{"id":28,"date":"2025-01-11T22:28:54","date_gmt":"2025-01-11T14:28:54","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=28"},"modified":"2025-01-11T22:34:44","modified_gmt":"2025-01-11T14:34:44","slug":"codeforce-1401-d-maximum-distributed-tree-%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%e8%b2%aa%e5%bf%83%e3%80%81dp","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=28","title":{"rendered":"D. Maximum Distributed Tree \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u8caa\u5fc3\u3001DP)"},"content":{"rendered":"\n

Codeforce 1401 D. Maximum Distributed Tree \u89e3\u6790(\u601d\u7dad\u3001DFS\u3001\u7d44\u5408\u3001\u8caa\u5fc3\u3001DP)<\/h1>\n

\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF1401D
\n\u984c\u76ee\u9023\u7d50<\/a><\/p>\n

\n

\u984c\u76ee<\/strong>
\n\u76f4\u63a5\u770b\u539f\u984c\u6bd4\u8f03\u6e05\u695a\uff0c\u7565\u3002<\/p>\n<\/blockquote>\n

\u524d\u8a00<\/h3>\n

\u9019\u6b21\u6bd4\u8cfd\u88ab\u7b2cC.\u984c\u641e\u5230\u526920\u5206\u9418\u53ef\u4ee5\u5bebD.\u9019\u984c\uff0c\u6bd4\u8cfd\u6642\u6c92\u5beb\u51fa\u4f86\uff0c\u6bd4\u5b8c\u4e86\u4ee5\u5f8c\u82b1\u4e86\u4e00\u500b\u591a\u5c0f\u6642Debug\u624dDe\u51fa\u4f86Orz\u3002<\/p>\n

\u60f3\u6cd5<\/h3>\n

\u8981\u6ce8\u610f\u5230\uff0c\u984c\u76ee\u4e2d\u7684distribution index<\/strong><\/em>\u5be6\u969b\u4e0a\u5c31\u662f\u628a\u6bcf\u689d\u8def\u5c0d\u65bc\u6bcf\u500b\u9ede\u5c0d\u4e92\u76f8\u62dc\u8a2a\u6642\uff0c\u6703\u88ab\u7d93\u904e\u5e7e\u6b21\uff0c\u4e58\u500b\u6b0a\u91cd\uff0c\u5168\u90e8\u52a0\u8d77\u4f86\u3002\u4f8b\u5982\u8aaa$(u,v)$\u9019\u689d\u908a\uff0c$u$\u90a3\u4e00\u7aef\u63a5\u4e86\u4e00\u500b\u7bc0\u9ede\u500b\u6578\u70ba$cnt_u$\u7684\u5b50\u6a39\uff0c$v$\u90a3\u4e00\u7aef\u63a5\u4e86\u4e00\u500b\u7bc0\u9ede\u500b\u6578\u70ba$cnt_v$\u7684\u5b50\u6a39(code\u4e2d\u6211\u662f\u7528$dp[.]$\u4f86\u5132\u5b58)\uff0c\u90a3\u9ebc\u7e3d\u5171\u6709$cnt_u\\times cnt_v$\u500b\u9ede\u5c0d\uff0c\u5728\u4e92\u76f8\u62dc\u8a2a\u6642\u6703\u7d93\u904e$(u,v)$\u9019\u689d\u908a\uff0c\u800cdistribution index<\/strong><\/em>\u5c31\u662f\u628a\u6240\u6709\u908a\u7684\u62dc\u8a2a\u6b21\u6578\u4e58\u4ee5\u4f60\u5206\u914d\u7684\u6b0a\u91cd\uff0c\u7136\u5f8c\u5168\u90e8\u52a0\u8d77\u4f86\u3002
\n\u800c\u5c0d\u65bc\u6bcf\u689d\u908a\uff0c\u5982\u679c\u8981\u627e\u5230\u5169\u500b\u7bc0\u9ede\u5206\u5225\u9023\u63a5\u5230\u591a\u5927\u7684\u5b50\u6a39(\u6ce8\u610f\uff0c\u9019\u908a\u6240\u8aaa\u7684\u5b50\u6a39\u4ee3\u8868\u7531\u7576\u524d\u9ede\u70ba\u6839\uff0c\u4e14\u4e0d\u6703\u7d93\u904e\u76ee\u524d\u8003\u616e\u7684\u908a\u7684\u5b50\u6a39)\uff0c\u6211\u5011\u53ef\u4ee5\u96a8\u4fbf\u9078\u4e00\u500b\u9ede$r$\u70ba\u6839\uff0c\u505a\u6a39\u4e0aDP\u7dad\u8b77\u6bcf\u500b\u9ede\u70ba\u6839\uff0c\u5f80\u4e0b\u7684\u5b50\u6a39(\u4e5f\u5c31\u662f\u4ee5$r$\u70ba\u6839\u4f86\u8aaa\uff0c\u6211\u5011\u8003\u616e\u7684\u5b50\u6a39\u4e0d\u6703\u5f80$r$\u63a5\u8fd1)\u7684\u7bc0\u9ede\u500b\u6578\u3002\u63a5\u8457\u5c31\u662f\u4e00\u4e9b\u7c21\u55ae\u7684\u5be6\u4f5c\u4e86\u3002
\n\u8981\u6ce8\u610f\u4ee5\u4e0b\u5e7e\u9ede:<\/p>\n

