虚树

对于每次询问，虚树由询问的特殊点以及它们的LCA组成

将两点之间的链的信息压缩成一条链

可知所有的LCA即DFS序相邻的特殊点的LCA

BZOJ2286（错误写法）

#include <cstdio>
#include <iostream>
#include <algorithm>
#define LL long long 
using namespace std;

  int dfn[250001],next[500001],cnt,nd[250001],des[500001],dep[250001],b[250001];
  int fa[250001][21],n,a[500001],sta[250001];
  LL len[500001],f[250001],mini[250001][21];

  int mycomp(int x,int y){
      return(dfn[x]<dfn[y]);
  }

  void addedge(int x,int y,LL le){
      next[++cnt]=nd[x];des[cnt]=y;len[cnt]=le;nd[x]=cnt;
  }

  void dfs(int po){
    dfn[po]=++cnt;
      for (int p=nd[po];p!=-1;p=next[p])
        if (dep[des[p]]==0){
          dep[des[p]]=dep[po]+1;
          fa[des[p]][0]=po;
          mini[des[p]][0]=len[p];
        dfs(des[p]);    
      }  
  }
  
  void LCA_init(){
      for (int i=1;i<=20;i++)
        for (int j=1;j<=n;j++)
          fa[j][i]=fa[fa[j][i-1]][i-1],
          mini[j][i]=min(mini[j][i-1],mini[fa[j][i-1]][i-1]);
  }
  
  int getlca(int x,int y,int typ){
      LL ret=1e18;
      if (dep[x]<dep[y]){
        int t=x;x=y;y=t;    
    }
    for (int i=20;i>=0;i--)
      if (dep[fa[x][i]]>=dep[y])
        ret=min(ret,mini[x][i]),x=fa[x][i];
    for (int i=20;i>=0;i--)
      if (fa[x][i]!=fa[y][i])
        ret=min(ret,mini[x][i]),x=fa[x][i],
        ret=min(ret,mini[y][i]),y=fa[y][i];
    if (x!=y)        
        ret=min(ret,mini[x][0]),x=fa[x][0],
        ret=min(ret,mini[y][0]),y=fa[y][0];
    if (typ) return(ret);else return(x);
  }
  
  void dp(int po){
      f[po]=0;
      for (int p=nd[po];p!=-1;p=next[p]){
        dp(des[p]);
      if (b[des[p]]) f[po]+=len[p];else f[po]+=min(len[p],f[des[p]]);
    }
  }

  int main(){
      scanf("%d",&n);
      for (int i=1;i<=n;i++) nd[i]=-1;
      for (int i=1;i<n;i++){
        int t1,t2;LL t3;
      scanf("%d%d%lld",&t1,&t2,&t3);
      addedge(t1,t2,t3);addedge(t2,t1,t3);
    } 
    
    cnt=0;
    dep[1]=1;
    dfs(1);
    LCA_init();
    int q;
    scanf("%d",&q);
    while (q--){
      int k;
      scanf("%d",&k);
      for (int i=1;i<=k;i++) scanf("%d",&a[i]);
      sort(a+1,a+k+1,mycomp);
      for (int i=1;i<k;i++)  a[i+k]=getlca(a[i],a[i+1],0);a[2*k]=1;
      for (int i=k+1;i<=2*k;i++) b[a[i]]=0;
      for (int i=1;i<=k;i++) b[a[i]]=1;
      sort(a+1,a+2*k+1,mycomp);    
      a[0]=-1e9;
      for (int i=1;i<=2*k;i++) nd[a[i]]=-1;
      int top=0;cnt=0;
      for (int i=1;i<=2*k;i++)
        if (a[i]!=a[i-1]){
          while (top&&getlca(sta[top],a[i],0)!=sta[top]) top--;
          if (top) addedge(sta[top],a[i],getlca(sta[top],a[i],1));
          sta[++top]=a[i];
        }
      dp(1);
      printf("%lld
",f[1]);    
    }
  }

 正确写法为按DFN递增插入节点，对上一个插入节点与当前节点LCA是否为上一个节点分类讨论

是则直接插入，否则插入LCA退栈

如下(BZOJ3611)

