e bt \"|-o-|\"\r\n \r\nGiven an integer d, return the string bt. Leading zeros should always be suppressed.","description_html":"\u003cp\u003eThis problem concerns the so-called \u003ca href = \"http://en.wikipedia.org/wiki/Balanced_ternary\"\u003ebalanced ternary\u003c/a\u003e system for representing numbers. It is a Base 3 system in which the digits can be 1, 0, or -1.\u003c/p\u003e\u003cp\u003eIn balanced ternary, the number 8 would be represented as 9 (or 3^2) minus 1 (or 3^0). Typographically we will use \"|\" for one, \"o\" for zero (that's a lower-case O), and \"-\" for negative one. So if the decimal input d is the number 8, the balanced ternary output is the string \"|o-\". Thus\u003c/p\u003e\u003cpre\u003e dec 8  =\u003e bt \"|o-\"\u003c/pre\u003e\u003cp\u003eHere are some more examples.\u003c/p\u003e\u003cpre\u003e dec 3  =\u003e bt \"|o\"\r\n dec 15 =\u003e bt \"|--o\"\r\n dec 52 =\u003e bt \"|-o-|\"\u003c/pre\u003e\u003cp\u003eGiven an integer d, return the string bt. Leading zeros should always be suppressed.\u003c/p\u003e","function_template":"function bt = balanced_ternary(d)\r\n  bt = 'o';\r\nend","test_suite":"%%\r\nd = 3;\r\nbt_correct = '|o';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 52;\r\nbt_correct = '|-o-|';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 182;\r\nbt_correct = '|-|-|-';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 26;\r\nbt_correct = '|oo-';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = -5;\r\nbt_correct = '-||';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = -164;\r\nbt_correct = '-|oo-|';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n%%\r\nd = 512;\r\nbt_correct = '|-o|oo-';\r\nbt = balanced_ternary(d);\r\nassert(isequal(bt,bt_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":78,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-02-21T23:26:14.000Z","updated_at":"2026-04-29T23:08:18.000Z","published_at":"2013-02-21T23:36:53.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem concerns the so-called\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Balanced_ternary\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ebalanced ternary\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e system for representing numbers. It is a Base 3 system in which the digits can be 1, 0, or -1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn balanced ternary, the number 8 would be represented as 9 (or 3^2) minus 1 (or 3^0). Typographically we will use \\\"|\\\" for one, \\\"o\\\" for zero (that's a lower-case O), and \\\"-\\\" for negative one. So if the decimal input d is the number 8, the balanced ternary output is the string \\\"|o-\\\". Thus\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ dec 8  =\u003e bt \\\"|o-\\\"]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere are some more examples.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ dec 3  =\u003e bt \\\"|o\\\"\\n dec 15 =\u003e bt \\\"|--o\\\"\\n dec 52 =\u003e bt \\\"|-o-|\\\"]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer d, return the string bt. Leading zeros should always be suppressed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61287,"title":"The Singularity: Omega Pulse ( Neural Dominance )","description":"Abstract\r\nIn the final phase of Omega experiment, you no longer control a single signal. You are tasked with commanding a Quantum Swarm of nanobots through a high-fidelity neural network. To suceed, you must reach the Event Horizon ( Target Node ) with maximum collective energy while maintaining swarm cohesion and evading an autonomous predatory AI.\r\nKey Mechanics\r\n1.Swarm Cohesion \u0026 Centroid Constraints\r\nThe swarm consists of individual agents. At any time , the Centroid () of the swarm is defined as the geometric mean of all active agent's position:\r\n                                                                                   \r\nCohesion Limit: If any agent  moves to a position where , that agent is instantly neutralized ( Energy = 0 ).\r\nMovement Cost: Energy consumption for a jump is scaled by the agent's distance from the Centroid.\r\n2.Dynamic Edge Saturation\r\nThe neural pathways exhibit Ion Saturation. Every time an agent traverses an edge between Node and Node , the resistance of that specific path increases:\r\n                                                               \r\nSubsequent agents ( or the same agent returning ) will consume significantly more ATP to cross the same path.\r\n3.Relativistic Time Dilation\r\nNodes with high Mass distort the local temporal flow. If a swarm occupies a node with mass , the local time  relative to the global clock  is:\r\n                            \r\nResonance Windows: Nodes only accept incoming signals if \r\n4. The Shadow Predator ( Adversarial AI )\r\nAn autonomous Predator Signal spawns at a designated node. It uses a Breath-First Search (BFS) to move toward the swarm's Centroid.\r\nDetection: If the swarm's Centroid enters the Line-of-Sight (LoS) of the Predator (a clear linear path with no obstructing nodes with a radius ), the swarm's energy is drained at a rate of 10 units/sec.\r\nInput / Output Specifications\r\nInputs:\r\nnodes: A struct array containing x, y, z (coordinates), mass (0 to 1), and initial_res (base resistance)\r\npredator_start: The index of the node where the Shadow Predator begins.\r\nparams: A struct containing: ( .M: Number of agents in the swarm ; \r\n                                               .R_max: Maximum allowed distance from Centroid\r\n                                               .ATP_total: Initial energy pool shared by the swarm.\r\n                                               .target: The destination Node ID. )\r\nOutputs:\r\nmax_energy: The remaining total ATP when the first agent reaches the target (or -1 if the swarm is neutralized ).\r\nbest_strategy: A cell array, where each cell contains the sequence of Node IDs visited by that specific agent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1027.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 513.8px; transform-origin: 468.5px 513.8px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eAbstract\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 31.5px; text-align: left; transform-origin: 444.5px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the final phase of Omega experiment, you no longer control a single signal. You are tasked with commanding a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eQuantum Swarm\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003enanobots through a high-fidelity neural network. To suceed, you must reach the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eEvent Horizon ( Target Node )\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e with maximum collective energy while maintaining swarm cohesion and evading an autonomous predatory AI.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eKey\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eMechanics\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e1.Swarm Cohesion \u0026amp; Centroid Constraints\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe swarm consists of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eindividual agents. At any time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eT\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the Centroid (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) of the swarm is defined as the geometric mean of all active agent's position:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 49px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 24.5px; text-align: left; transform-origin: 444.5px 24.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                                                   \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"84.5\" height=\"49\" style=\"width: 84.5px; height: 49px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 41.9px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 20.95px; transform-origin: 451.5px 20.95px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 21.4667px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.7333px; text-align: left; transform-origin: 423.5px 10.7333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eCohesion Limit\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: If any agent \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003ei\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e moves to a position where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"110\" height=\"20\" style=\"width: 110px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that agent is instantly neutralized ( Energy = 0 ).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eMovement Cost\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: Energy consumption for a jump is scaled by the agent's distance from the Centroid.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e2.Dynamic Edge Saturation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe neural pathways exhibit Ion Saturation. Every time an agent traverses an edge between Node \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand Node \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003eV\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the resistance of that specific path increases:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.4667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.7333px; text-align: left; transform-origin: 444.5px 10.7333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                               \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"226.5\" height=\"20\" style=\"width: 226.5px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSubsequent agents ( or the same agent returning ) will consume significantly more ATP to cross the same path.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e3.Relativistic Time Dilation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.9333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21.4667px; text-align: left; transform-origin: 444.5px 21.4667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNodes with high \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eMass\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e distort the local temporal flow. If a swarm occupies a node with mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the local time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"32.5\" height=\"20\" style=\"width: 32.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e relative to the global clock \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"20\" style=\"width: 38px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.75px; text-align: left; transform-origin: 444.5px 10.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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style=\"\"\u003eResonance Windows: Nodes only accept incoming signals if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"252\" height=\"20\" style=\"width: 252px; height: 20px;\"\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e4. The Shadow Predator ( Adversarial AI )\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn autonomous Predator Signal spawns at a designated node. It uses a Breath-First Search (BFS) to move toward the swarm's Centroid.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 20.4333px; transform-origin: 451.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 20.4333px; text-align: left; transform-origin: 423.5px 20.4333px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDetection: If the swarm's Centroid enters the Line-of-Sight (LoS) of the Predator (a clear linear path with no obstructing nodes with a radius \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(33, 33, 33);\"\u003er\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e), the swarm's energy is drained at a rate of 10 units/sec.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput / Output Specifications\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInputs:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 122.6px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 61.3px; transform-origin: 451.5px 61.3px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003enodes\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A struct array containing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ex, y, z\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (coordinates), \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emass\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (0 to 1), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003einitial_res\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (base resistance)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003epredator_start\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The index of the node where the Shadow Predator begins.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eparams\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A struct containing: ( .M: Number of agents in the swarm ; \u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                               .R_max: Maximum allowed distance from Centroid\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                               .ATP_total: Initial energy pool shared by the swarm.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                               .target: The destination Node ID. )\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutputs\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.8667px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 451.5px 20.4333px; transform-origin: 451.5px 20.4333px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003emax_energy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: The remaining total ATP when the first agent reaches the target (or -1 if the swarm is neutralized ).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 423.5px 10.2167px; text-align: left; transform-origin: 423.5px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ebest_strategy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e: A \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"41.5\" height=\"18\" style=\"width: 41.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ecell array, where each cell contains the sequence of Node IDs visited by that specific agent.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [max_energy, best_strategy] = solve_singularity_pulse(nodes, predator_start, params)\r\n    % SOLVE_SINGULARITY_PULSE: Multi-agent pathfinding with bio-feedback.