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=1;i<edge_num;i++){
        j=i-1;
        int x=e[i].w;
        int aa=e[i].a;
        int bb=e[i].b;
        
        while(j>=0&&e[j].w>x){
            e[j+1].a=e[j].a;
            e[j+1].b=e[j].b;
            e[j+1].w=e[j].w;
            j--;
        }
        e[j+1].a=aa;
        e[j+1].b=bb;
        e[j+1].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=0;i<vertex_num;i++){
        p[i]=i;//init the SET ID
    } 
    //sorting according to edge's weight
    sort();
    printf("
");
    for(i=0,j=0;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
",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[10];
    fgets(buf,10,fin);
    edge_num=atoi(buf);    
    fgets(buf,10,fin);
    vertex_num=atoi(buf);
    printf("edge_num:%d
",edge_num);
    printf("vertex_num:%d
",vertex_num);
    
    int i;
    for(i=0;i<edge_num;i++){
        int start,end,weight;//start point,end point and the weight of edge
        fgets(buf,10,fin);
        sscanf(buf,"%d %d %d",&start,&end,&weight);
        printf("start:%d end:%d weight:%d
",start,end,weight);
        e[i].a=start;
        e[i].b=end;
        e[i].w=weight;
    }
    Kruskal();

    return 0;
}