最小生成树和Kruskal算法

源代码

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>

#define MAXV 100
#define MaxSize 100
#define INF 65535

typedef struct{
    int edges[MAXV][MAXV];//领接矩阵数组
    int n, e;//顶点数，边数
} MatGraph;

typedef struct{
    int u;//边的起始顶点
    int v;//边的终止顶点
    int w;//边的权值
} Edge;

int cmp( const void *a ,const void *b)
{
return (*(Edge *)a).w > (*(Edge *)b).w ? 1 : -1;
}

void Kruskal(MatGraph g){
    int i, j, u1, v1, sn1, sn2, k;
    Edge E[MaxSize];
    int vset[MAXV];
    k = 0;
    for (i = 0; i < g.n;i++){
        for (j = 0; j <= i;j++){
            if(g.edges[i][j]>0&&g.edges[i][j]<INF){
                E[k].u = i;
                E[k].v = j;
                E[k].w = g.edges[i][j];
                k++;
            }
        }
    }
    qsort(E, k, sizeof(E[0]), cmp);//快排，需要定义cmp()函数
    for (i = 0; i < g.n;i++){
        vset[i] = i;
    }
    k = 1;
    j = 0;
    while(k<g.n){
        u1 = E[j].u;
        v1 = E[j].v;
        sn1 = vset[u1];
        sn2 = vset[v1];
        if(sn1!=sn2){
            printf("(%d,%d):%d\n", u1+1, v1+1, E[j].w);
            k++;
            for (i = 0; i < g.n;i++){
                if(vset[i]==sn2){
                    vset[i] = sn1;
                }
            }
        }
        j++;
    }
}

int main(void){
    FILE *pBanana;
    int i, j, w;
    bool dog[MAXV];
    MatGraph *apple = (MatGraph *)malloc(sizeof(MatGraph));
    if(apple==NULL){
        return 1;
    }
    memset((*apple).edges,INF,MAXV * MAXV * sizeof(int));
    memset(dog, false, sizeof(bool) * MAXV);
    (*apple).n = 0;
    (*apple).e = 0;
    pBanana = fopen("cat.txt", "r");
    while(!feof(pBanana)){
        fscanf(pBanana, "%d\t%d\t%d", &i, &j, &w);
        if(dog[i-1]==false){
            (*apple).n++;
            dog[i-1] = true;
        }
        (*apple).e++;
        (*apple).edges[i-1][j-1] = w;
        fgetc(pBanana);
    }
    (*apple).e /= 2;
    fclose(pBanana);
    Kruskal(*apple);
    getchar();//两个getchar()方便查看窗口
    getchar();
    return 0;
}

cat.txt

1   2   6
2   1   6
1   3   1
3   1   1
1   4   5
4   1   5
2   5   3
5   2   3
2   3   5
3   2   5
3   4   5
4   3   5
3   5   6
5   3   6
3   6   4
6   3   4
4   6   2
6   4   2
5   6   6
6   5   6

运行结果

TIM截图20180617170159.png