LG2495 「SDOI2011」消耗战 虚树

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;
}