3611: [Heoi2014]大工程

3611: [Heoi2014]大工程

链接

分析：

　　树形dp+虚树。

　　首先建立虚树，在虚树上dp。

　　dp：sum[i]为i的子树中所有询问点之间的和。siz[i]为i的子树中有多少询问点，mn[i]为i的子树中询问点到根的最小距离，mx为i的子树中询问点到根的最大距离。

　　具体过程见 https://www.luogu.org/blog/ShadowassIIXVIIIIV/solution-p4103

　　

代码：

 #include<cstdio>
 #include<algorithm>
 #include<cstring>
 #include<cmath>
 #include<iostream>

 using namespace std;

 const int N = ;
 const int INF = 1e9;

 int head[N<<],to[N<<],nxt[N<<];
 int siz[N],deth[N],fa[N],son[N],dfn[N],bel[N],sk[N],tag[N];
 int mn[N],mx[N],val[N],A[N];
 long long sum[N],Sum;
 int Time_index,Min,Max,TotE,top; 

 inline int read() {
     int x = ,f = ;char ch = getchar();
     for (; !isdigit(ch); ch=getchar()) if(ch=='-') f=-;
     for (; isdigit(ch); ch=getchar()) x=x*+ch-'';
     return x * f;
 }
 bool cmp_dfn(const int &a,const int &b) {
     return dfn[a] < dfn[b];
 }
 void Add_edge(int u,int v) {
     ++TotE; to[TotE] = v; nxt[TotE] = head[u]; head[u] = TotE;
     ++TotE; to[TotE] = u; nxt[TotE] = head[v]; head[v] = TotE;
 }
 void add_edge(int u,int v) {
     ++TotE; to[TotE] = v; val[TotE] = deth[v]-deth[u]; nxt[TotE] = head[u]; head[u] = TotE;
 }
 void dfs1(int u) {
     siz[u] = ;
     deth[u] = deth[fa[u]] + ; // 1的深度设为1。
     for (int i=head[u]; i; i=nxt[i]) {
         int v = to[i];
         if (v==fa[u]) continue;
         fa[v] = u;
         dfs1(v);
         siz[u] += siz[v];
         if (!son[u] || siz[son[u]] < siz[v]) son[u] = v;
     }
 }
 void dfs2(int u,int top) {
     bel[u] = top;
     dfn[u] = ++Time_index;
     if (!son[u]) return ;
     dfs2(son[u],top);
     for (int i=head[u]; i; i=nxt[i]) {
         int v = to[i];
         if (v==fa[u] || v==son[u]) continue;
         dfs2(v,v);
     }
 }
 int Lca(int u,int v) {
     while (bel[u] != bel[v]) {
         if (deth[bel[u]] < deth[bel[v]]) swap(u,v);
         u = fa[bel[u]];
     }
     if (deth[u] < deth[v]) return u;
     return v;
 }
 void Insert(int p) {
     int x = sk[top];
     if (x==) {sk[++top] = p; return;}
     int lca = Lca(x,p);
     while (lca != x) {
         int y = sk[--top];
         if (dfn[y] < dfn[lca]) {
             add_edge(lca,x);sk[++top] = lca; // !!!
             break;
         }
         add_edge(y,x);x = sk[top];
     }
     sk[++top] = p;
 }
 void DP(int u) {
     if (tag[u]) mx[u] = mn[u] = ,sum[u] = ,siz[u] = ;
     else mn[u] = INF,mx[u] = -INF,sum[u] = ,siz[u] = ;
     for (int i=head[u]; i; i=nxt[i]) {
         int v = to[i];
         DP(v);
         Min = min(Min,mn[u]+mn[v]+val[i]); mn[u] = min(mn[u],mn[v]+val[i]);
         Max = max(Max,mx[u]+mx[v]+val[i]); mx[u] = max(mx[u],mx[v]+val[i]);
         Sum += 1ll*siz[u]*(sum[v]+val[i]*siz[v])+1ll*siz[v]*sum[u]; //!!!
         sum[u] += sum[v]+val[i]*siz[v];
         siz[u] += siz[v];
     }
     tag[u] = head[u] = ;
 }
 int main () {

     int n = read();
     for (int i=; i<n; ++i) {
         int u = read(),v = read();
         Add_edge(u,v);
     }

     dfs1();
     dfs2(,);

     memset(head,,sizeof(head));

     int m = read();
     while (m--) {
         TotE = ;top = ;sk[++top] = ;

         int k = read();
         for (int i=; i<=k; ++i) A[i] = read(),tag[A[i]] = true;
         sort(A+,A+k+,cmp_dfn);

         if (A[] != ) sk[++top] = A[]; // 防止1加入两边。
         for (int i=; i<=k; ++i) Insert(A[i]);
         while (--top) add_edge(sk[top],sk[top+]);

         Sum = ,Min = INF,Max = -INF;
         DP();
         printf("%lld %d %d\n",Sum,Min,Max);
     }

     return ;
 }