bzoj1486HNOI2009最小圈

Posted 2020-06-13 AaronPolaris

1486: [HNOI2009]最小圈

Time Limit: 10 Sec  Memory Limit: 64 MB
Submit: 1778  Solved: 827
[Submit][Status][Discuss]

Description

Input

Output

Sample Input

Sample Output

HINT

Source

01分数规划+二分答案+spfa判负环

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#define F(i,j,n) for(int i=j;i<=n;i++)
#define D(i,j,n) for(int i=j;i>=n;i--)
#define ll long long
#define maxn 3005
#define maxm 10005
#define inf 1000000000
#define eps 1e-9
using namespace std;
struct edge{int next,to;double v,w;}e[maxm];
int n,m,cnt,head[maxn];
double dis[maxn];
bool flag,mark[maxn];
inline int read()
{
	int x=0,f=1;char ch=getchar();
	while (ch<'0'||ch>'9'){if (ch=='-') f=-1;ch=getchar();}
	while (ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
inline void add_edge(int x,int y)
{
	e[++cnt].next=head[x];
	e[cnt].to=y;
	head[x]=cnt;
}
inline void spfa(int x)
{
	if (mark[x]){flag=true;return;}
	mark[x]=true;
	for(int i=head[x],y;i;i=e[i].next)
		if (dis[x]+e[i].v<dis[y=e[i].to])
		{
			dis[y]=dis[x]+e[i].v;
			spfa(y);
			if (flag) return;
		}
	mark[x]=false;
}
inline bool judge()
{
	F(i,1,n) dis[i]=mark[i]=0;
	flag=false;
	F(i,1,n)
	{
		spfa(i);
		if (flag) return true;
	}
	return false;
}
int main()
{
	n=read();m=read();
	int x,y;double z,l=inf,r=-inf,mid;
	F(i,1,m)
	{
		x=read();y=read();scanf("%lf",&z);
		add_edge(x,y);
		e[i].w=z;
		l=min(l,z);
		r=max(r,z);
	}
	while (r-l>=eps)
	{
		mid=(l+r)/2;
		F(i,1,m) e[i].v=e[i].w-mid;
		if (judge()) r=mid;
		else l=mid;
	}
	printf("%.8lf\n",l);
	return 0;
}