{"id":76,"date":"2025-01-11T23:13:57","date_gmt":"2025-01-11T15:13:57","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=76"},"modified":"2025-01-11T23:13:57","modified_gmt":"2025-01-11T15:13:57","slug":"d-new-year-santa-network-%e8%a7%a3%e6%9e%90%e6%80%9d%e7%b6%ad%e3%80%81dfs%e3%80%81%e7%b5%84%e5%90%88%e3%80%81%e6%a8%b9%e7%8b%80dp","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=76","title":{"rendered":"D. New Year Santa Network \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u6a39\u72c0DP)"},"content":{"rendered":"\n

Codeforce 500 D. New Year Santa Network \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u6a39\u72c0DP)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF500D
\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

\u984c\u76ee<\/strong>
\n\u7d66\u4f60\u4e00\u68f5\u6709\u908a\u6b0a\u7684\u6a39\uff0c\u6c42\u73fe\u5728\u96a8\u6a5f\u53d6$3$\u9ede\uff0c\u6c42\u9019\u4e09\u9ede\u4e92\u76f8\u8ddd\u96e2\u7e3d\u548c\u7684\u671f\u671b\u503c\u3002<\/p>\n<\/blockquote>\n

\u524d\u8a00<\/h3>\n

\u4eca\u5929\u5beb\u7684\u984c\u76ee\u90fd\u662f\u770b\u89e3\u7b54\u5c31\u6703\u5beb\uff0c\u539f\u672c\u5c31\u6c92\u6709\u7684\u81ea\u4fe1\u5fc3\u53c8\u8981\u66f4\u4f4e\u4e86<\/p>\n

\u60f3\u6cd5<\/h3>\n

$3$\u500b\u9ede\u8981\u8003\u616e\u7684\u4e8b\u60c5\u592a\u591a\u4e86\uff0c\u9996\u5148\u53ea\u8981\u6ce8\u610f\u5230\u4ee5\u4e0b\u4e00\u4ef6\u4e8b\uff0c\u90a3\u9ebc\u5176\u4ed6\u7684\u4e8b\u60c5\u5c31\u548cCF1401D<\/a>\u6c92\u5169\u6a23\u4e86\u3002
\n\u6ce8\u610f\u5230($E(X)$\u4ee3\u8868$X$\u4e8b\u4ef6\u7684\u671f\u671b\u503c):$E(d(c_1,c_2)+d(c_2,c_3)+d(c_1,c_3))=E(d(c_1,c_2))+E(d(c_2,c_3))+E(d(c_1,c_3))$
\n\u4e14$c_1,c_2,c_3$\u90fd\u662f$dummy\\ variable$,\u6240\u4ee5$E(d(c_1,c_2))=E(d(c_2,c_3))=E(d(c_1,c_3))$
\n\u4e5f\u5c31\u662f\u8aaa\u6211\u5011\u53ea\u8981\u80fd\u7b97\u51fa\u96a8\u4fbf\u53d6\u5169\u9ede\u7684\u8ddd\u96e2\u671f\u671b\u503c\uff0c\u90a3\u9ebc\u6700\u5f8c\u7b54\u6848$\\times3$\u5c31\u597d\u3002<\/p>\n

(\u4ee5\u4e0b\u5167\u5bb9\u53ef\u4ee5\u53c3\u7167CF1401D<\/a>)
\n\u90a3\u9ebc\u6211\u5011\u53ea\u8981\u7b97\u51fa\u5982\u679c\u6240\u6709\u9ede\u5c0d\u7684\u8ddd\u96e2\u90fd\u88ab\u7b97\u4e00\u6b21\uff0c\u6bcf\u500b\u908a\u6703\u88ab\u7b97\u5e7e\u6b21\u5c31\u597d\u3002
\n\u7dad\u8b77\u6bcf\u500b\u5b50\u6a39\u6709\u5e7e\u500b\u9ede\u70ba$cnt[v]$\uff0c\u63a5\u8457\u679a\u8209\u908a${u,v,w}$\uff0c\u4fdd\u8b49$dep[u]<dep[v]$\uff0c\u9019\u500b\u908a\u6703\u88ab\u8d70\u904e\u7684\u6b21\u6578\u5c31\u662f\u9019\u689d\u908a\u9023\u63a5<\/strong>\u7684\u5169\u500b\u9ede\u96c6\u7684\u9ede\u7684\u6578\u91cf\u7684\u76f8\u4e58\uff0c\u4e5f\u5c31\u662f$cnt[v]\\times(n-cnt[v])$\u3002\u628a\u908a\u6b0a\u7e3d\u548c\u5132\u5b58\u5230\u4e00\u500b$long\\ long$\u88e1\uff0c\u7531\u65bc\u908a\u6b0a\u7e3d\u548c\u81f3\u591a\u662f$n\\times n^2\\times1000=10^{18}$(1000\u662f\u4e00\u689d\u908a\u7684\u6700\u5927\u908a\u6b0a)\uff0c\u6240\u4ee5\u5132\u5b58\u6c92\u6709\u554f\u984c\u3002
\n\u6bcf\u6b21\u4fee\u6539\u908a\u5c31\u55ae\u7d14\u7684\u628a\u9019\u689d\u908a\u7684\u8ca2\u737b\u91cd\u7b97\u4e00\u904d\u5c31\u597d\u3002<\/p>\n

