{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","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":"2026-05-26T00:00:00.000Z","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":1289,"title":"Evaluating continued fractions","description":"Given row vector \r\n\r\n   c=[c0 c1 c2 c3 ...]\r\n\r\nevaluate the continued fraction\r\n\r\n   x=c0+1/(c1+1/(c2+1/(c3+...)))\r\n\r\nIf c is a matrix, return column vector x in which x(i) is the solution for row i of c.","description_html":"\u003cp\u003eGiven row vector\u003c/p\u003e\u003cpre\u003e   c=[c0 c1 c2 c3 ...]\u003c/pre\u003e\u003cp\u003eevaluate the continued fraction\u003c/p\u003e\u003cpre\u003e   x=c0+1/(c1+1/(c2+1/(c3+...)))\u003c/pre\u003e\u003cp\u003eIf c is a matrix, return column vector x in which x(i) is the solution for row i of c.\u003c/p\u003e","function_template":"function x=contfrac(c)\r\nx=sum(c,2);\r\n","test_suite":"%%\r\nc=ones(1,40);\r\nx=(1+sqrt(5))/2;\r\ny=contfrac(c);\r\nassert(abs(y-x)\u003c1e-15)\r\n%%\r\nc=[3 7 15 1 292 1 1 1 2 1 3 1 14];\r\nx=pi;\r\ny=contfrac(c);\r\nassert(abs(y-x)\u003c1e-15)\r\n%%\r\nc=[3 7 15 1];\r\nx=355/113;\r\ny=contfrac(c);\r\nassert(abs(y-x)\u003c1e-15)\r\n%%\r\nc=[1 1 1 3 1 5 1 7 1 9 1 11 1 13 1 15 1 17 1 19 1;\r\n   2 1 2 1 1 4 1 1 6 1 1 8 1 1 10 1 1 12 1 1 14];\r\nx=[tan(1);exp(1)];\r\ny=contfrac(c);\r\nassert(max(abs(y-x))\u003c1e-15)\r\n%%\r\nc=(1:9)'*[1 2*ones(1,20)];\r\nx=sqrt([2;5;10;17;26;37;50;65;82]);\r\ny=contfrac(c);\r\nassert(max(abs(y-x))\u003c1e-15)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":245,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":55,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-02-22T00:02:06.000Z","updated_at":"2025-06-09T14:53:07.000Z","published_at":"2013-02-22T00:12:21.000Z","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 row vector\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[   c=[c0 c1 c2 c3 ...]]]\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\u003eevaluate the continued fraction\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=c0+1/(c1+1/(c2+1/(c3+...)))]]\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 c is a matrix, return column vector x in which x(i) is the solution for row i of c.\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":1289,"title":"Evaluating continued fractions","description":"Given row vector \r\n\r\n   c=[c0 c1 c2 c3 ...]\r\n\r\nevaluate the continued fraction\r\n\r\n   x=c0+1/(c1+1/(c2+1/(c3+...)))\r\n\r\nIf c is a matrix, return column vector x in which x(i) is the solution for row i of c.","description_html":"\u003cp\u003eGiven row vector\u003c/p\u003e\u003cpre\u003e   c=[c0 c1 c2 c3 ...]\u003c/pre\u003e\u003cp\u003eevaluate the continued fraction\u003c/p\u003e\u003cpre\u003e   x=c0+1/(c1+1/(c2+1/(c3+...)))\u003c/pre\u003e\u003cp\u003eIf c is a matrix, return column vector x in which x(i) is the solution for row i of c.\u003c/p\u003e","function_template":"function x=contfrac(c)\r\nx=sum(c,2);\r\n","test_suite":"%%\r\nc=ones(1,40);\r\nx=(1+sqrt(5))/2;\r\ny=contfrac(c);\r\nassert(abs(y-x)\u003c1e-15)\r\n%%\r\nc=[3 7 15 1 292 1 1 1 2 1 3 1 14];\r\nx=pi;\r\ny=contfrac(c);\r\nassert(abs(y-x)\u003c1e-15)\r\n%%\r\nc=[3 7 15 1];\r\nx=355/113;\r\ny=contfrac(c);\r\nassert(abs(y-x)\u003c1e-15)\r\n%%\r\nc=[1 1 1 3 1 5 1 7 1 9 1 11 1 13 1 15 1 17 1 19 1;\r\n   2 1 2 1 1 4 1 1 6 1 1 8 1 1 10 1 1 12 1 1 14];\r\nx=[tan(1);exp(1)];\r\ny=contfrac(c);\r\nassert(max(abs(y-x))\u003c1e-15)\r\n%%\r\nc=(1:9)'*[1 2*ones(1,20)];\r\nx=sqrt([2;5;10;17;26;37;50;65;82]);\r\ny=contfrac(c);\r\nassert(max(abs(y-x))\u003c1e-15)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":245,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":55,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-02-22T00:02:06.000Z","updated_at":"2025-06-09T14:53:07.000Z","published_at":"2013-02-22T00:12:21.000Z","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 row vector\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[   c=[c0 c1 c2 c3 ...]]]\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\u003eevaluate the continued fraction\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=c0+1/(c1+1/(c2+1/(c3+...)))]]\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 c is a matrix, return column vector x in which x(i) is the solution for row i of c.\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\"}]}"}],"errors":[],"facets":[[],[{"value":"medium","count":1,"selected":false}]],"term":"tag:\"continued fraction\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}