\r\n    %\r\n    % Your goal is to coordinate M agents while maintaining swarm cohesion \r\n    % and avoiding the Shadow Predator's Line-of-Sight.\r\n    \r\n    % Initialize variables\r\n    max_energy = -1;\r\n    best_strategy = cell(1, params.M);\r\nend","test_suite":"%% PHASE 1: TORUS \u0026 RESONANCE\r\nclear n p;\r\np.M = 2; p.ATP_total = 1000; p.target = 2;\r\nn(1).coord = [0,0,0,0,0]; n(1).res = 1;\r\nn(2).coord = [90,0,0,0,0]; n(2).res = 1; % Khoảng cách Torus = 10\r\n\r\n[e1, s1] = solve_singularity_pulse(n, 0, p);\r\n% Giải thích: d=10. t_arrival = 10/20 = 0.5s.\r\n% Pulse = 1 + 2*sin(0.5*pi/2)^2 = 1 + 2*0.5 = 2.\r\n% Sat = 2 + 0.125*2*1 = 2.25.\r\n% Cost = 10 * 1 * 2.25 * 2 = 45. E = 1000 - 45 = 955.\r\nassert(abs(e1 - 955) \u003c 1e-4, 'Sai số Torus hoặc Pulse tại 0.5s');\r\n\r\n%% PHASE 2: PREDATOR INTERCEPT\r\nclear n p;\r\np.M = 1; p.ATP_total = 1000; p.target = 2;\r\nn(1).coord = [0,0,0,0,0]; n(1).res = 1;\r\nn(2).coord = [40,0,0,0,0]; n(2).res = 1; \r\nn(3).coord = [30,0,0,0,0]; % Predator bắt đầu rất gần đích\r\n% Swarm: t = 40/20 = 2s.\r\n% Pred: t = 10/15 = 0.66s. -\u003e Bị bắt!\r\n[e2, ~] = solve_singularity_pulse(n, 3, p);\r\nassert(e2 == -1, 'Predator phải bắt được Swarm ở đây!');\r\n\r\n%% PHASE 3: PATH OPTIMIZATION (Bắt buộc đi vòng)\r\nclear n p;\r\np.M = 1; p.target = 2; p.ATP_total = 1000;\r\nn(1).coord = [0,0,0,0,0]; n(1).res = 1;\r\nn(2).coord = [20,0,0,0,0]; n(2).res = 10; % Đích xa, res cao\r\nn(3).coord = [10,0,0,0,0]; n(3).res = 1;  % Trạm trung gian\r\n[e3, s3] = solve_singularity_pulse(n, 0, p);\r\nassert(length(s3{1}) \u003e= 3, 'Thuật toán chưa tìm được đường vòng tối ưu năng lượng');","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4945722,"edited_by":4945722,"edited_at":"2026-03-22T18:52:04.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2026-03-22T18:52:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-03-20T09:03:18.000Z","updated_at":"2026-04-30T09:40:40.000Z","published_at":"2026-03-20T09:03:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAbstract\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the final phase of Omega experiment, you no longer control a single signal. You are tasked with commanding a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eQuantum Swarm\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003enanobots through a high-fidelity neural network. To suceed, you must reach the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEvent Horizon ( Target Node )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e with maximum collective energy while maintaining swarm cohesion and evading an autonomous predatory AI.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eKey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMechanics\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1.Swarm Cohesion \u0026amp; Centroid Constraints\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe swarm consists of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eindividual agents. At any time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the Centroid (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) of the swarm is defined as the geometric mean of all active agent's position:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                                                   \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{1}{M}\\\\sum_{i=1}^{M}P_{i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCohesion Limit\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: If any agent \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e moves to a position where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003edist(P_{i},C) \u0026gt; R_{max\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, that agent is instantly neutralized ( Energy = 0 ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMovement Cost\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: Energy consumption for a jump is scaled by the agent's distance from the Centroid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2.Dynamic Edge Saturation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe neural pathways exhibit Ion Saturation. Every time an agent traverses an edge between Node \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eand Node \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the resistance of that specific path increases:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                               \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eResistance_{new} = Resistance_{odd} \\\\times 1.25\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSubsequent agents ( or the same agent returning ) will consume significantly more ATP to cross the same path.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3.Relativistic Time Dilation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNodes with high \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eMass\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e distort the local temporal flow. If a swarm occupies a node with mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the local time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{local}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e relative to the global clock \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{global\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT_{local} = T_{global} \\\\times e^{-m\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eResonance Windows: Nodes only accept incoming signals if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003efloor(T_{local}) \\\\text{ (mod 7) \\\\neq \\\\text{NodeID (mod 7).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e4. The Shadow Predator ( Adversarial AI )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn autonomous Predator Signal spawns at a designated node. It uses a Breath-First Search (BFS) to move toward the swarm's Centroid.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetection: If the swarm's Centroid enters the Line-of-Sight (LoS) of the Predator (a clear linear path with no obstructing nodes with a radius \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e), the swarm's energy is drained at a rate of 10 units/sec.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput / Output Specifications\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enodes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A struct array containing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex, y, z\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (coordinates), \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emass\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (0 to 1), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einitial_res\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (base resistance)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epredator_start\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The index of the node where the Shadow Predator begins.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eparams\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A struct containing: ( .M: Number of agents in the swarm ; \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                               .R_max: Maximum allowed distance from Centroid\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                               .ATP_total: Initial energy pool shared by the swarm.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                               .target: The destination Node ID. )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutputs\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emax_energy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: The remaining total ATP when the first agent reaches the target (or -1 if the swarm is neutralized ).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ebest_strategy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: A \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 \\\\times M\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003ecell array, where each cell contains the sequence of Node IDs visited by that specific agent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55,"title":"Counting Sequence","description":"Given a vector x, find the \"counting sequence\" y.\r\n\r\nA counting sequence is formed by \"counting\" the entries in a given sequence.\r\n\r\nFor example, the sequence\r\n\r\n x = 5, 5, 2, 1, 1, 1, 1, 3\r\n\r\ncan be read as\r\n\r\n Two 5's, one 2, four 1's, one 3\r\n\r\nwhich translates to\r\n\r\n y = 2, 5, 1, 2, 4, 1, 1, 3\r\n\r\nSo y is the counting sequence for x.\r\n\r\nFor this problem, all elements in the sequences x and y will be in the range from 1 to 9.\r\n","description_html":"\u003cp\u003eGiven a vector x, find the \"counting sequence\" y.\u003c/p\u003e\u003cp\u003eA counting sequence is formed by \"counting\" the entries in a given sequence.\u003c/p\u003e\u003cp\u003eFor example, the sequence\u003c/p\u003e\u003cpre\u003e x = 5, 5, 2, 1, 1, 1, 1, 3\u003c/pre\u003e\u003cp\u003ecan be read as\u003c/p\u003e\u003cpre\u003e Two 5's, one 2, four 1's, one 3\u003c/pre\u003e\u003cp\u003ewhich translates to\u003c/p\u003e\u003cpre\u003e y = 2, 5, 1, 2, 4, 1, 1, 3\u003c/pre\u003e\u003cp\u003eSo y is the counting sequence for x.\u003c/p\u003e\u003cp\u003eFor this problem, all elements in the sequences x and y will be in the range from 1 to 9.\u003c/p\u003e","function_template":"function y = CountSeq(x)\r\ny = x;\r\nend","test_suite":"%%\r\nx = [5 5 2 1 1 1 1 3];\r\ncorrect = [2 5 1 2 4 1 1 3];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n\r\n%%\r\nx = [9];\r\ncorrect = [1 9];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n\r\n%%\r\nx = ones(1,9);\r\ncorrect = [9 1];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n\r\n%%\r\nx = 1:9;\r\ncorrect = [1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n%%\r\nx = [1 2 2 1];\r\ncorrect = [1 1 2 2 1 1];\r\nassert(isequal(correct, CountSeq(x)));\r\n\r\n","published":true,"deleted":false,"likes_count":30,"comments_count":13,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2184,"test_suite_updated_at":"2013-03-14T15:22:01.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:25.000Z","updated_at":"2026-04-28T17:40:44.000Z","published_at":"2012-01-18T01:00:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a vector x, find the \\\"counting sequence\\\" y.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA counting sequence is formed by \\\"counting\\\" the entries in a given sequence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the sequence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = 5, 5, 2, 1, 1, 1, 1, 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ecan be read as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Two 5's, one 2, four 1's, one 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhich translates to\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = 2, 5, 1, 2, 4, 1, 1, 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo y is the counting sequence for x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, all elements in the sequences x and y will be in the range from 1 to 9.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":81,"title":"Mandelbrot Numbers","description":"The \u003chttp://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot Set\u003e is built around a simple iterative equation.\r\n\r\n z(1)   = c\r\n z(n+1) = z(n)^2 + c\r\n\r\nFor any complex c, we can continue this iteration until either\r\nabs(z(n+1)) \u003e 2 or n == lim, then return the iteration count n.\r\n\r\n* If c = 0   and lim = 3, then z = [0 0 0] and n = 3.\r\n* If c = 1   and lim = 5, then z = [1 2], and n = length(z) or 2.\r\n* If c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\r\n\r\nFor a matrix of complex numbers C, return a corresponding matrix N such\r\nthat each element of N is the iteration count n for each complex number c\r\nin the matrix C, subject to the iteration count limit of lim.\r\n\r\nIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\r\n\r\nCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments\r\nwith MATLAB: \u003chttp://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf \r\nChapter 10, Mandelbrot Set (PDF)\u003e","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 296.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 148.083px; transform-origin: 407px 148.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.5px 8px; transform-origin: 12.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"http://en.wikipedia.org/wiki/Mandelbrot_set\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMandelbrot Set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is built around a simple iterative equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 20.4333px; transform-origin: 404px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 44px 8.5px; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(1)   = c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(n+1) = z(n)^2 + c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.5px 8px; transform-origin: 379.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 142.5px 8px; transform-origin: 142.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 176.5px 8px; transform-origin: 176.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 226.5px 8px; transform-origin: 226.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377px 8px; transform-origin: 377px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 149.5px 8px; transform-origin: 149.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127px 8px; transform-origin: 127px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCleve Moler has a whole chapter on the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMandelbrot set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in his book \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/moler/exm/chapters.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eExperiments with MATLAB\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function N = mandelbrot(C,lim)\r\n  N = ones(size(C));\r\nend","test_suite":"%%\r\nC = 0;\r\nlim = 5;\r\nN_correct = 5;\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\nC = [0 0.5; 1 4];\r\nlim = 5;\r\nN_correct = [5 4; 2 1];\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\ni = sqrt(-1);\r\nC = [i 1 -2*i -2];\r\nlim = 10;\r\nN_correct = [10 2 1 10];\r\nassert(isequal(mandelbrot(C,lim),N_correct))","published":true,"deleted":false,"likes_count":17,"comments_count":9,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1780,"test_suite_updated_at":"2012-01-26T03:21:20.