{"id":63006,"date":"2026-01-21T07:17:23","date_gmt":"2026-01-20T23:17:23","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/63006.html"},"modified":"2026-01-21T07:17:23","modified_gmt":"2026-01-20T23:17:23","slug":"%e6%b4%9b%e8%b0%b7-p3478%ef%bc%9apoi-2008-sta-station-%e2%86%90-%e6%8d%a2%e6%a0%b9dp","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/63006.html","title":{"rendered":"\u6d1b\u8c37 P3478\uff1a[POI 2008] STA-Station \u2190 \u6362\u6839DP"},"content":{"rendered":"

\u3010\u9898\u76ee\u6765\u6e90\u3011<\/span> https:\/\/www.luogu.com.cn\/problem\/P3478 \u3010\u9898\u76ee\u63cf\u8ff0\u3011 \u7ed9\u5b9a\u4e00\u4e2a n \u4e2a\u70b9\u7684\u6811，\u8bf7\u6c42\u51fa\u4e00\u4e2a\u7ed3\u70b9，\u4f7f\u5f97\u4ee5\u8fd9\u4e2a\u7ed3\u70b9\u4e3a\u6839\u65f6，\u6240\u6709\u7ed3\u70b9\u7684\u6df1\u5ea6\u4e4b\u548c\u6700\u5927\u3002 \u4e00\u4e2a\u7ed3\u70b9\u7684\u6df1\u5ea6\u4e4b\u548c\u5b9a\u4e49\u4e3a\u8be5\u8282\u70b9\u5230\u6839\u7684\u7b80\u5355\u8def\u5f84\u4e0a\u8fb9\u7684\u6570\u91cf\u3002 \u3010\u8f93\u5165\u683c\u5f0f\u3011 \u7b2c\u4e00\u884c\u6709\u4e00\u4e2a\u6574\u6570，\u8868\u793a\u6811\u7684\u7ed3\u70b9\u4e2a\u6570 n\u3002 \u63a5\u4e0b\u6765（n-1）\u884c，\u6bcf\u884c\u4e24\u4e2a\u6574\u6570 u，v，\u8868\u793a\u5b58\u5728\u4e00\u6761\u8fde\u63a5 u，v \u7684\u8fb9\u3002 \u3010\u8f93\u51fa\u683c\u5f0f\u3011 \u8f93\u51fa\u4e00\u884c\u4e00\u4e2a\u6574\u6570\u8868\u793a\u4f60\u9009\u62e9\u7684\u7ed3\u70b9\u7f16\u53f7\u3002\u5982\u679c\u6709\u591a\u4e2a\u7ed3\u70b9\u7b26\u5408\u8981\u6c42，\u8f93\u51fa\u4efb\u610f\u4e00\u4e2a\u5373\u53ef\u3002 \u3010\u8f93\u5165\u6837\u4f8b\u3011 8 1 4 5 6 4 5 6 7 6 8 2 4 3 4 \u3010\u8f93\u51fa\u6837\u4f8b\u3011 7 \u6216 8 \u3010\u6570\u636e\u8303\u56f4\u3011 \u5bf9\u4e8e\u5168\u90e8\u7684\u6d4b\u8bd5\u70b9，\u4fdd\u8bc11\u2264n\u2264<\/span>10^6<\/span>，1\u2264u,v\u2264n，\u7ed9\u51fa\u7684\u662f\u4e00\u68f5\u6811\u3002 \u3010\u7b97\u6cd5\u5206\u6790\u3011 \u25cf \u6362\u6839 DP \u662f\u6811\u5f62 DP \u7684\u4e00\u79cd\u91cd\u8981\u6280\u672f，\u7528\u4e8e\u89e3\u51b3\u9700\u8981\u4ee5\u6811\u4e2d\u200c<\/span>\u4e0d\u540c\u8282\u70b9\u4e3a\u6839\u200c<\/span>\u5206\u522b\u8ba1\u7b97\u7b54\u6848\u7684\u95ee\u9898\u3002\u5176\u6838\u5fc3\u601d\u60f3\u662f\u5728\u4e00\u6b21\u52a8\u6001\u89c4\u5212\u540e，\u901a\u8fc7\u200c<\/span>\u63a8\u5bfc\u51fa\u6362\u6839\u65f6\u7684\u72b6\u6001\u8f6c\u79fb\u516c\u5f0f\u200c<\/span>，\u9ad8\u6548\u5730\u8ba1\u7b97\u51fa\u6240\u6709\u8282\u70b9\u4f5c\u4e3a\u6839\u65f6\u7684\u7ed3\u679c，\u907f\u514d\u5bf9\u6bcf\u4e2a\u6839\u8282\u70b9\u90fd\u8fdb\u884c\u4e00\u6b21 O(n) \u7684\u6811\u5f62DP（\u90a3\u6837\u603b\u590d\u6742\u5ea6\u4e3a O(n\u00b2)）\u3002 \u25cf \u5bf9\u4e8e\u5927\u591a\u6570\u7b80\u5355\u7684\u6811\u5f62 