{"id":111,"date":"2010-08-29T08:27:47","date_gmt":"2010-08-29T00:27:47","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=111"},"modified":"2012-03-03T08:28:00","modified_gmt":"2012-03-03T00:28:00","slug":"poj-2515-birthday-cake","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/poj-2515-birthday-cake\/","title":{"rendered":"POJ 2515. Birthday Cake"},"content":{"rendered":"<h3>Brief description :<\/h3>\n<p>\u8ba1\u7b971^k+2^k+..+n^k\u3002<br \/>\n(1<=n<=10^41, 3<=k<=100)\n<!--more--><\/p>\n<h3>Analyse :<\/h3>\n<p>\u8fd9\u662f\u4e00\u4e2a\u91cd\u8981\u95ee\u9898\uff0c\u6211\u76ee\u524d\u75db\u5e76TLE\u7740\u3002<\/p>\n<pre lang=\"cpp\" file=\"1.cpp\">\r\n\/*\r\n    Author: xiaodao\r\n    Prog: POJ 2515. Birthday Cake\r\n    Status: Time Limited Error\r\n    Last modifiy: GMT +8 Aug. 29th 17:51\r\n*\/\r\n#include <iostream>\r\n#include \"bignum.h\"\r\nusing namespace std;\r\nconst int M = 1001;\r\nbignum D[M][M];\r\nbignum n; int m;\r\n\r\n\r\n\/\/ c(n, k)\r\nbignum c(int k){\r\n    bignum res = 1, nn = n;\r\n    for (int i=1;i<=k;i++){\r\n        res = res * nn; nn-=1;\r\n        res = res \/ i;\r\n    }\r\n    return res;\r\n}\r\n\r\n\r\n\/\/ s(n, m)\r\nbignum s(){\r\n    bignum res = 0;\r\n    for (int i=0;i<=m;i++)\r\n        res += D[i][0] * c(i+1);\r\n    return res;\r\n}\r\n\r\nvoid init(){\r\n    cin >> n >> m;\r\n    for (int i=0;i<=m;i++)\r\n        D[0][i] = pow(i+1, m);\r\n\r\n    for (int i=1;i<=m;i++)\r\n        for (int j=0;j<=m-i;j++)\r\n            D[i][j] = D[i-1][j+1] - D[i-1][j];\r\n}\r\n\r\nvoid patch(){\r\n    for (int i=0;i<=m;i++){\r\n        for (int j=0;j<=m-i;j++)\r\n            cout << D[i][j] << \" \";\r\n        cout << endl;\r\n    }\r\n}\r\n\r\n\r\nint main(){\r\n    int T; cin >> T;\r\n    while (T--){\r\n        init(); \/\/patch();\r\n        cout << s() << endl;\r\n    }\r\n}\r\n<\/pre>\n<h3>External link :<\/h3>\n<p><a href=\"http:\/\/acm.pku.edu.cn\/JudgeOnline\/problem?id=2515\">POJ 2515. Birthday Cake<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Brief description : \u8ba1\u7b971^k+2^k+..+n^k\u3002 (1<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[1],"tags":[],"class_list":["post-111","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-1N","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/111","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=111"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/111\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=111"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=111"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=111"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}