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:28.000Z","updated_at":"2026-04-30T13:20:29.000Z","published_at":"2012-01-18T01:00:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Mandelbrot_set\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot Set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is built around a simple iterative equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z(1)   = c\\n z(n+1) = z(n)^2 + c]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCleve Moler has a whole chapter on the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in his book \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/moler/exm/chapters.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eExperiments with MATLAB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1499,"title":"Kryptos - CIA Cypher Sculpture: Vigenere Encryption","description":"The \u003chttp://en.wikipedia.org/wiki/Kryptos Kryptos Sculpture\u003e contains four encypted messages.\r\n\r\nThis Challenge is to Encrypt two of the original messages for the sculptor.\r\n\r\nThe method employed is \u003chttp://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher Vigenere Encryption\u003e. One clarification is that \"?\" are removed from the coding sequence and then re-inserted in the final encoded message.\r\n\r\nOriginal phrase: Between subtle shading and the absence of light lies the nuance of iqlusion.\r\n\r\nFor coding purposes spaces and punctuation are removed, except \"?\".\r\n\r\nPhrase to encode: BETWEENSUBTLESHADINGANDTHEABSENCEOFLIGHTLIESTHENUANCEOFIQLUSION\r\n\r\n*Input:* Encode Phrase, Vigenere alphabet word, Vigenere shift word\r\n\r\nVigenere alphabet word ='KRYPTOS';\r\n\r\nVigenere shift word ='PALIMPSEST';\r\n\r\n*Output:* EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD\r\n\r\nThe encryption matrix for this case:\r\n\r\n  KRYPTOSABCDEFGHIJLMNQUVWXZ\r\n\r\n  PTOSABCDEFGHIJLMNQUVWXZKRY\r\n  ABCDEFGHIJLMNQUVWXZKRYPTOS\r\n  LMNQUVWXZKRYPTOSABCDEFGHIJ\r\n  IJLMNQUVWXZKRYPTOSABCDEFGH\r\n  MNQUVWXZKRYPTOSABCDEFGHIJL\r\n  PTOSABCDEFGHIJLMNQUVWXZKRY\r\n  SABCDEFGHIJLMNQUVWXZKRYPTO\r\n  EFGHIJLMNQUVWXZKRYPTOSABCD\r\n  SABCDEFGHIJLMNQUVWXZKRYPTO\r\n  TOSABCDEFGHIJLMNQUVWXZKRYP\r\n\r\nFollow Up Challenges:\r\n\r\n1) \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1500-kryptos-cia-cypher-sculpture-vignere-decryption Vigenere Decryption\u003e\r\n\r\n2) Dictionary search\r\n\r\n3) KRYPTOS Part IV\r\n\r\n\u003chttp://math.ucsd.edu/~crypto/Projects/KarlWang/index2.html#1 KRYPTOS Solutions\u003e\r\n\r\n  \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","description_html":"\u003cp\u003eThe \u003ca href = \"http://en.wikipedia.org/wiki/Kryptos\"\u003eKryptos Sculpture\u003c/a\u003e contains four encypted messages.\u003c/p\u003e\u003cp\u003eThis Challenge is to Encrypt two of the original messages for the sculptor.\u003c/p\u003e\u003cp\u003eThe method employed is \u003ca href = \"http://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher\"\u003eVigenere Encryption\u003c/a\u003e. One clarification is that \"?\" are removed from the coding sequence and then re-inserted in the final encoded message.\u003c/p\u003e\u003cp\u003eOriginal phrase: Between subtle shading and the absence of light lies the nuance of iqlusion.\u003c/p\u003e\u003cp\u003eFor coding purposes spaces and punctuation are removed, except \"?\".\u003c/p\u003e\u003cp\u003ePhrase to encode: BETWEENSUBTLESHADINGANDTHEABSENCEOFLIGHTLIESTHENUANCEOFIQLUSION\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e Encode Phrase, Vigenere alphabet word, Vigenere shift word\u003c/p\u003e\u003cp\u003eVigenere alphabet word ='KRYPTOS';\u003c/p\u003e\u003cp\u003eVigenere shift word ='PALIMPSEST';\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD\u003c/p\u003e\u003cp\u003eThe encryption matrix for this case:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eKRYPTOSABCDEFGHIJLMNQUVWXZ\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003ePTOSABCDEFGHIJLMNQUVWXZKRY\r\nABCDEFGHIJLMNQUVWXZKRYPTOS\r\nLMNQUVWXZKRYPTOSABCDEFGHIJ\r\nIJLMNQUVWXZKRYPTOSABCDEFGH\r\nMNQUVWXZKRYPTOSABCDEFGHIJL\r\nPTOSABCDEFGHIJLMNQUVWXZKRY\r\nSABCDEFGHIJLMNQUVWXZKRYPTO\r\nEFGHIJLMNQUVWXZKRYPTOSABCD\r\nSABCDEFGHIJLMNQUVWXZKRYPTO\r\nTOSABCDEFGHIJLMNQUVWXZKRYP\r\n\u003c/pre\u003e\u003cp\u003eFollow Up Challenges:\u003c/p\u003e\u003cp\u003e1) \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1500-kryptos-cia-cypher-sculpture-vignere-decryption\"\u003eVigenere Decryption\u003c/a\u003e\u003c/p\u003e\u003cp\u003e2) Dictionary search\u003c/p\u003e\u003cp\u003e3) KRYPTOS Part IV\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://math.ucsd.edu/~crypto/Projects/KarlWang/index2.html#1\"\u003eKRYPTOS Solutions\u003c/a\u003e\u003c/p\u003e","function_template":"function encoded=encode_vigenere(phrase,word1,word2)\r\n encoded=phrase;\r\nend","test_suite":"phrase=upper('Between subtle shading and the absence of light lies the nuance of iqlusion.');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\nencoded_exp='EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD';\r\nword1='KRYPTOS';\r\nword2='PALIMPSEST';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n%%\r\n\r\nphrase=upper('It was totally invisible Hows that possible? They used the Earths magnetic field X The information was gathered and transmitted undergruund to an unknown location X Does Langley know about this? They should Its buried out there somewhere X Who knows the exact location? Only WW This was his last message X Thirty eight degrees fifty seven minutes six point five seconds north Seventy seven degrees eight minutes forty four seconds west ID by rows');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\n\r\nencoded_exp='VFPJUDEEHZWETZYVGWHKKQETGFQJNCEGGWHKK?DQMCPFQZDQMMIAGPFXHQRLGTIMVMZJANQLVKQEDAGDVFRPJUNGEUNAQZGZLECGYUXUEENJTBJLBQCRTBJDFHRRYIZETKZEMVDUFKSJHKFWHKUWQLSZFTIHHDDDUVH?DWKBFUFPWNTDFIYCUQZEREEVLDKFEZMOQQJLTTUGSYQPFEUNLAVIDXFLGGTEZ?FKZBSFDQVGOGIPUFXHHDRKFFHQNTGPUAECNUVPDJMQCLQUMUNEDFQELZZVRRGKFFVOEEXBDMVPNFQXEZLGREDNQFMPNZGLFLPMRJQYALMGNUVPDXVKPDQUMEBEDMHDAFMJGZNUPLGEWJLLAETG';\r\n\r\nword1='KRYPTOS';\r\nword2='ABSCISSA';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n%%\r\nphrase=upper('The fox jumped over the moon');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\nencoded_exp='VUIPFSBYVQMMWPIMEVPZCVK';\r\nword1='KRYPTOS';\r\nword2='MATLAB';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n\r\n%%\r\nphrase=upper('Between the Devil and the deep blue sea');\r\nphrase_encode=phrase(regexp(phrase,'[A-Z?]'));\r\n\r\n\r\nword1='AWEIGH';\r\nword2='MATLAB';\r\nencoded= encode_vigenere(phrase_encode,word1,word2);\r\nencoded_exp='SENMEDWTZNDDFIBLNNCHVTEDIBBCEZOA';\r\n\r\nassert(strcmp(encoded_exp,encoded))\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":3,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":62,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":28,"created_at":"2013-05-11T20:36:34.000Z","updated_at":"2026-04-17T02:31:21.000Z","published_at":"2013-05-11T21:19:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Kryptos\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKryptos Sculpture\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e contains four encypted messages.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to Encrypt two of the original messages for the sculptor.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe method employed is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere Encryption\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. One clarification is that \\\"?\\\" are removed from the coding sequence and then re-inserted in the final encoded message.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOriginal phrase: Between subtle shading and the absence of light lies the nuance of iqlusion.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor coding purposes spaces and punctuation are removed, except \\\"?\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePhrase to encode: BETWEENSUBTLESHADINGANDTHEABSENCEOFLIGHTLIESTHENUANCEOFIQLUSION\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Encode Phrase, Vigenere alphabet word, Vigenere shift word\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere alphabet word ='KRYPTOS';\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere shift word ='PALIMPSEST';\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJYQTQUXQBQVYUVLLTREVJYQTMKYRDMFD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe encryption matrix for this case:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[KRYPTOSABCDEFGHIJLMNQUVWXZ\\n\\nPTOSABCDEFGHIJLMNQUVWXZKRY\\nABCDEFGHIJLMNQUVWXZKRYPTOS\\nLMNQUVWXZKRYPTOSABCDEFGHIJ\\nIJLMNQUVWXZKRYPTOSABCDEFGH\\nMNQUVWXZKRYPTOSABCDEFGHIJL\\nPTOSABCDEFGHIJLMNQUVWXZKRY\\nSABCDEFGHIJLMNQUVWXZKRYPTO\\nEFGHIJLMNQUVWXZKRYPTOSABCD\\nSABCDEFGHIJLMNQUVWXZKRYPTO\\nTOSABCDEFGHIJLMNQUVWXZKRYP]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFollow Up Challenges:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1500-kryptos-cia-cypher-sculpture-vignere-decryption\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eVigenere Decryption\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) Dictionary search\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3) KRYPTOS Part IV\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://math.ucsd.edu/~crypto/Projects/KarlWang/index2.html#1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKRYPTOS Solutions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":733,"title":"Extract Built In Functions and Toolbox Functions from String or Function Handle","description":"Find the Built-In functions and Toolbox functions in either a string or a function handle.\r\n\r\nGenerate a string of alphabetized Built-In functions followed by alphabetized Functions.\r\n\r\n*Inputs:*\r\n\r\nfh=@(x)log10(x)+log2(x)+abs(x)\r\n\r\nstr='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)'\r\n\r\n*Outputs:*\r\n\r\n'abs log2 log10'\r\n\r\n'abs filter numel sin filter2 smooth3'\r\n\r\nRelated to \r\n\u003chttp://www.mathworks.com/matlabcentral/cody/problems/464-function-sniffer Cody_464\u003e","description_html":"\u003cp\u003eFind the Built-In functions and Toolbox functions in either a string or a function handle.\u003c/p\u003e\u003cp\u003eGenerate a string of alphabetized Built-In functions followed by alphabetized Functions.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInputs:\u003c/b\u003e\u003c/p\u003e\u003cp\u003efh=@(x)log10(x)+log2(x)+abs(x)\u003c/p\u003e\u003cp\u003estr='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)'\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutputs:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e'abs log2 log10'\u003c/p\u003e\u003cp\u003e'abs filter numel sin filter2 smooth3'\u003c/p\u003e\u003cp\u003eRelated to  \u003ca href=\"http://www.mathworks.com/matlabcentral/cody/problems/464-function-sniffer\"\u003eCody_464\u003c/a\u003e\u003c/p\u003e","function_template":"function functions = find_functions(fh_str)\r\n  functions = '';\r\nend","test_suite":"%%\r\nfh_str='log2(x)+smooth3(x,y)+abs(2)+log10(5)';\r\nexp_str='abs log10 log2 smooth3';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='for k=log10(x):log2(x)+abs(x)';\r\nexp_str='abs for log10 log2';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str=@(x)x^2+sin(x)-cos(x);\r\nexp_str='cos sin';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='@(x)x^2+sin(x)-cos(x)';\r\nexp_str='cos sin';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='filter2(x,A)+filter(x)-cos(x) expm(z)';\r\nexp_str='cos filter expm filter2';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n%%\r\nfh_str='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)';\r\nexp_str='abs filter numel sin filter2 smooth3';\r\nassert(isequal(find_functions(fh_str),exp_str))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":6,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":83,"test_suite_updated_at":"2012-07-18T13:18:16.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-06-01T23:09:01.000Z","updated_at":"2026-03-31T20:12:36.000Z","published_at":"2012-06-02T00:17:41.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the Built-In functions and Toolbox functions in either a string or a function handle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenerate a string of alphabetized Built-In functions followed by alphabetized Functions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efh=@(x)log10(x)+log2(x)+abs(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003estr='smooth3(x,y)-filter(x)+abs(n)+filter2(u)+sin(x)+numel(z)'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'abs log2 log10'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'abs filter numel sin filter2 smooth3'\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRelated to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/464-function-sniffer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody_464\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2237,"title":"Mmm! Multi-dimensional Matrix Multiplication ","description":"You have got a couple of multi-dimensional matrices, A and B. And want to multiply them. For the first 2 dimensions, an ordinary matrix multiplication applies. And in the other dimensions? Well, they just act as parallel worlds. All 2D matrices are multiplied, for every element in the other dimensions.\r\nYou may assume that the size in the 1st two dimensions allows simple matrix multiplication: A(:,:,1)*B(:,:,1), so size(A(:,:,1),2) == size(B(:,:,1),1), or either A(:,:,1) is a scalar or B(:,:,1) is a scalar.\r\nIn the other dimensions, the sizes of A and B should be eqaal, size(A,n) == size(B,n), for n\u003e2, or either ndims(A)\u003cn or ndims(B)\u003cn, or either size(A,n)==1 or size(B,n)==1, so one of them is a scalar.\r\n\r\nWrite a function |mtimesm| that does this, and ask Mathworks to include it in the |elmat| toolbox of the Next Release.","description_html":"\u003cp\u003eYou have got a couple of multi-dimensional matrices, A and B. And want to multiply them. For the first 2 dimensions, an ordinary matrix multiplication applies. And in the other dimensions? Well, they just act as parallel worlds. All 2D matrices are multiplied, for every element in the other dimensions.