Author: lllyouo
Date: 20250425
tag: 二分答案、二分图、染色法
link: https://www.luogu.com.cn/problem/P1525

问题描述

link

分析

略

参考代码

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

const int N = 20010, M = 100010;
int h[N], e[M * 2], w[M * 2], ne[M * 2], idx;
int n, m, v[N];

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

bool dfs(int x, int color, int limit) {
    v[x] = color;
    for (int i = h[x]; i != -1; i = ne[i]) {
        if (w[i] > limit) {
            int y = e[i];
            if (!v[y]) {
                if (!dfs(y, 3 - color, limit)) return false;
            }
            else if (v[y] == color) return false;
        }
    }

    return true;
}

bool check(int mid) {
    memset(v, 0, sizeof v);
    for (int i = 1; i <= n; i++) {
        if (!v[i]) {
            if (!dfs(i, 1, mid)) return false;
        }
    }

    return true;
}

int main() {
    memset(h, -1, sizeof h);
    cin >> n >> m;
    for (int i = 1; i <= m; i++) {
        int a, b, c; cin >> a >> b >> c;
        add(a, b, c);
        add(b, a, c);
    }

    int l = 0, r = 1e9;
    while (l < r) {
        int mid = l + r >> 1;
        if (check(mid)) r = mid;
        else l = mid + 1;
    }
    cout << l << endl;

    return 0;
}