Kruskal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。
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程序(去除了原文中非标准的C语言代码):
#include运行结果:#include 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("\n\tImplementation of Kruskal's algorithm\n"); printf("\nEnter the no. of vertices:"); scanf("%d",&n); printf("\nEnter the cost adjacency matrix:\n"); 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\n"); 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\n",ne++,a,b,min); mincost +=min; } cost[a][b]=cost[b][a]=999; } printf("\n\tMinimum cost = %d\n",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;}
Implementation of Kruskal's algorithmEnter the no. of vertices:6Enter the cost adjacency matrix:0 3 1 6 0 03 0 5 0 3 01 5 0 5 6 46 0 5 0 0 20 3 6 0 0 60 0 4 2 6 0The edges of Minimum Cost Spanning Tree are1 edge (1,3) =12 edge (4,6) =23 edge (1,2) =34 edge (2,5) =35 edge (3,6) =4 Minimum cost = 13