{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","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":"2025-12-14T00:00:00.000Z","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":44076,"title":"GJam 2017 Kickstart: Vote (Small) ","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/6304486/dashboard#s=p1 GJam 2017 Kickstart Vote\u003e. This is the first 100 small cases with 0\u003c=M\u003cN\u003c=10.\r\n\r\n\u003chttp://code.google.com/codejam Google Code Jam 2017 Qualifier\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\r\n\r\nThe GJam story is given N and M votes, where N\u003eM, determine the number of voting sequences for which N is always in the lead divided by the total number of sequences(N+M)!.\r\n\r\n*Input:* [N,M], the quantity of votes to N and M\r\n\r\n*Output:* [V], the ratio of N always leading sequences to total sequences\r\n\r\n*Examples:* [N,M] [V]; [2,1] [0.33333333]\r\n\r\nFor the case [2,1] there are 6 sequences [N1N2M1,N2N1M1,N1M1N2,N2M1N1,M1N1N2,M1N2N1] with only the first two always having N in the lead.\r\n\r\n*Theory:* Brute force permutations and counting will not succeed in a timely manner for 0\u003c=M\u003cN\u003c=10 as 19! is a bit big to enumerate. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003chttp://code.google.com/codejam/contest/6304486/scoreboard#vf=1 GJam Kickstart solutions(C++,Python)\u003e. ","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/6304486/dashboard#s=p1\"\u003eGJam 2017 Kickstart Vote\u003c/a\u003e. This is the first 100 small cases with 0\u0026lt;=M\u0026lt;N\u0026lt;=10.\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://code.google.com/codejam\"\u003eGoogle Code Jam 2017 Qualifier\u003c/a\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\u003c/p\u003e\u003cp\u003eThe GJam story is given N and M votes, where N\u0026gt;M, determine the number of voting sequences for which N is always in the lead divided by the total number of sequences(N+M)!.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [N,M], the quantity of votes to N and M\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [V], the ratio of N always leading sequences to total sequences\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e [N,M] [V]; [2,1] [0.33333333]\u003c/p\u003e\u003cp\u003eFor the case [2,1] there are 6 sequences [N1N2M1,N2N1M1,N1M1N2,N2M1N1,M1N1N2,M1N2N1] with only the first two always having N in the lead.\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory:\u003c/b\u003e Brute force permutations and counting will not succeed in a timely manner for 0\u0026lt;=M\u0026lt;N\u0026lt;=10 as 19! is a bit big to enumerate. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003ca href = \"http://code.google.com/codejam/contest/6304486/scoreboard#vf=1\"\u003eGJam Kickstart solutions(C++,Python)\u003c/a\u003e.\u003c/p\u003e","function_template":"function val=vote(N,M)\r\n% 0\u003c=M\u003cN\u003c=10 Small\r\n% N\u003eM\u003e=0\r\n% Ratio of voter  [sequences sum(N_1:i)\u003esum(M_1:i) for all i] / (N+M)!\r\n val=0;\r\nend","test_suite":"%%\r\nv=vote(10,7);\r\nassert(abs(v-0.176470588)\u003c1e-8)\r\n%%\r\nv=vote(9,2);\r\nassert(abs(v-0.636363636)\u003c1e-8)\r\n%%\r\nv=vote(6,4);\r\nassert(abs(v-0.200000000)\u003c1e-8)\r\n%%\r\nv=vote(3,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(10,5);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(6,2);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(9,7);\r\nassert(abs(v-0.125000000)\u003c1e-8)\r\n%%\r\nv=vote(8,2);\r\nassert(abs(v-0.600000000)\u003c1e-8)\r\n%%\r\nv=vote(3,1);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(6,5);\r\nassert(abs(v-0.090909091)\u003c1e-8)\r\n%%\r\nv=vote(7,1);\r\nassert(abs(v-0.750000000)\u003c1e-8)\r\n%%\r\nv=vote(6,1);\r\nassert(abs(v-0.714285714)\u003c1e-8)\r\n%%\r\nv=vote(2,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(4,1);\r\nassert(abs(v-0.600000000)\u003c1e-8)\r\n%%\r\nv=vote(10,9);\r\nassert(abs(v-0.052631579)\u003c1e-8)\r\n%%\r\nv=vote(7,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(7,6);\r\nassert(abs(v-0.076923077)\u003c1e-8)\r\n%%\r\nv=vote(3,1);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(4,1);\r\nassert(abs(v-0.600000000)\u003c1e-8)\r\n%%\r\nv=vote(8,6);\r\nassert(abs(v-0.142857143)\u003c1e-8)\r\n%%\r\nv=vote(6,2);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(8,3);\r\nassert(abs(v-0.454545455)\u003c1e-8)\r\n%%\r\nv=vote(8,5);\r\nassert(abs(v-0.230769231)\u003c1e-8)\r\n%%\r\nv=vote(8,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(8,7);\r\nassert(abs(v-0.066666667)\u003c1e-8)\r\n%%\r\nv=vote(8,6);\r\nassert(abs(v-0.142857143)\u003c1e-8)\r\n%%\r\nv=vote(9,2);\r\nassert(abs(v-0.636363636)\u003c1e-8)\r\n%%\r\nv=vote(10,4);\r\nassert(abs(v-0.428571429)\u003c1e-8)\r\n%%\r\nv=vote(7,6);\r\nassert(abs(v-0.076923077)\u003c1e-8)\r\n%%\r\nv=vote(9,3);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(10,4);\r\nassert(abs(v-0.428571429)\u003c1e-8)\r\n%%\r\nv=vote(10,5);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(5,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(8,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(9,1);\r\nassert(abs(v-0.800000000)\u003c1e-8)\r\n%%\r\nv=vote(3,1);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(10,8);\r\nassert(abs(v-0.111111111)\u003c1e-8)\r\n%%\r\nv=vote(7,4);\r\nassert(abs(v-0.272727273)\u003c1e-8)\r\n%%\r\nv=vote(7,4);\r\nassert(abs(v-0.272727273)\u003c1e-8)\r\n%%\r\nv=vote(4,1);\r\nassert(abs(v-0.600000000)\u003c1e-8)\r\n%%\r\nv=vote(9,5);\r\nassert(abs(v-0.285714286)\u003c1e-8)\r\n%%\r\nv=vote(3,2);\r\nassert(abs(v-0.200000000)\u003c1e-8)\r\n%%\r\nv=vote(7,2);\r\nassert(abs(v-0.555555556)\u003c1e-8)\r\n%%\r\nv=vote