【HEOI2014】大工程

题面

虚树+贡献

题解

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<vector>
#include<stack>
#define ri register int
#define N 1000050
#define ll long long
using namespace std;
int n,q,m,cnt;
int a[2*N],yy[2*N],top;
int f[N][21],dep[N];
bool vis[N],imp[N];
int s;
ll sumdis,maxdis,mindis;

vector<int> to[N];

vector<int> son[N];
int siz[N],maxc[N],minc[N],nsmin[N];

int dfin[N],dfou[N];

void dfs(int x,int ff,int d) {
  f[x][0]=ff; dep[x]=d;
  for (ri i=1;i<=20;i++) f[x][i]=f[f[x][i-1]][i-1];
  dfin[x]=++cnt;
  for (ri i=to[x].size()-1;i>=0;i--) if (to[x][i]!=ff) dfs(to[x][i],x,d+1);
  dfou[x]=++cnt;
}

bool cmp1(int x,int y){
  return dfin[x]<dfin[y];
}

bool cmp2(int x,int y){
  int key1,key2;
  if (x>0) key1=dfin[x]; else key1=dfou[-x];
  if (y>0) key2=dfin[y]; else key2=dfou[-y];
  return key1<key2;
}

int lca(int u,int v){
  if (dep[u]<dep[v]) swap(u,v);
  for (ri i=20;i>=0;i--) if (dep[f[u][i]]>=dep[v]) u=f[u][i];
  if (u==v) return u;
  for (ri i=20;i>=0;i--) if (f[u][i]!=f[v][i]) u=f[u][i],v=f[v][i];
  return f[u][0];
}

void dp(int x) {
  if (imp[x]) siz[x]=1,minc[x]=0,maxc[x]=0; else siz[x]=0,minc[x]=7654321,maxc[x]=-7654321;
  nsmin[x]=7654321;
  for (ri i=son[x].size()-1;i>=0;i--) {
    dp(son[x][i]);
    siz[x]+=siz[son[x][i]];
    if (minc[son[x][i]]+dep[son[x][i]]-dep[x]<nsmin[x]) nsmin[x]=minc[son[x][i]]+dep[son[x][i]]-dep[x];
    if (minc[son[x][i]]+dep[son[x][i]]-dep[x]<minc[x]) minc[x]=minc[son[x][i]]+dep[son[x][i]]-dep[x];
    if (maxc[son[x][i]]+dep[son[x][i]]-dep[x]>maxc[x]) maxc[x]=maxc[son[x][i]]+dep[son[x][i]]-dep[x];
  }
}

void dp2(int x) {
  for (ri i=son[x].size()-1;i>=0;i--) dp2(son[x][i]);
  if (imp[x]) {
    if (maxc[x]>maxdis) maxdis=maxc[x];
    if (nsmin[x]<mindis) mindis=nsmin[x];
  }
  int s1=-7654321,s2=-7654321,b1=7654321,b2=7654321;
  for (ri i=son[x].size()-1;i>=0;i--) {
    maxc[son[x][i]]+=(dep[son[x][i]]-dep[x]);
    minc[son[x][i]]+=(dep[son[x][i]]-dep[x]);
    sumdis+=(siz[s]-siz[son[x][i]])*1LL*(siz[son[x][i]])*1LL*(dep[son[x][i]]-dep[x]);
    if (maxc[son[x][i]]>s1) s2=s1,s1=maxc[son[x][i]];else if (maxc[son[x][i]]>s2) s2=maxc[son[x][i]];
    if (minc[son[x][i]]<b1) b2=b1,b1=minc[son[x][i]];else if (minc[son[x][i]]<b2) b2=minc[son[x][i]];
  }
  if (s1+s2>maxdis) maxdis=s1+s2;
  if (b1+b2<mindis) mindis=b1+b2;
}

void view(int cur,int x){
  cout<<cur<<" "<<x<<endl;
  for (ri i=son[x].size()-1;i>=0;i--) cout<<son[x][i]<<" "; cout<<endl;
}

int main(){
  scanf("%d",&n);
  int u,v;
  for (ri i=1;i<n;i++) {
    scanf("%d %d",&u,&v);
    to[u].push_back(v);
    to[v].push_back(u);
  }
  cnt=0;
  dfs(1,1,1);
  scanf("%d",&q);
  for (ri ti=1;ti<=q;ti++) {
    scanf("%d",&m); 
    for (ri i=1;i<=m;i++) {
      scanf("%d",&a[i]);
      vis[a[i]]=1;
      imp[a[i]]=1;
    }
    sort(a+1,a+m+1,cmp1);
    cnt=m;
    for (ri i=1;i<m;i++) {
      int t=lca(a[i],a[i+1]);
      if (!vis[t]) vis[t]=1,a[++cnt]=t;
    }
    int cnt2=cnt;
    for (ri i=1;i<=cnt;i++) {
      a[++cnt2]=-a[i];
    }
    sort(a+1,a+cnt2+1,cmp2);
    //stack<int> yy;
    //while (!yy.empty()) yy.pop();
    top=0;
    for (ri i=1;i<=cnt2;i++) if (a[i]>0) yy[++top]=a[i];
    else {
      top--;
      if (top>0) son[yy[top]].push_back(-a[i]);
      else s=-a[i];
    }
    sumdis=0; maxdis=0; mindis=987654321;
    dp(s); dp2(s);
    printf("%lld %lld %lld
",sumdis,mindis,maxdis);
    for (ri i=1;i<=cnt2;i++) if (a[i]>0) vis[a[i]]=0,imp[a[i]]=0,son[a[i]].clear();
  }
}