\u7a0b\u5f0f\u78bc:<\/h3>\n
const int _n=1e5+10;  \nint t,n,a,b,l,q,r,w,fa[_n],cnt[_n],dep[_n];  \nll sum;  \nvector<PII> G[_n];  \nstruct E{int u,v,w;} e[_n];  \nll C(ll x){if(x<2ll)return 0;return x*(x-1)\/2ll;}  \nvoid dfs(int v,int faa,int d){  \n  fa[v]=faa,dep[v]=d,cnt[v]=1;  \n  rep(i,0,SZ(G[v]))if(G[v][i].fi!=faa)  \n    dfs(G[v][i].fi,v,d+1),cnt[v]+=cnt[G[v][i].fi];  \n}  \nmain(void) {ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);  \n  cin>>n;rep(i,1,n){cin>>a>>b>>l;a--,b--;G[a].pb({b,l}),G[b].pb({a,l});e[i]={a,b,l};}  \n  dfs(0,-1,0);rep(i,1,n){  \n    int u=e[i].u,v=e[i].v,w=e[i].w;  \n    if(dep[u]>dep[v])swap(u,v);  \n    sum+=1ll*cnt[v]*(n-cnt[v])*w;  \n  }  \n  cin>>q;while(q--){  \n    cin>>r>>w;int u=e[r].u,v=e[r].v;  \n    if(dep[u]>dep[v])swap(u,v);  \n    sum-=1ll*cnt[v]*(n-cnt[v])*e[r].w;  \n    sum+=1ll*cnt[v]*(n-cnt[v])*w;  \n    cout<<setprecision(20)<<3.0*sum\/(1.0*C(n))<<'\\n';  \n    e[r].w=w;  \n  }  \n  return 0;  \n}  \n<\/code><\/pre>\n
\u6a19\u982d\u3001\u6a21\u677f\u8acb\u9edeSubmission\u770b
\nSubmission<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_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},"version":2}},"categories":[3],"tags":[10,7,9,8,23,6],"class_list":["post-76","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-dfs","tag-ojcode","tag-8","tag-dp","tag-6"],"jetpack_publicize_connections":[],"yoast_head":"\nD. New Year Santa Network \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u6a39\u72c0DP) - Logic Formatting<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blog.seekrealthing.net\/blog\/?p=76\" \/>\n<meta property=\"og:locale\" content=\"zh_TW\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"D. New Year Santa Network \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u6a39\u72c0DP) - Logic Formatting\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blog.seekrealthing.net\/blog\/?p=76\" \/>\n<meta property=\"og:site_name\" content=\"Logic Formatting\" \/>\n<meta property=\"article:published_time\" content=\"2025-01-11T15:13:57+00:00\" \/>\n<meta name=\"author\" content=\"jeff\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005:\" \/>\n\t<meta name=\"twitter:data1\" content=\"jeff\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9810\u4f30\u95b1\u8b80\u6642\u9593\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 \u5206\u9418\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=76#article\",\"isPartOf\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=76\"},\"author\":{\"name\":\"jeff\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/person\/233e80a0fee3d4706f067f2e88c0b454\"},\"headline\":\"D. New Year Santa Network \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u6a39\u72c0DP)\",\"datePublished\":\"2025-01-11T15:13:57+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=76\"},\"wordCount\":87,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#organization\"},\"keywords\":[\"codeforce\",\"DFS\",\"ojcode\",\"\u601d\u7dad\",\"\u6a39\u72c0DP\",\"\u7d44\u5408\"],\"articleSection\":[\"ojcode\"],\"inLanguage\":\"zh-TW\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/blog.seekrealthing.net\/blog\/?p=76#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=76\",\"url\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=76\",\"name\":\"D. New Year Santa Network \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u6a39\u72c0DP) - Logic Formatting\",\"isPartOf\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#website\"},\"datePublished\":\"2025-01-11T15:13:57+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=76#breadcrumb\"},\"inLanguage\":\"zh-TW\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/blog.seekrealthing.net\/blog\/?p=76\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/?p=76#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9801\",\"item\":\"https:\/\/blog.seekrealthing.net\/blog\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"D. New Year Santa Network \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u6a39\u72c0DP)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#website\",\"url\":\"https:\/\/blog.seekrealthing.net\/blog\/\",\"name\":\"Logic Formatting\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/blog.seekrealthing.net\/blog\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"zh-TW\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#organization\",\"name\":\"Logic Formatting\",\"url\":\"https:\/\/blog.seekrealthing.net\/blog\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-TW\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/blog.seekrealthing.net\/blog\/wp-content\/uploads\/2025\/02\/android-chrome-512x512-1.png\",\"contentUrl\":\"https:\/\/blog.seekrealthing.net\/blog\/wp-content\/uploads\/2025\/02\/android-chrome-512x512-1.png\",\"width\":512,\"height\":512,\"caption\":\"Logic Formatting\"},\"image\":{\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/person\/233e80a0fee3d4706f067f2e88c0b454\",\"name\":\"jeff\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-TW\",\"@id\":\"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f9b571b28c252728386f0002b35d9cb9a9028f740b0f9ca5ad678e7eb21c4857?