\u7b80\u5355\u5197\u65a5<\/a> \u4e00\u4e0b\u5373\u53ef\u3002<\/p>\n\r\n#include <lastweapon\/number>\r\n\r\nusing namespace lastweapon;\r\n\r\nconst int N = int(5e1) + 9;\r\nInt Fact[N]; VVI Partition; VI cur;\r\nint n;\r\n\r\nvoid gen(int n = ::n, int s = 1){\r\n if (!n){\r\n Partition.PB(cur);\r\n }\r\n else if (n >= s){\r\n cur.PB(s); gen(n-s, s); cur.pop_back();\r\n gen(n, s+1);\r\n }\r\n}\r\n\r\nInt c(const VI P){\r\n\r\n Int z = Fact[n]; int c = 0, l = P.front();\r\n\r\n ECH(it, P){\r\n z \/= *it; if (*it != l){\r\n z \/= Fact[c]; l = *it;\r\n c = 1;\r\n }\r\n else{\r\n ++c;\r\n }\r\n }\r\n\r\n z \/= Fact[c];\r\n return z;\r\n}\r\n\r\nint g(const VI P){\r\n\r\n REP(i, SZ(P)) {\r\n w[i] = 0; vis[i] = 0;\r\n adj[i].clear();\r\n }\r\n\r\n int z = 0; REP(i, SZ(P)){\r\n z += P[i] \/ 2;\r\n REP(j, i) z += __gcd(P[i], P[j]);\r\n }\r\n return z;\r\n}\r\n\r\nInt binom(int n, int m) {\r\n return Fact[n] \/ (Fact[m] * Fact[n-m]);\r\n}\r\n\r\nint main(){\r\n\r\n#ifndef ONLINE_JUDGE\r\n \/\/freopen("in.txt", "r", stdin);\r\n \/\/freopen("out.txt", "w", stdout);\r\n#endif\r\n\r\n int k; RD(n, k, MOD); Fact[0] = 1; REP_1(i, n) Fact[i] = Fact[i-1] * i;\r\n\r\n gen();\r\n\r\n Int z = 0; ECH(it, Partition) if (SZ(*it) >= k) {\r\n Int zz = 0;\r\n REP(i, k) {\r\n Int d = binom(k, i) * pow(Int(k-i), SZ(*it));\r\n if (i&1) zz -= d; else zz += d;\r\n }\r\n z += zz * c(*it) * pow(Int(2), g(*it));\r\n }\r\n z \/= Fact[n];\r\n cout << z << endl;\r\n}\r\n\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"Ex. Count Unlabeled Graphs k = 1 \u7684\u60c5\u51b5\u4e0b\uff0c\u663e\u7136\u5c31\u662f\u65e0\u6807\u53f7\u56fe\u8ba1\u6570\u3002 \u6240\u4ee5\u505a\u6cd5\u4e5f\u5fc5\u7136\u4e0d\u4f1a\u5f31\u4e8e \u539f\u9898\u3002 \u56de\u5fc6\u539f\u9898\u4e2d\uff0c\u6211\u4eec\u5bf9\u70b9\u96c6\u7684\u5bf9\u79f0\u7fa4\uff0c\u6309\u7167 cycle index \u8fdb\u884c\u5206\u7c7b\uff0c\u518d\u53bb\u751f\u6210\u5bf9\u5e94\u7684\u8fb9\u7f6e\u6362\u7fa4\uff0c\u518d\u5f97\u5230\u8fb9\u7f6e\u6362\u7fa4\u7684 cycle index\u3002\u4e0d\u8fc7\u770b\u8d77\u6765\u8fd9\u91cc\u6211\u4eec\u65e2\u8981\u8003\u8651\u8fb9\u67d3\u8272\uff0c\u8fd8\u8981\u8003\u8651\u70b9\u67d3\u8272\uff0c\u597d\u5728\u5b83\u4eec\u7684\u7ed3\u6784\u90fd\u662f\u7528\u521d\u59cb\u7684\u70b9\u7fa4\u7684 cycle index \u6240\u51b3\u5b9a\u7684\uff0c\u53ef\u4ee5\u4e00\u8d77\u53c2\u4e0e\u8ba1\u7b97\u3002 \u6700\u540e\u518d \u7b80\u5355\u5197\u65a5 \u4e00\u4e0b\u5373\u53ef\u3002 #include <lastweapon\/number> using namespace lastweapon; const int N = int(5e1) + 9; Int Fact[N]; VVI Partition; VI cur; int n; void gen(int n = ::n, int s = 1){ if (!n){ Partition.PB(cur); } […]<\/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":[1],"tags":[],"class_list":["post-2877","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-Kp","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2877","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=2877"}],"version-history":[{"count":5,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2877\/revisions"}],"predecessor-version":[{"id":2882,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2877\/revisions\/2882"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=2877"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=2877"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=2877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}