{"id":796,"date":"2013-08-11T04:40:26","date_gmt":"2013-08-10T20:40:26","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=796"},"modified":"2013-08-15T02:40:25","modified_gmt":"2013-08-14T18:40:25","slug":"srm-584","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/srm-584\/","title":{"rendered":"SRM 584"},"content":{"rendered":"

600. Excavations<\/h2>\n

Brief description: <\/h3>\n

\u3002\u3002\u3002\u4e00\u4e2a\u53e4\u57ce\u9057\u8ff9 n \u4e2a\u5efa\u7b51\u3002\u3002\u6211\u4eec\u77e5\u9053\u8fd9\u4e9b\u5efa\u7b51\u7684\u7c7b\u578b\u548c\u63a9\u57cb\u7684\u6df1\u5ea6\u3002type\u3002depth\u3002
\n\u3002\u3002\u3002\u4f60\u6709\u4e00\u4e2a\u6700\u5927\u53ef\u4ee5\u6316 D \u7c73\u7684\u6316\u6398\u673a\u3002\u3002\u4f60\u4e0d\u77e5\u9053 D \u3002\u3002\u4f46\u662f\u4f60\u77e5\u9053\u4f60\u6070\u597d\u6316\u4e86 K \u6b21\u3002\u3002
\n\u3002\u3002\u5e76\u4e14\u6316\u4e0a\u6765\u7684\u5efa\u7b51\u79cd\u7c7b\u6070\u597d\u6709\u54ea\u4e9b \u3002\u3002found\u3002\u3002\u3002\u3002\u3002<\/p>\n

\u3002\u3002\u95ee\u54ea\u4e9b\u6316\u6398\u65b9\u6848\uff08K-tuples\uff09\u662f\u6709\u53ef\u80fd\u7684\u3002\u3002
\n<\/p>\n

Analysis: <\/h3>\n

\u3002\u3002\u3002\u9898\u76ee\u5f88\u7ed5\u3002\u3002\u5148\u660e\u786e\u70b9\u4e1c\u897f\u3002\u3002<\/p>\n

\u3002\u9996\u5148\u3002\u3002\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u65b9\u6848\u3002\u3002\u90fd\u81f3\u5c11\u8981\u8986\u76d6\u6240\u6709 found \u3002\u3002\u7136\u540e\u5bf9\u4e8e\u90a3\u4e9b\u672a\u51fa\u73b0\u5728 found \u91cc\u7684\u5143\u7d20\u3002\u3002
\n\u4ed6\u4eec\u7684 depth \u81f3\u5c11\u8981 \uff1e \u6240\u6709 found \u91cc\u51fa\u73b0\u7684\u6700\u5c0f\u503c\u3002\u5426\u5219\u4f1a\u6709\u4e0d\u8be5\u53d1\u73b0\u7684\u88ab\u53d1\u73b0\u3002\u3002\u3002\u3002
\n\u3002\u3002\u3002\u603b\u4e4b\u51fa\u73b0\u5728 found \u91cc\u548c\u6ca1\u51fa\u73b0\u5728 found \u91cc\u7684\u4e24\u7c7b\u5efa\u7b51\u3002\u3002\u662f\u8981\u5206\u5f00\u8003\u8651\u7684\u3002\u3002\u3002<\/p>\n

\u3002\u3002 \u7136\u540e\u4f3c\u4e4e\u4e0d\u53ef\u907f\u514d\u7684\u8981\u679a\u4e3e D\u3002\u3002\u3002\u5f53\u7136\u5176\u5b9e\u662f\u679a\u4e3e\u90a3\u4e2a\u88ab\u6316\u51fa\u6765\u7684\u6700\u6df1\u5143\u7d20\u3002\uff08\u79bb\u6563\u5316 + \u907f\u514d\u91cd\u590d\u8ba1\u6570\uff09\u3002\u3002\u3002
\n\u3002\u6df1\u5ea6\u786e\u5b9a\u4ee5\u540e\u3002\u3002\u53c8\u628a\u6240\u6709\u7684\u5143\u7d20\u5206\u4e3a\u4e86\u4e24\u7c7b\u3002\u3002\u8bbe\u5f53\u524d\u679a\u4e3e\u7684\u6df1\u5ea6\u4e3a d\u3002\u3002\u90a3\u4e48\u5bf9\u4e8e\u6240\u6709\u5927\u4e8e d \u7684\u5143\u7d20\u3002\u3002
\n\u3002\u3002\u3002\u4ed6\u51fa\u73b0\u4e0d\u51fa\u73b0\u5728 found \u91cc\u5176\u5b9e\u65e0\u5173\u7d27\u8981\u4e86\u3002\u3002\u53cd\u6b63\u770b\u4e0d\u89c1\u3002\u3002\u3002<\/p>\n

