{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":1409,"title":"Continued fractions","description":"Find a \u003chttp://en.wikipedia.org/wiki/Continued_fraction continued fraction\u003e approximation of x.","description_html":"\u003cp\u003eFind a \u003ca href = \"http://en.wikipedia.org/wiki/Continued_fraction\"\u003econtinued fraction\u003c/a\u003e approximation of x.\u003c/p\u003e","function_template":"function y = contfractions(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = pi;\r\ny_correct = '3 + 1/(7 + 1/(16))';\r\nassert(isequal(contfractions(x),y_correct))\r\n\r\n%%\r\nx = exp(1);\r\ny_correct = '3 + 1/(-4 + 1/(2 + 1/(5 + 1/(-2 + 1/(-7)))))';\r\nassert(isequal(contfractions(x),y_correct))\r\n\r\n%%\r\nx = sqrt(2);\r\ny_correct = '1 + 1/(2 + 1/(2 + 1/(2 + 1/(2 + 1/(2 + 1/(2 + 1/(2 + 1/(2))))))))';\r\nassert(isequal(contfractions(x),y_correct))\r\n\r\n%%\r\nx = (exp(1)-1)^-1;\r\ny_correct = '1 + 1/(-2 + 1/(-3 + 1/(2 + 1/(5 + 1/(-2 + 1/(-7 + 1/(2)))))))';\r\nassert(isequal(contfractions(x),y_correct))\r\n\r\n%%\r\nfiletext = fileread('contfractions.m');\r\nassert(isempty(strfind(filetext, 'switch')))\r\nassert(isempty(strfind(filetext, 'case')))","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":810,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":73,"test_suite_updated_at":"2013-04-07T19:37:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-04-02T00:27:11.000Z","updated_at":"2013-04-07T19:37:17.000Z","published_at":"2013-04-02T00:28:01.000Z","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\u003eFind 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/Continued_fraction\\\"\u003e\u003cw:r\u003e\u003cw:t\u003econtinued fraction\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e approximation of x.\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":55330,"title":"Convert Periodic Continued Fraction to Fractional Radical Representation","description":"Every periodic continued fraction can be prepresented by a number of the form  where p, q, and d are all integers with d\u003e0, , and d not a perfect square. Given the cointued fraction sequence, both the beginning sequence and cyclic part of the sequence [front, cyclic], output the unique p, q, and d (in reduced form). p and q can both be negative.","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: 63.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.75px; transform-origin: 407px 31.75px; 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 31.75px; text-align: left; transform-origin: 384px 31.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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=\"\"\u003eEvery periodic continued fraction can be prepresented by a number of the form \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"76.5\" height=\"21\" style=\"width: 76.5px; 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 where p, q, and d are all integers with d\u0026gt;0, \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\" 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and d not a perfect square. Given the cointued fraction sequence, both the beginning sequence and cyclic part of the sequence [front, cyclic], output the unique p, q, and d (in reduced form). p and q can both be negative.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Z=reverseContinuedFraction(Front,Cyclic)\r\n  Z=[p,q,d];\r\nend","test_suite":"%%\r\nf=[1 5];c=2;\r\nZc=[-18 -14 2];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc))\r\n%%\r\nf=[1 7 11];c=[1 1 5 7 9];\r\nZc=[206107,181290,585229];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc));\r\n%%\r\nf=[2 4 6 8 10];c=[1 3 5 7 9 11];\r\nZc=[-115159849,-51405893,465920];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc));\r\n%%\r\nf=[1 3 5 7 9];c=[2 4 6 8 10];\r\nZc=[-74808676,-56971998,5832226];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc));\r\n%%\r\nf=ones(1,4);c=[2 3 4];\r\nZc=[459,302,1093];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc));\r\n%%\r\nf=ones(1,8);c=[2 3 4];\r\nZc=[20943,12962,1093];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc));\r\n%%\r\nf=[1 8 9 7 7 7 4];c=[6 1 1 1 1];\r\nZc=[33600341839,29911810179,13];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc));\r\n%%\r\nrng(1);\r\nz=0;\r\nfor k=1:100\r\n    f=randperm(20,5);\r\n    c=randperm(10,6);\r\n    Z=reverseContinuedFraction(f,c);\r\n    z=z+sum(num2str(Z(1))-'0')+sum(num2str(Z(2))-'0')+sum(num2str(Z(3))-'0');\r\nend\r\nZc=13516;\r\nassert(isequal(z,Zc));\r\n%%\r\nrng(5);\r\nz=0;\r\nfor k=1:1000\r\n    f=randperm(20,5);\r\n    c=randperm(10,6);\r\n    Z=reverseContinuedFraction(f,c);\r\n    z=z+sum(num2str(Z(1))-'0')+sum(num2str(Z(2))-'0')+sum(num2str(Z(3))-'0');\r\nend\r\nZc=138319;\r\nassert(isequal(z,Zc));","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":145982,"edited_by":145982,"edited_at":"2022-09-01T22:16:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":"2022-09-01T22:16:01.