Author: lllyouo
Date: 2025-04-02
tag: 负环、01规划
link: https://www.acwing.com/problem/content/363/

问题描述

link

分析

略

参考代码

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

const int N = 1010, M = 5010;
int h[N], e[M], w[M], ne[M], idx;
int n, m, a[N], vis[N], cnt[N];
double dist[N];

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

bool check(double mid) {
    memset(dist, 0, sizeof dist);
    memset(cnt, 0, sizeof cnt);
    memset(vis, 0, sizeof vis);
    queue<int> q;
    
    for (int i = 1; i <= n; i++) {
        q.push(i);
        vis[i] = 1;
    }

    while (!q.empty()) {
        int k = q.front();
        q.pop();
        vis[k] = 0;

        for (int i = h[k]; i != -1; i = ne[i]) {
            int j = e[i];
            if (dist[j] > dist[k] + w[i] * mid - a[k]) {
                dist[j] = dist[k] + w[i] * mid - a[k];
                cnt[j] = cnt[k] + 1;
                
                if (cnt[j] >= n) return true;
                if (!vis[j]) {
                    q.push(j);
                    vis[j] = 1;
                }
            }
        }
    }

    return false;
}

int main() {
    memset(h, -1, sizeof h);
    cin >> n >> m;
    for (int i = 1; i <= n; i++) cin >> a[i];
    for (int i = 1; i <= m; i++) {
        int a, b, c; cin >> a >> b >> c;
        add(a, b, c);
    }
    
    double l = 0, r = 1000, eps = 1e-4;
    while (l + eps < r) {
        double mid = (l + r) / 2;
        if (check(mid)) l = mid;
        else r = mid;
    }
    printf("%.2lf\n", l);
    
    return 0;
}