洛谷P1967 [NOIP 2013 提高组] 货车运输 Kruskal重构树

题目链接：https://www.luogu.com.cn/problem/P1967

参考资料：https://www.cnblogs.com/qfxlzhe/p/15153705.html

示例程序：

#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e4 + 5, maxm = 5e4 + 5;

int n, m, q, f[maxn];
int fa[maxn][16], tr[maxn], idx, dep[maxn];
vector<int> g[maxn];

void init() {
    for (int i = 1; i < 2*n; i++)
        f[i] = fa[i][0] = i;
    idx = n;
}

int find(int x) {
    return x == f[x] ? x : f[x] = find(f[x]);
}

struct Edge {
    int u, v, w;

    bool operator < (const Edge &b) const {
        return w > b.w;
    }
} e[maxm];

void dfs(int u, int d) {
    dep[u] = d;
    for (auto v : g[u])
        dfs(v, d+1);
}

void kruskal_build_tree() {
    init();
    sort(e, e+m);
    for (int i = 0; i < m; i++) {
        int u = e[i].u, v = e[i].v, w = e[i].w;
        int x = find(u), y = find(v);
        if (x != y) {
            int z = ++idx;
            tr[z] = w;
            fa[z][0] = z;
            g[z].push_back(x);
            g[z].push_back(y);
            fa[x][0] = fa[y][0] = z;
            f[x] = f[y] = z;
        }
    }
    for (int i = 1; i <= idx; i++)
        if (fa[i][0] == i)
            dfs(i, 0);

    for (int i = 1; i < 16; i++)
        for (int u = 1; u <= idx; u++)
            fa[u][i] = fa[ fa[u][i-1] ][i-1];
}

int lca(int x, int y) {
    if (find(x) != find(y))
        return -1;

    if (dep[x] < dep[y])
        swap(x, y);
    for (int i = 15; i >= 0; i--)
        if (dep[ fa[x][i] ] >= dep[y])
            x = fa[x][i];
    if (x == y)
        return tr[x];
    for (int i = 15; i >= 0; i--)
        if (fa[x][i] != fa[y][i])
            x = fa[x][i], y = fa[y][i];
    x = fa[x][0];
    return tr[x];
}

int main() {
    scanf("%d%d", &n, &m);
    for (int i = 0; i < m; i++)
        scanf("%d%d%d", &e[i].u, &e[i].v, &e[i].w);
    kruskal_build_tree();
    scanf("%d", &q);
    while (q--) {
        int x, y;
        scanf("%d%d", &x, &y);
        printf("%d\n", lca(x, y));
    }
    return 0;
}