POJ 3621 Sightseeing Cows 最优比率环（01分数规划+负环）

àì夳堔傛蜴生んèń 2021-11-16 06:50 247阅读 0赞

## 题意：有向图G，节点权值为Fi,  边权值为Ti, 求一回路，使sum(Fi) / sum(Ti) 最大。 ##

## 分析：《算法竞赛进阶指南》P392。 ##

## 代码： ##

#include <queue>
    #include <cstdio>
    #include <cstring>
    #include <iostream>
    using namespace std;
    const int N = 1006, M = 5006;
    const double eps = 1e-6;
    int n, m, c[N], f[N], x[M], y[M], z[M];
    int Head[N], Edge[M], Next[M], tot;
    double Leng[M], d[N];
    bool v[N];
    
    void add(int x, int y, double z) {
    	Edge[++tot] = y;
    	Leng[tot] = z;
    	Next[tot] = Head[x];
    	Head[x] = tot;
    }
    
    bool spfa() {
    	queue<int> q;
    	for (int i = 1; i <= n; i++) {
    		q.push(i);
    		d[i] = 0;
    		v[i] = 1;
    	}
    	memset(c, 0, sizeof(c));
    	while (q.size()) {
    		int x = q.front();
    		q.pop();
    		v[x] = 0;
    		for (int i = Head[x]; i; i = Next[i]) {
    			int y = Edge[i];
    			if (d[y] > d[x] + Leng[i]) {
    				d[y] = d[x] + Leng[i];
    				if (++c[y] > n) return 1;
    				if (!v[y]) {
    					q.push(y);
    					v[y] = 1;
    				}
    			}
    		}
    	}
    	return 0;
    }
    
    bool pd(double w) {
    	tot = 0;
    	memset(Head, 0, sizeof(Head));
    	for (int i = 1; i <= m; i++)
    		add(x[i], y[i], w * z[i] - f[x[i]]);
    	return spfa();
    }
    
    int main() {
    	cin >> n >> m;
    	for (int i = 1; i <= n; i++)
    		scanf("%d", &f[i]);
    	for (int i = 1; i <= m; i++)
    		scanf("%d %d %d", &x[i], &y[i], &z[i]);
    	double l = 0, r = 1000;
    	while (r - l > eps) {
    		double mid = (l + r) / 2;
    		if (pd(mid)) l = mid;
    		else r = mid;
    	}
    	printf("%.2f", l);
    	return 0;
    }