最小生成树_Kruskal

http://www.cnblogs.com/ly772696417/archive/2012/03/19/2407172.html

#include "stdio.h"    #include "stdlib.h"   #include "io.h"  #include "math.h"  #include "time.h"#define OK 1#define ERROR 0#define TRUE 1#define FALSE 0typedef int Status;    /* Status是函数的类型,其值是函数结果状态代码，如OK等 */#define MAXEDGE 20#define MAXVEX 20#define INFINITY 65535typedef struct{    int arc[MAXVEX][MAXVEX];    int numVertexes, numEdges;}MGraph;typedef struct{    int begin;    int end;    int weight;}Edge;   /* 对边集数组Edge结构的定义 *//* 构件图 */void CreateMGraph(MGraph *G){    int i, j;    /* printf("请输入边数和顶点数:"); */    G->numEdges=15;    G->numVertexes=9;    for (i = 0; i < G->numVertexes; i++)/* 初始化图 */    {        for ( j = 0; j < G->numVertexes; j++)        {            if (i==j)                G->arc[i][j]=0;            else                G->arc[i][j] = G->arc[j][i] = INFINITY;        }    }    G->arc[0][1]=10;    G->arc[0][5]=11;     G->arc[1][2]=18;     G->arc[1][8]=12;     G->arc[1][6]=16;     G->arc[2][8]=8;     G->arc[2][3]=22;     G->arc[3][8]=21;     G->arc[3][6]=24;     G->arc[3][7]=16;    G->arc[3][4]=20;    G->arc[4][7]=7;     G->arc[4][5]=26;     G->arc[5][6]=17;     G->arc[6][7]=19;     for(i = 0; i < G->numVertexes; i++)    {        for(j = i; j < G->numVertexes; j++)        {            G->arc[j][i] =G->arc[i][j];        }    }}/* 交换权值 以及头和尾 */void Swapn(Edge *edges,int i, int j){    int temp;    temp = edges[i].begin;    edges[i].begin = edges[j].begin;    edges[j].begin = temp;    temp = edges[i].end;    edges[i].end = edges[j].end;    edges[j].end = temp;    temp = edges[i].weight;    edges[i].weight = edges[j].weight;    edges[j].weight = temp;}/* 对权值进行排序 */void sort(Edge edges[],MGraph *G){    int i, j;    for ( i = 0; i < G->numEdges; i++)    {        for ( j = i + 1; j < G->numEdges; j++)        {            if (edges[i].weight > edges[j].weight)            {                Swapn(edges, i, j);            }        }    }    printf("权排序之后的为:\n");    for (i = 0; i < G->numEdges; i++)    {        printf("(%d, %d) %d\n", edges[i].begin, edges[i].end, edges[i].weight);    }}/* 查找连线顶点的尾部下标 */int Find(int *parent, int f){    while ( parent[f] > 0)    {        f = parent[f];    }    return f;}/* 生成最小生成树 */void MiniSpanTree_Kruskal(MGraph G){    int i, j, n, m;    int k = 0;    int parent[MAXVEX];/* 定义一数组用来判断边与边是否形成环路 */        Edge edges[MAXEDGE];/* 定义边集数组,edge的结构为begin,end,weight,均为整型 */    /* 用来构建边集数组并排序********************* */    for ( i = 0; i < G.numVertexes-1; i++)    {        for (j = i + 1; j < G.numVertexes; j++)        {            if (G.arc[i][j]<INFINITY)            {                edges[k].begin = i;                edges[k].end = j;                edges[k].weight = G.arc[i][j];                k++;            }        }    }    sort(edges, &G);    /* ******************************************* */    for (i = 0; i < G.numVertexes; i++)        parent[i] = 0;    /* 初始化数组值为0 */    printf("打印最小生成树：\n");    for (i = 0; i < G.numEdges; i++)    /* 循环每一条边 */    {        n = Find(parent,edges[i].begin);        m = Find(parent,edges[i].end);        if (n != m) /* 假如n与m不等，说明此边没有与现有的生成树形成环路 */        {            parent[n] = m;    /* 将此边的结尾顶点放入下标为起点的parent中。 */                            /* 表示此顶点已经在生成树集合中 */            printf("(%d, %d) %d\n", edges[i].begin, edges[i].end, edges[i].weight);        }    }}int main(void){    MGraph G;    CreateMGraph(&G);    MiniSpanTree_Kruskal(G);    return 0;}