\u3002\u3002\u3002\u90a3\u4e48\u6211\u4eec\u518d\u679a\u4e3e\u5927\u4e8e d \u7684\u5143\u7d20\u5728 tuple \u91cc\u7684\u4e2a\u6570 i\u3002\u3002\u8fd9\u4e00\u90e8\u5206\u7684\u8ba1\u6570\u53ea\u9700\u8981\u7ec4\u5408\u6570\u5373\u53ef\u3002\u3002\u3002
\n\u3002\u3002\u5b50\u95ee\u9898\u662f\u5728\u8fd9\u4e9b\u5c0f\u4e8e d \u7684\u5143\u7d20\u4e2d\u9009\u53d6 k-1-i \u4e2a\u3002\u3002\u4fdd\u8bc1\u6bcf\u7c7b\u81f3\u5c11\u9009\u4e00\u4e2a\u7684\u65b9\u6848\u6570\u3002\u3002\u3002<\/p>\n

\u7b49\u7b49\u3002\u3002\u8fd9\u6837\u3002\u3002\u8fd8\u5f97\u7279\u5224\u90a3\u4e2a\u88ab\u6316\u51fa\u53bb\u5143\u7d20\u6070\u597d\u662f\u54ea\u4e2a\u79cd\u7c7b\u3002\u3002\u91cd\u6765\u3002\u3002<\/p>\n

\u3002\u6211\u4eec\u679a\u4e3e\u6700\u5c0f\u7684\u51fa\u73b0\u5728 tuple \u91cc\u7684\u4f46\u662f\u6ca1\u6709\u88ab\u53d1\u73b0\u7684\u4e0d\u5728 found \u4e2d\u7684\u90a3\u4e2a\u5143\u7d20\uff08\u6709\u53ef\u80fd\u4e0d\u5b58\u5728\uff09\u3002\u3002\u3002
\n\u3002\u3002\u5b50\u95ee\u9898\u662f\u5728\u6240\u6709\u5c0f\u4e8e d \u4e14\u51fa\u73b0\u5728 found \u7684\u5143\u7d20\u4e2d\u3002\u3002\u9009\u53d6 k \u4e2a\uff0c\u4f7f\u5f97\u6bcf\u4e00\u7c7b\u81f3\u5c11\u6709\u4e00\u4e2a\u3002\u3002\u3002
\n\u3002\u3002 \u5b50\u95ee\u9898\u7684 DP\u3002\u3002\u6bcf\u9636\u6bb5\u679a\u4e3e\u3002\u9009\u4e86\u51e0\u4e2a \u548c \u5176\u4e2d\u6700\u5c0f\u7684\u662f\u8c01 \u5373\u53ef\u3002<\/p>\n

