[HEOI2014]大工程【虚树+树形DP】

题目链接

---

  还不错，就是理解题意的时候理解的久了一些。题目中的距离实际上是每两个点在原树上的距离，而新建的结点是不会影响的，所以总的距离和是原树上任意两点的距离之和；最短距离呢，实际上就是最短边权了；最长距离，实际上就是新构成虚树上树的直径了，当然得是有效点的。

  所以，构建虚树，然后再进行一个树形DP就可以了。

#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <bitset>
//#include <unordered_map>
//#include <unordered_set>
#define lowbit(x) ( x&(-x) )
#define pi 3.141592653589793
#define e 2.718281828459045
#define INF 0x3f3f3f3f3f3f3f3f
#define HalF (l + r)>>1
#define lsn rt<<1
#define rsn rt<<1|1
#define Lson lsn, l, mid
#define Rson rsn, mid+1, r
#define QL Lson, ql, qr
#define QR Rson, ql, qr
#define myself rt, l, r
using namespace std;
typedef unsigned long long ull;
typedef unsigned int uit;
typedef long long ll;
const int maxN = 1e6 + 7;
int N, Q, qid[maxN << 1], LOG2[maxN];
struct Build_Graph
{
    int head[maxN], cnt;
    struct Eddge
    {
        int nex, to; ll val;
        Eddge(int a=-1, int b=0, ll c=0):nex(a), to(b), val(c) {}
    }edge[maxN << 1];
    inline void addEddge(int u, int v, int w)
    {
        edge[cnt] = Eddge(head[u], v, w);
        head[u] = cnt++;
    }
    inline void _add(int u, int v, int w) { addEddge(u, v, w); addEddge(v, u, w); }
    inline void init()
    {
        cnt = 0;
        for(int i=1; i<=N; i++) head[i] = -1;
    }
} Old, Now;
int dfn[maxN], tot, deep[maxN], fa[maxN][22];
inline bool cmp(int e1, int e2) { return dfn[e1] < dfn[e2]; }
ll up_toroot[maxN] = {0};
void pre_dfs(int u, int father)
{
    fa[u][0] = father; deep[u] = deep[father] + 1; dfn[u] = ++tot;
    for(int i=0; (1 << (i + 1)) < N; i++) fa[u][i + 1] = fa[fa[u][i]][i];
    for(int i=Old.head[u], v; ~i; i=Old.edge[i].nex)
    {
        v = Old.edge[i].to;
        if(v == father) continue;
        up_toroot[v] = Old.edge[i].val;
        if(u ^ 1) up_toroot[v] = min(up_toroot[v], up_toroot[u]);
        pre_dfs(v, u);
    }
}
inline int LCA(int u, int v)
{
    if(deep[u] < deep[v]) swap(u, v);
    int det = deep[u] - deep[v];
    for(int i=LOG2[det]; i>=0; i--)
    {
        if((det >> i) & 1) u = fa[u][i];
    }
    if(u == v) return u;
    for(int i=LOG2[N]; i>=0; i--)
    {
        if(fa[u][i] ^ fa[v][i])
        {
            u = fa[u][i];
            v = fa[v][i];
        }
    }
    return fa[u][0];
}
int Stap[maxN << 1], Stop;
inline void Insert(int u)
{
    if(!Stop) { Stap[++Stop] = u; return; }
    int lca = LCA(u, Stap[Stop]);
    if(lca == Stap[Stop]) { Stap[++Stop] = u; return; }
    while(Stop > 1 && dfn[lca] <= dfn[Stap[Stop - 1]])
    {
        Now.addEddge(Stap[Stop - 1], Stap[Stop], deep[Stap[Stop]] - deep[Stap[Stop - 1]]);
        Stop--;
    }
    if(lca ^ Stap[Stop])
    {
        Now.addEddge(lca, Stap[Stop], deep[Stap[Stop]] - deep[lca]);
        Stap[Stop] = lca;
    }
    Stap[++Stop] = u;
}
bool used[maxN];
int K, siz[maxN];
ll down_min[maxN], down_max[maxN], ans_sum, ans_min, ans_max;
#define Min_3(a, b, c) min(a, min(b, c))
#define Max_3(a, b, c) max(a, max(b, c))
void dfs(int u)
{
    siz[u] = used[u] ? 1 : 0;
    down_min[u] = INF; down_max[u] = -INF;
    for(int i=Now.head[u], v; ~i; i=Now.edge[i].nex)
    {
        v = Now.edge[i].to;
        dfs(v);
        ans_min = min(ans_min, down_min[u] + down_min[v] + Now.edge[i].val);
        ans_max = max(ans_max, down_max[u] + down_max[v] + Now.edge[i].val);
        down_min[u] = min(down_min[u], Now.edge[i].val + down_min[v]);
        down_max[u] = max(down_max[u], Now.edge[i].val + down_max[v]);
        siz[u] += siz[v];
    }
    if(used[u])
    {
        ans_min = min(ans_min, down_min[u]);
        down_min[u] = 0;
        ans_max = max(ans_max, down_max[u]);
        down_max[u] = max(down_max[u], 0LL);
    }
}
void sum_dfs(int u)
{
    for(int i=Now.head[u], v; ~i; i=Now.edge[i].nex)
    {
        v = Now.edge[i].to;
        sum_dfs(v);
        ans_sum += Now.edge[i].val * 1LL * (K - siz[v]) * siz[v];
    }
    Now.head[u] = -1;
}
inline void init()
{
    Old.init(); Now.init(); tot = 0;
    for(int i = 1, j = 2, k = 0; i <= N; i++)
    {
        if(i == j) { k++; j <<= 1; }
        LOG2[i] = k;
    }
}
int main()
{
    scanf("%d", &N);
    init();
    for(int i=1, u, v; i<N; i++)
    {
        scanf("%d%d", &u, &v);
        Old._add(u, v, 1);
    }
    deep[0] = 0;
    pre_dfs(1, 0);
    scanf("%d", &Q);
    for(int q=1; q<=Q; q++)
    {
        scanf("%d", &K);
        for(int i=1; i<=K; i++) scanf("%d", &qid[i]);
        Stop = 0;
        sort(qid + 1, qid + K + 1, cmp); Now.cnt = 0;
        for(int i=1; i<=K; i++) { Insert(qid[i]); used[qid[i]] = true; }
        while(Stop > 1)
        {
            Now.addEddge(Stap[Stop - 1], Stap[Stop], deep[Stap[Stop]] - deep[Stap[Stop - 1]]);
            Stop--;
        }
        ans_sum = 0; ans_max = -INF; ans_min = INF;
        dfs(Stap[1]);
        sum_dfs(Stap[1]);
        printf("%lld %lld %lld\n", ans_sum, ans_min, ans_max);
        for(int i=1; i<=K; i++) used[qid[i]] = false;
    }
    return 0;
}