BZOJ 3572 世界树(虚树)

http://www.lydsy.com/JudgeOnline/problem.php?id=3572

思路:建立虚树，然后可以发现，每条边不是同归属于一端，那就是切开，一半给上面，一半给下面。

 #include<algorithm>
 #include<cstdio>
 #include<cmath>
 #include<cstring>
 #include<iostream>
 #define N 300005
 int tot,go[N*],next[N*],first[N],sz,deep[N],tmp[N],tree[N];
 int son[N],dfn[N],fa[N][],bin[],ask[N],In[N],st[N],n,m,ans[N];
 int father[N],val[N];
 std::pair<int,int>near[N];
 int read(){
     int t=,f=;char ch=getchar();
     while (ch<''||ch>''){if (ch=='-') f=-;ch=getchar();}
     while (''<=ch&&ch<=''){t=t*+ch-'';ch=getchar();}
     return t*f;
 }
 void insert(int x,int y){
     tot++;
     go[tot]=y;
     next[tot]=first[x];
     first[x]=tot;
 }
 void add(int x,int y){
     insert(x,y);insert(y,x);
 }
 void dfs(int x){
     son[x]=;
     dfn[x]=++sz;
     for (int i=;i<=;i++)
      fa[x][i]=fa[fa[x][i-]][i-];
     for (int i=first[x];i;i=next[i]){
         int pur=go[i];
         if (pur==fa[x][]) continue;
         deep[pur]=deep[x]+;
         fa[pur][]=x;
         dfs(pur);
         son[x]+=son[pur];
     }
 }
 int find(int x,int dep){
     for (int i=;i>=;i--)
      if (deep[fa[x][i]]>=dep) x=fa[x][i];
     return x;
 }
 int lca(int x,int y){
     if (deep[x]<deep[y]) std::swap(x,y);
     int t=deep[x]-deep[y];
     for (int i=;i<=;i++)
      if (t&bin[i])
       x=fa[x][i];
     if (x==y) return x;
     for (int i=;i>=;i--)
      if (fa[x][i]!=fa[y][i])
       x=fa[x][i],y=fa[y][i];
     return fa[x][];
 }
 bool cmp(int a,int b){
     return dfn[a]<dfn[b];
 }
 void solve(){
     m=read();
     for (int i=;i<=m;i++){
         ask[i]=read(),tmp[i]=tree[i]=ask[i];
         near[ask[i]]=std::make_pair(,ask[i]);
         ans[ask[i]]=;
     }
     std::sort(ask+,ask++m,cmp);
     int top=,all=m;
     for (int i=;i<=m;i++){
         int p=ask[i];
         if (!top) father[p]=,st[++top]=p;
         else{
             int x=lca(st[top],p);
             father[p]=x;
             while (top&&deep[st[top]]>deep[x]){
                 if (deep[st[top-]]<=deep[x]){
                     father[st[top]]=x;
                 }
                 top--;
             }
             if (st[top]!=x){
                 father[x]=st[top];tree[++all]=x;
                 st[++top]=x;near[x]=std::make_pair(<<,);
             }
             st[++top]=p;
         }
     }
     std::sort(tree+,tree++all,cmp);
     for (int i=;i<=all;i++){
         int p=tree[i],f=father[p];
         val[p]=son[p];
         if (i>) In[p]=deep[p]-deep[f];
     }
     for (int i=all;i>;i--){
         int p=tree[i],f=father[p];
         near[f]=std::min(near[f],std::make_pair(near[p].first+In[p],near[p].second));
     }
     for (int i=;i<=all;i++){
         int p=tree[i],f=father[p];
         near[p]=std::min(near[p],std::make_pair(near[f].first+In[p],near[f].second));
     }
     for (int i=;i<=all;i++){
         int p=tree[i],f=father[p],sum=son[find(p,deep[f]+)]-son[p];
         if (f==) ans[near[p].second]+=n-son[p];
         else{
             val[f]-=sum+son[p];
             if (near[p].second==near[f].second) ans[near[p].second]+=sum;
             else{
                 int dis=(deep[p]-deep[f]-near[p].first+near[f].first)/;
                 if (dis+near[p].first==near[f].first+deep[p]-deep[f]-dis&&near[f].second<near[p].second) dis--;
                 int x=find(p,deep[p]-dis);
                 ans[near[p].second]+=son[x]-son[p];
                 ans[near[f].second]+=sum+son[p]-son[x];
             }
         }
     }
     for (int i=;i<=all;i++){
         ans[near[tree[i]].second]+=val[tree[i]];
     }
     for (int i=;i<=m;i++)
      printf("%d ",ans[tmp[i]]);
     puts("");
 }
 int main(){
     n=read();
     bin[]=;
     for (int i=;i<=;i++) bin[i]=bin[i-]*;
     for (int i=;i<n;i++){
         int x=read(),y=read();
         add(x,y);
     }
     dfs();
     int T=read();
     while (T--) solve();
 }