(5,2);\r\nassert(abs(v-0.428571429)\u003c1e-8)\r\n%%\r\nv=vote(2,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(5,3);\r\nassert(abs(v-0.250000000)\u003c1e-8)\r\n%%\r\nv=vote(10,1);\r\nassert(abs(v-0.818181818)\u003c1e-8)\r\n%%\r\nv=vote(8,6);\r\nassert(abs(v-0.142857143)\u003c1e-8)\r\n%%\r\nv=vote(9,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(10,7);\r\nassert(abs(v-0.176470588)\u003c1e-8)\r\n%%\r\nv=vote(8,4);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(2,1);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(8,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(8,6);\r\nassert(abs(v-0.142857143)\u003c1e-8)\r\n%%\r\nv=vote(6,1);\r\nassert(abs(v-0.714285714)\u003c1e-8)\r\n%%\r\nv=vote(8,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(9,3);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(7,6);\r\nassert(abs(v-0.076923077)\u003c1e-8)\r\n%%\r\nv=vote(10,4);\r\nassert(abs(v-0.428571429)\u003c1e-8)\r\n%%\r\nv=vote(5,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(5,2);\r\nassert(abs(v-0.428571429)\u003c1e-8)\r\n%%\r\nv=vote(10,1);\r\nassert(abs(v-0.818181818)\u003c1e-8)\r\n%%\r\nv=vote(7,4);\r\nassert(abs(v-0.272727273)\u003c1e-8)\r\n%%\r\nv=vote(6,2);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(6,3);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(4,3);\r\nassert(abs(v-0.142857143)\u003c1e-8)\r\n%%\r\nv=vote(10,9);\r\nassert(abs(v-0.052631579)\u003c1e-8)\r\n%%\r\nv=vote(10,6);\r\nassert(abs(v-0.250000000)\u003c1e-8)\r\n%%\r\nv=vote(7,2);\r\nassert(abs(v-0.555555556)\u003c1e-8)\r\n%%\r\nv=vote(9,5);\r\nassert(abs(v-0.285714286)\u003c1e-8)\r\n%%\r\nv=vote(2,1);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(8,4);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(7,5);\r\nassert(abs(v-0.166666667)\u003c1e-8)\r\n%%\r\nv=vote(10,6);\r\nassert(abs(v-0.250000000)\u003c1e-8)\r\n%%\r\nv=vote(5,3);\r\nassert(abs(v-0.250000000)\u003c1e-8)\r\n%%\r\nv=vote(10,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(8,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(4,2);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(1,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(8,6);\r\nassert(abs(v-0.142857143)\u003c1e-8)\r\n%%\r\nv=vote(10,3);\r\nassert(abs(v-0.538461538)\u003c1e-8)\r\n%%\r\nv=vote(4,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(9,8);\r\nassert(abs(v-0.058823529)\u003c1e-8)\r\n%%\r\nv=vote(6,5);\r\nassert(abs(v-0.090909091)\u003c1e-8)\r\n%%\r\nv=vote(10,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(7,2);\r\nassert(abs(v-0.555555556)\u003c1e-8)\r\n%%\r\nv=vote(5,2);\r\nassert(abs(v-0.428571429)\u003c1e-8)\r\n%%\r\nv=vote(5,1);\r\nassert(abs(v-0.666666667)\u003c1e-8)\r\n%%\r\nv=vote(9,1);\r\nassert(abs(v-0.800000000)\u003c1e-8)\r\n%%\r\nv=vote(5,1);\r\nassert(abs(v-0.666666667)\u003c1e-8)\r\n%%\r\nv=vote(5,3);\r\nassert(abs(v-0.250000000)\u003c1e-8)\r\n%%\r\nv=vote(6,4);\r\nassert(abs(v-0.200000000)\u003c1e-8)\r\n%%\r\nv=vote(6,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(6,1);\r\nassert(abs(v-0.714285714)\u003c1e-8)\r\n%%\r\nv=vote(4,2);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(10,1);\r\nassert(abs(v-0.818181818)\u003c1e-8)\r\n%%\r\nv=vote(7,6);\r\nassert(abs(v-0.076923077)\u003c1e-8)\r\n%%\r\nv=vote(6,5);\r\nassert(abs(v-0.090909091)\u003c1e-8)\r\n%%\r\nv=vote(5,4);\r\nassert(abs(v-0.111111111)\u003c1e-8)\r\n%%\r\nv=vote(6,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-02-25T22:45:25.000Z","updated_at":"2017-02-25T22:46:10.000Z","published_at":"2017-02-25T22:46:10.000Z","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\u003eThis Challenge is derived from\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://code.google.com/codejam/contest/6304486/dashboard#s=p1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2017 Kickstart Vote\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. This is the first 100 small cases with 0\u0026lt;=M\u0026lt;N\u0026lt;=10.\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:hyperlink w:docLocation=\\\"http://code.google.com/codejam\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGoogle Code Jam 2017 Qualifier\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\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\u003eThe GJam story is given N and M votes, where N\u0026gt;M, determine the number of voting sequences for which N is always in the lead divided by the total number of sequences(N+M)!.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [N,M], the quantity of votes to N and M\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [V], the ratio of N always leading sequences to total sequences\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [N,M] [V]; [2,1] [0.33333333]\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\u003eFor the case [2,1] there are 6 sequences [N1N2M1,N2N1M1,N1M1N2,N2M1N1,M1N1N2,M1N2N1] with only the first two always having N in the lead.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Brute force permutations and counting will not succeed in a timely manner for 0\u0026lt;=M\u0026lt;N\u0026lt;=10 as 19! is a bit big to enumerate. Determining the inherent mathematical pattern is usually the best way to succeed in GJam. \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://code.google.com/codejam/contest/6304486/scoreboard#vf=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam Kickstart solutions(C++,Python)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\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":44077,"title":"GJam 2017 Kickstart: Vote (Large) ","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/6304486/dashboard#s=p1 GJam 2017 Kickstart Vote\u003e. This is the first 100 large cases with 0\u003c=M\u003cN\u003c=2000.