UVa 11090 - Going in Cycle!! (01分数规划)

题目链接：https://onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&category=0&problem=2031&mosmsg=Submission+received+with+ID+26584370

求有向图平均权最小的回路

二分答案 \(x\)，将所有边都减去 \(x\)，看图中是否有负环即可

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

const int maxn = 105;
const double eps = 1e-3;

int T, n, m; 

int h[maxn], cnt = 0;
struct E{
	int to, next;
	double cost;
}e[maxn * maxn];
void add(int u, int v, double w){
	e[++cnt].to = v;
	e[cnt].cost = w;
	e[cnt].next = h[u];
	h[u] = cnt;
}

int in[maxn], tot[maxn]; double d[maxn];
bool spfa(double mid){
	queue<int> q;
	memset(tot, 0, sizeof(tot));
	memset(in, 0, sizeof(in));
	for(int i = 1 ; i <= n ; ++i) {
		d[i] = 0;
		in[i] = 1;
		q.push(i);
	}
	
	while(!q.empty()){
		int u = q.front(); q.pop(); in[u] = 0;
		for(int i = h[u] ; i != -1 ; i = e[i].next){
			int v = e[i].to;
			if(d[u] + e[i].cost - mid - d[v] < 0){
				d[v] = d[u] + e[i].cost - mid;
				
				if(!in[v]){
					in[v] = 1;
					q.push(v);
					++tot[v];
					if(tot[v] > n) return false;
				}
			}
		}
	}
	
	return true;
}

bool check(double x){
	return !spfa(x);
}

ll read(){ ll s = 0, f = 1; char ch = getchar(); while(ch < '0' || ch > '9'){ if(ch == '-') f = -1; ch = getchar(); } while(ch >= '0' && ch <= '9'){ s = s * 10 + ch - '0'; ch = getchar(); } return s * f; }

int main(){
	scanf("%d", &T);
	int kase = 0;
	while(T--){
		memset(h, -1, sizeof(h)); cnt = 0;
		scanf("%d%d", &n, &m);
		int u, v; double w;
		double L = 0, R = 0;
		for(int i = 1 ; i <= m ; ++i){
			scanf("%d%d%lf", &u, &v, &w);
			add(u, v, w);
			R = max(R, w * 1.0);
		}
		
		printf("Case #%d: ", ++kase);	
		if(!check(R + 1.0)) printf("No cycle found.\n");
		else {
			double ans = 0;
			while(R - L > eps){
				double mid = (R + L) / 2;
				if(check(mid)){
					R = mid;
				} else{
					L = mid;
				}
			}
			printf("%.2lf\n", L);
		}
	}
	return 0;
}