How Many Maos Does the Guanxi Worth

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 512000/512000 K (Java/Others)
Total Submission(s): 760    Accepted Submission(s): 290

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：1到n个人，在删除一个人（除第1个人和第n个人外)情况下,求打通关系从第一个1到第n人所花费最多的钱。

思路：枚举+dijkstra

收获：dijkstra应用。dijkstra：求单源最短路径，边权要为正。

#include <cstdio>
#include <iostream>
#include <cstdlib>
#include <algorithm>
#include <ctime>
#include <cmath>
#include <string>
#include <cstring>
#include <stack>
#include <queue>
#include <list>
#include <vector>
#include <map>
#include <set>
using namespace std;

const int INF=0x3f3f3f3f;
const double eps=1e-10;
const double PI=acos(-1.0);

const int maxn=5000;
int w[maxn][maxn];
int n, m;
int v[maxn];
int d[maxn];
int num[maxn];
int dijkstra(int k)
{
    memset(v, 0, sizeof(v));
    v[k] = 1;
    for(int i = 1; i <= n; i++) d[i] = (i==1 ? 0 : INF);
    for(int i = 1; i <= n; i++)
    {
        int x, m = INF;
        for(int j = 1; j <= n; j++) if(!v[j] && d[j]<=m) m = d[x=j];
        v[x]=1;
        for(int j = 1; j <= n; j++) d[j] = min(d[j], d[x] + w[x][j]);
    }
    return d[n];
}
int main()
{
    while(~scanf("%d%d", &n, &m))
    {
        if(n==0 && m==0)
            break;
        memset(w, INF, sizeof(w));
        int a, b, t;
        for(int i = 0; i < m; i++)
        {
            scanf("%d%d%d", &a, &b, &t);
            w[a][b] = w[b][a] = min(t, w[a][b]);
        }
        //int ans = INF;
        int cnt = 0;
        memset(num, INF, sizeof(num));
        for(int i = 2; i < n; i++) cnt = max(cnt, dijkstra(i));
        if(cnt == INF)
            printf("Inf\n");
        else
            printf("%d\n", cnt);
    }
    return 0;
}