3611: [Heoi2014]大工程
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：
1 #include<cstdio> 2 #include<algorithm> 3 #include<cstring> 4 #include<cmath> 5 #include<iostream> 6 7 using namespace std; 8 9 const int N = 1000100; 10 const int INF = 1e9; 11 12 int head[N<<1],to[N<<1],nxt[N<<1]; 13 int siz[N],deth[N],fa[N],son[N],dfn[N],bel[N],sk[N],tag[N]; 14 int mn[N],mx[N],val[N],A[N]; 15 long long sum[N],Sum; 16 int Time_index,Min,Max,TotE,top; 17 18 inline int read() { 19 int x = 0,f = 1;char ch = getchar(); 20 for (; !isdigit(ch); ch=getchar()) if(ch=='-') f=-1; 21 for (; isdigit(ch); ch=getchar()) x=x*10+ch-'0'; 22 return x * f; 23 } 24 bool cmp_dfn(const int &a,const int &b) { 25 return dfn[a] < dfn[b]; 26 } 27 void Add_edge(int u,int v) { 28 ++TotE; to[TotE] = v; nxt[TotE] = head[u]; head[u] = TotE; 29 ++TotE; to[TotE] = u; nxt[TotE] = head[v]; head[v] = TotE; 30 } 31 void add_edge(int u,int v) { 32 ++TotE; to[TotE] = v; val[TotE] = deth[v]-deth[u]; nxt[TotE] = head[u]; head[u] = TotE; 33 } 34 void dfs1(int u) { 35 siz[u] = 1; 36 deth[u] = deth[fa[u]] + 1; // 1的深度设为1。 37 for (int i=head[u]; i; i=nxt[i]) { 38 int v = to[i]; 39 if (v==fa[u]) continue; 40 fa[v] = u; 41 dfs1(v); 42 siz[u] += siz[v]; 43 if (!son[u] || siz[son[u]] < siz[v]) son[u] = v; 44 } 45 } 46 void dfs2(int u,int top) { 47 bel[u] = top; 48 dfn[u] = ++Time_index; 49 if (!son[u]) return ; 50 dfs2(son[u],top); 51 for (int i=head[u]; i; i=nxt[i]) { 52 int v = to[i]; 53 if (v==fa[u] || v==son[u]) continue; 54 dfs2(v,v); 55 } 56 } 57 int Lca(int u,int v) { 58 while (bel[u] != bel[v]) { 59 if (deth[bel[u]] < deth[bel[v]]) swap(u,v); 60 u = fa[bel[u]]; 61 } 62 if (deth[u] < deth[v]) return u; 63 return v; 64 } 65 void Insert(int p) { 66 int x = sk[top]; 67 if (x==1) {sk[++top] = p; return;} 68 int lca = Lca(x,p); 69 while (lca != x) { 70 int y = sk[--top]; 71 if (dfn[y] < dfn[lca]) { 72 add_edge(lca,x);sk[++top] = lca; // !!! 73 break; 74 } 75 add_edge(y,x);x = sk[top]; 76 } 77 sk[++top] = p; 78 } 79 void DP(int u) { 80 if (tag[u]) mx[u] = mn[u] = 0,sum[u] = 0,siz[u] = 1; 81 else mn[u] = INF,mx[u] = -INF,sum[u] = 0,siz[u] = 0; 82 for (int i=head[u]; i; i=nxt[i]) { 83 int v = to[i]; 84 DP(v); 85 Min = min(Min,mn[u]+mn[v]+val[i]); mn[u] = min(mn[u],mn[v]+val[i]); 86 Max = max(Max,mx[u]+mx[v]+val[i]); mx[u] = max(mx[u],mx[v]+val[i]); 87 Sum += 1ll*siz[u]*(sum[v]+val[i]*siz[v])+1ll*siz[v]*sum[u]; //!!! 88 sum[u] += sum[v]+val[i]*siz[v]; 89 siz[u] += siz[v]; 90 } 91 tag[u] = head[u] = 0; 92 } 93 int main () { 94 95 int n = read(); 96 for (int i=1; i<n; ++i) { 97 int u = read(),v = read(); 98 Add_edge(u,v); 99 } 100 101 dfs1(1); 102 dfs2(1,1); 103 104 memset(head,0,sizeof(head)); 105 106 int m = read(); 107 while (m--) { 108 TotE = 0;top = 0;sk[++top] = 1; 109 110 int k = read(); 111 for (int i=1; i<=k; ++i) A[i] = read(),tag[A[i]] = true; 112 sort(A+1,A+k+1,cmp_dfn); 113 114 if (A[1] != 1) sk[++top] = A[1]; // 防止1加入两边。 115 for (int i=2; i<=k; ++i) Insert(A[i]); 116 while (--top) add_edge(sk[top],sk[top+1]); 117 118 Sum = 0,Min = INF,Max = -INF; 119 DP(1); 120 printf("%lld %d %d ",Sum,Min,Max); 121 } 122 123 return 0; 124 }