【洛谷 P3199】 [HNOI2009]最小圈（分数规划，Spfa）

题目链接

一开始不理解为什么不能直接用\(Tarjan\)跑出换直接求出最小值，然后想到了“简单环”，恍然大悟。

二分答案，把所有边都减去\(mid\)，判是否存在负环，存在就\(r=mid\)。

别的题都卡dfs，这题卡bfs

#include <cstdio>
#include <queue>
#define INF 2147483647
using namespace std;
const int MAXN = 30010;
const int MAXM = 100010;
const double eps = 1e-10;
struct Edge{
	int next, to;
	double dis;
}e[MAXM];
int num, head[MAXN];
inline void Add(int from, int to, double dis){
	e[++num] = (Edge){ head[from], to, dis }; head[from] = num;
}
int a[MAXM], b[MAXN], T, n, m, v[MAXN], now;
double dis[MAXN], c[MAXN];
queue <int> q;
/*int bfs(int x){
	while(q.size()) q.pop();
	q.push(x); cnt[x] = 1; v[x] = 1; dis[x] = 0;
	while(q.size()){
		now = q.front(); q.pop(); v[now] = 0;
		for(int i = head[now]; i; i = e[i].next)
		   if(dis[e[i].to] > dis[now] + e[i].dis){
		   	 dis[e[i].to] = dis[now] + e[i].dis;
		   	 if(!v[e[i].to]){
		   	 	if(++cnt[e[i].to] >= n) return 1;
		   	 	v[e[i].to] = 1;
		   	 	q.push(e[i].to);
		   	 }
		   }
	}
	return 0;
}*/
int dfs(int u){
	v[u] = 1;
	for(int i = head[u]; i; i = e[i].next)
	   if(dis[e[i].to] > dis[u] + e[i].dis){
	   	 dis[e[i].to] = dis[u] + e[i].dis;
	   	 if(v[e[i].to]) return 1;
	   	 if(dfs(e[i].to)) return 1;
	   }
	v[u] = 0;
	return 0;
}
int check(){
	for(int i = 1; i <= n; ++i)
	   if(dfs(i))
	     return 1;
	return 0;
}
double l = -1e7, r = 1e7, mid;
int main(){
	scanf("%d%d", &n, &m);
	for(int i = 1; i <= m; ++i)
	   scanf("%d%d%lf", &a[i], &b[i], &c[i]);
	while(r - l > eps){
		mid = (l + r) / 2;
		for(int i = 1; i <= m; ++i)
		   Add(a[i], b[i], c[i] - mid);
		if(check()) r = mid;
		else l = mid;
		for(int i = 1; i <= n; ++i)
		   head[i] = v[i] = dis[i] = 0;
		num = 0;
	}
	printf("%.8lf\n", l);
	return 0;
}