[数据结构] 图的Kruskal算法实现

<pre name="code" class="cpp">#include <iostream>
using namespace std; 

#define MAX_V 100 //定义最大顶点个数
#define INF 1000 //表示正无穷 

typedef struct VertexType
{
    int number;//顶点标号

};//顶点类型

typedef struct MGraph//图的定义
{
    int matrix[MAX_V][MAX_V];//邻接矩阵
    int weight[MAX_V][MAX_V];//存放权值 
    int v;//顶点数
	int e;//边数
    VertexType vertax[MAX_V];//存放顶点信息
};//图的邻接矩阵类型

typedef struct Edge
{
	int v1;
	int v2;
	int weight;
};//边的存储类型 

void CreateMGragh(MGraph *G)
{
	int i,j,m,weight;
	cout << "请输入顶点数和边数:" << endl;
	cin >> G->v >> G->e ;
	cout << "请输入顶点信息:" << endl;
	for (i=0;i<G->v;i++)
	{
	    scanf("%d",&G->vertax[i].number);//输入顶点信息，建立顶点表
	}
	for (i=0;i<G->v;i++)//初始化邻接矩阵 
	  for (j=0;j<G->v;j++)
      { 
		  G->matrix[i][j]=0;
		  G->weight[i][j]=INF;//让所有权值不存在 
      }
    
	for(i=0;i<G->v;i++)//是结点自身指向自身权值为0 
	  for(j=0;j<G->v;j++)
	    if(i==j)
	      G->weight[i][j]=0;
	
	cout << "输入每条边的首尾顶点序号及权值:" << endl;
	for (m=0;m<G->e;m++)
	{
		cin >> i >> j >> weight;   // >> weight;
		G->matrix[i][j]=1;
		G->matrix[j][i]=1;
		G->weight[i][j]=weight;
		G->weight[j][i]=weight;
	}	
}

void DisplayMGragh(MGraph *G)//输出邻接矩阵G
{
    int i,j;
    for(i=0;i<G->v;i++)
    {
        for(j=0;j<G->v;j++)
          printf("%5d",G->matrix[i][j]);
        printf("\n");
    }
    cout << endl;
}

void DisplayMGragh_W(MGraph *G)//输出权值矩阵G
{
    int i,j;
    for(i=0;i<G->v;i++)
    {
        for(j=0;j<G->v;j++)
          printf("%5d",G->weight[i][j]);
        printf("\n");
    }
    cout << endl;
}

void Sort(Edge EdgeCount[], MGraph *G) // 给边进行升序排序 
{
	int i,j;
	Edge temp;
	for(i = 0; i < G->v; i++)
	{
		for(j = i; j <= G->v; j++)
		{
			if(EdgeCount[j].weight < EdgeCount[i].weight)
			{
				temp.v1 = EdgeCount[i].v1;
				temp.v2 = EdgeCount[i].v2;
				temp.weight = EdgeCount[i].weight;
				EdgeCount[i].v1 = EdgeCount[j].v1;
				EdgeCount[i].v2 = EdgeCount[j].v2;
				EdgeCount[i].weight = EdgeCount[j].weight;
				EdgeCount[j].v1 = temp.v1;
				EdgeCount[j].v2 = temp.v2;
				EdgeCount[j].weight = temp.weight;
			}
		}
	}
}

void Kruskal(MGraph *G) 
{
	Edge EdgeCount[10];//记录边数 
	int vset[MAX_V];
	int k = 0;
	int m = G->v;
	int i,j,s1,s2;
	   
	for(i = 0; i < G->v; i++)
	{
	  for(j = 0; j < G->v; j++)
	  {
	  	  if(G->matrix[i][j] != 0)//如果两条边是连通的 
	  	  {
	  	  	  if(i < j)
			  {
			      EdgeCount[k].v1 = i;
				  EdgeCount[k].v2 = j;
				  EdgeCount[k].weight = G->weight[i][j];
				  k++; 
			  }
	  	  }
	  }
	}
	
	Sort(EdgeCount, G);
		
    for (i=0;i<G->v;i++)//初始化辅助数组   
    {  
        vset[i]=i;  
    }  
    
    i = 0;
    
	while(m > 1)//最小生成树边数为顶点数-1 
	{
		s1 = vset[EdgeCount[i].v1];
		s2 = vset[EdgeCount[i].v2];
		
		if(s1 != s2)
		{
			cout << EdgeCount[i].v1 << "--" << EdgeCount[i].v2 << endl;
			m--;
			for(j = 0; j < G->v; j++)//改变连通分量的根节点 
			{
				if(vset[j] == s2)
				  vset[j] = s1;
			}
		}
		
		i++;		
	}
		
}

int main()
{
	MGraph *M;
	M = new MGraph;
	CreateMGragh(M);
	DisplayMGragh(M);
	
	DisplayMGragh_W(M);
	
        Kruskal(M);
	return 0;
}