DP \u95ee\u9898，\u5982\u8ba1\u7b97\u5b50\u6811\u5927\u5c0f\u3001\u8282\u70b9\u6df1\u5ea6\u3001\u7b80\u5355\u8def\u5f84\u7edf\u8ba1\u7b49，\u7b97\u6cd5\u901a\u5e38\u5bf9\u6bcf\u4e2a\u8282\u70b9\u6267\u884c\u5e38\u6570\u6b21\u64cd\u4f5c，\u56e0\u6b64\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a \u200cO(n)\u200c\u3002 \u25cf \u6362\u6839 DP \u901a\u5e38\u9075\u5faa\u4e00\u4e2a\u56fa\u5b9a\u7684\u4e24\u904d DFS \u6d41\u7a0b： （\u4e00）\u7b2c\u4e00\u6b21 DFS（\u56fa\u5b9a\u6839，\u6536\u96c6\u4fe1\u606f）\u200c （1）\u4efb\u9009\u4e00\u4e2a\u8282\u70b9（\u901a\u5e38\u4e3a 1 \u53f7\u8282\u70b9）\u4f5c\u4e3a\u521d\u59cb\u6839\u3002 （2）\u8fdb\u884c\u4e00\u6b21\u81ea\u5e95\u5411\u4e0a\u7684\u6811\u5f62 DP，\u8ba1\u7b97\u4ee5\u8be5\u8282\u70b9\u4e3a\u6839\u65f6，\u5404\u5b50\u6811\u7684\u72b6\u6001\u4fe1\u606f\u3002\u8fd9\u4e9b\u4fe1\u606f\u901a\u5e38\u5305\u62ec：\u5b50\u6811\u5927\u5c0f（siz[u]）\u3001\u5b50\u6811\u5185\u8282\u70b9\u5230\u6839\u7684\u8ddd\u79bb\u548c（dis[u]）\u3001\u6216\u5176\u4ed6\u4e0e\u95ee\u9898\u76f8\u5173\u7684\u5b50\u6811\u6700\u4f18\u89e3\u3002 （\u4e8c）\u7b2c\u4e8c\u6b21 DFS（\u6362\u6839，\u63a8\u5bfc\u5168\u5c40）\u200c （1）\u8fd9\u662f\u7b97\u6cd5\u7684\u5173\u952e\u3002\u57fa\u4e8e\u7b2c\u4e00\u6b21 DFS \u5f97\u5230\u7684\u4fe1\u606f，\u4ece\u521d\u59cb\u6839\u8282\u70b9\u5f00\u59cb，\u8fdb\u884c\u7b2c\u4e8c\u6b21 DFS\u3002 （2）\u5728\u904d\u5386\u8fc7\u7a0b\u4e2d，\u5f53\u4ece\u7236\u8282\u70b9 u \u8d70\u5411\u5b50\u8282\u70b9 v \u65f6，\u5229\u7528\u5df2\u77e5\u7684\u4ee5 u \u4e3a\u6839\u65f6\u7684\u5168\u5c40\u7b54\u6848 dp[u]，\u63a8\u5bfc\u51fa\u4ee5 v \u4e3a\u6839\u65f6\u7684\u5168\u5c40\u7b54\u6848 dp[v]\u3002 （3）\u8fd9\u4e2a\u63a8\u5bfc\u8fc7\u7a0b\u5c31\u662f \u200c\u201c<\/span>\u6362\u6839\u516c\u5f0f<\/span>\u201d\u200c，\u5b83\u5206\u6790\u4e86\u5f53\u6839\u4ece u \u79fb\u5230 v \u65f6，\u54ea\u4e9b\u8282\u70b9\u7684\u8d21\u732e\u53d1\u751f\u4e86\u53d8\u5316（\u4f8b\u5982，\u6df1\u5ea6\u589e\u52a0\u6216\u51cf\u5c11），\u5e76\u636e\u6b64\u66f4\u65b0\u7b54\u6848\u3002 \u25cf\u00a0\u7ecf\u5178\u793a\u4f8b：\u6240\u6709\u8282\u70b9\u5230\u5176\u4ed6\u8282\u70b9\u8ddd\u79bb\u4e4b\u548c \u8fd9\u662f\u4e00\u4e2a\u6700\u7ecf\u5178\u7684\u6362\u6839DP\u95ee\u9898，\u6e05\u6670\u5730\u5c55\u793a\u4e86\u6362\u6839\u516c\u5f0f\u7684\u63a8\u5bfc\u8fc7\u7a0b\u3002 （1）\u95ee\u9898\u200c：\u7ed9\u4e00\u68f5\u6811，\u6c42\u4ee5\u6bcf\u4e2a\u8282\u70b9\u4e3a\u6839\u65f6，\u6240\u6709\u8282\u70b9\u5230\u8be5\u6839\u8282\u70b9\u7684\u6df1\u5ea6\u4e4b\u548c\u3002 （2）\u5b9a\u4e49\u200c：siz[u]：\u4ee5 u \u4e3a\u6839\u7684\u5b50\u6811\u4e2d\u7684\u8282\u70b9\u6570\u3001dis[u]：\u4ee5 u \u4e3a\u6839\u65f6，\u6240\u6709\u8282\u70b9\u5230 u \u7684\u6df1\u5ea6\u4e4b\u548c\u3002<\/span><\/p>\n

