/*
Name:最小生成树kruskal算法
Author:wujilin
Description:用邻接矩阵做图
Date: 21-07-06 23:07
Copyright:wujilin
*/
#include<stdio.h>
#include<stdlib.h>
#define M 20
#define MAX 20
typedef struct
{
int begin;
int end;
int weight;
}edge;
typedef struct
{
int adj;
int weight;
}AdjMatrix[MAX][MAX];
typedef struct
{
AdjMatrix arc;
int vexnum, arcnum;
}MGraph;
void CreatGraph(MGraph *);//函数申明
void sort(edge* ,MGraph *);
void MiniSpanTree(MGraph *);
int Find(int *, int );
void Swapn(edge *, int, int);
void CreatGraph(MGraph *G)//构件图
{
int i, j,n, m;
printf("请输入边数和顶点数:");
scanf("%d %d",&G->arcnum,&G->vexnum);
for (i = 1; i <= G->vexnum; i++)//初始化图
{
for ( j = 1; j <= G->vexnum; j++)
{
G->arc[i][j].adj = G->arc[j][i].adj = 0;
}
}
for ( i = 1; i <= G->arcnum; i++)//输入边和权值
{
printf("\n请输入第%d边的2个顶点",i);
scanf("%d %d",&n,&m);
while(n < 0 || n > G->vexnum || m < 0 || n > G->vexnum)
{
printf("输入的数字不符合要求 请重新输入:");
scanf("%d%d",&n,&m);
}
G->arc[n][m].adj = G->arc[m][n].adj = 1;
getchar();
printf("\n请输入%d与%d之间的权值:", n, m);
scanf("%d",&G->arc[n][m].weight);
}
printf("邻接矩阵为:\n");
for ( i = 1; i <= G->vexnum; i++)
{
for ( j = 1; j <= G->vexnum; j++)
{
printf("%d ",G->arc[i][j].adj);
}
printf("\n");
}
}
void sort(edge edges[],MGraph *G)//对权值进行排序
{
int i, j;
for ( i = 1; i < G->arcnum; i++)
{
for ( j = i + 1; j <= G->arcnum; j++)
{
if (edges[i].weight > edges[j].weight)
{
Swapn(edges, i, j);
}
}
}
printf("权排序之后的为:\n");
for (i = 1; i < G->arcnum; i++)
{
printf("<< %d, %d >> %d\n", edges[i].begin, edges[i].end, edges[i].weight);
}
}
void Swapn(edge *edges,int i, int j)//交换权值 以及头和尾
{
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;
}
void MiniSpanTree(MGraph *G)//生成最小生成树
{
int i, j, n, m;
int k = 1;
int parent[M];
edge edges[M];
for ( i = 1; i < G->vexnum; i++)
{
for (j = i + 1; j <= G->vexnum; j++)
{
if (G->arc[i][j].adj == 1)
{
edges[k].begin = i;
edges[k].end = j;
edges[k].weight = G->arc[i][j].weight;
k++;
}
}
}
sort(edges, G);
for (i = 1; i <= G->arcnum; i++)
{
parent[i] = 0;
}
printf("最小生成树为:\n");
for (i = 1; i <= G->arcnum; i++)//核心部分
{
n = Find(parent, edges[i].begin);
m = Find(parent, edges[i].end);
if (n != m)
{
parent[n] = m;
printf("<< %d, %d >> %d\n", edges[i].begin, edges[i].end, edges[i].weight);
}
}
}
int Find(int *parent, int f)//找尾
{
while ( parent[f] > 0)
{
f = parent[f];
}
return f;
}
int main(void)//主函数
{
MGraph *G;
G = (MGraph*)malloc(sizeof(MGraph));
if (G == NULL)
{
printf("memory allcation failed,goodbye");
exit(1);
}
CreatGraph(G);
MiniSpanTree(G);
system("pause");
return 0;
}