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f9b571b28c252728386f0002b35d9cb9a9028f740b0f9ca5ad678e7eb21c4857?s=96&d=mm&r=g\",\"caption\":\"jeff\"},\"sameAs\":[\"http:\/\/150.230.63.147\/blog\"],\"url\":\"https:\/\/blog.seekrealthing.net\/blog\/?author=1\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"D. New Year Santa Network \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u6a39\u72c0DP) - Logic Formatting","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/blog.seekrealthing.net\/blog\/?p=76","og_locale":"zh_TW","og_type":"article","og_title":"D. New Year Santa Network \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u6a39\u72c0DP) - Logic Formatting","og_url":"https:\/\/blog.seekrealthing.net\/blog\/?p=76","og_site_name":"Logic Formatting","article_published_time":"2025-01-11T15:13:57+00:00","author":"jeff","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005:":"jeff","\u9810\u4f30\u95b1\u8b80\u6642\u9593":"2 \u5206\u9418"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/blog.seekrealthing.net\/blog\/?p=76#article","isPartOf":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/?p=76"},"author":{"name":"jeff","@id":"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/person\/233e80a0fee3d4706f067f2e88c0b454"},"headline":"D. New Year Santa Network \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u6a39\u72c0DP)","datePublished":"2025-01-11T15:13:57+00:00","mainEntityOfPage":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/?p=76"},"wordCount":87,"commentCount":0,"publisher":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/#organization"},"keywords":["codeforce","DFS","ojcode","\u601d\u7dad","\u6a39\u72c0DP","\u7d44\u5408"],"articleSection":["ojcode"],"inLanguage":"zh-TW","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/blog.seekrealthing.net\/blog\/?p=76#respond"]}]},{"@type":"WebPage","@id":"https:\/\/blog.seekrealthing.net\/blog\/?p=76","url":"https:\/\/blog.seekrealthing.net\/blog\/?p=76","name":"D. New Year Santa Network \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u6a39\u72c0DP) - Logic Formatting","isPartOf":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/#website"},"datePublished":"2025-01-11T15:13:57+00:00","breadcrumb":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/?p=76#breadcrumb"},"inLanguage":"zh-TW","potentialAction":[{"@type":"ReadAction","target":["https:\/\/blog.seekrealthing.net\/blog\/?p=76"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/blog.seekrealthing.net\/blog\/?p=76#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9801","item":"https:\/\/blog.seekrealthing.net\/blog"},{"@type":"ListItem","position":2,"name":"D. New Year Santa Network \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u6a39\u72c0DP)"}]},{"@type":"WebSite","@id":"https:\/\/blog.seekrealthing.net\/blog\/#website","url":"https:\/\/blog.seekrealthing.net\/blog\/","name":"Logic Formatting","description":"","publisher":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/blog.seekrealthing.net\/blog\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"zh-TW"},{"@type":"Organization","@id":"https:\/\/blog.seekrealthing.net\/blog\/#organization","name":"Logic Formatting","url":"https:\/\/blog.seekrealthing.net\/blog\/","logo":{"@type":"ImageObject","inLanguage":"zh-TW","@id":"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/logo\/image\/","url":"https:\/\/blog.seekrealthing.net\/blog\/wp-content\/uploads\/2025\/02\/android-chrome-512x512-1.png","contentUrl":"https:\/\/blog.seekrealthing.net\/blog\/wp-content\/uploads\/2025\/02\/android-chrome-512x512-1.png","width":512,"height":512,"caption":"Logic Formatting"},"image":{"@id":"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/person\/233e80a0fee3d4706f067f2e88c0b454","name":"jeff","image":{"@type":"ImageObject","inLanguage":"zh-TW","@id":"https:\/\/blog.seekrealthing.net\/blog\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f9b571b28c252728386f0002b35d9cb9a9028f740b0f9ca5ad678e7eb21c4857?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f9b571b28c252728386f0002b35d9cb9a9028f740b0f9ca5ad678e7eb21c4857?s=96&d=mm&r=g","caption":"jeff"},"sameAs":["http:\/\/150.230.63.147\/blog"],"url":"https:\/\/blog.seekrealthing.net\/blog\/?author=1"}]}},"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/76","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=76"}],"version-history":[{"count":1,"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/76\/revisions"}],"predecessor-version":[{"id":77,"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/76\/revisions\/77"}],"wp:attachment":[{"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=76"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=76"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.seekrealthing.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=76"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}