hdu5137(最短路)

How Many Maos Does the Guanxi Worth

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 512000/512000 K (Java/Others)
Total Submission(s): 1608    Accepted Submission(s): 622

Problem Description

"Guanxi" is a very important word in Chinese. It kind of means "relationship" or "contact". Guanxi can be based on friendship, but also can be built on money. So Chinese often say "I don't have one mao (0.1 RMB) guanxi with you." or "The guanxi between them is naked money guanxi." It is said that the Chinese society is a guanxi society, so you can see guanxi plays a very important role in many things.

Here is an example. In many cities in China, the government prohibit the middle school entrance examinations in order to relief studying burden of primary school students. Because there is no clear and strict standard of entrance, someone may make their children enter good middle schools through guanxis. Boss Liu wants to send his kid to a middle school by guanxi this year. So he find out his guanxi net. Boss Liu's guanxi net consists of N people including Boss Liu and the schoolmaster. In this net, two persons who has a guanxi between them can help each other. Because Boss Liu is a big money(In Chinese English, A "big money" means one who has a lot of money) and has little friends, his guanxi net is a naked money guanxi net -- it means that if there is a guanxi between A and B and A helps B, A must get paid. Through his guanxi net, Boss Liu may ask A to help him, then A may ask B for help, and then B may ask C for help ...... If the request finally reaches the schoolmaster, Boss Liu's kid will be accepted by the middle school. Of course, all helpers including the schoolmaster are paid by Boss Liu.

You hate Boss Liu and you want to undermine Boss Liu's plan. All you can do is to persuade ONE person in Boss Liu's guanxi net to reject any request. This person can be any one, but can't be Boss Liu or the schoolmaster. If you can't make Boss Liu fail, you want Boss Liu to spend as much money as possible. You should figure out that after you have done your best, how much at least must Boss Liu spend to get what he wants. Please note that if you do nothing, Boss Liu will definitely succeed.

 

Input

There are several test cases.

For each test case:

The first line contains two integers N and M. N means that there are N people in Boss Liu's guanxi net. They are numbered from 1 to N. Boss Liu is No. 1 and the schoolmaster is No. N. M means that there are M guanxis in Boss Liu's guanxi net. (3 <=N <= 30, 3 <= M <= 1000)

Then M lines follow. Each line contains three integers A, B and C, meaning that there is a guanxi between A and B, and if A asks B or B asks A for help, the helper will be paid C RMB by Boss Liu.

The input ends with N = 0 and M = 0.

It's guaranteed that Boss Liu's request can reach the schoolmaster if you do not try to undermine his plan.

 

Output

For each test case, output the minimum money Boss Liu has to spend after you have done your best. If Boss Liu will fail to send his kid to the middle school, print "Inf" instead.

 

Sample Input

4 5
1 2 3
1 3 7
1 4 50
2 3 4
3 4 2
3 2
1 2 30
2 3 10
0 0

 

Sample Output

50
Inf

题意：在中国存在很多关系，比如a和b有关系的话，如果a帮助了b那么a可以得到w元钱，反过来b帮助了a，b也可以得到w元，现在要在第1个点到第n个点之间让你去掉一个点，尽可能使1帮不到n或者使1得到n帮助的花费最大化。

思路：这题由于数据量比较小，所以直接枚举去掉2到第n-1个点就ok，不过枚举也是要有方法的，机智如我哈哈，只在spfa里面加上一个参数就搞定，并不需要实际的去去掉某一个点的所有边，在spfa里面加一个判断就行了。

#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include<string.h>
#include<algorithm>
#include<math.h>
#include<queue>
using namespace std;
typedef long long ll;
const int N=50,INF=999999999;
int n,m;
int tu[N][N];
int dis[N];
int spfa(int s,int qu)///这个qu参数就是表示去掉某一个点
{
    bool vis[N]= {0};
    queue<int>q;
    for(int i=0; i<=n; i++)
        dis[i]=INF;
    dis[s]=0;
    q.push(s);
    while(!q.empty())
    {
        int t=q.front();
        q.pop();
        vis[t]=0;
        for(int i=1; i<=n; i++)
        {
            if(i==qu)continue;///这句判断就是去点的关键，所有边都走不到这一个点了自然就相当于去掉了这个点
            if(dis[t]+tu[t][i]<dis[i])
            {

                dis[i]=dis[t]+tu[t][i];
                if(!vis[i])
                {
                    vis[i]=1;
                    q.push(i);
                }
            }
        }
    }
    return dis[n];
}

int main()
{
    while(~scanf("%d%d",&n,&m)&&m+n)
    {
        for(int i=1; i<=n; i++)
            for(int j=1; j<=n; j++)
                tu[i][j]=i==j?0:INF;
        while(m--)
        {
            int a,b,w;
            scanf("%d%d%d",&a,&b,&w);
            tu[a][b]=tu[b][a]=w;
        }
        int ans=-1;
        for(int i=2; i<n; i++)
        {
            int tem=spfa(1,i);
            ans=max(ans,tem);
        }
        if(ans>=INF)printf("Inf\n");
        else printf("%d\n",ans);
    }
    return 0;
}