    \n
  1. \u5c0d\u65bc\u67d0\u500b\u908a$(u,v)$\uff0c\u9019\u500b\u908a\u6703\u88ab\u7d93\u904e\u7684\u6b21\u6578\u70ba:$dp[v]\\times(n-dp[v])$ (\u5047\u8a2d$u$\u6bd4$v$\u6dfa\uff0c\u9700\u8981\u5148\u5728dfs\u6642\u7dad\u8b77\u6bcf\u500b\u9ede\u7684depth)<\/li>\n
  2. \u6700\u5f8c\u628a\u6b0a\u91cd\u5206\u914d\u5230\u908a\u4e0a\u6642\uff0c\u9996\u5148\u7576\u7136\u5169\u500b\u6578\u5217\u90fd\u8981\u5148\u6392\u5e8f\uff0c\u63a5\u8457\u8981\u8a18\u5f97\u8003\u616e$n-1>m$\u548c$n-1\\le m$\u7684\u60c5\u6cc1(\u6211\u5c31\u662f\u5728\u9019\u88e1\u5361\u4e86\u4e00\u500b\u591a\u5c0f\u6642)<\/li>\n<\/ol>\n

    \u7a0b\u5f0f\u78bc:<\/h3>\n
    int _n=1e5+10;  \nint t,n,m,p[_n],x,y,dp[_n],dep[_n];  \nVI G[_n];  \nPII e[_n];  \nll ecnt[_n];  \nvoid dfs(int v,int fa,int d){  \n  dep[v]=d;  \n  if(SZ(G[v])==1 and G[v][0]==fa){dp[v]=1;return;}  \n  int res=1;  \n  rep(i,0,SZ(G[v]))if(fa!=G[v][i])dfs(G[v][i],v,d+1),res+=dp[G[v][i]];  \n  dp[v]=res;  \n}  \nmain(void) {ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);  \n  cin>>t;while(t--){  \n    cin>>n;rep(i,0,n)G[i].clear();  \n    rep(i,0,n-1){cin>>x>>y;x--,y--;G[x].pb(y),G[y].pb(x);e[i]={x,y};}  \n    cin>>m;rep(i,0,m)cin>>p[i]; sort(p,p+m);  \n    dfs(0,-1,0); ll ans=0;rep(i,0,n-1){  \n      int u=e[i].fi,v=e[i].se;  \n      if(dep[u]>dep[v])swap(u,v);  \n      ecnt[i]=1ll*dp[v]*(n-dp[v]);  \n    } sort(ecnt,ecnt+n-1);  \n    int len=max(0,n-1-m);  \n    rep(i,0,len)ans+=ecnt[i],ans%=mod;  \n    if(n-1>m)rep(i,len,len+m)ans+=1ll*p[i-len]*ecnt[i],ans%=mod;  \n    if(m>=n-1){  \n      rep(i,0,n-2)ans+=1ll*p[i]*ecnt[i],ans%=mod;  \n      ll tmp=1;rep(i,n-2,m)tmp*=1ll*p[i],tmp%=mod;  \n      ans+=1ll*tmp*(ecnt[n-2]%mod); ans%=mod;  \n    }  \n    cout<<ans<<'\\n';  \n  }  \n  return 0;  \n}  \n<\/code><\/pre>\n
    \u6a19\u982d\u3001\u6a21\u677f\u8acb\u9edeSubmission\u770b
    \n    Submission<\/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":[10,7,4,9,8,6,5],"class_list":["post-28","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-dfs","tag-dp","tag-ojcode","tag-8","tag-6","tag-5"],"jetpack_publicize_connections":[],"yoast_head":"\nD. 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