{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-06-05T00:10:21.000Z","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":"2026-06-05T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":197,"title":"Recurrence relation","description":"A recurrence relation is given by\r\n\r\n  P(1)   := 1\r\n  P(n+1) := exp(1) - (n+1)*P(n)\r\n\r\nWrite a function that, given an integer |n|, returns |P(n)|. The |n| will be smaller than 100 in all test-suite problems and an absolute precision of 10*eps (~2e-15, i.e. almost machine precision) is required.","description_html":"\u003cp\u003eA recurrence relation is given by\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eP(1)   := 1\r\nP(n+1) := exp(1) - (n+1)*P(n)\r\n\u003c/pre\u003e\u003cp\u003eWrite a function that, given an integer \u003ctt\u003en\u003c/tt\u003e, returns \u003ctt\u003eP(n)\u003c/tt\u003e. The \u003ctt\u003en\u003c/tt\u003e will be smaller than 100 in all test-suite problems and an absolute precision of 10*eps (~2e-15, i.e. almost machine precision) is required.\u003c/p\u003e","function_template":"function pn = P(n)\r\n  pn = pi;\r\nend","test_suite":"%%\r\nassert(abs(P(1)-1)\u003c10*eps)\r\n%%\r\nassert(abs(P(2)-exp(1)+2)\u003c10*eps)\r\n%%\r\nassert(abs(P(3)-0.563436343081910)\u003c10*eps)\r\n%%\r\nassert(abs(P(10)-0.228001515486442)\u003c10*eps)\r\n%%\r\nassert(abs(P(20)-0.123803830762570)\u003c10*eps)\r\n%%\r\nassert(abs(P(50)-0.052293638299222)\u003c10*eps)\r\n%%\r\nassert(abs(P(99)-0.026916294692673)\u003c10*eps)\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":"2012-01-31T14:13:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-31T14:05:07.000Z","updated_at":"2026-05-25T04:11:35.000Z","published_at":"2012-01-31T21:44:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA recurrence relation is given by\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[P(1)   := 1\\nP(n+1) := exp(1) - (n+1)*P(n)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that, given an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, returns\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be smaller than 100 in all test-suite problems and an absolute precision of 10*eps (~2e-15, i.e. almost machine precision) is required.\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":197,"title":"Recurrence relation","description":"A recurrence relation is given by\r\n\r\n  P(1)   := 1\r\n  P(n+1) := exp(1) - (n+1)*P(n)\r\n\r\nWrite a function that, given an integer |n|, returns |P(n)|. The |n| will be smaller than 100 in all test-suite problems and an absolute precision of 10*eps (~2e-15, i.e. almost machine precision) is required.","description_html":"\u003cp\u003eA recurrence relation is given by\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eP(1)   := 1\r\nP(n+1) := exp(1) - (n+1)*P(n)\r\n\u003c/pre\u003e\u003cp\u003eWrite a function that, given an integer \u003ctt\u003en\u003c/tt\u003e, returns \u003ctt\u003eP(n)\u003c/tt\u003e. The \u003ctt\u003en\u003c/tt\u003e will be smaller than 100 in all test-suite problems and an absolute precision of 10*eps (~2e-15, i.e. almost machine precision) is required.\u003c/p\u003e","function_template":"function pn = P(n)\r\n  pn = pi;\r\nend","test_suite":"%%\r\nassert(abs(P(1)-1)\u003c10*eps)\r\n%%\r\nassert(abs(P(2)-exp(1)+2)\u003c10*eps)\r\n%%\r\nassert(abs(P(3)-0.563436343081910)\u003c10*eps)\r\n%%\r\nassert(abs(P(10)-0.228001515486442)\u003c10*eps)\r\n%%\r\nassert(abs(P(20)-0.123803830762570)\u003c10*eps)\r\n%%\r\nassert(abs(P(50)-0.052293638299222)\u003c10*eps)\r\n%%\r\nassert(abs(P(99)-0.026916294692673)\u003c10*eps)\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":"2012-01-31T14:13:25.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-31T14:05:07.000Z","updated_at":"2026-05-25T04:11:35.000Z","published_at":"2012-01-31T21:44:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA recurrence relation is given by\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[P(1)   := 1\\nP(n+1) := exp(1) - (n+1)*P(n)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that, given an integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, returns\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be smaller than 100 in all test-suite problems and an absolute precision of 10*eps (~2e-15, i.e. almost machine precision) is required.\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":"Tough Stuff","count":1,"selected":false}],[{"value":"medium","count":1,"selected":false}]],"term":"tag:\"numerical stability\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}