Kruskal算法的C语言程序

Kruskal算法是有关图的最小生成树的算法。Kruskal算法是两个经典的最小生成树算法之一，另外一个是Prim算法。

程序来源：Kruskal's Algorithm。

百度百科：Kruskal算法。

维基百科：Kruskal's Algorithm。

C语言程序（去除了原文中非标准的C语言代码）：

#include<stdio.h>
#include<stdlib.h>
int i,j,k,a,b,u,v,n,ne=1;
int min,mincost=0,cost[9][9],parent[9];
int find(int);
int uni(int,int);

int main()
{
    printf("
	Implementation of Kruskal's algorithm
");
    printf("
Enter the no. of vertices:");
    scanf("%d",&n);
    printf("
Enter the cost adjacency matrix:
");
    for(i=1;i<=n;i++)
    {
        for(j=1;j<=n;j++)
        {
            scanf("%d",&cost[i][j]);
            if(cost[i][j]==0)
                cost[i][j]=999;
        }
    }
    printf("The edges of Minimum Cost Spanning Tree are
");
    while(ne < n)
    {
        for(i=1,min=999;i<=n;i++)
        {
            for(j=1;j <= n;j++)
            {
                if(cost[i][j] < min)
                {
                    min=cost[i][j];
                    a=u=i;
                    b=v=j;
                }
            }
        }
        u=find(u);
        v=find(v);
        if(uni(u,v))
        {
            printf("%d edge (%d,%d) =%d
",ne++,a,b,min);
            mincost +=min;
        }
        cost[a][b]=cost[b][a]=999;
    }
    printf("
	Minimum cost = %d
",mincost);
}

int find(int i)
{
    while(parent[i])
    i=parent[i];
    return i;
}

int uni(int i,int j)
{
    if(i!=j)
    {
        parent[j]=i;
        return 1;
    }
    return 0;
}

运行结果：

	Implementation of Kruskal's algorithm

Enter the no. of vertices:6

Enter the cost adjacency matrix:
0 3 1 6 0 0
3 0 5 0 3 0
1 5 0 5 6 4
6 0 5 0 0 2
0 3 6 0 0 6
0 0 4 2 6 0
The edges of Minimum Cost Spanning Tree are
1 edge (1,3) =1
2 edge (4,6) =2
3 edge (1,2) =3
4 edge (2,5) =3
5 edge (3,6) =4

	Minimum cost = 13