\r\nconst int N = 60;\r\n\r\nLL Binom[N][N], dp[N][N];\r\nVI A[N]; int LIM, n, m;\r\n\r\nLL f(int n, int k){\r\n    if (n > k) return 0;\r\n    if (!n--) return k ? 0 : 1;\r\n    LL &res = dp[n][k];\r\n\r\n    if (!~res){\r\n        res = 0; REP_1(i, min(k, SZ(A[n]))) REP(j, SZ(A[n])-i+1){\r\n            if (A[n][j] >= LIM) break;\r\n            res += Binom[SZ(A[n])-j-1][i-1] * f(n, k-i);\r\n        }\r\n    }\r\n\r\n    return res;\r\n}\r\n\r\n\r\nclass Excavations {\r\npublic:\r\n\tlong long count(vector <int> kind, vector <int> depth, vector <int> found, int K) {\r\n\r\n        REP(i, N){Binom[i][0] = 1; REP_1(j, i) Binom[i][j] = Binom[i-1][j-1] + Binom[i-1][j];}\r\n        n = SZ(kind), m = SZ(found); REP(i, m+1) CLR(A[i]);\r\n        REP(i, n) A[find(ALL(found), kind[i]) - found.begin()].PB(depth[i]);\r\n        REP(i, m+1) SRT(A[i]);\r\n\r\n\t\tFLC(dp, -1); LIM = INF; LL res = f(m, K);\r\n\r\n\t\tDWN(i, SZ(A[m]), 0){\r\n\t\t    FLC(dp, -1), LIM = A[m][i];\r\n\t\t    REP_1(k, K-m) res += Binom[SZ(A[m])-i-1][k-1] * f(m, K-k);\r\n\t\t}\r\n\r\n\t\treturn res;\r\n\t}\r\n};\r\n<\/pre>\n
900. FoxTheLinguist<\/h2>\n
Brief description: <\/h3>\n
\u3002\u3002\u3002\u6709 m \u79cd\u8bed\u8a00\uff0c\u5f00\u59cb\u90fd\u662f 0 \u7ea7\u3002\u3002\u6709\u4e00\u4e9b\u8bfe\u7a0b\u3002\u3002\u8bfe\u7a0b\u662f\u5f62\u5982\u3002\u3002\u3002(Ai, Bj, w) \u7684\u5f62\u5f0f\u3002\u3002\uff08\u5982\u679c A \u8bed\u8a00\u591f i \u7ea7\u3002\u3002\u90a3\u4e48\u652f\u4ed8 w \u8d39\u7528\u3002\u3002\u53ef\u4ee5\u4ee4 B \u8bed\u8a00\u5230\u8fbe j \u7ea7\u3002\u3002\u3002
\n\u3002\u3002\u95ee\u6240\u6709\u8bed\u8a00\u90fd\u5230\u8fbe 9 \u7ea7\u3002\u3002\u81f3\u5c11\u9700\u8981\u591a\u5c11\u82b1\u8d39\u3002\u3002
\n<\/p>\n
Analysis: <\/h3>\n
\u3002\u3002\u6ce8\u610f\u5230\u662f\u6811\u5f62\u56fe\u5c31\u884c\u4e86\u3002\u3002
\n\u3002\u3002\u5efa\u6a21\u662f\u3002\u3002\u6bcf\u4e2a\u8bed\u8a00\u62c6\u6210 [0, 9] \u5341\u4e2a\u70b9\u3002\u3002 \u3002\u3002\u6dfb\u52a0\u4e00\u4e2a\u6839\u7ed3\u70b9\u3002\u3002\u8fde\u5230\u6240\u6709\u8bed\u8a00\u7684 0 \u7ea7\u3002\u3002\u4ee3\u4ef7\u4e3a 0\u3002\u3002
\n\u3002\u3002\u3002\u3002\u7136\u540e\u5bf9\u6bcf\u4e2a\u8bed\u8a00\u7684\u9664\u4e86 0 \u4ee5\u5916\u7684\u7b49\u7ea7\u3002\u3002\u90fd\u5411\u4f4e\u4e00\u7ea7\u8fde\u4e00\u6761\u4ee3\u4ef7\u4e3a 0 \u7684\u8fb9\u3002\u3002\u3002\u3002
\n\u3002\u3002\uff08\u3002\u5982\u679c\u8fb9\u7684\u5f62\u5f0f\u662f\u4ece\u4e00\u4e2a\u8bed\u8a00\u96c6\u5408\u5230\u53e6\u4e00\u4e2a\u8bed\u8a00\u8fd8\u80fd\u505a\u4e48\u3002\u3002<\/p>\n
External link: <\/h3>\n
https:\/\/apps.topcoder.com\/wiki\/display\/tc\/SRM+584<\/a>
\nhttps:\/\/gist.github.com\/lychees\/6202038<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
600. Excavations Brief description: \u3002\u3002\u3002\u4e00\u4e2a\u53e4\u57ce\u9057\u8ff9 n \u4e2a\u5efa\u7b51\u3002\u3002\u6211\u4eec\u77e5\u9053\u8fd9\u4e9b\u5efa\u7b51\u7684\u7c7b\u578b\u548c\u63a9\u57cb\u7684\u6df1\u5ea6\u3002type\u3002depth\u3002 \u3002\u3002\u3002\u4f60\u6709\u4e00\u4e2a\u6700\u5927\u53ef\u4ee5\u6316 D \u7c73\u7684\u6316\u6398\u673a\u3002\u3002\u4f60\u4e0d\u77e5\u9053 D \u3002\u3002\u4f46\u662f\u4f60\u77e5\u9053\u4f60\u6070\u597d\u6316\u4e86 K \u6b21\u3002\u3002 \u3002\u3002\u5e76\u4e14\u6316\u4e0a\u6765\u7684\u5efa\u7b51\u79cd\u7c7b\u6070\u597d\u6709\u54ea\u4e9b \u3002\u3002found\u3002\u3002\u3002\u3002\u3002 \u3002\u3002\u95ee\u54ea\u4e9b\u6316\u6398\u65b9\u6848\uff08K-tuples\uff09\u662f\u6709\u53ef\u80fd\u7684\u3002\u3002<\/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":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[17],"tags":[],"class_list":["post-796","post","type-post","status-publish","format-standard","hentry","category-topcoder"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-cQ","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/796","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=796"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/796\/revisions"}],"predecessor-version":[{"id":799,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/796\/revisions\/799"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=796"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=796"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=796"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}