问题描述

LG2495

题解

虚树

\(\mathrm{Code}\)

#include<bits/stdc++.h>
using namespace std;

#define int long long

template <typename Tp>
void read(Tp &x){
    x=0;char ch=1;int fh;
    while(ch!='-'&&(ch>'9'||ch<'0')) ch=getchar();
    if(ch=='-') ch=getchar(),fh=-1;
    else fh=1;
    while(ch>='0'&&ch<='9') x=(x<<1)+(x<<3)+ch-'0',ch=getchar();
    x*=fh;
}

const int maxn=250007;
const int INF=0x3f3f3f3f3f3f3f3fLL;

int n,T,k;
int tot,Head[maxn],to[maxn<<2],Next[maxn<<2],w[maxn<<2];

int size[maxn],son[maxn],mn[maxn];
int fa[maxn],dep[maxn],top[maxn];
int dfn[maxn],ind;

void add(int x,int y,int z){
    to[++tot]=y,Next[tot]=Head[x],Head[x]=tot,w[tot]=z;
}

void dfs1(int x,int f,int dp){
    fa[x]=f,dep[x]=dp,size[x]=1;
    int mx=-1;
    for(int i=Head[x];i;i=Next[i]){
        int y=to[i];
        if(y==f) continue;
        mn[y]=min(mn[x],w[i]);
        dfs1(y,x,dp+1);size[x]+=size[y];
        if(size[y]>mx) mx=size[y],son[x]=y;
    }
}

void dfs2(int x,int tp){
    top[x]=tp,dfn[x]=++ind;
    if(!son[x]) return;
    dfs2(son[x],tp);
    for(int i=Head[x];i;i=Next[i]){
        int y=to[i];
        if(y==fa[x]||y==son[x]) continue;
        dfs2(y,y);
    }
}

int lca(int x,int y){
    while(top[x]!=top[y]){
        if(dep[top[x]]<dep[top[y]]) swap(x,y);
        x=fa[top[x]];
    }
    if(dep[x]>dep[y]) swap(x,y);
    return x;
}

int s[maxn],ttop;
int a[maxn];
vector<int>v[maxn];

void insert(int x){
    if(ttop==1){s[++ttop]=x;return;}
    int lc=lca(x,s[ttop]);
    if(lc==s[ttop]) return;
    while(ttop>1&&dfn[s[ttop-1]]>=dfn[lc]){
        v[s[ttop-1]].push_back(s[ttop]);ttop--;
    }
    if(lc!=s[ttop]){v[lc].push_back(s[ttop]);s[ttop]=lc;}
    s[++ttop]=x;
}

bool comp(int a,int b){
    return dfn[a]<dfn[b];
}

int dp(int x){
    if(!v[x].size()) return mn[x];
    int res=0;
    for(int i=0;i<v[x].size();i++){
        res+=dp(v[x][i]);
    }
    v[x].clear();
    return min(res,mn[x]);
}

signed main(){
    read(n);mn[1]=INF;
    for(int i=1,x,y,z;i<n;i++){
        read(x);read(y);read(z);
        add(x,y,z);add(y,x,z);
    }
    dfs1(1,0,1);dfs2(1,1);
    read(T);
    while(T--){
        read(k);
        for(int i=1;i<=k;i++) read(a[i]);
        sort(a+1,a+k+1,comp);
        s[ttop=1]=1;
        for(int i=1;i<=k;i++) insert(a[i]);
        while(ttop>0) v[s[ttop-1]].push_back(s[ttop]),ttop--;
        printf("%lld\n",dp(1));
    }
    return 0;
}