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-20T17:36:46.000Z","updated_at":"2022-09-01T22:16:01.000Z","published_at":"2022-08-20T17:36:46.000Z","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 periodic continued fraction can be prepresented by a number of the form \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(p + \\\\sqrt{d})/q\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e where p, q, and d are all integers with d\u0026gt;0, \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\u003eq \\\\neq 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and d not a perfect square. Given the cointued fraction sequence, both the beginning sequence and cyclic part of the sequence [front, cyclic], output the unique p, q, and d (in reduced form). p and q can both be negative.\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":51580,"title":"Construct a continued fraction for a square root","description":null,"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: 483.917px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 241.958px; transform-origin: 407px 241.958px; 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: 190.983px 7.91667px; transform-origin: 190.983px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNumbers can be expressed as continued fractions of the form\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85.3333px; 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: 384px 42.6667px; text-align: left; transform-origin: 384px 42.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-69px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = a_0 + 1/(a_1 + 1/(a_2 + 1/(a_3 + 1/...)))\" style=\"width: 160.5px; height: 85.5px;\" width=\"160.5\" height=\"85.5\"\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: 141.192px 7.91667px; transform-origin: 141.192px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSome continued fractions—such as those for \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);\"\u003ee\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 13.6167px 7.91667px; transform-origin: 13.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand \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);\"\u003eπ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.033px 7.91667px; transform-origin: 206.033px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e--continue forever without a discernable pattern in the coefficients, while the coefficients of continued fractions for square roots eventually repeat. For example, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85.3333px; 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: 384px 42.6667px; text-align: left; transform-origin: 384px 42.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-69px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sqrt(2) = 1+(1/(2+1/(2+1/(2+1/...))))\" style=\"width: 153px; height: 85.5px;\" width=\"153\" height=\"85.5\"\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: 6.225px 7.91667px; transform-origin: 6.225px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eor\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 103px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 51.5px; text-align: left; transform-origin: 384px 51.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-87px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sqrt(14) = 3+1/(1+1/(2+1/(1+1/(6+1/...))))\" style=\"width: 185px; height: 103px;\" width=\"185\" height=\"103\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 10.625px; text-align: left; transform-origin: 384px 10.625px; 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: 228.192px 7.91667px; transform-origin: 228.192px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a non-square integer and returns the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABsAAAAoCAYAAAAPOoFWAAABC0lEQVRYhe2VTRGDMBBGnwcc1AAGogAFOMABDrCABiTEQy2gAQv0wO6Q0oSkkB46kzeTA1nYb3/YBAqFQqHwN9RAB/SAkT0jz3VOEQvMImaAEXgCq6xHDqFWnM1AdbCtju2nQq7YcFeocZwZj/0RsSdTAYs4mgLvaNYL/qyT6dmjDv1lVuw24qOLiWlWIUfGCaa/I5biyBLPPAm3hI3H3rFnnrVfR7GWbQwm3ss8sldBT5RJ9k+pHTErkVfiQOdNMxtlHf9YDThp/jRyd03sJVsO+6HvfW3w0kiEHZ/nXuzwXdiqkOW8PEPbEBqbrCQPcw50Bmu+6NlV9JZoyXAbxNALdeDmwBcKhWu8ANZGYx8ObIHOAAAAAElFTkSuQmCC\" style=\"width: 13.5px; height: 20px;\" width=\"13.5\" 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: 74.2917px 7.91667px; transform-origin: 74.2917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e until the values repeat. \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: 135.758px 7.91667px; transform-origin: 135.758px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem celebrates my finally cracking \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/groups/25/problems/1215\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 1215\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: 178.892px 7.91667px; transform-origin: 178.892px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by James. If you struggle with Test 8, as I did, remember that MATLAB cannot represent decimals with infinite precision.