解题：HNOI 2014 世界树

题面

首先建虚树

DFS求虚树上每个点所属的点和到它所属点的距离，然后在=考虑虚树所有的边(对应原树一条链)。如果两个端点所属节点不同就倍增出分界点统计答案，否则不用管(之后会统计到的)；注意根节点特殊讨论。

 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 using namespace std;
 const int N=,K=,inf=1e9;
 int T,n,m,t1,t2,cnt,tot,top;
 int p[N],noww[N],goal[N];
 int siz[N],dep[N],dfn[N],upt[N][K],oth[N][K];
 int a[N],b[N],c[N],d[N],bel[N],stk[N],ans[N];
 bool cmp(int a,int b)
 {
     return dfn[a]<dfn[b];
 }
 void Link(int f,int t)
 {
     noww[++cnt]=p[f];
     goal[cnt]=t,p[f]=cnt;
 }
 void DFS(int nde,int fth,int dth)
 {
     siz[nde]=,dep[nde]=dth;
     upt[nde][]=fth,dfn[nde]=++tot;
     for(int i=;i<=&&upt[nde][i-];i++)
         upt[nde][i]=upt[upt[nde][i-]][i-];
     for(int i=p[nde];i;i=noww[i])
         if(goal[i]!=fth)
             DFS(goal[i],nde,dth+),siz[nde]+=siz[goal[i]];
 }
 void Calc(int nde,int fth)
 {
     oth[nde][]=siz[fth]-siz[nde];
     for(int i=;i<=&&upt[nde][i-];i++)
         oth[nde][i]=oth[nde][i-]+oth[upt[nde][i-]][i-];
     for(int i=p[nde];i;i=noww[i])
         if(goal[i]!=fth) Calc(goal[i],nde);
 }
 int LCA(int x,int y)
 {
     if(dep[x]<dep[y]) swap(x,y);
     for(int i=;dep[x]!=dep[y];i--)
         if(dep[upt[x][i]]>=dep[y]) x=upt[x][i];
     if(x==y) return x;
     for(int i=;~i;i--)
         if(upt[x][i]!=upt[y][i])
             x=upt[x][i],y=upt[y][i];
     return upt[x][];
 }
 int Dis(int x,int y)
 {
     int lca=LCA(x,y);
     return dep[x]+dep[y]-*dep[lca];
 }
 bool Check(int a,int b,int d)
 {
     return c[a]+d<c[b]||(c[a]+d==c[b]&&bel[a]<bel[b]);
 }
 void Insert(int nde)
 {
     if(!top) stk[++top]=nde;
     else
     {
         int lca=LCA(nde,stk[top]);
         if(lca!=stk[top])
         {
             while(top>&&dfn[lca]<=dfn[stk[top-]])
                 Link(stk[top-],stk[top]),top--;
             if(dfn[lca]<dfn[stk[top]])
                 Link(lca,stk[top]),top--;
             if(lca!=stk[top])
                 stk[++top]=lca;
         }
         stk[++top]=nde;
     }
 }
 int Upt(int nde,int gal)
 {
     int ret=;
     for(int i=;~i;i--)
         if(gal&(<<i))
             ret+=oth[nde][i],nde=upt[nde][i];
     return ret;
 }
 void DFS1(int nde)
 {
     if(!bel[nde]) c[nde]=inf;
     for(int i=p[nde];i;i=noww[i])
     {
         int g=goal[i],dd=dep[g]-dep[nde]; DFS1(g);
         if(Check(g,nde,dd)) c[nde]=c[g]+dd,bel[nde]=bel[g];
     }
 }
 void DFS2(int nde,int lst)
 {
     int dd=dep[nde]-dep[lst];
     if(lst&&Check(lst,nde,dd))
         c[nde]=c[lst]+dd,bel[nde]=bel[lst];
     for(int i=p[nde];i;i=noww[i])
         DFS2(goal[i],nde),d[nde]+=d[goal[i]];
     if(!lst) ans[bel[nde]]+=n-d[nde];
     else if(bel[nde]!=bel[lst])
     {
         int cut=c[nde]+c[lst]+dd,chk=cut%||bel[nde]<bel[lst],tmp;
         tmp=Upt(nde,cut/-c[nde]-(chk^));
         ans[bel[nde]]+=siz[nde]-d[nde]+tmp,d[nde]=siz[nde]+tmp;
     }
 }
 void Clear(int nde)
 {
     for(int i=p[nde];i;i=noww[i])
         Clear(goal[i]);
     bel[nde]=p[nde]=c[nde]=d[nde]=;
 }
 int main()
 {
     scanf("%d",&n);
     for(int i=;i<n;i++)
         scanf("%d%d",&t1,&t2),Link(t1,t2),Link(t2,t1);
     DFS(,,),Calc(,),memset(p,,sizeof p);
     scanf("%d",&T);
     while(T--)
     {
         scanf("%d",&m),cnt=top=;
         for(int i=;i<=m;i++) scanf("%d",&a[i]),b[i]=a[i];
         sort(a+,a++m,cmp);  stk[top=]=a[],bel[a[]]=a[];
         for(int i=;i<=m;i++) Insert(a[i]),bel[a[i]]=a[i];
         while(top>) Link(stk[top-],stk[top]),top--;
         DFS1(stk[]),DFS2(stk[],);
         for(int i=;i<=m;i++)
             printf("%d ",ans[b[i]]),ans[b[i]]=;
         Clear(stk[]),puts("");
     }
     return ;
 }