最小生成树之Kruskal算法

用Kruskal方法解决无向连通图最小生成树问题：

1所有的点初始化的时候自成一个集合

2所有的边按照权值大小，从小到大排序

3选取权值小的边加入现有集合中，且加入后必须不构成环路，加入后，记录点的祖先

4重复步骤3，直到所有的点都被放入一个集合中

 /*
 desription:use Kruskal method to solve mini span tree problem
 copyright:Hou Shengtao
 data:2016/12/7
 */
 #include<stdio.h>
 #include<stdlib.h>
 #define max 100
 #define INF 999
 int edge_num,vertex_num;
 int p[max];//record SET ID
 struct edge{
     int a;
     int b;
     int w;
 }e[max];
 void sort(){
     int i,j;

     for(i=;i<edge_num;i++){
         j=i-;
         int x=e[i].w;
         int aa=e[i].a;
         int bb=e[i].b;

         while(j>=&&e[j].w>x){
             e[j+].a=e[j].a;
             e[j+].b=e[j].b;
             e[j+].w=e[j].w;
             j--;
         }
         e[j+].a=aa;
         e[j+].b=bb;
         e[j+].w=x;
     }
 }
 //find() use to find the ancester node
 int find(int x){
     return x==p[x]?x:(p[x]=find(p[x]));
 }
 //unioned() use to pass the ancester ID to its children
 //so that all the mini tree vertex have the same ID
 void unioned(int x,int y){
     p[find(x)]=find(y);
 }
 void Kruskal(){
     //init
     int i,j;
     for(i=;i<vertex_num;i++){
         p[i]=i;//init the SET ID
     }
     //sorting according to edge's weight
     sort();
     printf("\n");
     for(i=,j=;i<vertex_num&&j<edge_num;i++,j++){
         if(find(e[j].a)==find(e[j].b))continue;//form circle,skip

         unioned(e[j].a,e[j].b);

         printf("start:%d end:%d weight:%d\n",e[j].a,e[j].b,e[j].w);
     }
 }

 int main(){

     FILE *fin  = fopen ("mst.in", "r");
     FILE *fout = fopen ("mst.out", "w");

     char buf[];
     fgets(buf,,fin);
     edge_num=atoi(buf);
     fgets(buf,,fin);
     vertex_num=atoi(buf);
     printf("edge_num:%d\n",edge_num);
     printf("vertex_num:%d\n",vertex_num);

     int i;
     for(i=;i<edge_num;i++){
         int start,end,weight;//start point,end point and the weight of edge
         fgets(buf,,fin);
         sscanf(buf,"%d %d %d",&start,&end,&weight);
         printf("start:%d end:%d weight:%d\n",start,end,weight);
         e[i].a=start;
         e[i].b=end;
         e[i].w=weight;
     }
     Kruskal();

     return ;
 }