{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-07-05T00:54:32.000Z","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":"2026-07-05T00:00:00.000Z","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":42938,"title":"Project Euler: Problem 18, Maximum path sum I","description":"By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.\r\n\r\n       3*\r\n     7*  4\r\n   2   4*  6\r\n 8   5   9*  3\r\n \r\n3 + 7 + 4 + 9 = 23\r\n\r\nFind the maximum total from top to bottom of a given triangle.\r\n","description_html":"\u003cp\u003eBy starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.\u003c/p\u003e\u003cpre\u003e       3*\r\n     7*  4\r\n   2   4*  6\r\n 8   5   9*  3\u003c/pre\u003e\u003cp\u003e3 + 7 + 4 + 9 = 23\u003c/p\u003e\u003cp\u003eFind the maximum total from top to bottom of a given triangle.\u003c/p\u003e","function_template":"function s = maxPathSum(tr)\r\n    % tr: lower triangular matrix\r\n  s = inf;\r\nend","test_suite":"%%\r\nx = [3 0 0 0\r\n  7 4 0 0\r\n  2 4 6 0\r\n  8 5 9 3];\r\nassert(isequal(maxPathSum(x),23))\r\n\r\n%%\r\nassert(isequal(maxPathSum(tril(magic(10))),891))\r\n\r\n%%\r\nassert(isequal(maxPathSum(tril(magic(100)^2)),251716502500))\r\n\r\n%%\r\nassert(isequal(maxPathSum(tril(mod(magic(1000),997))),741570))\r\n\r\n%%\r\nassert(isequal(maxPathSum(tril(gallery('integerdata',1e4,5e3,4))),37455089))","published":true,"deleted":false,"likes_count":4,"comments_count":2,"created_by":85274,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":149,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-08-30T10:52:35.000Z","updated_at":"2026-06-15T07:02:49.000Z","published_at":"2016-08-30T10:53:42.000Z","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\u003eBy starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.\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[       3*\\n     7*  4\\n   2   4*  6\\n 8   5   9*  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\u003e3 + 7 + 4 + 9 = 23\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\u003eFind the maximum total from top to bottom of a given triangle.\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\"}]}"}],"problem_search":{"problems":[{"id":42938,"title":"Project Euler: Problem 18, Maximum path sum I","description":"By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.\r\n\r\n       3*\r\n     7*  4\r\n   2   4*  6\r\n 8   5   9*  3\r\n \r\n3 + 7 + 4 + 9 = 23\r\n\r\nFind the maximum total from top to bottom of a given triangle.\r\n","description_html":"\u003cp\u003eBy starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.\u003c/p\u003e\u003cpre\u003e       3*\r\n     7*  4\r\n   2   4*  6\r\n 8   5   9*  3\u003c/pre\u003e\u003cp\u003e3 + 7 + 4 + 9 = 23\u003c/p\u003e\u003cp\u003eFind the maximum total from top to bottom of a given triangle.\u003c/p\u003e","function_template":"function s = maxPathSum(tr)\r\n    % tr: lower triangular matrix\r\n  s = inf;\r\nend","test_suite":"%%\r\nx = [3 0 0 0\r\n  7 4 0 0\r\n  2 4 6 0\r\n  8 5 9 3];\r\nassert(isequal(maxPathSum(x),23))\r\n\r\n%%\r\nassert(isequal(maxPathSum(tril(magic(10))),891))\r\n\r\n%%\r\nassert(isequal(maxPathSum(tril(magic(100)^2)),251716502500))\r\n\r\n%%\r\nassert(isequal(maxPathSum(tril(mod(magic(1000),997))),741570))\r\n\r\n%%\r\nassert(isequal(maxPathSum(tril(gallery('integerdata',1e4,5e3,4))),37455089))","published":true,"deleted":false,"likes_count":4,"comments_count":2,"created_by":85274,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":149,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-08-30T10:52:35.000Z","updated_at":"2026-06-15T07:02:49.000Z","published_at":"2016-08-30T10:53:42.000Z","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\u003eBy starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.\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[       3*\\n     7*  4\\n   2   4*  6\\n 8   5   9*  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\u003e3 + 7 + 4 + 9 = 23\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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