<虚树+树型DP> SDOI2011消耗战

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

using namespace std;

typedef long long LL;
const int MAXN = 25e4 + 10;

inline LL in()
{
    LL x = 0, flag = 1; char ch = getchar();
    while (ch < '0' || ch > '9') { if (ch == '-') flag = 1; ch = getchar(); }
    while (ch >= '0' && ch <= '9') x = (x << 3) + (x << 1) + (ch ^ 48), ch = getchar();
    return x * flag;
}

int n, m;

struct Gra
{
    int head[MAXN], nume;
    struct Adj { int nex, to; LL w; } adj[MAXN << 1] ;
    void clear()
        {
            memset(head, 0, sizeof head);
            nume = 0;
        }
    void addedge(int from, int to, LL w)
        {
            adj[++ nume] = (Adj) { head[from], to, w } ;
            head[from] = nume ;
        }
    void link(int from, int to, LL w)
        {
            addedge(from, to, w);
            addedge(to, from, w);
        }
} g[2];
int dep[MAXN], up[21][MAXN], lg[MAXN], dfn[MAXN], ind;
LL mn[MAXN];
void DFS(int u, int fa)
{
    dfn[u] = ++ ind;
    dep[u] = dep[fa] + 1;
    up[0][u] = fa;
    for (int i = 1; (1 << i) <= dep[u]; ++ i)
        up[i][u] = up[i - 1][up[i - 1][u]];
    for (int i = g[0].head[u]; i; i = g[0].adj[i].nex)
    {
        int v = g[0].adj[i].to;
        if (v == fa) continue;
        mn[v] = min(mn[u], g[0].adj[i].w);
        DFS(v, u);
    }
}
int lca(int x, int y)
{
    if (dep[x] > dep[y]) swap(x, y);
    while (dep[x] != dep[y]) y = up[lg[dep[y] - dep[x]]][y];
    if (x == y) return x;
    for (int i = lg[dep[x]]; i >= 0; -- i)
        if (up[i][x] != up[i][y]) x = up[i][x], y = up[i][y];
    return up[0][x];
}

int key[MAXN], stk[MAXN], top;
bool iskey[MAXN];
void insert(int u)
{
    if (top == 1) return  (void) (stk[++ top] = u);
    int LCA = lca(u, stk[top]);
    if (LCA == stk[top]) return (void) (stk[++ top] = u);
    while (top > 1 && dep[LCA] <= dep[stk[top - 1]])
    {
        g[1].addedge(stk[top - 1], stk[top], 0);
        -- top;
    }
    if (LCA != stk[top]) g[1].addedge(LCA, stk[top], 0), stk[top] = LCA;
    stk[++ top] = u;
}
LL search(int u)
{
    LL ret = 0;
    for (int i = g[1].head[u]; i; i = g[1].adj[i].nex)
    {
        int v = g[1].adj[i].to;
        ret += search(v);
    }
    if (iskey[u] || ret > mn[u] * 1LL) ret = mn[u];
    iskey[u] = false; g[1].head[u] = 0;
    return ret;
}

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

int main()
{
    n = in();
    for (int i = 1; i <= n; ++ i) lg[i] = lg[i - 1] + ((2 << lg[i - 1]) == i);
    for (int i = 1; i < n; ++ i)
    {
        int u = in(), v = in(); LL w = in();
        g[0].link(u, v, w);
    }
    mn[1] = 1e18;
    DFS(1, 0);
    m = in();
    while (m --)
    {
        int q = in();
        for (int i = 1; i <= q; ++ i) key[i] = in(), iskey[key[i]] = true ;
        sort(key + 1, key + q + 1, cmp);
        top = 0;
        stk[++ top] = 1;
        for (int i = 1; i <= q; ++ i) insert(key[i]);
        while (top > 1) g[1].addedge(stk[top - 1], stk[top], 0), -- top;
        g[1].nume = 0;
        printf("%lld\n", search(1));
    }
    return 0;
}

原文地址：https://www.cnblogs.com/ikihsiguoyr/p/10805036.html