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = sqrtContinuedFraction(n)\r\n  a = f(n);\r\nend","test_suite":"%%\r\nn = 2;\r\na_correct = [1 2];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 3;\r\na_correct = [1 1 2];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 7;\r\na_correct = [2 1 1 1 4];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 14;\r\na_correct = [3 1 2 1 6];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 29;\r\na_correct = [5 2 1 1 2 10];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 61;\r\na_correct = [7 1 4 3 1 2 2 1 3 4 1 14];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 73;\r\na_correct = [8 1 1 5 5 1 1 16];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 151;\r\na_correct = [12 3 2 7 1 3 4 1 1 1 11 1 1 1 4 3 1 7 2 3 24];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 513;\r\na_correct = [22 1 1 1 5 1 4 5 2 5 4 1 5 1 1 1 44];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 777;\r\na_correct = [27 1 6 1 54];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 1201;\r\na_correct = [34 1 1 1 9 4 4 2 1 1 1 7 13 1 2 1 2 1 1 4 22 1 7 1 2 2 2 2 1 7 1 22 4 1 1 2 1 2 1 13 7 1 1 1 2 4 4 9 1 1 1 68];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 3456;\r\na_correct = [58 1 3 1 2 2 6 1 12 5 29 5 12 1 6 2 2 1 3 1 116];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 8888;\r\na_correct = [94 3 1 1 1 1 1 3 188];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 10001;\r\na_correct = [100 200];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 42867;\r\na_correct = [207 23 414];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 100001;\r\na_correct = [316 4 2 1 3 2 7 2 6 1 2 1 1 4 3 1 16 3 39 4 1 21 126 2 4 8 2 3 1 3 2 2 2 1 9 5 1 2 3 15 7 1 5 3 1 3 1 1 1 1 24 1 2 4 1 1 1 1 11 3 13 7 1 1 5 15 1 1 1 2 2 2 1 5 1 18 1 10 1 1 4 1 1 6 9 3 2 15 2 1 1 1 2 9 1 78 6 1 1 32 1 2 1 56 1 2 1 32 1 1 6 78 1 9 2 1 1 1 2 15 2 3 9 6 1 1 4 1 1 10 1 18 1 5 1 2 2 2 1 1 1 15 5 1 1 7 13 3 11 1 1 1 1 4 2 1 24 1 1 1 1 3 1 3 5 1 7 15 3 2 1 5 9 1 2 2 2 3 1 3 2 8 4 2 126 21 1 4 39 3 16 1 3 4 1 1 2 1 6 2 7 2 3 1 2 4 632];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = randi(50)^2+1;\r\na = sqrtContinuedFraction(n);\r\nb = repmat(flip(a(2:end)),1,25);\r\ny = 0;\r\nfor k = 1:length(b)\r\n    y = 1/(b(k)+y); \r\nend\r\nassert(abs(y+a(1)-sqrt(n))\u003c1e-13)","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-30T02:08:02.000Z","updated_at":"2026-03-15T12:36:12.000Z","published_at":"2021-04-30T02:24:34.000Z","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:t\u003eNumbers can be expressed as continued fractions of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"x = a_0 + 1/(a_1 + 1/(a_2 + 1/(a_3 + 1/...)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex =a_0+\\\\frac{1}{a_1+\\\\frac{1}{a_2+\\\\frac{1}{a_3+\\\\frac{1}{\\\\ddots}\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\u003eSome continued fractions—such as those 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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"e\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\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\u003cw:r\u003e\u003cw:t\u003eand \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=\\\"pi\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e--continue forever without a discernable pattern in the coefficients, while the coefficients of continued fractions for square roots eventually repeat. For 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:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sqrt(2) = 1+(1/(2+1/(2+1/(2+1/...))))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sqrt{2} =1+\\\\frac{1}{2+\\\\frac{1}{2+\\\\frac{1}{2+\\\\frac{1}{\\\\ddots}\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\u003eor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"sqrt(14) = 3+1/(1+1/(2+1/(1+1/(6+1/...))))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sqrt{14} =3+\\\\frac{1}{1+\\\\frac{1}{2+\\\\frac{1}{1+\\\\frac{1}{6+\\\\frac{1}{\\\\ddots}\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 non-square integer and returns the values 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\u003ea_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e until the values repeat. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 celebrates my finally cracking \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/25/problems/1215\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 1215\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e by James. If you struggle with Test 8, as I did, remember that MATLAB cannot represent decimals with infinite precision.\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":1409,"title":"Continued fractions","description":"Find a \u003chttp://en.wikipedia.org/wiki/Continued_fraction continued fraction\u003e approximation of x.","description_html":"\u003cp\u003eFind a \u003ca href = \"http://en.wikipedia.org/wiki/Continued_fraction\"\u003econtinued fraction\u003c/a\u003e approximation of x.