dfs \u5e8f\u6c42 lca<\/a> \u8fd9\u6837\u7684\u9ad8\u7ea7\u77e5\u8bc6\uff0c\u4f46\u770b\u8d77\u6765\u8fd9\u4e2a\u9898\u770b\u8d77\u6765\u907f\u514d\u4e0d\u4e86\u500d\u589e\u7956\u5148\uff0c\u6240\u4ee5\u8fd8\u662f\u7528\u500d\u589e\u7956\u5148\u6c42 lca \u5427\uff01<\/p>\n\u9996\u5148\u8fd8\u662f dfs \u5404\u79cd\u9884\u5904\u7406\uff0c\u8fd9\u91cc\u8fd8\u8981\u9700\u8981\u4e24\u6b21 dfs\uff0c\u56e0\u4e3a\u9700\u8981\u8dd1\u6811\u5f62 dp \u6c42\u51fa dn[x] \u548c up[x]\uff0c\u5206\u522b\u8868\u793a\u5411\u4e0b\u3001\u5411\u4e0a\u7684\u8ddd\u79bb\u548c\u3002<\/p>\n
\u6839\u636e\u8def\u5f84\u7684\u5947\u5076\u6027\uff0c\u4e2d\u70b9\u53ef\u80fd\u5728\u4e24\u70b9\u4e4b\u95f4\u4e5f\u53ef\u80fd\u6070\u597d\u843d\u5728\u67d0\u4e2a\u70b9\u4e0a\u3002
\n\u5bf9\u4e8e\u90a3\u6837\u7684\u60c5\u51b5\uff0c\u5b83\u4efb\u610f\u8fde\u5411 x \u6216\u8005 y \u90fd\u53ef\uff0c\u4f46\u662f\u8fd9\u6837\u8ba8\u8bba\u7684\u8bdd\u611f\u89c9\u60c5\u51b5\u6709\u70b9\u591a\u538b\u529b\u6709\u70b9\u5927…<\/p>\n
\u4e8e\u662f\u6211\u4eec\u9700\u8981\u8bbe\u8ba1\u4e00\u4e2a\u5b50\u51fd\u6570 ff(x, y)\uff0c\u8868\u793a\u6c42\u51fa\u6240\u6709\u5230 x \u7684\u4f46\u4e0d\u7ecf\u8fc7 y \u7684\u8def\u5f84\u548c\uff01
\n\u8fd9\u6837\u7684\u8bdd\u65e0\u8bba\u5982\u4f55\u6211\u4eec\u90fd\u53ef\u4ee5\u6c42\u4e24\u4e2a\u5206\u5272\u70b9\uff0c\u907f\u514d\u8ba8\u8bba\u8def\u5f84\u7684\u5947\u5076\u6027\uff0c\u800c\u662f\u53ea\u8981\u5904\u7406\u4e00\u4e0b\u4e24\u8fb9\u6df1\u5ea6\u4e00\u6837\u7684\u60c5\u51b5\uff0c\u538b\u529b\u5927\u5e45\u51cf\u8f7b\uff01<\/p>\n
\u6700\u540e\u53ea\u8981\u8003\u8651\u600e\u4e48\u6c42 ff(x, y)\uff0c\u6709\u4e09\u79cd\u60c5\u51b5\uff0c\u65e0\u8bba\u54ea\u4e00\u79cd\u6211\u4eec\u90fd\u5148\u52a0\u4e0a dn[x]+up[x]\u3002
\n\u7b2c\u4e00\u79cd\u662f x \u662f y \u7684\u7956\u5148\uff0c\u90a3\u4e48\u4e0d\u4ec5\u8981\u51cf\u53bb dn[y]\uff0c\u5e76\u4e14 y \u5b50\u6811\u7684\u6240\u6709\u70b9\u8fd8\u8981\u7ee7\u7eed\u51cf\u53bb\u5c11\u7b97\u7684\u8ddd\u79bb\uff0c\u4e5f\u5c31\u662f sz[y] * (dep[y]-dep[x])\u3002
\n\u7b2c\u4e8c\u79cd\u662f y \u662f x \u7684\u7956\u5148\uff0c\u6b64\u65f6\u8981\u5148\u6c42\u51fa y \u4e00\u5708\u4f46\u4e0d\u5305\u542b x \u6240\u5728\u5206\u652f\u7684\u548c\uff0c\u6211\u4eec\u9700\u8981\u5148\u6c42\u51fa y \u7684\u5b69\u5b50\u4e2d\u662f x \u7956\u5148\u7684\u8282\u70b9 w\uff0c\u90a3\u4e48\u5c31\u662f\u51cf\u53bb dn[y]-dn[w]-sz[w]\uff0c\u7136\u540e\u518d\u7ee7\u7eed\u51cf\u53bb\u5c11\u7b97\u7684\uff0c\u4e5f\u5c31\u662f (LL)(n-sz[w]) * (dep[x]-dep[y])\u3002
\n\u6700\u540e\u4e00\u79cd\u60c5\u51b5\u662f\u6709\u53e6\u4e00\u4e2a lca\uff0c\u8fd9\u79cd\u60c5\u51b5\u53ef\u4ee5\u5408\u5e76\u5230\u60c5\u51b5\u4e00\uff0c\u53ea\u8981\u628a\u8ddd\u79bb\u51fd\u6570\u6539\u6210 (dep[x]+dep[y]-2*dep[l]) \u5373\u53ef\u3002<\/p>\n
