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| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 8220 | Accepted: 2757 |
Description
Farmer John has decided to reward his cows for their hard work by taking them on a tour of the big city! The cows must decide how best to spend their free time.
Fortunately, they have a detailed city map showing the L (2 ≤ L ≤ 1000) major landmarks (conveniently numbered 1.. L) and the P (2 ≤ P ≤ 5000) unidirectional cow paths that join them. Farmer John will drive the cows to a starting landmark of their choice, from which they will walk along the cow paths to a series of other landmarks, ending back at their starting landmark where Farmer John will pick them up and take them back to the farm. Because space in the city is at a premium, the cow paths are very narrow and so travel along each cow path is only allowed in one fixed direction.
While the cows may spend as much time as they like in the city, they do tend to get bored easily. Visiting each new landmark is fun, but walking between them takes time. The cows know the exact fun values Fi (1 ≤ Fi ≤ 1000) for each landmark i.
The cows also know about the cowpaths. Cowpath i connects landmark L1i to L2i (in the direction L1i -> L2i ) and requires time Ti (1 ≤ Ti ≤ 1000) to traverse.
In order to have the best possible day off, the cows want to maximize the average fun value per unit time of their trip. Of course, the landmarks are only fun the first time they are visited; the cows may pass through the landmark more than once, but they do not perceive its fun value again. Furthermore, Farmer John is making the cows visit at least two landmarks, so that they get some exercise during their day off.
Help the cows find the maximum fun value per unit time that they can achieve.
Input
* Line 1: Two space-separated integers: L and P
* Lines 2..L+1: Line i+1 contains a single one integer: Fi
* Lines L+2..L+P+1: Line L+i+1 describes cow path i with three space-separated integers: L1i , L2i , and Ti
Output
* Line 1: A single number given to two decimal places (do not perform explicit rounding), the maximum possible average fun per unit time, or 0 if the cows cannot plan any trip at all in accordance with the above rules.
Sample Input
5 7 30 10 10 5 10 1 2 3 2 3 2 3 4 5 3 5 2 4 5 5 5 1 3 5 2 2
Sample Output
6.00
Source
题目大意就是找到一个环使得顶点权值之和与边权之和的比率最大
首先，需要注意的是题目要求可以从任意一点开始，网上很多解题报告默认的从1点开始，虽然过了此题，但是显然是不太对的
由于题目是求的max，那么在边权变形后，用 SPFA求最长路，看是否出现正环， 然后根据这个进行二分查找。
ac代码#include<stdio.h>
#include<string.h>
#include <queue>
#include<iostream>
#define eps 1e-6
#define INF 0xfffffff
using namespace std;
int head[1010],cnt,n,m,vis[1010],c[1010];
struct s
{
int u,v,w,next;
}edge[100100];
double val[1010],d[1010];
void add(int u,int v,int w)
{
edge[cnt].u=u;
edge[cnt].v=v;
edge[cnt].w=w;
edge[cnt].next=head[u];
head[u]=cnt++;
}
int spfa(double mid)
{
int i;
queue<int>q;
for(i=1;i<=n;i++)
{
vis[i]=c[i]=1;
q.push(i);
d[i]=0;
}
while(!q.empty())
{
int u=q.front();
q.pop();
vis[u]=0;
for(i=head[u];i!=-1;i=edge[i].next)
{
int v=edge[i].v;
double w=val[u]-mid*edge[i].w;
if(d[v]<d[u]+w)
{
d[v]=d[u]+w;
if(!vis[v])
{
q.push(v);
vis[v]=1;
c[v]++;
if(c[v]>n)
return 1;
}
}
}
}
return 0;
}
int main()
{
// int n,m;
while(scanf("%d%d",&n,&m)!=EOF)
{
int i;
cnt=0;
memset(head,-1,sizeof(head));
for(i=1;i<=n;i++)
{
scanf("%lf",&val[i]);
}
for(i=0;i<m;i++)
{
int u,v,w;
scanf("%d%d%d",&u,&v,&w);
add(u,v,w);
}
double low=0,high=1000;
while(high-low>eps)
{
double mid=(high+low)/2;
if(spfa(mid))
low=mid;
else
high=mid;
}
printf("%.2lf\n",low);
}
}POJ 题目3621 Sightseeing Cows（SPFA）
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原文地址：http://blog.csdn.net/yu_ch_sh/article/details/45445633