\r\n\r\n\u003chttp://code.google.com/codejam Google Code Jam 2017 Qualifier\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\r\n\r\nThe GJam story is given N and M votes, where N\u003eM, determine the number of voting sequences for which N is always in the lead divided by the total number of sequences(N+M)!.\r\n\r\n*Input:* [N,M], the quantity of votes to N and M\r\n\r\n*Output:* [V], the ratio of N always leading sequences to total sequences\r\n\r\n*Examples:* [N,M] [V]; [2,1] [0.33333333]\r\n\r\nFor the case [2,1] there are 6 sequences [N1N2M1,N2N1M1,N1M1N2,N2M1N1,M1N1N2,M1N2N1] with only the first two always having N in the lead.\r\n\r\n*Theory:* Brute force permutations and counting will not succeed in a timely manner for 0\u003c=M\u003cN\u003c=2000 as 2000! may be a bit large. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003chttp://code.google.com/codejam/contest/6304486/scoreboard#vf=1 GJam Kickstart solutions(C++,Python)\u003e. ","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/6304486/dashboard#s=p1\"\u003eGJam 2017 Kickstart Vote\u003c/a\u003e. This is the first 100 large cases with 0\u0026lt;=M\u0026lt;N\u0026lt;=2000.\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://code.google.com/codejam\"\u003eGoogle Code Jam 2017 Qualifier\u003c/a\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\u003c/p\u003e\u003cp\u003eThe GJam story is given N and M votes, where N\u0026gt;M, determine the number of voting sequences for which N is always in the lead divided by the total number of sequences(N+M)!.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [N,M], the quantity of votes to N and M\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [V], the ratio of N always leading sequences to total sequences\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e [N,M] [V]; [2,1] [0.33333333]\u003c/p\u003e\u003cp\u003eFor the case [2,1] there are 6 sequences [N1N2M1,N2N1M1,N1M1N2,N2M1N1,M1N1N2,M1N2N1] with only the first two always having N in the lead.\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory:\u003c/b\u003e Brute force permutations and counting will not succeed in a timely manner for 0\u0026lt;=M\u0026lt;N\u0026lt;=2000 as 2000! may be a bit large. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003ca href = \"http://code.google.com/codejam/contest/6304486/scoreboard#vf=1\"\u003eGJam Kickstart solutions(C++,Python)\u003c/a\u003e.\u003c/p\u003e","function_template":"function val=vote(N,M)\r\n% 0\u003c=M\u003cN\u003c=2000 Large\r\n% N\u003eM\u003e=0\r\n% Ratio of voter  [sequences sum(N_1:i)\u003esum(M_1:i) for all i] / (N+M)!\r\n val=0;\r\nend","test_suite":"%%\r\nv=vote(821,455);\r\nassert(abs(v-0.286833856)\u003c1e-8)\r\n%%\r\nv=vote(1548,733);\r\nassert(abs(v-0.357299430)\u003c1e-8)\r\n%%\r\nv=vote(858,291);\r\nassert(abs(v-0.493472585)\u003c1e-8)\r\n%%\r\nv=vote(1595,28);\r\nassert(abs(v-0.965495995)\u003c1e-8)\r\n%%\r\nv=vote(1174,995);\r\nassert(abs(v-0.082526510)\u003c1e-8)\r\n%%\r\nv=vote(1476,454);\r\nassert(abs(v-0.529533679)\u003c1e-8)\r\n%%\r\nv=vote(690,333);\r\nassert(abs(v-0.348973607)\u003c1e-8)\r\n%%\r\nv=vote(1230,896);\r\nassert(abs(v-0.157102540)\u003c1e-8)\r\n%%\r\nv=vote(533,149);\r\nassert(abs(v-0.563049853)\u003c1e-8)\r\n%%\r\nv=vote(1941,1758);\r\nassert(abs(v-0.049472830)\u003c1e-8)\r\n%%\r\nv=vote(1976,339);\r\nassert(abs(v-0.707127430)\u003c1e-8)\r\n%%\r\nv=vote(2000,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(398,93);\r\nassert(abs(v-0.621181263)\u003c1e-8)\r\n%%\r\nv=vote(1659,1028);\r\nassert(abs(v-0.234834388)\u003c1e-8)\r\n%%\r\nv=vote(1894,961);\r\nassert(abs(v-0.326795096)\u003c1e-8)\r\n%%\r\nv=vote(1388,874);\r\nassert(abs(v-0.227232538)\u003c1e-8)\r\n%%\r\nv=vote(1354,1149);\r\nassert(abs(v-0.081901718)\u003c1e-8)\r\n%%\r\nv=vote(1778,1287);\r\nassert(abs(v-0.160195759)\u003c1e-8)\r\n%%\r\nv=vote(886,283);\r\nassert(abs(v-0.515825492)\u003c1e-8)\r\n%%\r\nv=vote(1431,822);\r\nassert(abs(v-0.270306258)\u003c1e-8)\r\n%%\r\nv=vote(679,544);\r\nassert(abs(v-0.110384301)\u003c1e-8)\r\n%%\r\nv=vote(1405,1150);\r\nassert(abs(v-0.099804305)\u003c1e-8)\r\n%%\r\nv=vote(1228,379);\r\nassert(abs(v-0.528313628)\u003c1e-8)\r\n%%\r\nv=vote(1607,1129);\r\nassert(abs(v-0.174707602)\u003c1e-8)\r\n%%\r\nv=vote(1265,457);\r\nassert(abs(v-0.469221835)\u003c1e-8)\r\n%%\r\nv=vote(1885,1572);\r\nassert(abs(v-0.090540931)\u003c1e-8)\r\n%%\r\nv=vote(1451,1348);\r\nassert(abs(v-0.036798857)\u003c1e-8)\r\n%%\r\nv=vote(1712,975);\r\nassert(abs(v-0.274283588)\u003c1e-8)\r\n%%\r\nv=vote(921,494);\r\nassert(abs(v-0.301766784)\u003c1e-8)\r\n%%\r\nv=vote(1966,354);\r\nassert(abs(v-0.694827586)\u003c1e-8)\r\n%%\r\nv=vote(1299,536);\r\nassert(abs(v-0.415803815)\u003c1e-8)\r\n%%\r\nv=vote(1872,874);\r\nassert(abs(v-0.363437728)\u003c1e-8)\r\n%%\r\nv=vote(1831,1125);\r\nassert(abs(v-0.238836265)\u003c1e-8)\r\n%%\r\nv=vote(1101,822);\r\nassert(abs(v-0.145085803)\u003c1e-8)\r\n%%\r\nv=vote(1057,526);\r\nassert(abs(v-0.335439040)\u003c1e-8)\r\n%%\r\nv=vote(1761,639);\r\nassert(abs(v-0.467500000)\u003c1e-8)\r\n%%\r\nv=vote(1111,137);\r\nassert(abs(v-0.780448718)\u003c1e-8)\r\n%%\r\nv=vote(445,425);\r\nassert(abs(v-0.022988506)\u003c1e-8)\r\n%%\r\nv=vote(670,362);\r\nassert(abs(v-0.298449612)\u003c1e-8)\r\n%%\r\nv=vote(1009,737);\r\nassert(abs(v-0.155784651)\u003c1e-8)\r\n%%\r\nv=vote(2000,1);\r\nassert(abs(v-0.999000500)\u003c1e-8)\r\n%%\r\nv=vote(1504,28);\r\nassert(abs(v-0.963446475)\u003c1e-8)\r\n%%\r\nv=vote(1821,560);\r\nassert(abs(v-0.529609408)\u003c1e-8)\r\n%%\r\nv=vote(1521,1373);\r\nassert(abs(v-0.051140290)\u003c1e-8)\r\n%%\r\nv=vote(823,361);\r\nassert(abs(v-0.390202703