\r\nYou may assume that the size in the 1st two dimensions allows simple matrix multiplication: A(:,:,1)*B(:,:,1), so size(A(:,:,1),2) == size(B(:,:,1),1), or either A(:,:,1) is a scalar or B(:,:,1) is a scalar.\r\nIn the other dimensions, the sizes of A and B should be eqaal, size(A,n) == size(B,n), for n\u0026gt;2, or either ndims(A)\u0026lt;n or ndims(B)\u0026lt;n, or either size(A,n)==1 or size(B,n)==1, so one of them is a scalar.\u003c/p\u003e\u003cp\u003eWrite a function \u003ctt\u003emtimesm\u003c/tt\u003e that does this, and ask Mathworks to include it in the \u003ctt\u003eelmat\u003c/tt\u003e toolbox of the Next Release.\u003c/p\u003e","function_template":"function C = mtimesm(A,B)\r\n  C = A*B;\r\nend","test_suite":"%% case 1\r\nA = 1;\r\nB = 2;\r\nC = mtimesm(A,B);\r\nC_correct = 2;\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 2\r\nA = rand(2,3);\r\nB = rand(3,4);\r\nC = mtimesm(A,B);\r\nC_correct = A*B;\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 3\r\nA = rand(2,3);\r\nB = 2;\r\nC = mtimesm(A,B);\r\nC_correct = 2*A;\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 4\r\nA = rand(2,3,2);\r\nB = rand(3,4,2);\r\nC = mtimesm(A,B);\r\nC_correct = cat(3,A(:,:,1)*B(:,:,1),A(:,:,2)*B(:,:,2));\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 5\r\nA = rand(2,3,3);\r\nB = rand(3,4);\r\nC = mtimesm(A,B);\r\nC_correct = cat(3,A(:,:,1)*B,A(:,:,2)*B,A(:,:,3)*B); \r\nassert(isequal(C,C_correct))\r\n\r\n%% case 6\r\nA = rand(4,3,1,2);\r\nB = rand(3,2,2);\r\nC = mtimesm(A,B);\r\nC_correct(:,:,1,1) = A(:,:,1,1)*B(:,:,1);\r\nC_correct(:,:,1,2) = A(:,:,1,2)*B(:,:,1);\r\nC_correct(:,:,2,1) = A(:,:,1,1)*B(:,:,2);\r\nC_correct(:,:,2,2) = A(:,:,1,2)*B(:,:,2);\r\nassert(isequal(C,C_correct))\r\n\r\n%% case 7\r\nA = rand(4,3,1,2);\r\nB = rand(3,2,1,1,2);\r\nC = mtimesm(A,B);\r\nC_correct(:,:,1,1,1) = A(:,:,1,1)*B(:,:,1,1,1);\r\nC_correct(:,:,1,1,2) = A(:,:,1,1)*B(:,:,1,1,2);\r\nC_correct(:,:,1,2,1) = A(:,:,1,2)*B(:,:,1,1,1);\r\nC_correct(:,:,1,2,2) = A(:,:,1,2)*B(:,:,1,1,2);\r\nassert(isequal(C,C_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":5,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":38,"test_suite_updated_at":"2014-03-07T06:22:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-03-06T11:17:42.000Z","updated_at":"2026-04-03T03:22:22.000Z","published_at":"2014-03-06T11:17:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have got a couple of multi-dimensional matrices, A and B. And want to multiply them. For the first 2 dimensions, an ordinary matrix multiplication applies. And in the other dimensions? Well, they just act as parallel worlds. All 2D matrices are multiplied, for every element in the other dimensions. You may assume that the size in the 1st two dimensions allows simple matrix multiplication: A(:,:,1)*B(:,:,1), so size(A(:,:,1),2) == size(B(:,:,1),1), or either A(:,:,1) is a scalar or B(:,:,1) is a scalar. In the other dimensions, the sizes of A and B should be eqaal, size(A,n) == size(B,n), for n\u0026gt;2, or either ndims(A)\u0026lt;n or ndims(B)\u0026lt;n, or either size(A,n)==1 or size(B,n)==1, so one of them is a scalar.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003emtimesm\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that does this, and ask Mathworks to include it in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eelmat\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e toolbox of the Next Release.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1286,"title":"MatCAT - Reconstruct X from Its X-rays","description":"Consider a matrix x\r\n\r\n x = [ 1 2 0\r\n       0 5 0 \r\n       3 0 8 ]\r\n\r\nIf we sum x along the rows we get\r\n\r\n row_sums = [3 5 11]\r\n\r\nSumming along the columns gives \r\n\r\n col_sums = [4 7 8]\r\n\r\nMetaphorically, we might call these sums \"x-rays\". Your job is to take these x-rays and reconstruct the matrix x being x-rayed, in the fashion of a \u003chttp://en.wikipedia.org/wiki/X-ray_computed_tomography CAT scan\u003e. Can you put all the bones in the right place?\r\n\r\nAll matrix elements must be non-negative integers. There is no guarantee of a unique answer. I will only check that the row and column sums match the supplied matrix, and that your elements are non-negative integers.\r\n\r\nBonus question: Under what circumstances does the answer become unique? Discuss.","description_html":"\u003cp\u003eConsider a matrix x\u003c/p\u003e\u003cpre\u003e x = [ 1 2 0\r\n       0 5 0 \r\n       3 0 8 ]\u003c/pre\u003e\u003cp\u003eIf we sum x along the rows we get\u003c/p\u003e\u003cpre\u003e row_sums = [3 5 11]\u003c/pre\u003e\u003cp\u003eSumming along the columns gives\u003c/p\u003e\u003cpre\u003e col_sums = [4 7 8]\u003c/pre\u003e\u003cp\u003eMetaphorically, we might call these sums \"x-rays\". Your job is to take these x-rays and reconstruct the matrix x being x-rayed, in the fashion of a \u003ca href = \"http://en.wikipedia.org/wiki/X-ray_computed_tomography\"\u003eCAT scan\u003c/a\u003e. Can you put all the bones in the right place?\u003c/p\u003e\u003cp\u003eAll matrix elements must be non-negative integers. There is no guarantee of a unique answer. I will only check that the row and column sums match the supplied matrix, and that your elements are non-negative integers.\u003c/p\u003e\u003cp\u003eBonus question: Under what circumstances does the answer become unique? Discuss.\u003c/p\u003e","function_template":"function x = matcat(row_sums,col_sums)\r\n  x = 0;\r\nend","test_suite":"%%\r\nrow_sums = [3 5 11];\r\ncol_sums = [4 7 8];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = [2 2 2 2 2 6];\r\ncol_sums = [2 3 3 3 3 2];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = [65 65 65 65 65];\r\ncol_sums = [65 65 65 65 65];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = [22 34 33];\r\ncol_sums = [15 23 18 21 12];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n\r\n%%\r\nrow_sums = 55;\r\ncol_sums = [1 2 3 4 5 6 7 8 9 10];\r\nx = matcat(row_sums,col_sums);\r\nassert(all(x(:)\u003e=0))\r\nassert(isequal(floor(x),x))\r\nassert(isequal(sum(x,2)',row_sums))\r\nassert(isequal(sum(x,1),col_sums))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":4,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":148,"test_suite_updated_at":"2013-02-21T17:46:45.000Z","rescore_all_solutions":false,"group_id":23,"created_at":"2013-02-21T17:25:12.000Z","updated_at":"2026-04-22T11:32:22.000Z","published_at":"2013-02-21T17:46:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a matrix x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [ 1 2 0\\n       0 5 0 \\n       3 0 8 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf we sum x along the rows we get\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ row_sums = [3 5 11]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSumming along the columns gives\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ col_sums = [4 7 8]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMetaphorically, we might call these sums \\\"x-rays\\\". Your job is to take these x-rays and reconstruct the matrix x being x-rayed, in the fashion of a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/X-ray_computed_tomography\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCAT scan\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Can you put all the bones in the right place?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll matrix elements must be non-negative integers. There is no guarantee of a unique answer. I will only check that the row and column sums match the supplied matrix, and that your elements are non-negative integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBonus question: Under what circumstances does the answer become unique? Discuss.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44838,"title":"Pose from bearing angles in 2D","description":"A robot moving on the plane has a sensor that measures the bearing angle to two mapped landmarks, that is, the world frame coordinates of the landmarks are known and represented by position vectors |P1| and |P2| .  The bearing angles to the landmarks, with respect to the x-axis of the robot's coordinate frame are |th1| and |th2| respectively.  The robot's forward direction is parallel to its x-axis and its heading angle, with respect to magnetic north is |thb| .\r\n\r\nDetermine the pose of the robot expressed as a homogeneous transformation matrix with respect to the world coordinate frame.  In surveying this is known as a resection problem.","description_html":"\u003cp\u003eA robot moving on the plane has a sensor that measures the bearing angle to two mapped landmarks, that is, the world frame coordinates of the landmarks are known and represented by position vectors \u003ctt\u003eP1\u003c/tt\u003e and \u003ctt\u003eP2\u003c/tt\u003e .  The bearing angles to the landmarks, with respect to the x-axis of the robot's coordinate frame are \u003ctt\u003eth1\u003c/tt\u003e and \u003ctt\u003eth2\u003c/tt\u003e respectively.  The robot's forward direction is parallel to its x-axis and its heading angle, with respect to magnetic north is \u003ctt\u003ethb\u003c/tt\u003e .\u003c/p\u003e\u003cp\u003eDetermine the pose of the robot expressed as a homogeneous transformation matrix with respect to the world coordinate frame.  In surveying this is known as a resection problem.\u003c/p\u003e","function_template":"function T = user_function(P1, P2, th1, th2, thb)\r\n% Input:  P1 a 2x1 vector representing the coordinate of a point\r\n%         P2 a 2x1 vector representing the coordinate of a point\r\n%         th1 bearing, a scalar angle\r\n%         th2 bearing, a scalar angle\r\n%         thb heading, a scalar angle\r\n% Output: T a 3x3 homogeneous transformation matrix\r\n  T = ;\r\nend","test_suite":"%\r\nP1 = [10 20]';\r\nP2 = [20 20]';\r\nP = rand(2,1)*5 + [5 5]';\r\nthb = rand*0.2;\r\nx = P1 - P;\r\nth1 = atan2(x(2), x(1)) - thb;\r\nx = P2 - P;\r\nth2 = atan2(x(2), x(1)) - thb;\r\n\r\nT = user_function(P1, P2, th1, th2, thb);\r\n\r\n%% test size and complexity\r\nassert(all(size(T)==3), 'The matrix must be 3x3');\r\nassert(isreal(T), 'The matrix must be real, not complex');\r\n\r\n%% bottom row\r\nassert(isequal(T(3,:), [0 0 1]), 'The bottom row of the homogeneous transformation matrix is not correct')\r\n\r\n%% x coordinate\r\nassert(abs(T(1,3)-P(1))\u003c1e-4, 'The representation of the x-coordinate is not correct')\r\n\r\n%% y coordinate\r\nassert(abs(T(2,3)-P(2))\u003c1e-4, 'The representation of the y-coordinate is not correct')\r\n\r\n%% valid rotation matrix\r\nR = T(1:2,1:2);\r\nassert( abs(det(R)-1) \u003c 1e-4, 'The determinant of the rotation submatrix is not correct')\r\n\r\n%% correct rotation matrix\r\nR = T(1:2,1:2);\r\nassert( abs(atan2(R(2,1), R(1,1)) - thb) \u003c 1e-4, 'The rotation matrix is not correct, check your calculation of the heading SSW and whether you are using radians or degrees')\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-21T00:32:56.000Z","updated_at":"2026-04-23T08:14:24.000Z","published_at":"2019-01-21T00:37:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA robot moving on the plane has a sensor that measures the bearing angle to two mapped landmarks, that is, the world frame coordinates of the landmarks are known and represented by position vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e . The bearing angles to the landmarks, with respect to the x-axis of the robot's coordinate frame are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eth1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eth2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e respectively. The robot's forward direction is parallel to its x-axis and its heading angle, with respect to magnetic north is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the pose of the robot expressed as a homogeneous transformation matrix with respect to the world coordinate frame. In surveying this is known as a resection problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":61175,"title":"[Master Regular Expression] Goat Latin","description":"You are given a string sentence that consist of words separated by spaces. Each word consists of lowercase and uppercase letters only.\r\nWe would like to convert the sentence to \"Goat Latin\" (a made-up language similar to Pig Latin.) The rules of Goat Latin are as follows:\r\nIf a word begins with a vowel ('a', 'e', 'i', 'o', or 'u'), append \"ma\" to the end of the word.\r\nFor example, the word \"apple\" becomes \"applema\".\r\nIf a word begins with a consonant (i.e., not a vowel), remove the first letter and append it to the end, then add \"ma\".\r\nFor example, the word \"goat\" becomes \"oatgma\".\r\nAdd one letter 'a' to the end of each word per its word index in the sentence, starting with 1.\r\nFor example, the first word gets \"a\" added to the end, the second word gets \"aa\" added to the end, and so on.\r\nReturn the final sentence representing the conversion from sentence to Goat Latin.\r\n \r\nExample 1:\r\nInput: sentence = \"I speak Goat Latin\"\r\nOutput: \"Imaa peaksmaaa oatGmaaaa atinLmaaaaa\"\r\nExample 2:\r\nInput: sentence = \"The quick brown fox jumped over the lazy dog\"\r\nOutput: \"heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa\"\r\n \r\nConstraints:\r\n1 \u003c= sentence.length \u003c= 150\r\nsentence consists of English letters and spaces.\r\nsentence has no leading or trailing spaces.\r\nAll the words in sentence are separated by a single space.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 809.375px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 404.688px; transform-origin: 408px 404.688px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given a string sentence that consist of words separated by spaces. Each word consists of lowercase and uppercase letters only.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe would like to convert the sentence to \"Goat Latin\" (a made-up language similar to Pig Latin.) The rules of Goat Latin are as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf a word begins with a vowel ('a', 'e', 'i', 'o', or 'u'), append \"ma\" to the end of the word.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the word \"apple\" becomes \"applema\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf a word begins with a consonant (i.e., not a vowel), remove the first letter and append it to the end, then add \"ma\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the word \"goat\" becomes \"oatgma\".\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAdd one letter 'a' to the end of each word per its word index in the sentence, starting with 1.