#include <cstdio>
#include <iostream>
#include <algorithm>
#define LL long long 
using namespace std;

  int dfn[1000001],next[2000001],des[2000001],nd[1000001],len[2000001],cnt;
  int dep[1000001],fa[1000001][21],n,b[1000001],maxi[1000001],mini[1000001],k;
  int a[1000001],sta[1000001],ansmin,ansmax;
  LL f[1000001],g[1000001],ans; 

  int mycomp(int x,int y){
      return(dfn[x]<dfn[y]);
  }

  void addedge1(int x,int y){
      next[++cnt]=nd[x];des[cnt]=y;nd[x]=cnt;
      next[++cnt]=nd[y];des[cnt]=x;nd[y]=cnt;
  }
  
  void addedge(int x,int y,int le){
      next[++cnt]=nd[x];des[cnt]=y;len[cnt]=le;nd[x]=cnt;
  }
  
  void dfs(int po){
      dfn[po]=++cnt;
      for (int p=nd[po];p!=-1;p=next[p])
        if (!dep[des[p]]){
          dep[des[p]]=dep[po]+1;
          fa[des[p]][0]=po;
        dfs(des[p]);    
      }
  }
  
  void LCA_ini(){
      for (int i=1;i<=20;i++)
        for (int j=1;j<=n;j++)
          fa[j][i]=fa[fa[j][i-1]][i-1];
  }
  
  int getlca(int x,int y){
    if (dep[x]<dep[y]){
      int t=x;x=y;y=t;
    }
    
    for (int i=20;i>=0;i--)
      if (dep[fa[x][i]]>=dep[y])
        x=fa[x][i];
    for (int i=20;i>=0;i--)
      if (fa[x][i]!=fa[y][i])
        x=fa[x][i],y=fa[y][i];
    if (x==y) return(x);else return(fa[x][0]);        
  }
  
  int dis(int x,int y){
      return(dep[x]+dep[y]-2*dep[getlca(x,y)]);
  } 
  
  void dp(int po){
      if (b[po]){
        f[po]++;maxi[po]=0;mini[po]=0;
    }
    for (int p=nd[po];p!=-1;p=next[p]){
      dp(des[p]);
      ansmax=max(ansmax,maxi[po]+maxi[des[p]]+len[p]);
      maxi[po]=max(maxi[des[p]]+len[p],maxi[po]);    
      ansmin=min(ansmin,mini[po]+mini[des[p]]+len[p]);
      mini[po]=min(mini[des[p]]+len[p],mini[po]);    
      ans+=(g[po]+(LL)f[po]*(LL)len[p])*(LL)f[des[p]]+(LL)g[des[p]]*(LL)f[po];
      f[po]+=f[des[p]];
      g[po]+=g[des[p]]+(LL)len[p]*f[des[p]];
    }
    if (b[po])      ansmax=max(ansmax,maxi[po]);
    if (b[po]&&mini[po]>0) ansmin=min(ansmin,mini[po]);
  }
  
  void solve(){
      scanf("%d",&k);
      cnt=0;
      int nowk=k;
      for (int i=1;i<=k;i++) scanf("%d",&a[i]),nd[a[i]]=-1;nd[1]=-1;
      sort(a+1,a+nowk+1,mycomp);
      int top;
      sta[top=1]=1;
      for (int i=1;i<=k;i++){
        if (getlca(a[i],sta[top])==sta[top]) {if (a[i]!=sta[top]) sta[++top]=a[i];continue;}
        int otop=top;
        while (getlca(a[i],sta[top])!=sta[top]) top--;
        for (int j=top+1;j<otop;j++) addedge(sta[j],sta[j+1],dis(sta[j],sta[j+1]));
        int newin=getlca(a[i],sta[top+1]);
        if (newin==sta[top]){
            addedge(sta[top],sta[top+1],dis(sta[top+1],sta[top]));
          sta[++top]=a[i];
      }else{
          nd[newin]=-1;
          addedge(newin,sta[top+1],dis(sta[top+1],newin));
          sta[++top]=a[++nowk]=newin;
          sta[++top]=a[i];
      }
    } 
    for (int i=2;i<=top;i++) addedge(sta[i-1],sta[i],dis(sta[i],sta[i-1]));
    a[++nowk]=1;
    
    for (int i=1;i<=nowk;i++) {
      maxi[a[i]]=-1e9,mini[a[i]]=1e9,f[a[i]]=g[a[i]]=0;
    }
    for (int i=k+1;i<=nowk;i++) b[a[i]]=0;
    for (int i=1;i<=k;i++) b[a[i]]=1;
    ans=0;ansmin=1e9;ansmax=-1e9;
    dp(1);
    printf("%lld %d %d
",ans,ansmin,ansmax);
  }

  int main(){
      scanf("%d",&n);
      for (int i=1;i<=n;i++) nd[i]=-1;
      for (int i=1;i<n;i++){
        int t1,t2;
      scanf("%d%d",&t1,&t2);
      addedge1(t1,t2);    
    }
    
    dep[1]=1;cnt=0;
    dfs(1);
    LCA_ini();
    
    int q;
    scanf("%d",&q);
    while (q--)   
      solve();
  }