)\u003c1e-8)\r\n%%\r\nv=vote(836,140);\r\nassert(abs(v-0.713114754)\u003c1e-8)\r\n%%\r\nv=vote(1763,1599);\r\nassert(abs(v-0.048780488)\u003c1e-8)\r\n%%\r\nv=vote(1288,162);\r\nassert(abs(v-0.776551724)\u003c1e-8)\r\n%%\r\nv=vote(417,357);\r\nassert(abs(v-0.077519380)\u003c1e-8)\r\n%%\r\nv=vote(1020,122);\r\nassert(abs(v-0.786339755)\u003c1e-8)\r\n%%\r\nv=vote(1617,1576);\r\nassert(abs(v-0.012840589)\u003c1e-8)\r\n%%\r\nv=vote(1493,780);\r\nassert(abs(v-0.313682358)\u003c1e-8)\r\n%%\r\nv=vote(1868,34);\r\nassert(abs(v-0.964248160)\u003c1e-8)\r\n%%\r\nv=vote(1452,1240);\r\nassert(abs(v-0.078751857)\u003c1e-8)\r\n%%\r\nv=vote(2,1);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(584,242);\r\nassert(abs(v-0.414043584)\u003c1e-8)\r\n%%\r\nv=vote(1610,1196);\r\nassert(abs(v-0.147540984)\u003c1e-8)\r\n%%\r\nv=vote(1423,1296);\r\nassert(abs(v-0.046708349)\u003c1e-8)\r\n%%\r\nv=vote(975,479);\r\nassert(abs(v-0.341127923)\u003c1e-8)\r\n%%\r\nv=vote(1000,80);\r\nassert(abs(v-0.851851852)\u003c1e-8)\r\n%%\r\nv=vote(1227,1035);\r\nassert(abs(v-0.084880637)\u003c1e-8)\r\n%%\r\nv=vote(1812,260);\r\nassert(abs(v-0.749034749)\u003c1e-8)\r\n%%\r\nv=vote(1875,1294);\r\nassert(abs(v-0.183338593)\u003c1e-8)\r\n%%\r\nv=vote(1882,826);\r\nassert(abs(v-0.389955687)\u003c1e-8)\r\n%%\r\nv=vote(1401,1348);\r\nassert(abs(v-0.019279738)\u003c1e-8)\r\n%%\r\nv=vote(1449,494);\r\nassert(abs(v-0.491507977)\u003c1e-8)\r\n%%\r\nv=vote(1807,512);\r\nassert(abs(v-0.558430358)\u003c1e-8)\r\n%%\r\nv=vote(1118,432);\r\nassert(abs(v-0.442580645)\u003c1e-8)\r\n%%\r\nv=vote(1168,184);\r\nassert(abs(v-0.727810651)\u003c1e-8)\r\n%%\r\nv=vote(1421,980);\r\nassert(abs(v-0.183673469)\u003c1e-8)\r\n%%\r\nv=vote(1265,270);\r\nassert(abs(v-0.648208469)\u003c1e-8)\r\n%%\r\nv=vote(1474,1172);\r\nassert(abs(v-0.114134543)\u003c1e-8)\r\n%%\r\nv=vote(606,556);\r\nassert(abs(v-0.043029260)\u003c1e-8)\r\n%%\r\nv=vote(1,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(1543,124);\r\nassert(abs(v-0.851229754)\u003c1e-8)\r\n%%\r\nv=vote(1935,1383);\r\nassert(abs(v-0.166365280)\u003c1e-8)\r\n%%\r\nv=vote(1969,1150);\r\nassert(abs(v-0.262584162)\u003c1e-8)\r\n%%\r\nv=vote(1394,1223);\r\nassert(abs(v-0.065341995)\u003c1e-8)\r\n%%\r\nv=vote(961,203);\r\nassert(abs(v-0.651202749)\u003c1e-8)\r\n%%\r\nv=vote(1453,318);\r\nassert(abs(v-0.640880858)\u003c1e-8)\r\n%%\r\nv=vote(1979,818);\r\nassert(abs(v-0.415087594)\u003c1e-8)\r\n%%\r\nv=vote(333,302);\r\nassert(abs(v-0.048818898)\u003c1e-8)\r\n%%\r\nv=vote(1830,1041);\r\nassert(abs(v-0.274817137)\u003c1e-8)\r\n%%\r\nv=vote(1163,620);\r\nassert(abs(v-0.304542905)\u003c1e-8)\r\n%%\r\nv=vote(1446,514);\r\nassert(abs(v-0.475510204)\u003c1e-8)\r\n%%\r\nv=vote(1229,1116);\r\nassert(abs(v-0.048187633)\u003c1e-8)\r\n%%\r\nv=vote(1590,1215);\r\nassert(abs(v-0.133689840)\u003c1e-8)\r\n%%\r\nv=vote(990,252);\r\nassert(abs(v-0.594202899)\u003c1e-8)\r\n%%\r\nv=vote(948,918);\r\nassert(abs(v-0.016077170)\u003c1e-8)\r\n%%\r\nv=vote(2000,1999);\r\nassert(abs(v-0.000250063)\u003c1e-8)\r\n%%\r\nv=vote(1077,717);\r\nassert(abs(v-0.200668896)\u003c1e-8)\r\n%%\r\nv=vote(1296,801);\r\nassert(abs(v-0.236051502)\u003c1e-8)\r\n%%\r\nv=vote(1807,370);\r\nassert(abs(v-0.660082683)\u003c1e-8)\r\n%%\r\nv=vote(253,218);\r\nassert(abs(v-0.074309979)\u003c1e-8)\r\n%%\r\nv=vote(789,452);\r\nassert(abs(v-0.271555197)\u003c1e-8)\r\n%%\r\nv=vote(1647,203);\r\nassert(abs(v-0.780540541)\u003c1e-8)\r\n%%\r\nv=vote(1807,15);\r\nassert(abs(v-0.983534577)\u003c1e-8)\r\n%%\r\nv=vote(1503,929);\r\nassert(abs(v-0.236019737)\u003c1e-8)\r\n%%\r\nv=vote(1111,266);\r\nassert(abs(v-0.613652869)\u003c1e-8)\r\n%%\r\nv=vote(1534,564);\r\nassert(abs(v-0.462345091)\u003c1e-8)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-02-25T22:52:35.000Z","updated_at":"2017-02-25T22:53:48.000Z","published_at":"2017-02-25T22:53:48.000Z","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\u003eThis Challenge is derived from\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://code.google.com/codejam/contest/6304486/dashboard#s=p1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2017 Kickstart Vote\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. This is the first 100 large cases with 0\u0026lt;=M\u0026lt;N\u0026lt;=2000.\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:hyperlink w:docLocation=\\\"http://code.google.com/codejam\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGoogle Code Jam 2017 Qualifier\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\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\u003eThe GJam story is given N and M votes, where N\u0026gt;M, determine the number of voting sequences for which N is always in the lead divided by the total number of sequences(N+M)!.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [N,M], the quantity of votes to N and M\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [V], the ratio of N always leading sequences to total sequences\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [N,M] [V]; [2,1] [0.33333333]\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\u003eFor the case [2,1] there are 6 sequences [N1N2M1,N2N1M1,N1M1N2,N2M1N1,M1N1N2,M1N2N1] with only the first two always having N in the lead.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Brute force permutations and counting will not succeed in a timely manner for 0\u0026lt;=M\u0026lt;N\u0026lt;=2000 as 2000! may be a bit large. Determining the inherent mathematical pattern is usually the best way to succeed in GJam. \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://code.google.com/codejam/contest/6304486/scoreboard#vf=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam Kickstart solutions(C++,Python)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\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":{"errors":[],"problems":[{"id":44076,"title":"GJam 2017 Kickstart: Vote (Small) ","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/6304486/dashboard#s=p1 GJam 2017 Kickstart Vote\u003e. This is the first 100 small cases with 0\u003c=M\u003cN\u003c=10.