\u003c/p\u003e","function_template":"function y = contfractions(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = pi;\r\ny_correct = '3 + 1/(7 + 1/(16))';\r\nassert(isequal(contfractions(x),y_correct))\r\n\r\n%%\r\nx = exp(1);\r\ny_correct = '3 + 1/(-4 + 1/(2 + 1/(5 + 1/(-2 + 1/(-7)))))';\r\nassert(isequal(contfractions(x),y_correct))\r\n\r\n%%\r\nx = sqrt(2);\r\ny_correct = '1 + 1/(2 + 1/(2 + 1/(2 + 1/(2 + 1/(2 + 1/(2 + 1/(2 + 1/(2))))))))';\r\nassert(isequal(contfractions(x),y_correct))\r\n\r\n%%\r\nx = (exp(1)-1)^-1;\r\ny_correct = '1 + 1/(-2 + 1/(-3 + 1/(2 + 1/(5 + 1/(-2 + 1/(-7 + 1/(2)))))))';\r\nassert(isequal(contfractions(x),y_correct))\r\n\r\n%%\r\nfiletext = fileread('contfractions.m');\r\nassert(isempty(strfind(filetext, 'switch')))\r\nassert(isempty(strfind(filetext, 'case')))","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":810,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":73,"test_suite_updated_at":"2013-04-07T19:37:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-04-02T00:27:11.000Z","updated_at":"2013-04-07T19:37:17.000Z","published_at":"2013-04-02T00:28:01.000Z","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\u003eFind 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/Continued_fraction\\\"\u003e\u003cw:r\u003e\u003cw:t\u003econtinued fraction\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e approximation of x.\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":55330,"title":"Convert Periodic Continued Fraction to Fractional Radical Representation","description":"Every periodic continued fraction can be prepresented by a number of the form  where p, q, and d are all integers with d\u003e0, , and d not a perfect square. Given the cointued fraction sequence, both the beginning sequence and cyclic part of the sequence [front, cyclic], output the unique p, q, and d (in reduced form). p and q can both be negative.","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: 63.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.75px; transform-origin: 407px 31.75px; 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 31.75px; text-align: left; transform-origin: 384px 31.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-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=\"\"\u003eEvery periodic continued fraction can be prepresented by a number of the form \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"76.5\" height=\"21\" style=\"width: 76.5px; 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 where p, q, and d are all integers with d\u0026gt;0, \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\" 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and d not a perfect square. Given the cointued fraction sequence, both the beginning sequence and cyclic part of the sequence [front, cyclic], output the unique p, q, and d (in reduced form). p and q can both be negative.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Z=reverseContinuedFraction(Front,Cyclic)\r\n  Z=[p,q,d];\r\nend","test_suite":"%%\r\nf=[1 5];c=2;\r\nZc=[-18 -14 2];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc))\r\n%%\r\nf=[1 7 11];c=[1 1 5 7 9];\r\nZc=[206107,181290,585229];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc));\r\n%%\r\nf=[2 4 6 8 10];c=[1 3 5 7 9 11];\r\nZc=[-115159849,-51405893,465920];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc));\r\n%%\r\nf=[1 3 5 7 9];c=[2 4 6 8 10];\r\nZc=[-74808676,-56971998,5832226];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc));\r\n%%\r\nf=ones(1,4);c=[2 3 4];\r\nZc=[459,302,1093];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc));\r\n%%\r\nf=ones(1,8);c=[2 3 4];\r\nZc=[20943,12962,1093];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc));\r\n%%\r\nf=[1 8 9 7 7 7 4];c=[6 1 1 1 1];\r\nZc=[33600341839,29911810179,13];\r\nassert(isequal(reverseContinuedFraction(f,c),Zc));\r\n%%\r\nrng(1);\r\nz=0;\r\nfor k=1:100\r\n    f=randperm(20,5);\r\n    c=randperm(10,6);\r\n    Z=reverseContinuedFraction(f,c);\r\n    z=z+sum(num2str(Z(1))-'0')+sum(num2str(Z(2))-'0')+sum(num2str(Z(3))-'0');\r\nend\r\nZc=13516;\r\nassert(isequal(z,Zc));\r\n%%\r\nrng(5);\r\nz=0;\r\nfor k=1:1000\r\n    f=randperm(20,5);\r\n    c=randperm(10,6);\r\n    Z=reverseContinuedFraction(f,c);\r\n    z=z+sum(num2str(Z(1))-'0')+sum(num2str(Z(2))-'0')+sum(num2str(Z(3))-'0');\r\nend\r\nZc=138319;\r\nassert(isequal(z,Zc));","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":145982,"edited_by":145982,"edited_at":"2022-09-01T22:16:01.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":"2022-09-01T22:16:01.