E90 换根DP P6419 COCI2014-2015#1 Kamp

// 换根DP O(n)
#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#define int long long
using namespace std;

int read(){
  int s=0; char c=getchar();
  while(isdigit(c))s=s*10+c-'0',c=getchar();
  return s;
}
const int N=500005;
struct E{int v,w;};
vector<E> e[N];
int n,m,a[N],sz[N],d1[N],d2[N],pos[N],up[N];
int f[N],g[N];

void dfs(int u,int fa){
  sz[u]=a[u];
  for(E i:e[u]){
    int v=i.v,w=i.w;
    if(v==fa) continue;
    dfs(v,u);
    if(sz[v]){
      f[u]+=f[v]+2*w;
      if(d1[u]<d1[v]+w)
        d2[u]=d1[u],d1[u]=d1[v]+w,pos[u]=v;
      else if(d2[u]<d1[v]+w) d2[u]=d1[v]+w;
    }
    sz[u]+=sz[v];
  }
}
void dfs2(int u,int fa){
  for(E i:e[u]){
    int v=i.v,w=i.w;
    if(v==fa) continue;
    if(m-sz[v]){
      g[v]=g[u]+(f[u]-f[v]);
      if(!sz[v]) g[v]+=2*w;
      if(pos[u]==v) up[v]=max(up[u],d2[u])+w;
      else up[v]=max(up[u],d1[u])+w;
    }
    dfs2(v,u);
  }
}
signed main(){
  n=read();m=read();
  for(int i=1,x,y,w;i<n;i++){
    x=read(),y=read(),w=read();
    e[x].push_back({y,w});
    e[y].push_back({x,w});
  }
  for(int i=1;i<=m;i++) a[read()]++;
  dfs(1,0);
  dfs2(1,0);
  for(int i=1;i<=n;i++)
    printf("%lld\n",f[i]+g[i]-max(up[i],d1[i]));
}