poj 2485 Highways(最小生成树中求最大权值)

探讨如何在给定村庄间距离的情况下,构建一个所有村庄都相互连通且任意两点间只通过高速公路可达的最小最大边权重问题。介绍了一种有效算法实现,通过不断选择当前未连接村庄间的最短路径来逐步构建完整的高速公路网络。

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<div class="ptt" lang="en-US">                                                                                                                                              Highways</div><div class="plm"><table align="center"><tbody><tr><td><strong>Time Limit:</strong> 1000MS</td><td width="10px"> </td><td><strong>Memory Limit:</strong> 65536K</td></tr><tr><td><strong>Total Submissions:</strong> 28287</td><td width="10px"> </td><td><strong>Accepted:</strong> 12880</td></tr></tbody></table></div><p class="pst">Description</p><div class="ptx" lang="en-US">The island nation of Flatopia is perfectly flat. Unfortunately, Flatopia has no public highways. So the traffic is difficult in Flatopia. The Flatopian government is aware of this problem. They're planning to build some highways so that it will be possible to drive between any pair of towns without leaving the highway system. 

Flatopian towns are numbered from 1 to N. Each highway connects exactly two towns. All highways follow straight lines. All highways can be used in both directions. Highways can freely cross each other, but a driver can only switch between highways at a town that is located at the end of both highways. 

The Flatopian government wants to minimize the length of the longest highway to be built. However, they want to guarantee that every town is highway-reachable from every other town.</div><p class="pst">Input</p><div class="ptx" lang="en-US">The first line of input is an integer T, which tells how many test cases followed.
The first line of each case is an integer N (3 <= N <= 500), which is the number of villages. Then come N lines, the i-th of which contains N integers, and the j-th of these N integers is the distance (the distance should be an integer within [1, 65536]) between village i and village j. There is an empty line after each test case.</div><p class="pst">Output</p><div class="ptx" lang="en-US">For each test case, you should output a line contains an integer, which is the length of the longest road to be built such that all the villages are connected, and this value is minimum.</div><p class="pst">Sample Input</p><pre class="sio">1

3
0 990 692
990 0 179
692 179 0

Sample Output

692



#include<stdio.h>
#include<string.h>
int INF = 0x3f3f3f3f;
int main()
{
    int t;
    int n,m;
    int i,j,k;
    int map[550][550];
    bool book[550];
    int dis[550];
    scanf("%d",&t);
    while( t-- )
    {
        scanf("%d",&n);
        //memset(map,0,sizeof(map));
        memset(book,0,sizeof(book));
        memset(dis,0,sizeof(dis));
        for(i = 1; i <=n ;i++)
        {
            for( j = 1; j <=n ;j++)
                scanf("%d",&map[i][j]);
        }
        book[1]=1;
        for( i = 1; i <= n; i++)
            dis[i] = map[1][i];
        int step = 1;
        int max = -1;
        int min;
        while(step < n)
        {
           min =  INF;
           for( i=1; i <=n; i++)
           {
               if(!book[i]&&dis[i]<min)
               {
                   min = dis[i];
                   j = i;
               }
           }
           book[j] = 1;
           step++;

           if(max < min)
              max=min;

              for( k = 1; k <= n; k++)
              {
                  if(!book[k] && dis[k] > map[j][k])
                    dis[k]=map[j][k];
              }


        }
        printf("%d\n",max);
    }
    return 0;
}

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