\"\"<\/p>\n

（3）\u6b65\u9aa4\u200c： \u7b2c\u4e00\u6b21 DFS\u200c：\u4ee5\u8282\u70b9 1 \u4e3a\u6839，\u8ba1\u7b97 siz[u] \u548c\u521d\u59cb\u7684 dis[1]\u3002 \u6362\u6839\u516c\u5f0f\u63a8\u5bfc\u200c：\u5f53\u6839\u4ece u \u6362\u5230\u5176\u5b50\u8282\u70b9 v \u65f6，\u6240\u6709\u5728 v \u5b50\u6811\u4e2d\u7684\u8282\u70b9，\u5230\u65b0\u6839 v \u7684\u8ddd\u79bb\u6bd4\u5230\u65e7\u6839 u \u7684\u8ddd\u79bb\u200c\u51cf\u5c111\u200c\u3002\u8fd9\u90e8\u5206\u8d21\u732e\u603b\u5171\u51cf\u5c11 siz[v]\u3002\u6240\u6709\u4e0d\u5728 v \u5b50\u6811\u4e2d\u7684\u8282\u70b9（\u5171 n – siz[v] \u4e2a），\u5230\u65b0\u6839 v \u7684\u8ddd\u79bb\u6bd4\u5230\u65e7\u6839 u \u7684\u8ddd\u79bb\u200c\u589e\u52a01\u200c\u3002\u8fd9\u90e8\u5206\u8d21\u732e\u603b\u5171\u589e\u52a0 n – siz[v]\u3002 \u56e0\u6b64，<\/span>dis[v] = dis[u] – siz[v] + (n – siz[v]) = dis[u] + n – 2 * siz[v]<\/span>\u3002 \u7b2c\u4e8c\u6b21 DFS\u200c：\u5e94\u7528\u6b64\u516c\u5f0f，\u5373\u53ef\u4ece dp[1] \u9012\u63a8\u8ba1\u7b97\u51fa\u6240\u6709\u8282\u70b9\u7684 dis[i]\u3002<\/span> \u25cf \u672c\u9898\u6570\u636e\u91cf\u8fbe\u5230\u4e86 10^6，\u6240\u4ee5\u5728\u4ee3\u7801\u4e2d\u52a0\u5165\u5982\u4e0b\u8bed\u53e5（https:\/\/blog.csdn.net\/hnjzsyjyj\/article\/details\/143176072），\u907f\u514d TLE\u3002<\/p>\n