\r\n#include <lastweapon\/io>\r\nusing namespace lastweapon;\r\nconst int N = int(2e5) + 9, LV = 20;\r\nint fa[LV][N], dep[N], sz[N]; LL dn[N], up[N];\r\nVI adj[N]; int n;\r\n\r\nint move_up(int x, int d) {\r\n for (int lv=0;d;++lv,d>>=1)\r\n if (d&1) x = fa[lv][x];\r\n return x;\r\n}\r\ninline int lca(int x, int y) {\r\n if (dep[y] < dep[x]) swap(x, y); y = move_up(y, dep[y] - dep[x]); if (x == y) return x;\r\n DWN(lv, LV, 0) if (fa[lv][x] != fa[lv][y]) x = fa[lv][x], y = fa[lv][y];\r\n return fa[0][x];\r\n}\r\nvoid dfs1(int u = 1, int p = 0) {\r\n sz[u] = 1;\r\n for (auto v: adj[u]) if (v != p) {\r\n dep[v] = dep[u] + 1;\r\n fa[0][v] = u; for (int lv=0;fa[lv+1][v]=fa[lv][fa[lv][v]];++lv);\r\n dfs1(v, u);\r\n sz[u] += sz[v];\r\n dn[u] += dn[v] + sz[v];\r\n }\r\n}\r\nvoid dfs2(int u = 1, int p = 0) {\r\n for (auto v: adj[u]) if (v != p) {\r\n up[v] = up[u] + dn[u] + n - dn[v] - 2*sz[v];\r\n dfs2(v, u);\r\n }\r\n}\r\nint sub(int u, int v) {\r\n return move_up(v, dep[v]-dep[u]-1);\r\n}\r\n\r\nLL ff(int x, int y) {\r\n \/\/ y\r\n \/\/ x\r\n \/\/ z x\r\n \/\/x y y\r\n LL z = dn[x] + up[x]; int l = lca(x, y);\r\n if (l == y) {\r\n int w = sub(y, x);\r\n z -= up[y] + (dn[y] - dn[w] - sz[w]) + (LL)(n-sz[w])*(dep[x]-dep[y]);\r\n } else {\r\n z -= dn[y] + (LL)sz[y]*(dep[x]+dep[y]-2*dep[l]);\r\n }\r\n return z;\r\n}\r\n\r\n\/\/ 1\r\n\/\/ 6 4 8\r\n\/\/ 75 2\r\n\/\/ 3\r\n\r\nLL f(int a, int b) {\r\n\r\n if (a == b) return dn[a] + up[a];\r\n if (dep[a] < dep[b]) swap(a, b);\r\n int l = lca(a, b), d = dep[a] + dep[b] - 2*dep[l];\r\n int ma = move_up(a, d\/2), mb = ma == l ? move_up(b, d\/2-1) : fa[0][ma];\r\n LL z = ff(a, mb) + ff(b, ma);\r\n return z;\r\n}\r\n\r\nint main() {\r\n\r\n#ifndef ONLINE_JUDGE\r\n freopen("in.txt", "r", stdin);\r\n \/\/freopen("\/Users\/minakokojima\/Documents\/GitHub\/ACM-Training\/Workspace\/out.txt", "w", stdout);\r\n#endif\r\n\r\n RD(n); DO(n-1) {\r\n int x, y; RD(x, y);\r\n adj[x].PB(y);\r\n adj[y].PB(x);\r\n }\r\n\r\n dfs1(); dfs2();\r\n\r\n Rush {\r\n int a, b; RD(a, b);\r\n printf("%lld\\n", f(a, b));\r\n }\r\n}\r\n\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"Problem F. Rook Score \u6211\u4eec\u8bb0\u5f55\u6bcf\u4e00\u884c\u548c\u6bcf\u4e00\u5217\u7684\u548c R[], C[]\uff0c\u90a3\u4e48\u7b54\u6848\u662f\u67d0\u4e2a R[] + C[] – X[][] \u6ce8\u610f\u8fd9\u91cc X[][] \u53ef\u80fd\u5728\u8f93\u5165\u91cc\uff0c\u4e5f\u53ef\u80fd\u4e0d\u5728\uff0c\u524d\u8005\u53ea\u6709 O(n) \u79cd\uff0c \u540e\u8005\u5bf9\u6bcf\u4e00\u4e2a R\uff0c\u6211\u4eec\u53ea\u8981\u627e\u5176\u4e2d\u6700\u5927\u7684 C\uff0c\u6240\u4ee5\u5176\u5b9e\u4e5f\u53ea\u6709 O(n) \u79cd\u3002 \u6392\u5e8f\u540e\u4e8c\u91cd\u5faa\u73af\u52a0\u4e2a\u526a\u679d\u5373\u53ef\u3002 #include <lastweapon\/io> using namespace lastweapon; const int N = int(2e5) + 9; set<PII> P; map<int, LL> R, C; vector<pair<LL, int>> RR, CC; int r[N], c[N], x[N]; int n; int main() { #ifndef […]<\/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-2620","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-Gg","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2620","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=2620"}],"version-history":[{"count":18,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2620\/revisions"}],"predecessor-version":[{"id":2700,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2620\/revisions\/2700"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=2620"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=2620"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=2620"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}