kruskal 克鲁斯卡尔 With Prim 普里姆 最小生成树算法

// Kruskal.cpp: 定义控制台应用程序的入口点。//#include "stdafx.h"#include <stdio.h>#include <stdlib.h>#include<limits.h>#define VEX 7#define EDGE 11typedef struct{    int arc[VEX][VEX];    //二维数组里面存储的是边的权重，下标为节点的序号    //例如  arc[0][3]=7 节点0--> 节点3  边的权重为7    int numVertexes, numEdges;//顶点数，边数}MGraph ,*MGraphP;typedef struct{    int begin;    int end;    int weight;}Edge,*EdgeP;//对边集数组Edge结构的定义//qsort 比较条件int cmp(void const *a, void const * b){    return (*(EdgeP)a).weight - (*(EdgeP)b).weight;}//创建图的邻接矩阵void CreateMGraph(MGraphP G){        int i, j;        G->numEdges = EDGE;//单边数量        G->numVertexes = VEX;//节点数量 下标0~6        //初始化图的边的权重数组        for (i = 0; i < G->numVertexes; i++) {            for (j = 0; j < G->numVertexes; j++) {                if (i == j)                    G->arc[i][j] = 0;                else                    G->arc[i][j] = G->arc[j][i] = INT_MAX;            }        }        //向边的权重数组中附上真正的值        G->arc[0][1] = 7;        G->arc[0][3] = 5;        G->arc[1][2] = 8;        G->arc[1][3] = 9;        G->arc[1][4] = 7;        G->arc[2][4] = 5;        G->arc[3][4] = 15;        G->arc[3][5] = 6;        G->arc[4][5] = 8;        G->arc[4][6] = 9;        G->arc[5][6] = 11;        //<3,2> 和<2，3>公用一条边，双向图        // 对角线两边 对等化        for (i = 0; i < G->numVertexes; i++)            //第一趟0字辈全部遍历完…… ，所以就j就可以从i开始 ，而不用从0开始        {            for (j = i; j < G->numVertexes; j++) {                G->arc[j][i] = G->arc[i][j];            }        }}int Find(int * parent, int i)//传入的是一个记录父亲节点坐标的数组，i是需要索引 最根上 父节点的下标，//返回最根上父节点的坐标{    while (parent[i] >= 0)    {        i = parent[i];    }    return i;}void MiniSpanTree_Kruskal(MGraph G){    int parent[VEX];    Edge edges[EDGE];    //初始化边数组    int k = 0;    int begin, end;    int begin_par, end_par;    for (int i = 0; i < G.numVertexes-1; i++)    {        for (int j = i + 1; j < G.numVertexes; j++)        {            if (G.arc[i][j] < INT_MAX)            {                edges[k].begin = i;                edges[k].end = j;                edges[k].weight = G.arc[i][j];                k++;            }        }    }    //初始化parent数组    for (int i = 0; i < G.numVertexes; i++)    {        parent[i] = -1;    }    qsort(edges, G.numEdges, sizeof(Edge),cmp);//对edges数组进行从小到大排序    //记录父节点信息，生成最小生成树    for (int i = 0; i < k ; i++)    {        begin = edges[i].begin;        end = edges[i].end;        begin_par = Find(parent, begin);        end_par = Find(parent, end);        if (begin_par != end_par)//如果不成环，将最小的权重添加进生成树中        {            parent[end_par] = begin_par;            //如果最根父节点不一样，将最根父节点连在一起 成树             //将独立的节点结构 纳入树的结构中        /*        o   o               o——o        |   |   ------>      |  |        o   o               o  o        */            printf("(%d, %d) %d\n", begin, end, edges[i].weight);        }    }}void Prim(MGraph G){    int lowcost[VEX];//下标为节点 标志 值为 目前所探测到的最短路径    //INT_MAX 表示还没探测到 0 表示已经纳入生成树的节点了    for (int i = 0; i < VEX; i++)    {        lowcost[i] = INT_MAX;    }    int parent[VEX];    //-1表示已经纳入生成树的节点了 INT_MAX 表示还没探测到    //下标为节点标志 值为最短路径的源节点,    for (int i = 0; i < VEX; i++)    {        parent[i] =INT_MAX ;    }    int current_id = 0;    int min;    for (int i = 0; i < VEX - 1; i++)    {        for (int j = 0; j < VEX; j++)        {            if (j != current_id)//找到更小的路径，就替换            {                if (G.arc[current_id][j] < lowcost[j]&&lowcost[j]>0)                {                    lowcost[j] = G.arc[current_id][j];                    parent[j] = current_id;//到j节点最小的路径是从current_id 节点发出的                }                }            else            {                lowcost[j] = 0;            }        }        min = INT_MAX;        for (int j = 0; j < VEX; j++)        {            if (lowcost[j] > 0 && lowcost[j] < INT_MAX)            {                if (lowcost[j] < min)                {                    min = lowcost[j];                    current_id = j;                }            }        }        printf("<%d,%d> weight:%d\n", parent[current_id], current_id, G.arc[parent[current_id]][current_id]);    }}int main(){    MGraphP gp = (MGraphP)malloc(sizeof(MGraph));    CreateMGraph(gp);    MiniSpanTree_Kruskal(*gp);    Prim(*gp);    system("pause");    return 0;}