ios::sync_with_stdio(0);
\ncin.tie(0);
\ncout.tie(0); <\/p>\n

\u5f53\u7136，\u4e5f\u53ef\u4ee5\u4f7f\u7528\u201c\u5feb\u8bfb（<\/span>https:\/\/blog.csdn.net\/hnjzsyjyj\/article\/details\/120131534）\u201d\u51fd\u6570，\u4ee3\u7801\u5982\u4e0b\u3002<\/span><\/p>\n

int read() { \/\/fast read
\n int x=0,f=1;
\n char c=getchar();
\n while(c<'0' || c>'9') { \/\/!isdigit(c)
\n if(c=='-') f=-1;
\n c=getchar();
\n }
\n while(c>='0' && c<='9') { \/\/isdigit(c)
\n x=x*10+c-'0';
\n c=getchar();
\n }
\n return x*f;
\n} <\/p>\n

\u3010\u7b97\u6cd5\u4ee3\u7801：<\/span>\u90bb\u63a5\u8868\u5b58\u56fe<\/span>\u3011<\/span><\/p>\n

#include <bits\/stdc++.h>
\nusing namespace std;<\/p>\n

const int N=1e6+5;
\ntypedef long long LL;
\nLL siz[N],dis[N],imx;
\nvector<int> g[N];
\nint n,id;<\/p>\n

void dfs1(int u,int fa) {
\n siz[u]=1;
\n for(int v:g[u]) {
\n if(v==fa) continue;
\n dfs1(v,u);
\n siz[u]+=siz[v];
\n dis[u]+=dis[v]+siz[v];
\n }
\n return;
\n}<\/p>\n

void dfs2(int u,int fa) {
\n for(int v:g[u]) {
\n if(v==fa) continue;
\n dis[v]=dis[u]-siz[v]+n-siz[v];
\n if(dis[v]>imx) {
\n imx=dis[v];
\n id=v;
\n } else if(dis[v]==imx) id=min(id,v);
\n dfs2(v,u);
\n }
\n}<\/p>\n

int main() {
\n ios::sync_with_stdio(0);
\n cin.tie(0);
\n cout.tie(0);
\n cin>>n;
\n for(int i=1; i<n; i++) {
\n int u,v;
\n cin>>u>>v;
\n g[u].push_back(v);
\n g[v].push_back(u);
\n }<\/p>\n

dfs1(1,-1);
\n imx=dis[1], id=1;
\n dfs2(1,-1);
\n cout<<id<<endl;<\/p>\n

return 0;
\n}<\/p>\n

\/*
\nin:
\n8
\n1 4
\n5 6
\n4 5
\n6 7
\n6 8
\n2 4
\n3 4<\/p>\n

out:
\n7
\n*\/ <\/p>\n

\u3010\u53c2\u8003\u6587\u732e\u3011<\/span> https:\/\/blog.csdn.net\/hnjzsyjyj\/article\/details\/157134513 https:\/\/mp.weixin.qq.com\/s\/efEtbnK1O7NI06k6wtmSmg https:\/\/www.cnblogs.com\/LYFmobai\/p\/10219339.html \u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"

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