虛樹入門
題目傳送門
虛樹的主要思想就是對於一棵樹，僅僅保留有用的點，重新構建一棵樹。
#include<bits/stdc++.h>
#define il inline
#define pb push_back
#define ms(_data,v) memset(_data,v,sizeof(_data))
#define SZ(a) int((a).size())
using namespace std;
typedef long long ll;
const ll inf=0x3f3f3f3f;
const int N=250005;
template <typename _Tp> il void read(_Tp&x) {
char ch;bool flag=0;x=0;
while(ch=getchar(),!isdigit(ch)) if(ch=='-')flag=1;
while(isdigit(ch)) x=x*10+ch-'0',ch=getchar();
if(flag) x=-x;
}
//il int Add(int &x,ll y) {return x=x+y>=mod?x+y-mod:x+y;}
//il int Mul(int &x,ll y) {return x=x*y>=mod?x*y%mod:x*y;}
struct node{
int to,w;
};
vector<node> G[N];
int n,m,a[N],dfn[N],topf[N],siz[N],son[N];
int s[N],top,deep[N],fa[N],ID=0;
ll mn[N];
void dfs1(int x, int f) {
siz[x]=1; fa[x]=f;
for(auto tp:G[x]) {
int to=tp.to,w=tp.w;
if(to==f) continue;
deep[to]=deep[x]+1;
mn[to]=min(mn[x],(ll)w);
dfs1(to,x);
siz[x]+=siz[to];
if(siz[to]>siz[son[x]]) son[x] = to;
}
}
void dfs2(int x, int topfa) {
topf[x]=topfa;
dfn[x]=++ID;
if(!son[x]) return ;
dfs2(son[x], topfa);
for(auto tp:G[x])
if(!topf[tp.to]) dfs2(tp.to, tp.to);
}
int Lca(int x, int y) {
while(topf[x]!=topf[y]) {
if(deep[topf[x]]<deep[topf[y]]) swap(x, y);
x = fa[topf[x]];
}
if(deep[x]<deep[y]) swap(x, y);
return y;
}
vector<int> mp[N];
il void add_edge(int u,int v){
mp[u].pb(v);
}
il void add(int x){
if(top==1){
s[++top]=x;
return;
}
int lca=Lca(x,s[top]);
if(lca==s[top]) return;
while(top>1 && dfn[s[top-1]]>=dfn[lca]) add_edge(s[top-1],s[top]),top--;
if(lca!=s[top]) add_edge(lca,s[top]),s[top] = lca;
s[++top]=x;
}
il ll solve(int x) {
if(mp[x].size()==0) return mn[x];
ll sum=0;
for(auto to:mp[x]) sum+=solve(to);
mp[x].clear();
return min(sum,(ll)mn[x]);
}
il bool cmp(int x,int y){
return dfn[x]<dfn[y];
}
int main(){
// std::ios::sync_with_stdio(0);cin.tie(0);
mn[1]=1e18;
read(n);
for(int i=1,u,v,w;i<=n-1;++i){
read(u),read(v),read(w);
G[u].pb({v,w});
G[v].pb({u,w});
}
deep[1]=1;
dfs1(1,0);
dfs2(1,1);
read(m);
int k;
while(m--){
read(k);
for(int i=1;i<=k;++i) read(a[i]);
sort(a+1,a+k+1,cmp);
top=1;
s[top]=1;
for(int i=1;i<=k;++i) add(a[i]);
while(top>0) add_edge(s[top-1],s[top]),top--;
printf("%lld\n",solve(1));
}
return 0;
}