\r\n\r\n\u003chttp://code.google.com/codejam Google Code Jam 2017 Qualifier\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\r\n\r\nThe GJam story is given N and M votes, where N\u003eM, determine the number of voting sequences for which N is always in the lead divided by the total number of sequences(N+M)!.\r\n\r\n*Input:* [N,M], the quantity of votes to N and M\r\n\r\n*Output:* [V], the ratio of N always leading sequences to total sequences\r\n\r\n*Examples:* [N,M] [V]; [2,1] [0.33333333]\r\n\r\nFor the case [2,1] there are 6 sequences [N1N2M1,N2N1M1,N1M1N2,N2M1N1,M1N1N2,M1N2N1] with only the first two always having N in the lead.\r\n\r\n*Theory:* Brute force permutations and counting will not succeed in a timely manner for 0\u003c=M\u003cN\u003c=10 as 19! is a bit big to enumerate. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003chttp://code.google.com/codejam/contest/6304486/scoreboard#vf=1 GJam Kickstart solutions(C++,Python)\u003e. ","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/6304486/dashboard#s=p1\"\u003eGJam 2017 Kickstart Vote\u003c/a\u003e. This is the first 100 small cases with 0\u0026lt;=M\u0026lt;N\u0026lt;=10.\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://code.google.com/codejam\"\u003eGoogle Code Jam 2017 Qualifier\u003c/a\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\u003c/p\u003e\u003cp\u003eThe GJam story is given N and M votes, where N\u0026gt;M, determine the number of voting sequences for which N is always in the lead divided by the total number of sequences(N+M)!.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [N,M], the quantity of votes to N and M\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [V], the ratio of N always leading sequences to total sequences\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e [N,M] [V]; [2,1] [0.33333333]\u003c/p\u003e\u003cp\u003eFor the case [2,1] there are 6 sequences [N1N2M1,N2N1M1,N1M1N2,N2M1N1,M1N1N2,M1N2N1] with only the first two always having N in the lead.\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory:\u003c/b\u003e Brute force permutations and counting will not succeed in a timely manner for 0\u0026lt;=M\u0026lt;N\u0026lt;=10 as 19! is a bit big to enumerate. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003ca href = \"http://code.google.com/codejam/contest/6304486/scoreboard#vf=1\"\u003eGJam Kickstart solutions(C++,Python)\u003c/a\u003e.\u003c/p\u003e","function_template":"function val=vote(N,M)\r\n% 0\u003c=M\u003cN\u003c=10 Small\r\n% N\u003eM\u003e=0\r\n% Ratio of voter  [sequences sum(N_1:i)\u003esum(M_1:i) for all i] / (N+M)!\r\n val=0;\r\nend","test_suite":"%%\r\nv=vote(10,7);\r\nassert(abs(v-0.176470588)\u003c1e-8)\r\n%%\r\nv=vote(9,2);\r\nassert(abs(v-0.636363636)\u003c1e-8)\r\n%%\r\nv=vote(6,4);\r\nassert(abs(v-0.200000000)\u003c1e-8)\r\n%%\r\nv=vote(3,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(10,5);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(6,2);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(9,7);\r\nassert(abs(v-0.125000000)\u003c1e-8)\r\n%%\r\nv=vote(8,2);\r\nassert(abs(v-0.600000000)\u003c1e-8)\r\n%%\r\nv=vote(3,1);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(6,5);\r\nassert(abs(v-0.090909091)\u003c1e-8)\r\n%%\r\nv=vote(7,1);\r\nassert(abs(v-0.750000000)\u003c1e-8)\r\n%%\r\nv=vote(6,1);\r\nassert(abs(v-0.714285714)\u003c1e-8)\r\n%%\r\nv=vote(2,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(4,1);\r\nassert(abs(v-0.600000000)\u003c1e-8)\r\n%%\r\nv=vote(10,9);\r\nassert(abs(v-0.052631579)\u003c1e-8)\r\n%%\r\nv=vote(7,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(7,6);\r\nassert(abs(v-0.076923077)\u003c1e-8)\r\n%%\r\nv=vote(3,1);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(4,1);\r\nassert(abs(v-0.600000000)\u003c1e-8)\r\n%%\r\nv=vote(8,6);\r\nassert(abs(v-0.142857143)\u003c1e-8)\r\n%%\r\nv=vote(6,2);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(8,3);\r\nassert(abs(v-0.454545455)\u003c1e-8)\r\n%%\r\nv=vote(8,5);\r\nassert(abs(v-0.230769231)\u003c1e-8)\r\n%%\r\nv=vote(8,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(8,7);\r\nassert(abs(v-0.066666667)\u003c1e-8)\r\n%%\r\nv=vote(8,6);\r\nassert(abs(v-0.142857143)\u003c1e-8)\r\n%%\r\nv=vote(9,2);\r\nassert(abs(v-0.636363636)\u003c1e-8)\r\n%%\r\nv=vote(10,4);\r\nassert(abs(v-0.428571429)\u003c1e-8)\r\n%%\r\nv=vote(7,6);\r\nassert(abs(v-0.076923077)\u003c1e-8)\r\n%%\r\nv=vote(9,3);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(10,4);\r\nassert(abs(v-0.428571429)\u003c1e-8)\r\n%%\r\nv=vote(10,5);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(5,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(8,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(9,1);\r\nassert(abs(v-0.800000000)\u003c1e-8)\r\n%%\r\nv=vote(3,1);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(10,8);\r\nassert(abs(v-0.111111111)\u003c1e-8)\r\n%%\r\nv=vote(7,4);\r\nassert(abs(v-0.272727273)\u003c1e-8)\r\n%%\r\nv=vote(7,4);\r\nassert(abs(v-0.272727273)\u003c1e-8)\r\n%%\r\nv=vote(4,1);\r\nassert(abs(v-0.600000000)\u003c1e-8)\r\n%%\r\nv=vote(9,5);\r\nassert(abs(v-0.285714286)\u003c1e-8)\r\n%%\r\nv=vote(3,2);\r\nassert(abs(v-0.200000000)\u003c1e-8)\r\n%%\r\nv=vote(7,2);\r\nassert(abs(v-0.555555556)\u003c1e-8)\r\n%%\r\nv=vote(5,2);\r\nassert(abs(v-0.428571429)\u003c1e