poj 2485 Highways

Highways

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 26150		Accepted: 11932

Description

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.

Input

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.

Output

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.

Sample Input

1

3
0 990 692
990 0 179
692 179 0

Sample Output

692

/*求最小生成树的最大权边*/

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int MAX=550;
const int INF=0xfffffff;
int g[MAX][MAX];
int vis[MAX]; //标记数组，没有加入时为0，加入后为1
int dis[MAX]; //记录树到每个顶点的最小距离，会不断更新
int t,n;
int prim(int start)
{
    int i,j,k,Min,Max=0;
    memset(vis,0,sizeof(vis));
    vis[start]=1;//将第一个顶点加入树
    for(i=0;i<n;i++)
    {
        dis[i]=g[start][i]; //计算其他顶点距离第一个顶点的最小距离
    }
    for(i=1;i<n;i++)  // 注意循环次数
    {
        Min=INF,k=-1;
        for(j=0;j<n;j++) //找最小边
        {
            if(!vis[j]&&dis[j]<Min)
            {
                Min=dis[j];
                k=j;
            }
        }
        vis[k]=1;
        Max=max(Min,Max);  // 更新树的最大权值
        for(j=0;j<n;j++)  //更新权值
        {
            if(!vis[j]&&dis[j]>g[k][j])
                dis[j]=g[k][j];
        }
    }
    return Max;
}
int main()
{
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        memset(dis,INF,sizeof(dis));
        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
                scanf("%d",&g[i][j]);
        }
        printf("%d
",prim(0));
    }
    return 0;
}