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-08-20T17:36:46.000Z","updated_at":"2022-09-01T22:16:01.000Z","published_at":"2022-08-20T17:36:46.000Z","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 periodic continued fraction can be prepresented by a number of the form \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(p + \\\\sqrt{d})/q\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e where p, q, and d are all integers with d\u0026gt;0, \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\u003eq \\\\neq 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and d not a perfect square. Given the cointued fraction sequence, both the beginning sequence and cyclic part of the sequence [front, cyclic], output the unique p, q, and d (in reduced form). p and q can both be negative.\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":51580,"title":"Construct a continued fraction for a square root","description":null,"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: 483.917px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 241.958px; transform-origin: 407px 241.958px; 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: 190.983px 7.91667px; transform-origin: 190.983px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNumbers can be expressed as continued fractions of the form\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85.3333px; 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: 384px 42.6667px; text-align: left; transform-origin: 384px 42.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-69px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = a_0 + 1/(a_1 + 1/(a_2 + 1/(a_3 + 1/...)))\" style=\"width: 160.5px; height: 85.5px;\" width=\"160.5\" height=\"85.5\"\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: 141.192px 7.91667px; transform-origin: 141.192px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSome continued fractions—such as those for \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);\"\u003ee\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-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 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\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: 13.6167px 7.91667px; transform-origin: 13.6167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand \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);\"\u003eπ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.033px 7.91667px; transform-origin: 206.033px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e--continue forever without a discernable pattern in the coefficients, while the coefficients of continued fractions for square roots eventually repeat. For example, \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85.3333px; 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: 384px 42.6667px; text-align: left; transform-origin: 384px 42.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-69px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sqrt(2) = 1+(1/(2+1/(2+1/(2+1/...))))\" style=\"width: 153px; height: 85.5px;\" width=\"153\" height=\"85.5\"\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: 6.225px 7.91667px; transform-origin: 6.225px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eor\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 103px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 51.5px; text-align: left; transform-origin: 384px 51.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-87px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"sqrt(14) = 3+1/(1+1/(2+1/(1+1/(6+1/...))))\" style=\"width: 185px; height: 103px;\" width=\"185\" height=\"103\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; 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 10.625px; text-align: left; transform-origin: 384px 10.625px; 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: 228.192px 7.91667px; transform-origin: 228.192px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a non-square integer and returns the values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABsAAAAoCAYAAAAPOoFWAAABC0lEQVRYhe2VTRGDMBBGnwcc1AAGogAFOMABDrCABiTEQy2gAQv0wO6Q0oSkkB46kzeTA1nYb3/YBAqFQqHwN9RAB/SAkT0jz3VOEQvMImaAEXgCq6xHDqFWnM1AdbCtju2nQq7YcFeocZwZj/0RsSdTAYs4mgLvaNYL/qyT6dmjDv1lVuw24qOLiWlWIUfGCaa/I5biyBLPPAm3hI3H3rFnnrVfR7GWbQwm3ss8sldBT5RJ9k+pHTErkVfiQOdNMxtlHf9YDThp/jRyd03sJVsO+6HvfW3w0kiEHZ/nXuzwXdiqkOW8PEPbEBqbrCQPcw50Bmu+6NlV9JZoyXAbxNALdeDmwBcKhWu8ANZGYx8ObIHOAAAAAElFTkSuQmCC\" style=\"width: 13.5px; height: 20px;\" width=\"13.5\" 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: 74.2917px 7.91667px; transform-origin: 74.2917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e until the values repeat. \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: 135.758px 7.91667px; transform-origin: 135.758px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem celebrates my finally cracking \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/groups/25/problems/1215\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003eCody Problem 1215\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: 178.892px 7.91667px; transform-origin: 178.892px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e by James. If you struggle with Test 8, as I did, remember that MATLAB cannot represent decimals with infinite precision.