How Many Maos Does the Guanxi Worth （dijkstra）

最新推荐文章于 2019-02-11 18:15:04 发布

原创最新推荐文章于 2019-02-11 18:15:04 发布 · 449 阅读

0 ·

CC 4.0 BY-SA版权

文章标签：

#acm #dijkstra

本文介绍了一种算法问题，目标是最小化刘老板利用金钱关系让其孩子进入好中学的成本，或使其计划失败。通过枚举关系网中的关键节点并计算最小花费。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

How Many Maos Does the Guanxi Worth

"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

Sample Output

50
Inf

题意：刘老板想通过关系让儿子上学，但是王老板不认识校长，只能通过关系，刘老板每次找一个人就得向这个人付钱，正义的你看到这样的情况很气愤，于是你决定说服一个人且只能说服一个人不帮助刘老板，让刘老板的计划失败或者花的钱更多

这道题想了好久，思路完全错了，应该就是枚举然后选出最大的就可以了！

#include <cstdio>  
#include <cstring>  
#define INF 0x3f3f3f3f  
int map[50][50];  
int dis[50];  
int vis[50];  
int n,m;  
void dj()  
{  
    vis[1]=1;  
    for(int i=1;i<=n;i++)  
    {  
        dis[i]=map[1][i];  
    }  
    for(int i=0;i<n;i++)  
    {  
        int min=INF;  
        int pos=-1;  
        for(int j=1;j<=n;j++)  
        {  
            if(vis[j]==0&&min>dis[j])  
            {  
                min=dis[j];  
                pos=j;  
            }  
        }  
        if(pos==-1)  
        return ;  
        vis[pos]=1;  
        dis[pos]=min;  
        for(int j=1;j<=n;j++)  
        {  
            if(vis[j]==0&&dis[j]>dis[pos]+map[pos][j])  
            {  
                dis[j]=dis[pos]+map[pos][j];  
            }  
        }  
    }  
}  
int main()  
{  
    while(scanf("%d%d",&n,&m)!=EOF)  
    {  
        if(n==0&&m==0)  
        break;  
        for(int i=1;i<=n;i++)  
        {  
            for(int j=i;j<=n;j++)  
            {  
                if(i==j)  
                map[i][j]=0;  
                else  
                {  
                    map[i][j]=INF;  
                    map[j][i]=INF;  
                }  
            }  
        }  
        for(int i=0;i<m;i++)  
        {  
            int x,y,z;  
            scanf("%d%d%d",&x,&y,&z);  
            if(map[x][y]>z)  
            {  
                map[x][y]=z;  
            }  
                map[y][x]=z;  
        }  
        int ans=-1;  
        for(int i=2;i<n;i++) 
        {  
            memset(vis,0,sizeof(vis));  
            vis[i]=1;    
            dj();  
            if(ans<dis[n])//¸üÐÂans   
            {  
                ans=dis[n];  
            }  
        }  
        if(ans==INF)//ÎÞ·¨ÁªÍ¨   
        {  
            printf("Inf\n");  
        }  
        else  
        {  
            printf("%d\n",ans);  
        }  
    }  
    return 0;  
}