Problem 53094. Easy Sequences 51: Positive Gaussian Primes

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>A </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Gaussian_integer#Gaussian_primes\"><w:r><w:t>Gaussian Prime</w:t></w:r></w:hyperlink><w:r><w:t> is a gaussian integer that cannot be decomposed as product of two non-unit gaussian integers (the complex units being: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>1</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>-1</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>i</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>-i</w:t></w:r></w:customXml><w:r><w:t>). We say that a gaussian prime </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>p+qi</w:t></w:r></w:customXml><w:r><w:t>, is positive, if </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>p&gt;0</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>q\\ge0</w:t></w:r></w:customXml><w:r><w:t>. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Write a function that counts the number of elements of set, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>S_{GP+}</w:t></w:r></w:customXml><w:r><w:t>,</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>of all positive gaussian primes </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>p+qi</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, such that </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>p</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>q</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> are both </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\le n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n=10</w:t></w:r></w:customXml><w:r><w:t>, the complete set of positive gaussian primes are as follows: </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>S_{GP+} = \\{\\ 3,\\ 7,\\ 1+i,\\ 1+2i,\\ 1+4i,\\ 1+6i,\\ 1+10i,\\ 2+i,\\ 2+3i,\\ 2+5i,\\ 2+7i,\\ 3+2i,\\ 3+8i,\\\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 3+10i\\ 4+i,\\ 4+5i,\\ 4+9i,\\ 5+2i,\\ 5+4i,\\ 5+6i,\\ 5+8i,\\ 6+i,\\ 6+5i,\\ 7+2i,\\ 7+8i,\\\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 7+10i,\\ 8+3i,\\ 8+5i,\\ 8+7i,\\ 9+4i,\\ 9+10i,\\ 10+i,\\ 10+3i,\\ 10+7i, 10+9i\\ \\}</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Therefore, for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n=10</w:t></w:r></w:customXml><w:r><w:t> the function should return </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>35</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div 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; "><div style="block-size: 226.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 113.25px; transform-origin: 407px 113.25px; vertical-align: baseline; "><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.5px 8px; transform-origin: 6.5px 8px; unicode-bidi: normal; ">A <a target='_blank' href = "https://en.wikipedia.org/wiki/Gaussian_integer#Gaussian_primes">Gaussian Prime</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 316px 8px; transform-origin: 316px 8px; unicode-bidi: normal; "> is a gaussian integer that cannot be decomposed as product of two non-unit gaussian integers (the complex units being: 1<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; ">, <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACoAAAAkCAYAAAD/yagrAAAAhUlEQVRYhe3XUQmAMBhF4ZPFAhYwgQlsYIM1sIsRDGMGK8wHBwoqCv5uE+8H99nDGMJARCS2MnXAlQYYgT51yJmaJdCHZRnaAW1Y1qFbCrWmUGsKtWYSWhksSqh/uClW6PBwdz7+rzsag0KtKdSSYw0dgSJtzl7DcoJHvzTHB95PIiLyshkwkls8t0LQOAAAAABJRU5ErkJggg==" style="width: 21px; height: 18px;" width="21" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; ">, i<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; "> and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACMAAAAkCAYAAAAD3IPhAAAAxElEQVRYhe2WUQ3DIBBAn4c6wEANoGAKcICDOsBCNUxCxVQDFroPYHQLfGxdel1yL7mEpgl5Oe4OQFGU/8YAo7QEgAW2HE7YhYkqswi7MGSJlYsclXJJDKmLHBBINRMkZTypaEsn3aRkCgtVZhB2IfLFfLE/iHdGalamT2S2gxEbe/rd/5Zsl+Vg3Dt79kRPp2SlJXoq+5vaC7u83NRG2OVZL2v+tsAsJVOyEkgtHhEcemXYrXkt+o5xpKOapUUURVEuwwPb9lEUVsiTiwAAAABJRU5ErkJggg==" style="width: 17.5px; height: 18px;" width="17.5" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 102px 8px; transform-origin: 102px 8px; unicode-bidi: normal; ">). We say that a gaussian prime <img src="data:image/png;base64,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" style="width: 40.5px; height: 18px;" width="40.5" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.5px 8px; transform-origin: 44.5px 8px; unicode-bidi: normal; ">, is positive, if <img src="data:image/png;base64,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" style="width: 38px; height: 18px;" width="38" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; "> and <img src="data:image/png;base64,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" style="width: 36.5px; height: 18px;" width="36.5" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; ">. </div><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 209px 8px; transform-origin: 209px 8px; unicode-bidi: normal; ">Write a function that counts the number of elements of set, <img src="data:image/png;base64,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" style="width: 31px; height: 20px;" width="31" height="20"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-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; ">,<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 109px 8px; transform-origin: 109px 8px; unicode-bidi: normal; ">of all positive gaussian primes <img src="data:image/png;base64,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" style="width: 40.5px; height: 18px;" width="40.5" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; ">, such that p<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17px 8px; transform-origin: 17px 8px; unicode-bidi: normal; "> and q<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.5px 8px; transform-origin: 33.5px 8px; unicode-bidi: normal; "> are both <img src="data:image/png;base64,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" style="width: 25px; height: 18px;" width="25" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-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; ">.</div><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-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; ">For example, for <img src="data:image/png;base64,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" style="width: 44px; height: 18px;" width="44" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 240.5px 8px; transform-origin: 240.5px 8px; unicode-bidi: normal; ">, the complete set of positive gaussian primes are as follows: </div><div style="block-size: 63.5px; 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 31.75px; text-align: left; transform-origin: 384px 31.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-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; "> <img src="data:image/png;base64,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" style="width: 610px; height: 63.5px;" width="610" height="63.5"></div><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; ">Therefore, for <img src="data:image/png;base64,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" style="width: 44px; height: 18px;" width="44" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 85px 8px; transform-origin: 85px 8px; unicode-bidi: normal; "> the function should return <img src="data:image/png;base64,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" style="width: 18px; height: 18px;" width="18" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-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; ">.</div></div></div>

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Last Solution submitted on Mar 19, 2023

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Michael Sisco on 25 Dec 2021

I have a solution that works and the entire test suite can run in 18 seconds on my laptop, but takes a little over 45 seconds to run on the server, so the server times out on the test cases.

I'm stumped trying to figure out how I can optimize this code any further.

Michael Sisco on 25 Dec 2021

I just re-ran the solution and this time it worked. I must have gotten a slow core the first time I ran it. ;-)

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Problem 53094. Easy Sequences 51: Positive Gaussian Primes

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Problem 53094. Easy Sequences 51: Positive Gaussian Primes

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