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = sqrtContinuedFraction(n)\r\n  a = f(n);\r\nend","test_suite":"%%\r\nn = 2;\r\na_correct = [1 2];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 3;\r\na_correct = [1 1 2];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 7;\r\na_correct = [2 1 1 1 4];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 14;\r\na_correct = [3 1 2 1 6];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 29;\r\na_correct = [5 2 1 1 2 10];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 61;\r\na_correct = [7 1 4 3 1 2 2 1 3 4 1 14];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 73;\r\na_correct = [8 1 1 5 5 1 1 16];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 151;\r\na_correct = [12 3 2 7 1 3 4 1 1 1 11 1 1 1 4 3 1 7 2 3 24];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 513;\r\na_correct = [22 1 1 1 5 1 4 5 2 5 4 1 5 1 1 1 44];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 777;\r\na_correct = [27 1 6 1 54];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 1201;\r\na_correct = [34 1 1 1 9 4 4 2 1 1 1 7 13 1 2 1 2 1 1 4 22 1 7 1 2 2 2 2 1 7 1 22 4 1 1 2 1 2 1 13 7 1 1 1 2 4 4 9 1 1 1 68];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 3456;\r\na_correct = [58 1 3 1 2 2 6 1 12 5 29 5 12 1 6 2 2 1 3 1 116];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 8888;\r\na_correct = [94 3 1 1 1 1 1 3 188];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 10001;\r\na_correct = [100 200];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 42867;\r\na_correct = [207 23 414];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = 100001;\r\na_correct = [316 4 2 1 3 2 7 2 6 1 2 1 1 4 3 1 16 3 39 4 1 21 126 2 4 8 2 3 1 3 2 2 2 1 9 5 1 2 3 15 7 1 5 3 1 3 1 1 1 1 24 1 2 4 1 1 1 1 11 3 13 7 1 1 5 15 1 1 1 2 2 2 1 5 1 18 1 10 1 1 4 1 1 6 9 3 2 15 2 1 1 1 2 9 1 78 6 1 1 32 1 2 1 56 1 2 1 32 1 1 6 78 1 9 2 1 1 1 2 15 2 3 9 6 1 1 4 1 1 10 1 18 1 5 1 2 2 2 1 1 1 15 5 1 1 7 13 3 11 1 1 1 1 4 2 1 24 1 1 1 1 3 1 3 5 1 7 15 3 2 1 5 9 1 2 2 2 3 1 3 2 8 4 2 126 21 1 4 39 3 16 1 3 4 1 1 2 1 6 2 7 2 3 1 2 4 632];\r\nassert(isequal(sqrtContinuedFraction(n),a_correct))\r\n\r\n%%\r\nn = randi(50)^2+1;\r\na = sqrtContinuedFraction(n);\r\nb = repmat(flip(a(2:end)),1,25);\r\ny = 0;\r\nfor k = 1:length(b)\r\n    y = 1/(b(k)+y); \r\nend\r\nassert(abs(y+a(1)-sqrt(n))\u003c1e-13)","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-30T02:08:02.000Z","updated_at":"2026-03-15T12:36:12.000Z","published_at":"2021-04-30T02:24:34.000Z","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:t\u003eNumbers can be expressed as continued fractions of the form\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"x = a_0 + 1/(a_1 + 1/(a_2 + 1/(a_3 + 1/...)))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex =a_0+\\\\frac{1}{a_1+\\\\frac{1}{a_2+\\\\frac{1}{a_3+\\\\frac{1}{\\\\ddots}\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\u003eSome continued fractions—such as those 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\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"e\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ee\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\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\u003cw:r\u003e\u003cw:t\u003eand \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=\\\"pi\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e--continue forever without a discernable pattern in the coefficients, while the coefficients of continued fractions for square roots eventually repeat. For 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:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"sqrt(2) = 1+(1/(2+1/(2+1/(2+1/...))))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sqrt{2} =1+\\\\frac{1}{2+\\\\frac{1}{2+\\\\frac{1}{2+\\\\frac{1}{\\\\ddots}\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\u003eor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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=\\\"sqrt(14) = 3+1/(1+1/(2+1/(1+1/(6+1/...))))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\sqrt{14} =3+\\\\frac{1}{1+\\\\frac{1}{2+\\\\frac{1}{1+\\\\frac{1}{6+\\\\frac{1}{\\\\ddots}\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 non-square integer and returns the values 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\u003ea_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e until the values repeat. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\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 celebrates my finally cracking \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/25/problems/1215\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 1215\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e by James. If you struggle with Test 8, as I did, remember that MATLAB cannot represent decimals with infinite precision.\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\"}]}"}],"term":"tag:\"continued fractions\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"continued 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