-8)\r\n%%\r\nv=vote(2,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(5,3);\r\nassert(abs(v-0.250000000)\u003c1e-8)\r\n%%\r\nv=vote(10,1);\r\nassert(abs(v-0.818181818)\u003c1e-8)\r\n%%\r\nv=vote(8,6);\r\nassert(abs(v-0.142857143)\u003c1e-8)\r\n%%\r\nv=vote(9,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(10,7);\r\nassert(abs(v-0.176470588)\u003c1e-8)\r\n%%\r\nv=vote(8,4);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(2,1);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(8,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(8,6);\r\nassert(abs(v-0.142857143)\u003c1e-8)\r\n%%\r\nv=vote(6,1);\r\nassert(abs(v-0.714285714)\u003c1e-8)\r\n%%\r\nv=vote(8,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(9,3);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(7,6);\r\nassert(abs(v-0.076923077)\u003c1e-8)\r\n%%\r\nv=vote(10,4);\r\nassert(abs(v-0.428571429)\u003c1e-8)\r\n%%\r\nv=vote(5,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(5,2);\r\nassert(abs(v-0.428571429)\u003c1e-8)\r\n%%\r\nv=vote(10,1);\r\nassert(abs(v-0.818181818)\u003c1e-8)\r\n%%\r\nv=vote(7,4);\r\nassert(abs(v-0.272727273)\u003c1e-8)\r\n%%\r\nv=vote(6,2);\r\nassert(abs(v-0.500000000)\u003c1e-8)\r\n%%\r\nv=vote(6,3);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(4,3);\r\nassert(abs(v-0.142857143)\u003c1e-8)\r\n%%\r\nv=vote(10,9);\r\nassert(abs(v-0.052631579)\u003c1e-8)\r\n%%\r\nv=vote(10,6);\r\nassert(abs(v-0.250000000)\u003c1e-8)\r\n%%\r\nv=vote(7,2);\r\nassert(abs(v-0.555555556)\u003c1e-8)\r\n%%\r\nv=vote(9,5);\r\nassert(abs(v-0.285714286)\u003c1e-8)\r\n%%\r\nv=vote(2,1);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(8,4);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(7,5);\r\nassert(abs(v-0.166666667)\u003c1e-8)\r\n%%\r\nv=vote(10,6);\r\nassert(abs(v-0.250000000)\u003c1e-8)\r\n%%\r\nv=vote(5,3);\r\nassert(abs(v-0.250000000)\u003c1e-8)\r\n%%\r\nv=vote(10,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(8,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(4,2);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(1,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(8,6);\r\nassert(abs(v-0.142857143)\u003c1e-8)\r\n%%\r\nv=vote(10,3);\r\nassert(abs(v-0.538461538)\u003c1e-8)\r\n%%\r\nv=vote(4,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(9,8);\r\nassert(abs(v-0.058823529)\u003c1e-8)\r\n%%\r\nv=vote(6,5);\r\nassert(abs(v-0.090909091)\u003c1e-8)\r\n%%\r\nv=vote(10,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(7,2);\r\nassert(abs(v-0.555555556)\u003c1e-8)\r\n%%\r\nv=vote(5,2);\r\nassert(abs(v-0.428571429)\u003c1e-8)\r\n%%\r\nv=vote(5,1);\r\nassert(abs(v-0.666666667)\u003c1e-8)\r\n%%\r\nv=vote(9,1);\r\nassert(abs(v-0.800000000)\u003c1e-8)\r\n%%\r\nv=vote(5,1);\r\nassert(abs(v-0.666666667)\u003c1e-8)\r\n%%\r\nv=vote(5,3);\r\nassert(abs(v-0.250000000)\u003c1e-8)\r\n%%\r\nv=vote(6,4);\r\nassert(abs(v-0.200000000)\u003c1e-8)\r\n%%\r\nv=vote(6,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(6,1);\r\nassert(abs(v-0.714285714)\u003c1e-8)\r\n%%\r\nv=vote(4,2);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(10,1);\r\nassert(abs(v-0.818181818)\u003c1e-8)\r\n%%\r\nv=vote(7,6);\r\nassert(abs(v-0.076923077)\u003c1e-8)\r\n%%\r\nv=vote(6,5);\r\nassert(abs(v-0.090909091)\u003c1e-8)\r\n%%\r\nv=vote(5,4);\r\nassert(abs(v-0.111111111)\u003c1e-8)\r\n%%\r\nv=vote(6,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-02-25T22:45:25.000Z","updated_at":"2017-02-25T22:46:10.000Z","published_at":"2017-02-25T22:46:10.000Z","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\u003eThis Challenge is derived from\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://code.google.com/codejam/contest/6304486/dashboard#s=p1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2017 Kickstart Vote\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. This is the first 100 small cases with 0\u0026lt;=M\u0026lt;N\u0026lt;=10.\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:hyperlink w:docLocation=\\\"http://code.google.com/codejam\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGoogle Code Jam 2017 Qualifier\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\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\u003eThe GJam story is given N and M votes, where N\u0026gt;M, determine the number of voting sequences for which N is always in the lead divided by the total number of sequences(N+M)!.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [N,M], the quantity of votes to N and M\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [V], the ratio of N always leading sequences to total sequences\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [N,M] [V]; [2,1] [0.33333333]\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\u003eFor the case [2,1] there are 6 sequences [N1N2M1,N2N1M1,N1M1N2,N2M1N1,M1N1N2,M1N2N1] with only the first two always having N in the lead.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Brute force permutations and counting will not succeed in a timely manner for 0\u0026lt;=M\u0026lt;N\u0026lt;=10 as 19! is a bit big to enumerate. Determining the inherent mathematical pattern is usually the best way to succeed in GJam. \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://code.google.com/codejam/contest/6304486/scoreboard#vf=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam Kickstart solutions(C++,Python)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\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":44077,"title":"GJam 2017 Kickstart: Vote (Large) ","description":"This Challenge is derived from \u003chttp://code.google.com/codejam/contest/6304486/dashboard#s=p1 GJam 2017 Kickstart Vote\u003e. This is the first 100 large cases with 0\u003c=M\u003cN\u003c=2000.