Author: lllyouo
Date: 20250325
tag: 最近公共祖先
link: https://www.luogu.com.cn/problem/P10930

问题描述

link

分析

略

参考代码

#include <bits/stdc++.h>
using namespace std;

const int N = 500010, M = 2 * N;
int h[N], e[M], w[N], ne[M], idx;
int n, m, t, num;
int d[N], f[N][25], dfn[N];
long long dis[N];
set<pair<int, int>> st;

void add(int a, int b, int c) {
    e[idx] = b;
    w[idx] = c;
    ne[idx] = h[a];
    h[a] = idx++;
}

void dfs(int x) {
    dfn[x] = ++num;
    for (int i = h[x]; i != -1; i = ne[i]) {
        int y = e[i];
        if (!dfn[y]) {
            dis[y] = dis[x] + w[i];
            dfs(y);
        }
    }
}

void bfs() {
    queue<int> q;
    q.push(1);
    d[1] = 1;

    while (q.size()) {
        int x = q.front();
        q.pop();

        for (int i = h[x]; i != -1; i = ne[i]) {
            int y = e[i];
            if (d[y]) continue;
            d[y] = d[x] + 1;
            f[y][0] = x;
            for (int k = 1; k <= t; k++) {
                f[y][k] = f[f[y][k - 1]][k - 1];
            }
            q.push(y);
        }
    }
}

int lca(int x, int y) {
    if (d[x] < d[y]) swap(x, y);
    for (int i = t; i >= 0; i--) {
        if (d[f[x][i]] >= d[y]) x = f[x][i];
    }
    if (x == y) return x;

    for (int i = t; i >= 0; i--) {
        if (f[x][i] != f[y][i]) {
            x = f[x][i];
            y = f[y][i];
        }
    }

    return f[x][0];
}

long long get_dis(int x, int y) {
    return dis[x] + dis[y] - 2 * dis[lca(x, y)];
}

int pre(int x) {
    auto it = st.lower_bound(make_pair(dfn[x], x));
    if (it == st.begin()) it = st.end();
    return (--it)->second;
}

int suf(int x) {
    auto it = st.upper_bound(make_pair(dfn[x], x));
    if (it == st.end()) it = st.begin();
    return it->second;
}

int main() {
    memset(h, -1, sizeof h);
    scanf("%d", &n);
    for (int i = 1; i < n; i++) {
        int a, b, c; scanf("%d%d%d", &a, &b, &c);
        add(a, b, c);
        add(b, a, c);
    }

    t = int(log(n) / log(2)) + 1;
    dfs(1);
    bfs();

    long long ans = 0;
    scanf("%d", &m);
    while(m--) {
        char op[2];
        int x;
        scanf("%s", op);
        if (op[0] == '+') {
            scanf("%d", &x);
            if (st.empty()) ans = 0;
            else if (st.size() == 1) ans = 2 * get_dis(st.begin()->second, x);
            else {
                int l = pre(x), r = suf(x);
                ans += get_dis(l, x) + get_dis(x, r) - get_dis(l, r);
            }
            st.insert(make_pair(dfn[x], x));
        } else if (op[0] == '-') {
            scanf("%d", &x);
            st.erase(make_pair(dfn[x], x));
            if (st.size() <= 1) ans = 0;
            else {
                int l = pre(x), r = suf(x);
                ans -= get_dis(l, x) + get_dis(x, r) - get_dis(l, r);
            }
        } else {
            printf("%lld\n", ans / 2);
        }
    }

    return 0;
}