问题描述
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;
}