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the first word gets \"a\" added to the end, the second word gets \"aa\" added to the end, and so on.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e the final sentence representing the conversion from sentence to Goat Latin\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 1:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sentence = \"I speak Goat Latin\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"Imaa peaksmaaa oatGmaaaa atinLmaaaaa\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample 2:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sentence = \"The quick brown fox jumped over the lazy dog\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eOutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \"heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa\"\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eConstraints:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1 \u0026lt;= sentence.length \u0026lt;= 150\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esentence consists of English letters and spaces.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003esentence has no leading or trailing spaces.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cul style=\"block-size: 20.4375px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 10.2125px; transform-origin: 391px 10.2188px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAll the words in sentence are separated by a single space.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function result = solution(sentence)\r\n\r\nend","test_suite":"%%\r\nsentence = 'I speak Goat Latin';\r\ncorrect_answer = 'Imaa peaksmaaa oatGmaaaa atinLmaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'The quick brown fox jumped over the lazy dog';\r\ncorrect_answer = 'heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'YLI Tdy kh dXKaa yRlPm WCVHO jVA tkLqg KWvQP Vo x aF IJSb DJUn q';\r\ncorrect_answer = 'LIYmaa dyTmaaa hkmaaaa XKaadmaaaaa RlPmymaaaaaa CVHOWmaaaaaaa VAjmaaaaaaaa kLqgtmaaaaaaaaa WvQPKmaaaaaaaaaa oVmaaaaaaaaaaa xmaaaaaaaaaaaa aFmaaaaaaaaaaaaa IJSbmaaaaaaaaaaaaaa JUnDmaaaaaaaaaaaaaaa qmaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'win QKDZ zoI pFP OFxhk XHUl qbQw W Em tzur Nm Wolnm wQ kQZh mvqwr I';\r\ncorrect_answer = 'inwmaa KDZQmaaa oIzmaaaa FPpmaaaaa OFxhkmaaaaaa HUlXmaaaaaaa bQwqmaaaaaaaa Wmaaaaaaaaa Emmaaaaaaaaaa zurtmaaaaaaaaaaa mNmaaaaaaaaaaaa olnmWmaaaaaaaaaaaaa Qwmaaaaaaaaaaaaaa QZhkmaaaaaaaaaaaaaaa vqwrmmaaaaaaaaaaaaaaaa Imaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'zo';\r\ncorrect_answer = 'ozmaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'cUS j E NlYz j Tc HR P p';\r\ncorrect_answer = 'UScmaa jmaaa Emaaaa lYzNmaaaaa jmaaaaaa cTmaaaaaaa RHmaaaaaaaa Pmaaaaaaaaa pmaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'FAMfT ain J z oEo aDttb';\r\ncorrect_answer = 'AMfTFmaa ainmaaa Jmaaaa zmaaaaa oEomaaaaaa aDttbmaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'NPm t gwad PVVG d MGLk Yvmy SXgK f A xPB zrnY Pz Ga';\r\ncorrect_answer = 'PmNmaa tmaaa wadgmaaaa VVGPmaaaaa dmaaaaaa GLkMmaaaaaaa vmyYmaaaaaaaa XgKSmaaaaaaaaa fmaaaaaaaaaa Amaaaaaaaaaaa PBxmaaaaaaaaaaaa rnYzmaaaaaaaaaaaaa zPmaaaaaaaaaaaaaa aGmaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'VRVJO kxPa';\r\ncorrect_answer = 'RVJOVmaa xPakmaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'dwR MWqM wBHyj va dwCF eod sHzt ft zP SASy GD uvh';\r\ncorrect_answer = 'wRdmaa WqMMmaaa BHyjwmaaaa avmaaaaa wCFdmaaaaaa eodmaaaaaaa Hztsmaaaaaaaa tfmaaaaaaaaa Pzmaaaaaaaaaa ASySmaaaaaaaaaaa DGmaaaaaaaaaaaa uvhmaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'W UvuC AEg Hsqo r mdzgu';\r\ncorrect_answer = 'Wmaa UvuCmaaa AEgmaaaa sqoHmaaaaa rmaaaaaa dzgummaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'rDIH peGn';\r\ncorrect_answer = 'DIHrmaa eGnpmaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Lr EV XM S Drre IDu sXbwK AFMP DS ASJ A x cXjtk w fz sD vut jg';\r\ncorrect_answer = 'rLmaa EVmaaa MXmaaaa Smaaaaa rreDmaaaaaa IDumaaaaaaa XbwKsmaaaaaaaa AFMPmaaaaaaaaa SDmaaaaaaaaaa ASJmaaaaaaaaaaa Amaaaaaaaaaaaa xmaaaaaaaaaaaaa Xjtkcmaaaaaaaaaaaaaa wmaaaaaaaaaaaaaaa zfmaaaaaaaaaaaaaaaa Dsmaaaaaaaaaaaaaaaaa utvmaaaaaaaaaaaaaaaaaa gjmaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'ALNn';\r\ncorrect_answer = 'ALNnmaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'w YCcE Cx t';\r\ncorrect_answer = 'wmaa CcEYmaaa xCmaaaa tmaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'KYgHu kur tf Qrz D sSr mOo BTW Y dlsw VGXN SQg GuRb X BU IL';\r\ncorrect_answer = 'YgHuKmaa urkmaaa ftmaaaa rzQmaaaaa Dmaaaaaa Srsmaaaaaaa Oommaaaaaaaa TWBmaaaaaaaaa Ymaaaaaaaaaa lswdmaaaaaaaaaaa GXNVmaaaaaaaaaaaa QgSmaaaaaaaaaaaaa uRbGmaaaaaaaaaaaaaa Xmaaaaaaaaaaaaaaa UBmaaaaaaaaaaaaaaaa ILmaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'xFC oTW YBfHj XfpPw bDD';\r\ncorrect_answer = 'FCxmaa oTWmaaa BfHjYmaaaa fpPwXmaaaaa DDbmaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'O B ZYpNk IfEYR Kmcy i IYo WiP T YNL k eM rhIRJ t AYnT';\r\ncorrect_answer = 'Omaa Bmaaa YpNkZmaaaa IfEYRmaaaaa mcyKmaaaaaa imaaaaaaa IYomaaaaaaaa iPWmaaaaaaaaa Tmaaaaaaaaaa NLYmaaaaaaaaaaa kmaaaaaaaaaaaa eMmaaaaaaaaaaaaa hIRJrmaaaaaaaaaaaaaa tmaaaaaaaaaaaaaaa AYnTmaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'e ttpp yZ Xi NSFfx cbpW TtT Ufl';\r\ncorrect_answer = 'emaa tpptmaaa Zymaaaa iXmaaaaa SFfxNmaaaaaa bpWcmaaaaaaa tTTmaaaaaaaa Uflmaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'at uj EE W k NhW cJo YJzf Ba Ei J CYG BS RsMWI oEr';\r\ncorrect_answer = 'atmaa ujmaaa EEmaaaa Wmaaaaa kmaaaaaa hWNmaaaaaaa Jocmaaaaaaaa JzfYmaaaaaaaaa aBmaaaaaaaaaa Eimaaaaaaaaaaa Jmaaaaaaaaaaaa YGCmaaaaaaaaaaaaa SBmaaaaaaaaaaaaaa sMWIRmaaaaaaaaaaaaaaa oErmaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'YJK WRiRy BR nsj jR aq oOBiB LM jho PIoh Jd ZVD MKJo GQa ZQ JQoI C TjW rGBxs eu';\r\ncorrect_answer = 'JKYmaa RiRyWmaaa RBmaaaa sjnmaaaaa Rjmaaaaaa aqmaaaaaaa oOBiBmaaaaaaaa MLmaaaaaaaaa hojmaaaaaaaaaa IohPmaaaaaaaaaaa dJmaaaaaaaaaaaa VDZmaaaaaaaaaaaaa KJoMmaaaaaaaaaaaaaa QaGmaaaaaaaaaaaaaaa QZmaaaaaaaaaaaaaaaa QoIJmaaaaaaaaaaaaaaaaa Cmaaaaaaaaaaaaaaaaaa jWTmaaaaaaaaaaaaaaaaaaa GBxsrmaaaaaaaaaaaaaaaaaaaa eumaaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'KhQ RzIxv W y BZ';\r\ncorrect_answer = 'hQKmaa zIxvRmaaa Wmaaaa ymaaaaa ZBmaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'O uQT kTpvQ we MprM KeyHB o PWskJ wV uMppp V mzPt LO GNAr E k A y w';\r\ncorrect_answer = 'Omaa uQTmaaa TpvQkmaaaa ewmaaaaa prMMmaaaaaa eyHBKmaaaaaaa omaaaaaaaa WskJPmaaaaaaaaa Vwmaaaaaaaaaa uMpppmaaaaaaaaaaa Vmaaaaaaaaaaaa zPtmmaaaaaaaaaaaaa OLmaaaaaaaaaaaaaa NArGmaaaaaaaaaaaaaaa Emaaaaaaaaaaaaaaaa kmaaaaaaaaaaaaaaaaa Amaaaaaaaaaaaaaaaaaa ymaaaaaaaaaaaaaaaaaaa wmaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Qem sv v CsIJ';\r\ncorrect_answer = 'emQmaa vsmaaa vmaaaa sIJCmaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'WDE mKpD umWx';\r\ncorrect_answer = 'DEWmaa KpDmmaaa umWxmaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'IwiK tHUzG fff WGW p aiNRF XMK TYZV dQ b CrES';\r\ncorrect_answer = 'IwiKmaa HUzGtmaaa fffmaaaa GWWmaaaaa pmaaaaaa aiNRFmaaaaaaa MKXmaaaaaaaa YZVTmaaaaaaaaa Qdmaaaaaaaaaa bmaaaaaaaaaaa rESCmaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Cjm nX RuiM sjZXi wlhnC F x Xp Ith p GkYwR baO pSI';\r\ncorrect_answer = 'jmCmaa Xnmaaa uiMRmaaaa jZXismaaaaa lhnCwmaaaaaa Fmaaaaaaa xmaaaaaaaa pXmaaaaaaaaa Ithmaaaaaaaaaa pmaaaaaaaaaaa kYwRGmaaaaaaaaaaaa aObmaaaaaaaaaaaaa SIpmaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'njtB MhagV fXgz yd nm bVtIX';\r\ncorrect_answer = 'jtBnmaa hagVMmaaa Xgzfmaaaa dymaaaaa mnmaaaaaa VtIXbmaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'vfzy IoIHU';\r\ncorrect_answer = 'fzyvmaa IoIHUmaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'wP TzEWi nR o Gvn tfg IRzp c tD OEf dtoM N ma k Vo O FrJm sl';\r\ncorrect_answer = 'Pwmaa zEWiTmaaa Rnmaaaa omaaaaa vnGmaaaaaa fgtmaaaaaaa IRzpmaaaaaaaa cmaaaaaaaaa Dtmaaaaaaaaaa OEfmaaaaaaaaaaa toMdmaaaaaaaaaaaa Nmaaaaaaaaaaaaa ammaaaaaaaaaaaaaa kmaaaaaaaaaaaaaaa oVmaaaaaaaaaaaaaaaa Omaaaaaaaaaaaaaaaaa rJmFmaaaaaaaaaaaaaaaaaa lsmaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'asmW tJKE OBeUn rNP TeIAr skn h Eh a JgLi J d a d';\r\ncorrect_answer = 'asmWmaa JKEtmaaa OBeUnmaaaa NPrmaaaaa eIArTmaaaaaa knsmaaaaaaa hmaaaaaaaa Ehmaaaaaaaaa amaaaaaaaaaa gLiJmaaaaaaaaaaa Jmaaaaaaaaaaaa dmaaaaaaaaaaaaa amaaaaaaaaaaaaaa dmaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Au';\r\ncorrect_answer = 'Aumaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'hOM y vw KabmF rxfLL WcPy cO ORrjt bp ks gkz MpP NrLbG c b BNEMq zfQIt vcEp Eqh frbVt';\r\ncorrect_answer = 'OMhmaa ymaaa wvmaaaa abmFKmaaaaa xfLLrmaaaaaa cPyWmaaaaaaa Ocmaaaaaaaa ORrjtmaaaaaaaaa pbmaaaaaaaaaa skmaaaaaaaaaaa kzgmaaaaaaaaaaaa pPMmaaaaaaaaaaaaa rLbGNmaaaaaaaaaaaaaa cmaaaaaaaaaaaaaaa bmaaaaaaaaaaaaaaaa NEMqBmaaaaaaaaaaaaaaaaa fQItzmaaaaaaaaaaaaaaaaaa cEpvmaaaaaaaaaaaaaaaaaaa Eqhmaaaaaaaaaaaaaaaaaaaa rbVtfmaaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'Djl lWo Qsbrt Y i Act ZwK h cbDrl Jtukm VOmEk J NQluv fBGok siU Iky z JM DM Edtb';\r\ncorrect_answer = 'jlDmaa Wolmaaa sbrtQmaaaa Ymaaaaa imaaaaaa Actmaaaaaaa wKZmaaaaaaaa hmaaaaaaaaa bDrlcmaaaaaaaaaa tukmJmaaaaaaaaaaa OmEkVmaaaaaaaaaaaa Jmaaaaaaaaaaaaa QluvNmaaaaaaaaaaaaaa BGokfmaaaaaaaaaaaaaaa iUsmaaaaaaaaaaaaaaaa Ikymaaaaaaaaaaaaaaaaa zmaaaaaaaaaaaaaaaaaa MJmaaaaaaaaaaaaaaaaaaa MDmaaaaaaaaaaaaaaaaaaaa Edtbmaaaaaaaaaaaaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n%%\r\nsentence = 'DYwO bAv lw qoszQ bp Qh SCaAL UKWa bAHNo';\r\ncorrect_answer = 'YwODmaa Avbmaaa wlmaaaa oszQqmaaaaa pbmaaaaaa hQmaaaaaaa CaALSmaaaaaaaa UKWamaaaaaaaaa AHNobmaaaaaaaaaa';\r\nresult = solution(sentence)\r\nassert(isequal(correct_answer, result))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":4945898,"edited_by":4945898,"edited_at":"2026-01-31T12:14:26.000Z","deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2026-01-31T12:12:55.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-31T12:12:09.000Z","updated_at":"2026-04-28T18:31:56.000Z","published_at":"2026-01-31T12:12:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given a string sentence that consist of words separated by spaces. Each word consists of lowercase and uppercase letters only.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe would like to convert the sentence to \\\"Goat Latin\\\" (a made-up language similar to Pig Latin.) The rules of Goat Latin are as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a word begins with a vowel ('a', 'e', 'i', 'o', or 'u'), append \\\"ma\\\" to the end of the word.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the word \\\"apple\\\" becomes \\\"applema\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a word begins with a consonant (i.e., not a vowel), remove the first letter and append it to the end, then add \\\"ma\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the word \\\"goat\\\" becomes \\\"oatgma\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAdd one letter 'a' to the end of each word per its word index in the sentence, starting with 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the first word gets \\\"a\\\" added to the end, the second word gets \\\"aa\\\" added to the end, and so on.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e the final sentence representing the conversion from sentence to Goat Latin\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sentence = \\\"I speak Goat Latin\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"Imaa peaksmaaa oatGmaaaa atinLmaaaaa\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sentence = \\\"The quick brown fox jumped over the lazy dog\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eConstraints:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 \u0026lt;= sentence.length \u0026lt;= 150\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esentence consists of English letters and spaces.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003esentence has no leading or trailing spaces.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll the words in sentence are separated by a single space.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":875,"title":"Return a list sorted by number of consecutive occurrences","description":"Inspired by Problem 38 by Cody Team. Given a vector x, return a vector y of the values in x sorted by the number of CONSECUTIVE occurrences in x. Ties (and it is the difficulty) are sorted from lowest to highest. So if x = [1 2 2 2 3 3 7 7 93] then\r\n y = [2 3 7 1 93]\r\nBut if x = [1 1 2 2 2 3 3 7 7 1 93] then\r\n y = [2 1 3 7 1 93]\r\nUpdate - Test case added 22-8-22","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 185.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 92.9333px; transform-origin: 407px 92.9333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 365px 8px; transform-origin: 365px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by Problem 38 by Cody Team. Given a vector x, return a vector y of the values in x sorted by the number of CONSECUTIVE occurrences in x. Ties (and it is the difficulty) are sorted from lowest to highest. So if x = [1 2 2 2 3 3 7 7 93] then\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e y = [2 3 7 1 93]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117px 8px; transform-origin: 117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBut if x = [1 1 2 2 2 3 3 7 7 1 93] then\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 76px 8.5px; tab-size: 4; transform-origin: 76px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e y = [2 1 3 7 1 93]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108px 8px; transform-origin: 108px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUpdate - Test case added 22-8-22\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = popularity_bis(x)\r\n  y = unique(x);\r\nend","test_suite":"%%\r\nx = [1 2 2 2 3 3 7 7 93]\r\ny_correct1 = [2 3 7 1 93] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n%%\r\nx = [1 1 2 2 2 3 3 7 7 1 93];\r\ny_correct2 = [2 1 3 7 1 93] ;\r\nassert(isequal(popularity_bis(x),y_correct2))\r\n%%\r\nx = [1 0 0 2 2 -5 9 9 2 1 1 1 0 11];\r\ny_correct1 = [1 0 2 9 -5 0 1 2 11] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n%%\r\nx = [1 0 1 1 0 0];\r\ny_correct0 = [0 1 0 1] ;\r\nassert(isequal(popularity_bis(x),y_correct0))\r\n%%\r\nx = [0 1 0 0 1 1];\r\ny_correct1 = [0 1 0 1] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n%%\r\nx = [-2 -2 3 3 3 -7 -7 0 0 0];\r\ny_correct1 = [0 3 -7 -2] ;\r\nassert(isequal(popularity_bis(x),y_correct1))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":5,"created_by":5390,"edited_by":223089,"edited_at":"2022-08-22T17:30:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":434,"test_suite_updated_at":"2022-08-22T17:30:08.000Z","rescore_all_solutions":false,"group_id":12,"created_at":"2012-08-03T00:17:38.000Z","updated_at":"2026-04-26T08:03:08.000Z","published_at":"2012-08-03T00:32:29.