poj 1797 Heavy Transportation 最短路

poj 1797 Heavy Transportation 最短路

Heavy Transportation

Time Limit: 3000MS		Memory Limit: 30000K
Total Submissions: 5123		Accepted: 1393

Description

Background
Hugo Heavy is happy. After the breakdown of the Cargolifter project he can now expand business. But he needs a clever man who tells him whether there really is a way from the place his customer has build his giant steel crane to the place where it is needed on which all streets can carry the weight.
Fortunately he already has a plan of the city with all streets and bridges and all the allowed weights.Unfortunately he has no idea how to find the the maximum weight capacity in order to tell his customer how heavy the crane may become. But you surely know.

Problem
You are given the plan of the city, described by the streets (with weight limits) between the crossings, which are numbered from 1 to n. Your task is to find the maximum weight that can be transported from crossing 1 (Hugo's place) to crossing n (the customer's place). You may assume that there is at least one path. All streets can be travelled in both directions.

Input

The first line contains the number of scenarios (city plans). For each city the number n of street crossings (1 <= n <= 1000) and number m of streets are given on the first line. The following m lines contain triples of integers specifying start and end crossing of the street and the maximum allowed weight, which is positive and not larger than 1000000. There will be at most one street between each pair of crossings.

Output

The output for every scenario begins with a line containing "Scenario #i:", where i is the number of the scenario starting at 1. Then print a single line containing the maximum allowed weight that Hugo can transport to the customer. Terminate the output for the scenario with a blank line.

Sample Input

1
3 3
1 2 3
1 3 4
2 3 5

Sample Output

Scenario #1:
4
给定n个点，及m条边的最大负载，求顶点1到顶点n的最大流。

用Dijkstra算法解之，只是需要把“最短路”的定义稍微改变一下，

A到B的路长定义为路径上边权最小的那条边的长度，

而最短路其实是A到B所有路长的最大值。

   
   
   
   

    
    
    
    
    
    
    
    //
    
    
    
    Heavy Transportation

    
    
    
    //
    
    
    
    Dijkstra
    
    
    
    

    
    
    
    #include 
    
    
    
    <
    
    
    
    iostream
    
    
    
    >
    
    
    
    
#include
    
    
    
    <
    
    
    
    stdio.h
    
    
    
    >
    
    
    
    

    
    
    
    using
    
    
    
     
    
    
    
    namespace
    
    
    
     std;

    
    
    
    const
    
    
    
     
    
    
    
    int
    
    
    
     MAXS
    
    
    
    =
    
    
    
    1005
    
    
    
    ;

    
    
    
    int
    
    
    
     n;

    
    
    
    int
    
    
    
     mat[MAXS][MAXS];

    
    
    
    int
    
    
    
     asd[MAXS];

    
    
    
    int
    
    
    
     s[MAXS];

    
    
    
    int
    
    
    
     min(
    
    
    
    int
    
    
    
     a,
    
    
    
    int
    
    
    
     b)
    
    
    
    
    
    
    
    {return a<b?a:b;}
    
    
    
    

    
    
    
    int
    
    
    
     Dijkstra()

    
    
    
    
    
    
    
    {
    int i,j;
    for(i=1;i<n;i++)
    {
        asd[i]=mat[0][i];
        s[i]=0;
    }
    s[0]=1;
    asd[0]=0;
    for(i=0;i<n-1;i++)
    {
        int max=0;
        int u=0;
        for(j=1;j<n;j++)
        {
            if(s[j]==0 && asd[j]>max)
            {
                u=j;
                max=asd[j];
            }
        }
        if(u==0)
            break;
        s[u]=1;
        asd[u]=max;
        for(j=1;j<n;j++)
        {
            if (s[j]==0 && asd[j]<min(asd[u],mat[u][j]))
            {
                asd[j]=min(asd[u],mat[u][j]);
                
            }
        }
    }
    return asd[n-1];

}
    
    
    
    

    
    
    
    int
    
    
    
     main()

    
    
    
    
    
    
    
    {
    
    int t,m;
    int i,j;
    scanf("%d",&t);
    int v1,v2;
    int value;
    for (int s=1;s<=t;s++)
    {
        scanf("%d%d",&n,&m);
        for(i=0;i<n;i++)
            for (j=0;j<n;j++)
            {
                mat[i][j]=0;
            }
        while (m--)
        {
            scanf("%d%d%d",&v1,&v2,&value);
            mat[v1-1][v2-1]=mat[v2-1][v1-1]=value;
            
        }
        printf("Scenario #%d:\n%d\n\n",s,Dijkstra());

    }
    return 0;
}