\r\n\r\n\u003chttp://code.google.com/codejam Google Code Jam 2017 Qualifier\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\r\n\r\nThe GJam story is given N and M votes, where N\u003eM, determine the number of voting sequences for which N is always in the lead divided by the total number of sequences(N+M)!.\r\n\r\n*Input:* [N,M], the quantity of votes to N and M\r\n\r\n*Output:* [V], the ratio of N always leading sequences to total sequences\r\n\r\n*Examples:* [N,M] [V]; [2,1] [0.33333333]\r\n\r\nFor the case [2,1] there are 6 sequences [N1N2M1,N2N1M1,N1M1N2,N2M1N1,M1N1N2,M1N2N1] with only the first two always having N in the lead.\r\n\r\n*Theory:* Brute force permutations and counting will not succeed in a timely manner for 0\u003c=M\u003cN\u003c=2000 as 2000! may be a bit large. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003chttp://code.google.com/codejam/contest/6304486/scoreboard#vf=1 GJam Kickstart solutions(C++,Python)\u003e. ","description_html":"\u003cp\u003eThis Challenge is derived from \u003ca href = \"http://code.google.com/codejam/contest/6304486/dashboard#s=p1\"\u003eGJam 2017 Kickstart Vote\u003c/a\u003e. This is the first 100 large cases with 0\u0026lt;=M\u0026lt;N\u0026lt;=2000.\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://code.google.com/codejam\"\u003eGoogle Code Jam 2017 Qualifier\u003c/a\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\u003c/p\u003e\u003cp\u003eThe GJam story is given N and M votes, where N\u0026gt;M, determine the number of voting sequences for which N is always in the lead divided by the total number of sequences(N+M)!.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [N,M], the quantity of votes to N and M\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e [V], the ratio of N always leading sequences to total sequences\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e [N,M] [V]; [2,1] [0.33333333]\u003c/p\u003e\u003cp\u003eFor the case [2,1] there are 6 sequences [N1N2M1,N2N1M1,N1M1N2,N2M1N1,M1N1N2,M1N2N1] with only the first two always having N in the lead.\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory:\u003c/b\u003e Brute force permutations and counting will not succeed in a timely manner for 0\u0026lt;=M\u0026lt;N\u0026lt;=2000 as 2000! may be a bit large. Determining the inherent mathematical pattern is usually the best way to succeed in GJam.   \u003ca href = \"http://code.google.com/codejam/contest/6304486/scoreboard#vf=1\"\u003eGJam Kickstart solutions(C++,Python)\u003c/a\u003e.\u003c/p\u003e","function_template":"function val=vote(N,M)\r\n% 0\u003c=M\u003cN\u003c=2000 Large\r\n% N\u003eM\u003e=0\r\n% Ratio of voter  [sequences sum(N_1:i)\u003esum(M_1:i) for all i] / (N+M)!\r\n val=0;\r\nend","test_suite":"%%\r\nv=vote(821,455);\r\nassert(abs(v-0.286833856)\u003c1e-8)\r\n%%\r\nv=vote(1548,733);\r\nassert(abs(v-0.357299430)\u003c1e-8)\r\n%%\r\nv=vote(858,291);\r\nassert(abs(v-0.493472585)\u003c1e-8)\r\n%%\r\nv=vote(1595,28);\r\nassert(abs(v-0.965495995)\u003c1e-8)\r\n%%\r\nv=vote(1174,995);\r\nassert(abs(v-0.082526510)\u003c1e-8)\r\n%%\r\nv=vote(1476,454);\r\nassert(abs(v-0.529533679)\u003c1e-8)\r\n%%\r\nv=vote(690,333);\r\nassert(abs(v-0.348973607)\u003c1e-8)\r\n%%\r\nv=vote(1230,896);\r\nassert(abs(v-0.157102540)\u003c1e-8)\r\n%%\r\nv=vote(533,149);\r\nassert(abs(v-0.563049853)\u003c1e-8)\r\n%%\r\nv=vote(1941,1758);\r\nassert(abs(v-0.049472830)\u003c1e-8)\r\n%%\r\nv=vote(1976,339);\r\nassert(abs(v-0.707127430)\u003c1e-8)\r\n%%\r\nv=vote(2000,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(398,93);\r\nassert(abs(v-0.621181263)\u003c1e-8)\r\n%%\r\nv=vote(1659,1028);\r\nassert(abs(v-0.234834388)\u003c1e-8)\r\n%%\r\nv=vote(1894,961);\r\nassert(abs(v-0.326795096)\u003c1e-8)\r\n%%\r\nv=vote(1388,874);\r\nassert(abs(v-0.227232538)\u003c1e-8)\r\n%%\r\nv=vote(1354,1149);\r\nassert(abs(v-0.081901718)\u003c1e-8)\r\n%%\r\nv=vote(1778,1287);\r\nassert(abs(v-0.160195759)\u003c1e-8)\r\n%%\r\nv=vote(886,283);\r\nassert(abs(v-0.515825492)\u003c1e-8)\r\n%%\r\nv=vote(1431,822);\r\nassert(abs(v-0.270306258)\u003c1e-8)\r\n%%\r\nv=vote(679,544);\r\nassert(abs(v-0.110384301)\u003c1e-8)\r\n%%\r\nv=vote(1405,1150);\r\nassert(abs(v-0.099804305)\u003c1e-8)\r\n%%\r\nv=vote(1228,379);\r\nassert(abs(v-0.528313628)\u003c1e-8)\r\n%%\r\nv=vote(1607,1129);\r\nassert(abs(v-0.174707602)\u003c1e-8)\r\n%%\r\nv=vote(1265,457);\r\nassert(abs(v-0.469221835)\u003c1e-8)\r\n%%\r\nv=vote(1885,1572);\r\nassert(abs(v-0.090540931)\u003c1e-8)\r\n%%\r\nv=vote(1451,1348);\r\nassert(abs(v-0.036798857)\u003c1e-8)\r\n%%\r\nv=vote(1712,975);\r\nassert(abs(v-0.274283588)\u003c1e-8)\r\n%%\r\nv=vote(921,494);\r\nassert(abs(v-0.301766784)\u003c1e-8)\r\n%%\r\nv=vote(1966,354);\r\nassert(abs(v-0.694827586)\u003c1e-8)\r\n%%\r\nv=vote(1299,536);\r\nassert(abs(v-0.415803815)\u003c1e-8)\r\n%%\r\nv=vote(1872,874);\r\nassert(abs(v-0.363437728)\u003c1e-8)\r\n%%\r\nv=vote(1831,1125);\r\nassert(abs(v-0.238836265)\u003c1e-8)\r\n%%\r\nv=vote(1101,822);\r\nassert(abs(v-0.145085803)\u003c1e-8)\r\n%%\r\nv=vote(1057,526);\r\nassert(abs(v-0.335439040)\u003c1e-8)\r\n%%\r\nv=vote(1761,639);\r\nassert(abs(v-0.467500000)\u003c1e-8)\r\n%%\r\nv=vote(1111,137);\r\nassert(abs(v-0.780448718)\u003c1e-8)\r\n%%\r\nv=vote(445,425);\r\nassert(abs(v-0.022988506)\u003c1e-8)\r\n%%\r\nv=vote(670,362);\r\nassert(abs(v-0.298449612)\u003c1e-8)\r\n%%\r\nv=vote(1009,737);\r\nassert(abs(v-0.155784651)\u003c1e-8)\r\n%%\r\nv=vote(2000,1);\r\nassert(abs(v-0.999000500)\u003c1e-8)\r\n%%\r\nv=vote(1504,28);\r\nassert(abs(v-0.963446475)\u003c1e-8)\r\n%%\r\nv=vote(1821,560);\r\nassert(abs(v-0.529609408)\u003c1e-8)\r\n%%\r\nv=vote(