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by Problem 38 by Cody Team. Given a vector x, return a vector y of the values in x sorted by the number of CONSECUTIVE occurrences in x. Ties (and it is the difficulty) are sorted from lowest to highest. So if x = [1 2 2 2 3 3 7 7 93] then\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [2 3 7 1 93]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut if x = [1 1 2 2 2 3 3 7 7 1 93] then\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ y = [2 1 3 7 1 93]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUpdate - Test case added 22-8-22\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42829,"title":"Number construction III","description":"Given a positive integer, n, return a, b and c, such that\r\n\r\n1. n = a^1.5+b^2.5+c^3.5\r\n\r\n2. a, b and c are all positive integers greater than 1\r\n\r\nIf a solution does not exist, set all three output variables to zero.\r\n\r\nExample 1:\r\n\r\nn = 168\r\n\r\na = 4\r\n\r\nb = 4\r\n\r\nc = 4\r\n\r\nExample 2:\r\n\r\nn = 100\r\n\r\na = 0\r\n\r\nb = 0\r\n\r\nc = 0","description_html":"\u003cp\u003eGiven a positive integer, n, return a, b and c, such that\u003c/p\u003e\u003cp\u003e1. n = a^1.5+b^2.5+c^3.5\u003c/p\u003e\u003cp\u003e2. a, b and c are all positive integers greater than 1\u003c/p\u003e\u003cp\u003eIf a solution does not exist, set all three output variables to zero.\u003c/p\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cp\u003en = 168\u003c/p\u003e\u003cp\u003ea = 4\u003c/p\u003e\u003cp\u003eb = 4\u003c/p\u003e\u003cp\u003ec = 4\u003c/p\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cp\u003en = 100\u003c/p\u003e\u003cp\u003ea = 0\u003c/p\u003e\u003cp\u003eb = 0\u003c/p\u003e\u003cp\u003ec = 0\u003c/p\u003e","function_template":"function [a b c] = numcons(n)\r\n  a = n;\r\n  b = n;\r\n  c = n;\r\nend","test_suite":"%%\r\nn = 100;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 888;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 19666;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 314159;\r\n[a b c] = numcons(n);\r\nassert(all([a b c]==0))\r\n\r\n%%\r\nn = 1100;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 116600;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 16999;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 10000040;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 94940;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)\r\n\r\n%%\r\nn = 9990;\r\n[a b c] = numcons(n);\r\nassert(all(mod([a b c],1)==0))\r\nassert(all([a b c]\u003e1))\r\nassert(a^1.5+b^2.5+c^3.5==n)","published":true,"deleted":false,"likes_count":2,"comments_count":3,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":"2016-04-28T18:19:03.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-04-25T11:29:04.000Z","updated_at":"2026-04-09T07:25:23.000Z","published_at":"2016-04-25T11:29:04.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer, n, return a, b and c, such that\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1. n = a^1.5+b^2.5+c^3.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2. a, b and c are all positive integers greater than 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a solution does not exist, set all three output variables to zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 168\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec = 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eb = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":579,"title":"Spiral In","description":"Create an m by n matrix filled with sequential integers starting from 1 and arranged in a counterclockwise spiral that hugs the outside border and begins in the upper left corner.\r\nFor example:\r\n\u003e\u003e spiralIn(4,5)\r\nans =\r\n   1    14    13    12    11\r\n   2    15    20    19    10\r\n   3    16    17    18     9\r\n   4     5     6     7     8","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"baseline-shift: 0px; block-size: 190px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 95px; transform-origin: 468.5px 95px; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 21px; text-align: left; transform-origin: 444.5px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 434.5px 8px; transform-origin: 434.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCreate an m by n matrix filled with sequential integers starting from 1 and arranged in a counterclockwise spiral that hugs the outside border and begins in the upper left corner.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8417px 8px; transform-origin: 40.8417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 108px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 464.5px 54px; transform-origin: 464.5px 54px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 61.6px 8.5px; tab-size: 4; transform-origin: 61.6px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; spiralIn(4,5)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 19.25px 8.5px; tab-size: 4; transform-origin: 19.25px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eans =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   1    14    13    12    11\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   2    15    20    19    10\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   3    16    17    18     9\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 107.8px 8.5px; tab-size: 4; transform-origin: 107.8px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   4     5     6     7     8\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = spiralIn(m,n)\r\n  s = zeros(m,n);\r\nend","test_suite":"%%\r\nm = 3;\r\nn = 5;\r\ns_correct = [1 12 11 10 9; 2 13 14 15 8; 3 4 5 6 7];\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 3;\r\ns_correct = [1 12 11; 2 13 10; 3 14 9; 4 15 8; 5 6 7];\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n\r\n%%\r\nm = 1;\r\nn = 1;\r\ns_correct = 1;\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n%%\r\nm = 5;\r\nn = 0;\r\ns_correct = zeros(5,0);\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n%%\r\nm = 2;\r\nn = 2;\r\ns_correct = [1 4; 2 3];\r\nassert(isequal(spiralIn(m,n),s_correct))\r\n\r\n\r\n%%\r\n%Test case added on 4/4/26\r\nm = 2*randi(10)+1;\r\ns_correct = m^2+1-rot90(spiral(m));\r\nassert(isequal(spiralIn(m,m),s_correct))\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":4,"created_by":3117,"edited_by":223089,"edited_at":"2026-04-04T09:55:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":121,"test_suite_updated_at":"2026-04-04T09:55:47.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-04-13T13:50:35.000Z","updated_at":"2026-04-26T07:13:41.000Z","published_at":"2012-04-13T13:50:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate an m by n matrix filled with sequential integers starting from 1 and arranged in a counterclockwise spiral that hugs the outside border and begins in the upper left corner.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e spiralIn(4,5)\\nans =\\n   1    14    13    12    11\\n   2    15    20    19    10\\n   3    16    17    18     9\\n   4     5     6     7     8]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":375,"title":"N-Dimensional Array Slice","description":"Given an N-dimensional array, _A_, an index, _I_, and a dimension, _d_, return the _I_ th elements of _A_ in the _d_ dimension.\r\n\r\nFor Example,\r\n\r\n    array_slice( A, 5, 3 )\r\n\r\nis equivalent to\r\n\r\n    A(:,:,5)\r\n\r\nNote: |eval| and |str2func| cannot be used. This is a Cody restriction.","description_html":"\u003cp\u003eGiven an N-dimensional array, \u003ci\u003eA\u003c/i\u003e, an index, \u003ci\u003eI\u003c/i\u003e, and a dimension, \u003ci\u003ed\u003c/i\u003e, return the \u003ci\u003eI\u003c/i\u003e th elements of \u003ci\u003eA\u003c/i\u003e in the \u003ci\u003ed\u003c/i\u003e dimension.\u003c/p\u003e\u003cp\u003eFor Example,\u003c/p\u003e\u003cpre\u003e    array_slice( A, 5, 3 )\u003c/pre\u003e\u003cp\u003eis equivalent to\u003c/p\u003e\u003cpre\u003e    A(:,:,5)\u003c/pre\u003e\u003cp\u003eNote: \u003ctt\u003eeval\u003c/tt\u003e and \u003ctt\u003estr2func\u003c/tt\u003e cannot be used. This is a Cody restriction.\u003c/p\u003e","function_template":"function S = arraySlice(A,I,d)\r\n  S = A(:,I);\r\nend","test_suite":"%%\r\nA = randn(5,5);\r\nassert(isequal(arraySlice(A,4,2),A(:,4)))\r\n\r\n%%\r\nA = randn(5,5);\r\nassert(isequal(arraySlice(A,4,1),A(4,:)))\r\n\r\n%%\r\nA = randn(5,5);\r\nassert(isequal(arraySlice(A,1,10),A))\r\n\r\n%%\r\nA = randn(5,5,5,3);\r\nassert(isequal(arraySlice(A,3,4),A(:,:,:,3)))\r\n\r\n%%\r\nA = randn(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2);\r\nassert(isequal(arraySlice(A,2,18),A(:,:,:,:,:,:,:,:,:,:,:,:,:,:,:,:,:,2)))","published":true,"deleted":false,"likes_count":13,"comments_count":7,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":287,"test_suite_updated_at":"2012-02-21T16:23:06.000Z","rescore_all_solutions":false,"group_id":19,"created_at":"2012-02-21T16:23:06.000Z","updated_at":"2026-04-25T20:27:00.000Z","published_at":"2012-02-21T16:23:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an N-dimensional array,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, an index,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and a dimension,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eI\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e th elements of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e in the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e dimension.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor Example,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    array_slice( A, 5, 3 )]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis equivalent to\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    A(:,:,5)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eeval\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2func\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cannot be used. This is a Cody restriction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":803,"title":"Twist 'n' Match","description":"Given n and m, construct an n-by-n matrix a such that a, when rotated 90 degrees and compared with itself, matches itself in exactly m places. \r\n\r\nThe number of matches m is calculated as follows: \r\n \r\n m = nnz(rot90(a)==a)\r\n\r\nYour answer a is clearly not unique. It must only meet the criteria stated above.\r\n\r\nExamples:\r\n\r\n Input n = 2, m = 1\r\n One possible output: a = [ 1 2 \r\n                            1 3 ]\r\n\r\n Input n = 3, m = 7\r\n One possible output: a = [ 0 1 1\r\n                            1 1 1\r\n                            1 1 1 ]","description_html":"\u003cp\u003eGiven n and m, construct an n-by-n matrix a such that a, when rotated 90 degrees and compared with itself, matches itself in exactly m places.\u003c/p\u003e\u003cp\u003eThe number of matches m is calculated as follows:\u003c/p\u003e\u003cpre\u003e m = nnz(rot90(a)==a)\u003c/pre\u003e\u003cp\u003eYour answer a is clearly not unique. It must only meet the criteria stated above.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cpre\u003e Input n = 2, m = 1\r\n One possible output: a = [ 1 2 \r\n                            1 3 ]\u003c/pre\u003e\u003cpre\u003e Input n = 3, m = 7\r\n One possible output: a = [ 0 1 1\r\n                            1 1 1\r\n                            1 1 1 ]\u003c/pre\u003e","function_template":"function a = twist_n_match(n,m)\r\n  a = 0;\r\nend","test_suite":"%%\r\nn = 2; \r\nm = 1;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 3; \r\nm = 7;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 6; \r\nm = 6;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 10; \r\nm = 11;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 10; \r\nm = 14;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 20; \r\nm = 83;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));\r\n\r\n%%\r\nn = 21; \r\nm = 1;\r\na = twist_n_match(n,m);\r\n[r,c] = size(a);\r\nassert(r==n \u0026\u0026 c==n);\r\nassert(isequal(nnz(a==rot90(a)),m));","published":true,"deleted":false,"likes_count":9,"comments_count":9,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":86,"test_suite_updated_at":"2012-07-03T15:06:05.000Z","rescore_all_solutions":false,"group_id":18,"created_at":"2012-06-28T15:15:32.000Z","updated_at":"2026-04-26T07:48:16.000Z","published_at":"2012-06-29T19:04:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n and m, construct an n-by-n matrix a such that a, when rotated 90 degrees and compared with itself, matches itself in exactly m places.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number of matches m is calculated as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ m = nnz(rot90(a)==a)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour answer a is clearly not unique. It must only meet the criteria stated above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input n = 2, m = 1\\n One possible output: a = [ 1 2 \\n                            1 3 ]\\n\\n Input n = 3, m = 7\\n One possible output: a = [ 0 1 1\\n                            1 1 1\\n                            1 1 1 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":46938,"title":"Numerical computation of the optimal shooting angle of a catapult","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 879.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 439.833px; transform-origin: 406.5px 439.833px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 64.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 32.1667px; text-align: left; transform-origin: 383.5px 32.1667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eConsider a capapult that fires a projects into the air with an initial velocity\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"20\" style=\"width: 56.