1521,1373);\r\nassert(abs(v-0.051140290)\u003c1e-8)\r\n%%\r\nv=vote(823,361);\r\nassert(abs(v-0.390202703)\u003c1e-8)\r\n%%\r\nv=vote(836,140);\r\nassert(abs(v-0.713114754)\u003c1e-8)\r\n%%\r\nv=vote(1763,1599);\r\nassert(abs(v-0.048780488)\u003c1e-8)\r\n%%\r\nv=vote(1288,162);\r\nassert(abs(v-0.776551724)\u003c1e-8)\r\n%%\r\nv=vote(417,357);\r\nassert(abs(v-0.077519380)\u003c1e-8)\r\n%%\r\nv=vote(1020,122);\r\nassert(abs(v-0.786339755)\u003c1e-8)\r\n%%\r\nv=vote(1617,1576);\r\nassert(abs(v-0.012840589)\u003c1e-8)\r\n%%\r\nv=vote(1493,780);\r\nassert(abs(v-0.313682358)\u003c1e-8)\r\n%%\r\nv=vote(1868,34);\r\nassert(abs(v-0.964248160)\u003c1e-8)\r\n%%\r\nv=vote(1452,1240);\r\nassert(abs(v-0.078751857)\u003c1e-8)\r\n%%\r\nv=vote(2,1);\r\nassert(abs(v-0.333333333)\u003c1e-8)\r\n%%\r\nv=vote(584,242);\r\nassert(abs(v-0.414043584)\u003c1e-8)\r\n%%\r\nv=vote(1610,1196);\r\nassert(abs(v-0.147540984)\u003c1e-8)\r\n%%\r\nv=vote(1423,1296);\r\nassert(abs(v-0.046708349)\u003c1e-8)\r\n%%\r\nv=vote(975,479);\r\nassert(abs(v-0.341127923)\u003c1e-8)\r\n%%\r\nv=vote(1000,80);\r\nassert(abs(v-0.851851852)\u003c1e-8)\r\n%%\r\nv=vote(1227,1035);\r\nassert(abs(v-0.084880637)\u003c1e-8)\r\n%%\r\nv=vote(1812,260);\r\nassert(abs(v-0.749034749)\u003c1e-8)\r\n%%\r\nv=vote(1875,1294);\r\nassert(abs(v-0.183338593)\u003c1e-8)\r\n%%\r\nv=vote(1882,826);\r\nassert(abs(v-0.389955687)\u003c1e-8)\r\n%%\r\nv=vote(1401,1348);\r\nassert(abs(v-0.019279738)\u003c1e-8)\r\n%%\r\nv=vote(1449,494);\r\nassert(abs(v-0.491507977)\u003c1e-8)\r\n%%\r\nv=vote(1807,512);\r\nassert(abs(v-0.558430358)\u003c1e-8)\r\n%%\r\nv=vote(1118,432);\r\nassert(abs(v-0.442580645)\u003c1e-8)\r\n%%\r\nv=vote(1168,184);\r\nassert(abs(v-0.727810651)\u003c1e-8)\r\n%%\r\nv=vote(1421,980);\r\nassert(abs(v-0.183673469)\u003c1e-8)\r\n%%\r\nv=vote(1265,270);\r\nassert(abs(v-0.648208469)\u003c1e-8)\r\n%%\r\nv=vote(1474,1172);\r\nassert(abs(v-0.114134543)\u003c1e-8)\r\n%%\r\nv=vote(606,556);\r\nassert(abs(v-0.043029260)\u003c1e-8)\r\n%%\r\nv=vote(1,0);\r\nassert(abs(v-1.000000000)\u003c1e-8)\r\n%%\r\nv=vote(1543,124);\r\nassert(abs(v-0.851229754)\u003c1e-8)\r\n%%\r\nv=vote(1935,1383);\r\nassert(abs(v-0.166365280)\u003c1e-8)\r\n%%\r\nv=vote(1969,1150);\r\nassert(abs(v-0.262584162)\u003c1e-8)\r\n%%\r\nv=vote(1394,1223);\r\nassert(abs(v-0.065341995)\u003c1e-8)\r\n%%\r\nv=vote(961,203);\r\nassert(abs(v-0.651202749)\u003c1e-8)\r\n%%\r\nv=vote(1453,318);\r\nassert(abs(v-0.640880858)\u003c1e-8)\r\n%%\r\nv=vote(1979,818);\r\nassert(abs(v-0.415087594)\u003c1e-8)\r\n%%\r\nv=vote(333,302);\r\nassert(abs(v-0.048818898)\u003c1e-8)\r\n%%\r\nv=vote(1830,1041);\r\nassert(abs(v-0.274817137)\u003c1e-8)\r\n%%\r\nv=vote(1163,620);\r\nassert(abs(v-0.304542905)\u003c1e-8)\r\n%%\r\nv=vote(1446,514);\r\nassert(abs(v-0.475510204)\u003c1e-8)\r\n%%\r\nv=vote(1229,1116);\r\nassert(abs(v-0.048187633)\u003c1e-8)\r\n%%\r\nv=vote(1590,1215);\r\nassert(abs(v-0.133689840)\u003c1e-8)\r\n%%\r\nv=vote(990,252);\r\nassert(abs(v-0.594202899)\u003c1e-8)\r\n%%\r\nv=vote(948,918);\r\nassert(abs(v-0.016077170)\u003c1e-8)\r\n%%\r\nv=vote(2000,1999);\r\nassert(abs(v-0.000250063)\u003c1e-8)\r\n%%\r\nv=vote(1077,717);\r\nassert(abs(v-0.200668896)\u003c1e-8)\r\n%%\r\nv=vote(1296,801);\r\nassert(abs(v-0.236051502)\u003c1e-8)\r\n%%\r\nv=vote(1807,370);\r\nassert(abs(v-0.660082683)\u003c1e-8)\r\n%%\r\nv=vote(253,218);\r\nassert(abs(v-0.074309979)\u003c1e-8)\r\n%%\r\nv=vote(789,452);\r\nassert(abs(v-0.271555197)\u003c1e-8)\r\n%%\r\nv=vote(1647,203);\r\nassert(abs(v-0.780540541)\u003c1e-8)\r\n%%\r\nv=vote(1807,15);\r\nassert(abs(v-0.983534577)\u003c1e-8)\r\n%%\r\nv=vote(1503,929);\r\nassert(abs(v-0.236019737)\u003c1e-8)\r\n%%\r\nv=vote(1111,266);\r\nassert(abs(v-0.613652869)\u003c1e-8)\r\n%%\r\nv=vote(1534,564);\r\nassert(abs(v-0.462345091)\u003c1e-8)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2017-02-25T22:52:35.000Z","updated_at":"2017-02-25T22:53:48.000Z","published_at":"2017-02-25T22:53:48.000Z","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\u003eThis Challenge is derived from\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://code.google.com/codejam/contest/6304486/dashboard#s=p1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGJam 2017 Kickstart Vote\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. This is the first 100 large cases with 0\u0026lt;=M\u0026lt;N\u0026lt;=2000.\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:hyperlink w:docLocation=\\\"http://code.google.com/codejam\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGoogle Code Jam 2017 Qualifier\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is March 7, 2017. Typically four challenges with small and large aspects with 27 hours to complete.\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\u003eThe GJam story is given N and M votes, where N\u0026gt;M, determine the number of voting sequences for which N is always in the lead divided by the total number of sequences(N+M)!.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [N,M], the quantity of votes to N and M\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [V], the ratio of N always leading sequences to total sequences\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [N,M] [V]; [2,1] [0.33333333]\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\u003eFor the case [2,1] there are 6 sequences [N1N2M1,N2N1M1,N1M1N2,N2M1N1,M1N1N2,M1N2N1] with only the first two always having N in the lead.\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Brute force permutations and counting will not succeed in a timely manner for 0\u0026lt;=M\u0026lt;N\u0026lt;=2000 as 2000! may be a bit large. 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