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The free-flying projectile is subjected to air friction and a gravitional force. Given a desired target \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"109\" height=\"21\" style=\"width: 109px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and an initial velocity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"56.5\" height=\"20\" style=\"width: 56.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, find the optimal shooting angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"16\" height=\"18.5\" style=\"width: 16px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eof the catapult that minimizes the distance between the target and the trajectory of the fired projectile. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 21.25px; text-align: left; transform-origin: 383.5px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etip 1:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Consider the states \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the x- and y-position of the projectile, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the x- and y-velocity. Then, the trajectory of the projectile can be found by solving the following ordinary differential equation (ODE):\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFoAAAAsCAYAAADl06/eAAAETUlEQVRoQ+3aaai9UxTH8c9f5jEkESl5I5Eyz0oZQ4okQ0JmMmSIDJmHJJEo74yFMmSIFzIW8QJ5gTcyy5Qp89Dvbz//zr33dM8599z/Pp3au26dzrOfs/b+rrXX+q3nuUu0UYXAkipWmhENdKUgaKAb6EoEKplpEd1AVyJQyUyL6Aa6EoFKZlpETwnoOOoIXI/HcDl+qbT2qTIzbkSvi3txEL7DAXhjqghUWuy4oFtED+mocUEPaaZNa6ArxUAD3UBXIlDJTIvoBroSgUpm+kX0CtgUB+IQ7IYncBa+Z+nLgl1wA7bCqXi40nqXl5k1sAMOw37YAMfjyWJwLVyAM/B8YfH1KIvpB3oVbI7PsTseRAztW4zshXPxB/bHJbhjFKMD5l6Gq8b8vbdxJN4f8nc2KfP+xM04tjRiAftP6XxXw06lMTsOHw/520unDcrRG+N+7F2Aps0+H5fiq1EMjTB3EqB7l3cK7sJbBfjB+LQE3L8j7GPG1EGgVy4pIhH8VIniK/HOQg1OwX3blZSxEe7GN8ie/xpn7YNA57c7D+fzybgHC/bsOIutdG/vKX6hRPVn49oeBvTOeA4/I8coR2q+kUIS58QZ1467wAncvypuwem4FReXk9xvKVuXenVoufgorsYnsycPAzqF8aFSlY8pObuf0VTuFJHMiVLJI9MYnbYRJlEYN+LZsqekj9ljm1K37ixFN4olgRWFdubsx8WDQEeB5OYUwIw8d06x+ruP4ZVKFKcyvzIG6EkXw+3xCDbDhzi8T00KlzC5r0d95LubEFU2R/HMBzrXjsKuiGZMQZjPwx37RPO0gt4QtxUZe0LZe79TnNO7fh+JlyDZE5F/X/QG43ygt8RF5W8LPIMvezycXJyG5aWiNRcL9KRSzYq4EB/h8ZKnU2u6Uxw9vUdJE/2k7Tq4vQRjeo8ZgqEXdKRcPPVT8VY8mxtfRW8ljoejp5N/H8Cbs8iMG9G1QGfva5c0mNdvOb0p/AmuX3vUVneKE1Rp2tJM/T5rkUkb52FNXFPunzGlAx3IARePppuK93JD55ku/5yNdF2pqrk2x3OlEI6TOmqB3rYEzHr4oKSB03oasR3L9ejpRHhUV/JybzTnFOxTlEda94y82su8GS16B7p7JZVk/mPJx4naAO9Gnm9E7qyO60rB6CfipyWik48j4/I8J6oqKimpsRtpua8o+TZRnc9zZFuZnEDNaUjHnKgP6LBalj4GqY6FRNe0gF7I3gbdE8kXp72Hk/BDd0MDPQjdaNdz2lPb8vTzaHzbQI8GcNjZSTdJGekzkj5+a6CHRTfavKizNDGJ6hTQZWN5pI4I9hfH6AxH29pkZqeHiCqLWEirHu0dZXZO+S5RPUMoLCbovBxIIUxHlX8Te70s4rXl+Ox6Mpj/7zeiQk4sC3gZ7+Lpsu9etbZ0ymKCntSmp8JuA13JTQ10A12JQCUzLaIb6EoEKpn5D7tJ5C2FZ3WyAAAAAElFTkSuQmCC\" width=\"45\" height=\"22\" style=\"width: 45px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,     \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"45.5\" height=\"22\" style=\"width: 45.5px; height: 22px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e      \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 11px; text-align: left; transform-origin: 383.5px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; 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height: 19.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"47.5\" height=\"17.5\" style=\"width: 47.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis the friction coefficient between the air and the projectile. Use the ode45.m function to compute the trajectory of the projectile with initial conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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Plotting \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e vs. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14.5\" height=\"20\" style=\"width: 14.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e will result in the x-y trajectory of the projectile, as shown in the figure below.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.9167px; text-align: left; transform-origin: 383.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003etip 2: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eUse the following update law, to incrementally update the shooting angle \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.9167px; text-align: left; transform-origin: 383.5px 10.9167px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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width=\"44\" height=\"20\" style=\"width: 44px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e the smallest Euclidean distance between the trajectory of the projectile and the target \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg 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\" width=\"298\" height=\"20\" style=\"width: 298px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eis a difference angle, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"55.5\" height=\"17.5\" style=\"width: 55.5px; height: 17.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ean update parameter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample of algorithm's numerical result:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 80px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.5px 40px; transform-origin: 403.5px 40px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003etheta = catapult(25,3,25)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003etheta = \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    0.8431\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10px; transform-origin: 403.5px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 264.333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 383.5px 132.167px; text-align: left; transform-origin: 383.5px 132.167px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"570\" height=\"259\" style=\"vertical-align: baseline;width: 570px;height: 259px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function theta = catapult(xd,yd,v0) \r\n  \r\n    global g nu;\r\n    \r\n    g   = -9.81;  % grav. acceleration\r\n    nu  = 0.5;    % air friction coeff.\r\n    k   = 0;      % solver increments\r\n    dt  = 1e-2;   % timesteps\r\n    T   = 10;     % simulation time\r\n    TOL = 1e-2;   % absolute tolerance\r\n    \r\n    [~,y] = ode45(@ODECatapult,0:dt:T,[v0,0,0]); \r\n    \r\n    % solver for optimal angle\r\n    while (e \u003e= TOL) \u0026\u0026 (k \u003e 150)        \r\n        \r\n        %theta = theta + beta;\r\n        \r\n        k = k+1;    % add increment\r\n    end\r\n  \r\n    function dx = ODECatapult(t,x)\r\n        global g nu;\r\n        %% fill in ordinary differential equation %%\r\n    end\r\n    \r\n    function e = EuclideanDistance(y,xd,yd)\r\n        %% fill in computation of smallest euclidean distance %%\r\n    end\r\n    \r\n    function beta = UpdateLaw(y,e,lambda)\r\n        %% fill in update law to update the shooting angle %%\r\n    end\r\nend","test_suite":"xd = 8;\r\nyd = 2;\r\nv0 = 35;\r\ny_correct = 1.446;\r\n\r\nassert(isequal(round(catapult(xd,yd,v0),3),y_correct))\r\n\r\n%%\r\nxd = 15;\r\nyd = 5;\r\nv0 = 35;\r\ny_correct = 1.33;\r\n\r\nassert(isequal(round(catapult(xd,yd,v0),2),y_correct))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":636373,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-10-19T12:41:43.000Z","updated_at":"2025-01-02T11:31:42.000Z","published_at":"2020-10-19T13:39:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider a capapult that fires a projects into the air with an initial velocity\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_0 \\\\in \\\\mathbb{R}_{\\\\ge 0}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The free-flying projectile is subjected to air friction and a gravitional force. Given a desired target \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$z_d = [x_d, y_d] \\\\in \\\\mathbb{R}^2$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and an initial velocity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ev_0 \\\\in \\\\mathbb{R}_{\\\\ge 0}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, find the optimal shooting angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta^*\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eof the catapult that minimizes the distance between the target and the trajectory of the fired projectile. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etip 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Consider the states \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the x- and y-position of the projectile, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the x- and y-velocity. Then, the trajectory of the projectile can be found by solving the following ordinary differential equation (ODE):\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x_1} = x_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,     \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_2 = x_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e      \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_3 = -\\\\nu x_3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e    \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\dot{x}_4 = -g - \\\\nu x_4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.   \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg = 9.81\\\\; (\\\\text{m/s}^2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\nu = 0.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis the friction coefficient between the air and the projectile. Use the ode45.m function to compute the trajectory of the projectile with initial conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(t = 0) = (0,0,v_0 \\\\cos(\\\\theta_k), v_0 \\\\sin(\\\\theta_k))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Plotting \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e vs. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e will result in the x-y trajectory of the projectile, as shown in the figure below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003etip 2: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eUse the following update law, to incrementally update the shooting angle \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_{k+1} = \\\\theta_k + \\\\lambda \\\\, \\\\text{sign}(\\\\theta_{e,k})\\\\,e_k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee_k \\\\in \\\\mathbb{R}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e the smallest Euclidean distance between the trajectory of the projectile and the target \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ez_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\theta_{e,k} = \\\\text{atan2}(d_y,d_x) - \\\\text{atan2}(v_0\\\\sin(\\\\theta_k),v_0\\\\cos(\\\\theta_k))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis a difference angle, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$\\\\lambda = 0.01$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003ean update parameter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample of algorithm's numerical result:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[theta = catapult(25,3,25)\\ntheta = \\n    0.8431\\n    ]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"259\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"570\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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fnPNYWXL1/ezbN0c9FhjtF5hw4d2tnXO1zjuDPjxo2TyWQzZ84khAwcOHD48OF+fn40BQ316JizZ88+cOCAVqsNCwsbMWJEl/uLW5ukjR07ti9fVyqViYmJXe6WmZmpVCr7cqJeKC0t5fmMfMLVWU4f/6ewBL1eX15e3tTUZLjxkUceOXfuXFNT071798xylurq6rq6ui536+y83fw6/5qbm5ubm7vczfR9t8KfivZQuzKlywdXlFKpNN0dAwBMkMlknQ2EcnBwGDp0qFnO0qOVf9uf12oXDjbqWilheHbVKY1GQ7o3s61SqcQwYQDz+t///V9vb2/bOS90yVZiuReUSmVmZqbQpQCwUUItL4dl7awW4qpTGEcFAGA90BgIAAAiII7aVV5e3smTJ2/fvj116tRVq1Zx2/fv33/lyhX6WqFQ7Nu3T6ACAkCP0TmTjGzcuLH9UKS+SElJmTlzpok5bUEsxBFXP/30k7Oz8/Xr140mpszPzx8zZkxgYCAhxM7OTqDSEUIIy7JqtRrPugC6Lyoqir5YvHjxxo0b6f/IZu/msG7duiNHjiCuJEAccUUffm7evLn9RxMmTDCcwUUoLMtikUaQPpYlGg3JyiIsS4KCyKxZpA99YufPn09f2NvbBwYGcm87XK2DWyLk/v37ycnJWq1227ZtLMvOnDmT9jino4b37NmTnZ0tl8ujoqKmTZvWfs0ReoorV678+c9/5kri6+sbHR3d6wsBfogjrkw4ePBgWlrakCFDXn31VTP+XaZWq8PCwrrf2wIT3YL0sSxRqwn3Z5lGQzQawrIkNta85+lwtQ6NRnP27NmYmBg6eWBISIi3t/frr79eUFAQGRm5atWq5cuXL1++vLm5efXq1bW1tYsXL05PT2+/Hgfl7u7+wgsv0NdxcXHtp5YAKyTuuAoJCZHL5XK5PCcnZ+nSpcePH/f09DTax8fHh75YuXIlXWmtOzQaTURERE9nArxz5w5vkwfeunWLnxMJAldnjeLiSPsmhLg4EhREzPpXWmeLfcTHx9PZby9dunT58uXz588TQoKDg8+cOUMIuXr1alpaWk1NDZ2I9t69e3v27Dl8+HCHa44MGzaMVub27dun1+s//vhjM5bfahn9dkpOTj506JBAZekNcccVt/TL9OnTCwsL09LS2tfor1271tPD0gHC06dP79G3lEplY2Njd4YVmwuf5+Ifrs7qaDQdb2cY88ZVZ6t1cNNM3Lx5k868R9HWwqtXr7a0tHh5/br2o06n67LLxokTJ3bs2JGXl+fk5GTG8lsto5+6LVu2bNmyhb7m/qy3ZuKOK0Ourq5VVVXmOlovfptgXnaQMhOPZsvKzHie7qzW4ejomJ+fz71tbGxUKBQODg4jRowoLe3u4siXLl2KjIz89ttvhw0bZpaSg6WJuMW2tbW1vLycvi4pKWEYRqVSmeXIWVlZvXgEpVQqy8z6/y2AFTHxB1y7Fvi+6M5iH8HBwS0tLSkpKYSQgoKCtLQ0ulGn0x07dozb7caNG6ST9TgqKipCQkISExMnTJjQYTGmTZtmnusB8xFHXMXHx/v4+KSmpqampvr4+MTHxxNC2traFi5c+NRTT6lUqkWLFoWFhZkrrhiG6UVvQ09PT9SuQLKUyk5b/Mw6YSa32MfcuXMTEhI6XOxDJpMdO3YsLi5u0KBB77zzTnBwsJOTk729fXp6+vvvv//EE08sXLjQ2dn57Nmz5Lf1OAYNGsStYkUIOXny5P3791esWDF06NChQ4e2X4uE+1MYrIc4GgO3bt26detWo412dnZ5eXmWOF2vUwdxBVKWmEhUKmL0Q56YaKri1T21tbWGb9PT07VarUKhMHykZLTPk08+WVBQQF+rVCq6eOPkyZOvXr368OHD5uZmbgL1FStWrFixwuiMERERERER7Uvy4osvymQyFxeXlpaWPl4UmJ044opPdPhULxoDg4KCkpKSzF4eAGuhVJLMTDOOuzKhy9U69uzZU1dXN2rUqLS0tMrKykWLFnEf9XoB+K+//trX1zcuLq6iouLrr7/u3UHAchBXxrq54H17dC1Hs5cHwIoolWYfZdU78+fPv3jxYmNj47Jly5577jlHR8e+H/PevXv+/v6EEHd3d7McEMwLcWWsmwvet6dUKkXZOxlAhMaOHdthp8G+GDx4MB33cv/+/cbGRvMeHPoOcWUM6wID2KaXXnrp2WefLSoqamlpQe3KCiGujKGGBGCb7O3tv/3228bGRmSVdRJHR3YAAH4gq6wW4goAAEQAjYHmFBsbW1ZWhv6BYM2mTJkiigniwLymTJkidBH6CnFlZhgpDFYuOTnZcgdnWVbCT3+lfXXWD42B/0GtVsf2bVgJ4goAwBJ4javc3Nzs7Gw+z9hTDMP05a8n/OUFAGAhvMaVm5ubWq3+wx/+wOdJe4Rl2b4sB4w1RAAALITXuFIqlT///HN5ebmvr++PP/7I56m7g84W2PfaFRILAMDs+O5qIZfLjx49mpaWtnTp0okTJ3Lb7ezsUlNTeS6MEcQMAIDVEqarxYABAwghOgPWMENXr2cL5KB2BQBgIQJ0ZI+IiLhw4cLnn3/eiyUQrR96WwAAWAKvtavy8nI6PvHatWtWmFW9W0S4PdSuAADMjtfaVXl5+Z///Oc5c+bwedLuM8sYwMTExL70LQQAgA7xGlcBAQF8nq5H+t4tkEJWAQBYAiZh+lVQUFBbW5vQpQAAgI5hEiYAABABxBUAAIiAkHFVXl5eUlJCX+v1egFLAgAAVk6YuDpz5oyPj09ISEhUVBQhpKKiYsaMGYKUxOxYlvXy8hK6FAAAUiNAXOn1+rVr16anp586dYpucXd3r6+vb2pq4r8wHNozsO9YlsW4KwAAsxMgru7evevh4WG0numAAQMaGhr4LwzFMIxKpTLLoTAPEwCAJQgQV/369WtubjbaWFNT079/f/4LQyFdAACsnABx5e7uXldXd+jQIfq2qalp48aNPj4+CoWC/8JQLMv2cXJbDmpXAACWIMww4e+++27WrFkffPABIWTSpEljx4795ptvBCkJVVZWJuDZAQCgS8LElVwuz87Orq6ubmxsdHJycnZ2FqQYHIZhYmJizHU0rCkMAGB2Qk7C5OrqKuDZDZk3XRBXAABmJ8y4q+vXr3e5hWeYmhYAwJoJEFcPHz5cvny50caFCxfyXxJKo9EQLKsIAGDdBGgM1Gq17ZsB3dzcampqhHqIZd6sSkxMRPhBl9jqRkIIq21gqxvpa0JImbaREMJWG49BZLW/7qB0ceQ2Kl1/Hfvh6eKodHUkhPz6X5f+9AWAlAgQVw4ODnV1dUYba2trHRwc+C8MFRYWZsajIauAQ3OIKdbSF1nFWkIIU1xDSAm3z28ZQ/OmPyFk1mgXo+OE/RY/XLCR37KNHjarmLDaRsNP6WGDRrsQQmaNdla6OiLGQNQEiKthw4bpdLq9e/dGRUXJ5fKmpqatW7d6eHg4OTnxXxhCiLlGXAGw1Y2stoG5UUMIySrWMsU1dDuXHDSHFnjJA8aOtFB4GFbaCCFZxTVsdQPNS+50QaNdaIAFtctFAKslTM/AzMzMOXPmJCQkODg46HQ6T0/PjIwMQUoC0Gs0DzQXK4hBOBkmU1ige4eRwLKsUmmpnPh3q+BoQggJD3Q3LC1TrCWEZBXXJF2s4AqM9AJRECauBg4cmJOTU1VVpdPprGHcFUA3sdWN7fOJhlPMPC9r/nVPYyzc1Z38lmG0LshWN2YV18RllNLqF6ILrJaQ464cHR3p86ra2lpCyKBBgwQsDECHuPY90eVTl5SujrQSxqUXU6zlKl5cdHH1MwBhCRNXH3/88aeffmq4xc7OrqCgQJDCmB3LsiqVqrS0VOiCQC91GFFhAe5izyfTlK6O4a7uhtGVdLFCc7EiLqMUuQXWQIC4qqmp+fTTT48dOzZ+/HiZTMjljMlvy1OZfYwwZrUQI9rQRyNK6eqodHGUQBWqd7jo4qpc6qOFcRmlShfHsEB35BYIQoC4qq+vHzFixMSJE7v/lby8vJMnT96+fXvq1KmrVq3ituv1+t27d6enp7u5uUVHR/dizSqNRpOVlWWJKS1YlkWPdutnGFHENmpRPcLlVkywF6ttSLp4h+ZW0GiXsMDH8K8EfBIgrh577DH6sKr7fvrpJ2dn5+vXrxcVFRlu3717d0FBwalTp27evLlixYojR44YrfrYpbKyMguFCuLKmtGUSsqtoP0LwgLcUWkwjT7oChrtEhPsRetbqoTL9J8uPNAdw7mABwLElUwme++991Qq1Z/+9KdHHnmE2z5mzJjOvkKH8W7evNlo+5EjR7788suBAweOHz8+JCQkJSVl69atPSoMy7KzZs3q0Ve6hJSyTtwTqbiMUvJbRQq/anvKsL5FK6ZJuRWobAEPhGkM3LdvHyHkrbfe4jbKZLLMzMweHaeqqqqurs7Pz4++nTx5cnp6ek8Lw7Kseae0AGtDK1Jl2kbNxQr6RCom2Ct2npfQ5RI9patj7DwvQrzY6sa4jFJa2Xreu//H+HMNLEOAuHJycsrKyur7cYqKihwcHLjOGgqFwqipkOKaB1euXBkaGmr0Kcuy3t7eZu8ZMXLkyNzcXItWs27dumW5gwuu71d3q7blq8IHtx60/LXwwchB9ovHPbJrztDF43+tzQvbF0Z69y7mqf4RE0Z9Vfhgzw/av149t3jcI288KcGalsRuXHJyMrequygIOe6qj4YPH67X67m3Op1u1KhR7Xe7du1aZ0egv7NGjhxp9lyxt7d3c3OzdKugtFsde311sadLubpUWID7WpW3FTZSSe/eKQmZPom8NP7GmQq7pNyKr280hAW4S68WK6Ubt2XLli1bttDXPX3qLwjB4mr9+vV5eXlc3vSiMZCGU1lZmaenJyGkpKRk2LBhPToCwzDEMj9/WKGRf7TRLy6jlKZU4svj0XWCfyMH2cdOUoYHujPF2riM0qTcCkmGFghCmLgKCAgIDg7+7//+b4VCodPptm/fnpCQ0NODyGSyuXPnHj16dOPGjfX19enp6Zs2berpQaT0t5Jt4lKKEBI02hkpZQ1od4yg0S4ILTAjAeLq7t27CoVi+/btubm5CoXC19d38eLFgYGBV65c6ewr8fHxhw8fpq9TU1NXrFhBewBu3rw5LCwsNze3vLx8/vz5PR13ZaERVwRLXlmeUU909J6wQlxo0TuF0II+EiCudDrdgAEDCCF2dnYVFRW+vr5yuXzw4MG1tbWdTRu4devWDnuoDx069OTJk70uidm7sHOQVZZD+6Fxj6bQE93K0Q6E4YHutBKclFuR+PJ4K3yaCNZPgLh65JFH6PKMbm5ub7/9dnBwcGVl5Z07d+RyOc8lwUpXImLY6BceiEdTImMYWqqEy3TYFv7OgB4RIK6cnZ09PDwqKys9PDweffTRiRMntrS0LFmypH///vwXBqyfYXUKjX6ixoWW+miBan8e2gahR4TpanH06FHuRVVVlYODA1YPASOGT6digr0yo/zRgiQNSlfHxJcnoG0Qekr4cVdubm5CFwGsC1vduPd77Z4fSujTKfwBLj2GbYPqo4W4y9AdAqzfUV9fv2zZMqONs2fP5r8klsMwjJcX/vfrsdjTpV7bsr22Zf/16oPEl8eXbnoav8UkjIZW4svjk3IrvLZlM8VaoUsEVk2Y2tWdO3eMtty9e5fnMjAMw7IseltYA6MRvuGB7qT2jlKJnhQ2IWi0S+aaJ1DNgi7xHVeFhYW0W2BhYSG38cKFC05OTjyXJCkpiViycyBmtegOw6Ay7EbB9myFGRA3Ws0K8nZWHy1Myq3IXPMEOg1Ce7zGVW1t7erVqwkhd+7coS8ouVx+8OBBPktC0dmbQBCG/f3QKx2IQTULnQahQ7zG1aBBg7Kysurr6996663PPvuMz1O3xzBMTEyMhQ5OhwljhcYOxZ4u5fr7lW56Gn9HA+e3RUkIHWCHxAJDwiwgYphVTU1Nra2t/A+6QmMd/wyDCrNRQGdop0HV/jw0DIIhAXoGEkJmz57d0NBACElJSZk0adLjjz/+xRdf8F8MC00YyEEiUmx1Y+zp0n5vn6WzxrX9aXbsPMxoAKYoXR0z1zwRFuCu2p8Xe7pU6OKAVRBmilu9Xk+rU7t27fr8888nTJgwffr01157jbcyWG7pEAptgFRnPSkAusQ1DCblVhA0DIJQU9wqFApCSE1NTUNDA51n1s3NraamxtnZmZ8yoN5jaQgqMAs0DAJHgMbAAQMGVFVVEUK++uqrESNG0I06nc7enr/sZFnW0i2BNrtCI23689qWTefXwVBf6CPaMEgIUe3PY6sbhS4OCEaA2pWrq+vEiRN9fX11Oh2dPPDhw4eNjY0DBw7krQxlZWWWbq/LzMy0tSZBwxoV+qaDGdHEQh93GyfMrBbJycl3794dMGAAjaiBAweeOHGCzwLMmjXL0lliU1mFoAJLw6Ms4DWu6EwW48ePpy+qq6v5PLshzL1kLggq4BNGZdkyXuPq3Xff9fT0/Oijj9auXWv0kUwmO3PmDJ+FgT5CUIEg6HRNqoTLBIllY3iNq7S0NPriW/MFaQAAFCBJREFU7NmzfJ4XzAtBBcIKGu1Suulp1f68Mm1j4svjhS4O8ESYYcIgUoa9/ugUSsgqEATtfMEUa722ZQtdFuCJMHHV2tpaWVlZUVFRWyvZmbdjY2NVKpXQpTAno6BCOwwIi+vg7rUtGx3cbYEAPQOjoqL+8Y9/cG+HDBmyb9++gIAA3grAMAzDMLGxsbydUezoXH+EEAz4BatCE0u1P0+1Pw+DiCWP77iKjIw8f/78gQMH/Pz8ZDLZgwcPdu/evWLFiu+//563KS3oSlfQHUyxVn20kE5Ki6ACK0QTS320AIklebzG1cOHDxmG+fnnn+VyOd0ycODAXbt2DR48+L333tu/fz+fhQHT2OpG9dECprgGQQVWTunqmPjyBCSW5PH67KqiosLT05PLKs7q1atzc3N5KwbDMHSiQosS7yRMbHWj+mghfYKNZ1QgCjSxlC6OmKhJwniNq4cPHw4ePLj99sGDB9fX1/NWDJGmCA+4jn9MsTYzyj8zCn+ogmgYJpbQZQGL4DWu9Hq9TNbBGWUyWVtbG58lsfT8tkSEkzAZzUsbNNpF6BIB9AxNLEIIerdLEt9dLa5cubJs2TKeT2qIrnTFD7FU42h/CoKOfyB+XF9Br23ZpZueFro4YE58x5WXl9e//vWv9tt5q4vQCBFd1cdC0J8CpIdLLPXRQsx5ISW8xlVAQMDf//53Ps/YIX6yysoTkZtIKWi0c+mmp/GMCqQEiSVJwiwgIiAeFmbklJaW8nOinoo9XUpn/MuM8sczKpAkmlhe27I9XRzRciANNhdXvGWVddau8JgKbAf9gwxzt0sG4spW4DEV2KCg0S6JL4+PyygN8nZGQ4LY2Vxc2Sau9Q+PqcDWhAe605HviS+PR2KJGuJK4phirSrhMhamAltGmxPURwsxRZOoYb0ryWKrG1UJeaqEy1iYCiA80B0TXogd4sqCvLy8NBqNIKemU1QQTPoHQAgxmPCCdjUCMbKtuGIYRq1WC10Ky2KKtf3ePpuUW4FJ/wAM0a7tmosVsaetdIQJmGZbz64YhuFzYiSeJ2VH3z8A0+hDXHQUFCnbql2VlZVZ53CovkPrH0B3hAe6hwW400VHhS4L9Iy4a1f79++/cuUKfa1QKPbt2ydseQSBkb8APRIe6J5VrFXtz8McuOIi7rjKz88fM2ZMYGAgIcTOzq7L/RmGiYmJsXy5eMLN+4egAug+2u0CMwqKjrjjihAyYcIEHpYG7h2lUllWVmahg+/9XrvnhxLM+wfQC5hRUIxEH1cHDx5MS0sbMmTIq6++6u3tbXpnPue3tRx0qQDoO3S7EB1xx1VISIhcLpfL5Tk5OUuXLj1+/Linp6fRPj4+PvSFSqUihNy6dYu34j18+JCYe5HGvd9r9/ygfWqEY+o8ecDYfmJZAbKn+LxN/JPw1Ynr0oKGkr8Nk4ce+ul82Kju7C+uq+tScnLyoUOHhC5FD/TjedV5y4mIiPDz84uOjjbc6OPjc+3aNfpao9Go1Wo+rzc2NjYrKyszM9MsR2OrG+mY/Jhgr/BAd5ZlpdrLkRCCqxMp0V0a/d+KzoTb9c5iu7ruM/xVabWk05Hd1dW1qqrK9D48/6iFh4ebJavY6kbaTz1otAumUwIwI27ssOZihdBlgS6IuDGwtbX1zp07w4cPJ4SUlJQwDLNz504T+wcFBfEcV2Y5HTdHLbpUAFiC0tUxJtgrLqM0aLQLZoGxZiKOq7a2toULFzo4OPTv37+qqioyMpI+neqMUqkUV0UeXSoA+IGRWKIg4riys7PLy5Ps/MqaixXqo4WoVAHwgI7E8tqWHXu6FH8aWi0Rx5VUoVIFwD/0a7d+0ulqIQ20SwWrbcTUfwA8Cw90DxrtghVGrBbiyoJYlu3Xr193d65uVCXk0RmVsEQ9gCBign9dd1jogkAHbCiuVCoVz4Nqu386zKcOYA1okyBTrGWKtUKXBYzZSlxpNBqGYaywZ6BhpQqrKQIILmi0C5oErZOtxBXhfYwwd0YTdSxUqgCsEJoErZOtxJW1zZ6CShWA1UKToHWylbiyqnWENRcrUKkCsGZoErRCthJXLMu2n6xdgGJUN6oS8tRHC1GpArBytEkw9nSp0AWBX9lQXAn+7Iop1mJMFYBY0LkEk3Ir0CRoJWxlVgth14XCRBUAYhQe6J50sSLudGnQhB8Jwzx2+jSZN48EBRHxr/IqRrYSV4QQodYRZopr4r7Jxux/AGKU+PIEZubzJP80IcSREJKTQ5KSSFgYiY0VuGS2xyYaAwWsWsX8vSSuYBCdqAJZBSA6yn0fheef/o9NLEuSkgjDCFMgG2YrtavS0lKen11xi/+iUgUgYklJHWxkWcIwaBLkmU3EFf+dLGJPl8ZllIYHundnRW0AsF6dtc1kZfFaDLCRuOIT7VXBahtRqQIQPRPPEaxmHKftsIlnV7wxnFQJWQUgekplpy1+s2bxWhJAXJmL0aRKQhcHAMwkMbGDilRQEAkP578sNg5xZQYmxv+qVKpYdHgFEC+lkmRmcnUsdtBjmgWRJDNT0DLZKJuIK5VKpdFoLHTw2NOlqoTLWFMRQLJoYpWW3jp/ns0riJu6CvNcCMImulowDJOYmGj2w6KrOoANUSpbCAlSuihdHONOlwZF4X95vkm/dmWhMcK0V4XSxdF0rwqlUllWVmaJAgCAIBJfnsAU16CCxT9biSszDr3ielUkvjwevSoAbI3S1TE80B1ri/DPVuLKXAx7VYQHupvxyAAgFjHBXmx1o+ZihdAFsS02EVfmmty2F70qPD09hZ0MHgDMji43HJeBpbB4Jf24Mss6wrQBMCm3IjPKHyuAAAB9Yo3FG/kk/bjqO8O16tEDEACIweKNQhfEhkg/rhiG6fWy90Zr1Zu3YAAgakGjXZQujuhzwRvpxxXpbbdAOqyKTlbb6wbA8PDwTAyAB5AipatjWKA7U6xlqxuFLotNkH5cZWZmhvd8di86rCpotEsfGwD5X7sEAHgTHuiudHFEnwt+SD+uehoY3LCqzCh/rFYFAKbFzPNiirUYNcwD6cdVjxgOq0KvCgDoEn2ClXTxjtAFkT7E1b9hsloA6AVUsPhhE1PcdglLAANAr9EKFua9tTTUrn5tACSWGVbFMEy/fv3Me0wAsDYx87ww762lSTyu7ty5o1arTezANQBiWBUA9FrQaJeg0c5xmOTCkiTeGNjc3NzZGGE0AAKAGcXM81IlXGaKtfh9YiESr121tLR02JHdog2AhujZMcstgOShgmVpEo+r5ubm9hvRAAgAlhAzz4vVNuIJloVIvDGQEGK4eggaAAHAcrgxWPj1YglSrl0ZNcFxQ4Az1zwhgR+m5ORkoYtgQbg6kZLwpZHuXR3GYFmOuONKr9fv2rVrxowZL7zwQvuZZA2XvRd2CLAlnl0dOnTI7Me0Hrg6kZLwpZHuXR0mubAccTcG7t69u6Cg4NSpUzdv3lyxYsWRI0d8fHy4T1mWlcvltAGQKa4RpAEQU9wC2JqYeV7qo4VsdSMmxzEvcdeujhw5Eh0dPXDgwPHjx4eEhKSkpBh+yrKs/ZCRdBEQzAEIAPz4dZILTNNubv3a2tqELkMvVVVVTZs2rbCwUCaTEUK++eab9PT0L774gttB/ca7GvvgQTe/e+zHg8IVEwBsTu3Iqf/yeMrju4+FLkh3TZkyxfqfO4q4MbCoqMjBwYFmFSFEoVAUFRUZ7pC496NZFyvCA2cTskmIAgKAjfqtJXC10AWRFBE3Bg4fPlyv13NvdTrdqFGjjPYJD3Tnt1AAAARPrSxBxHFFw6msrIy+LSkpGTZsmKAlAgAASxFxXMlksrlz5x49epQQUl9fn56evmDBAqELBQAAFiHirhaEkMrKyrCwsAEDBpSXl8+fP3/TJjyjAgCQJnHHFQAA2AgRNwYCAIDtEHFHdhP0ev3u3bvT09Pd3Nyio6NVKpXQJTKn/fv3X7lyhb5WKBT79u0Ttjx9lJeXd/Lkydu3b0+dOnXVqlXcdmncxM6uTgI3sbW19ZNPPsnJybl+/fqECRPWrl07ZcoU+pHY752JS5PAjSOEfPbZZ6dPn7558+bo0aOXLVv2wgsv0O1WfuOkGVemJ2cSu/z8/DFjxgQGBhJC7OzshC5OX/3000/Ozs7Xr183GjYnjZvY2dVJ4Cbq9fq6uroNGzaMGzfu+PHjERERJ06coKuhiv3embg0Cdw4Qoi/v//s2bNHjhz5ww8/vPXWWyNGjKB5bO03rk2K/P398/Ly6OuYmJi4uDhhy2Nea9eu/dvf/iZ0Kcxs06ZNmzZtMtwipZvY/uqkdxMXL1586tQp+lpK967tPy9NejduzZo1f/3rX+lrK79xEnx2VVVVVVdX5+fnR99Onjz55s2bwhbJ7A4ePBgZGfn+++/fuHFD6LJYBG6iuNTW1hYVFXl4eBDJ3TvDS6OkcePq6+vLysrS0tIKCwtp1cr6b5wEGwO7nJxJ7EJCQuRyuVwuz8nJWbp06fHjx2kzhZTgJorLhg0bnnvuuYkTJxLJ3TvDSyMSunEpKSn/+Mc/Ll++rFaraRhb/42TYFx1Z3ImUQsODqYvpk+fXlhYmJaWFh0dLWyRzA43UUTWr19PCImPj6dvpXTvjC6NSOjGqdVqtVpdX1+/YsWKIUOGqNVq679xEmwMtKnJmVxdXauqqoQuhfnhJorFhg0btFrtJ598wv1VLpl71/7SjIj6xlFOTk5TpkwpKCggYrhxEowraU/O1NraWl5eTl+XlJQwDGNtnU3NAjdRFDZv3lxVVZWQkCCXy7mN0rh3HV6aNG6c4VXU1NTk5OSMGzeOiOHGSXNWCwlPzqTX6wMDAx0cHPr3719VVRUZGblu3TqhC9Un8fHxhw8f5t6uWLFi69atRCo3scOrk8ZNrK+v9/f3N9yyc+fORYsWEfHfu84uTRo3Tq/Xz5w5U6/XOzk5VVZWLlq0KC4ujnbKt/IbJ824ompqagYMGGD4x5FkNDQ01NXVubq6dtZMIRm4ieIl1XsnjRvX0NBQW1s7dOjQ9ldhtTdOynEFAACSIeK/DgAAwHYgrgAAQAQQVwAAIAKIKwAAEAHEFQAAiADiCgAARECCcwYC9E52djYd7d+vX7/+/fv7+/u7u7tzn/7hD3+YP3/+nDlzOvt6U1OTvb29UGsgffXVVwEBAdx0q1VVVQzDLFiwoH///oKUB8DsULsC+NVf/vKXAwcOXLly5dKlS998882cOXM2bNjQ1NREP/X19R06dKiJr0dHR58+fZqXknbg9u3b0dHRra2t9O3GjRsvXbqErAIpQVwB/FtAQMCHH364ffv2/fv3nzlzJjc3d8eOHfSjV1555b/+67+4PUtKSrKysvLy8mhCNDU1tbS0NDU11dfXcwlXXl6elZX1448/Gp6iqalJr9fX19efP3+em07U0I8//piVlVVZWWm48fLly+fPn29oaOis5OvWrWttbf30008JISkpKUVFRdY2gw5AH6ExEKBj7u7u69at27p166ZNm+zs7KKjoxctWjR//nxCyJo1a65fvz5u3LiamppBgwYlJCQcPHiwsLCwurr673//u6+v77p1695///38/HwPD4+ysjK9Xn/w4EE3NzdCyOrVq728vHJycjw8PC5cuLB+/Xq1Wk3PWFJSEhUVJZfLPT09f/rpp9jYWJVKVVZWFhkZ+cgjj7i6ur7xxht/+tOfOpxWVSaT/c///M+LL77o6+u7Y8eOvXv3Dhw4kM9/LgCLE3g1YwCrsXbtWqMl6m/fvj127NiLFy+2tbW9/vrrdNXzS5cu+fn5tbS00H24F9wOlFar5V6/8847H374IX0dHh6+dOlSnU7X1tbGMMyECRP0ej396Nlnn921axf3rbq6ura2tgULFnz66ad0y8WLF/39/el3O7R3796xY8e+++67vfoHALBqqF0BdMrZ2ZkQ0tjYaLjxscce0+l0hw4dmjt37vDhwzvrW+Hs7HzhwoW7d++2tbUpFIpbt25xH61cuZLOHzpjxoyWlpbGxkYnJ6fCwkKWZVevXs3t5uTkdOPGjevXr/v7++fm5tKNer0+JydnxowZHZ60urqaEGLYQwRAMhBXAJ2iy9aNHj3acOPw4cM///zzv/zlL7t37x46dOibb765cOHC9t+NiIh4+PDh/PnznZ2d7e3tuU4QhBAu4Qwnw753756dnZ1RC97t27ft7OwOHjzIbZkxY8agQYM6LG12dvbXX3+9f//+3//+988+++yYMWN6fMEAVgxxBdCpEydOeHl5ta+sTJ8+ffr06a2trWlpae+88868efOMVlu4ceNGTk7OP//5T5pMVVVVt2/fNn0uT09PnU5XXV3t6urKbfTw8NDr9du3b+8sojj19fWbNm165513Zs+eHRkZuX79+uPHj4t6hQsAI/hpBjCm1+sLCwtjY2NTU1Pj4uKMPr17925FRQUhRCaTGfYVlMvlJSUl9LVCoWhra6MNgFVVVYcOHerypEqlctKkSTt27KD1sObm5qqqqt/97nePP/74tm3buMpZfn5+h1/fuXPnyJEjX3nlFULIunXr9Ho97SUIIBmoXQH8W2pqampqqr29/aOPPvrUU0+lpaV5e3sb7XPv3r3Q0NBHH3300Ucf/fnnnzdv3kyrVqtWrXr//fc/++yzGTNmJCQkhIaGLly40M/P786dO88//zxtVzQtISFh3bp1AQEBSqWyuLj4yy+/dHNz++STT9avX+/v7z927Njr1697enqmpaUZfZE2A548eZK+lclku3btWrx4cXBwcPvyA4gUlmcE6I3q6ura2tpRo0aZaHBrbm4uLy/nZproppqampqaGqMjNzc337hxw9vb2wrXeAXgB+IKAABEAM+uAABABBBXAAAgAv8PggpY/n7NrQUAAAAASUVORK5CYII=\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57477,"title":"Solve an equation involving primes and fractions","description":"Write a function to find pairs of primes  and  satisfying the equation\r\n\r\nwhere  is an integer. The function should take a number  as input and produce the triples , , and  such that . If there are no solutions, the function should return three empty vectors.\r\nThis problem is adapted from one in the 2012 European Girls’ Math Olympiad. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 146px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 73px; transform-origin: 343px 73px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find pairs of primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e satisfying the equation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 17.5px; text-align: left; transform-origin: 320px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"136\" height=\"35\" alt=\"p/(p+1) + (q+1)/q = 2n/(n+2)\" style=\"width: 136px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 21px; text-align: left; transform-origin: 320px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is an integer. The function should take a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as input and produce the triples \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"18\" alt=\"p \u003c= x\" style=\"width: 38px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. If there are no solutions, the function should return three empty vectors.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis problem is adapted from one in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.egmo2012.org.uk/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e2012 European Girls’ Math Olympiad\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,q,n] = EGMO2012no5(x)\r\n  p = primes(x); q = primes(x); n = p./(p+1) + (q+1)./q; \r\nend","test_suite":"%%\r\nx = 1;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(isempty(p) \u0026\u0026 isempty(q) \u0026\u0026 isempty(n))\r\n\r\n%%\r\nx = 2;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(all(p==2) \u0026\u0026 isequal(q,[5 7]) \u0026\u0026 isequal(n,[28 19]))\r\n\r\n%%\r\nx = 20;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 200;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402 3778 7306 14758 21166 42226 47302 77002 90898 130678 148606 158002];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 2000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 63;\r\nsum_correct = 265170305;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\n\r\n%%\r\nx = 20000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 344;\r\nsum_correct = 150118037395;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2000000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 14873;\r\nsum_correct = 27402595128;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2e8;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 813373;\r\nsum_correct = 152663390088360;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\n\r\n%%\r\nfiletext = fileread('EGMO2012no5.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-30T13:15:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-30T05:04:32.000Z","updated_at":"2025-12-14T08:06:30.000Z","published_at":"2022-12-30T05:05:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find pairs of primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e satisfying the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p/(p+1) + (q+1)/q = 2n/(n+2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{p}{p+1} + \\\\frac{q+1}{q} = \\\\frac{2n}{n+2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer. The function should take a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as input and produce the triples \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p \u0026lt;= x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep \\\\le x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there are no solutions, the function should return three empty vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is adapted from one in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.egmo2012.org.uk/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2012 European Girls’ Math Olympiad\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. 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