[数据结构] 图的Prim算法实现

图的Prim算法实现最小生成树

#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

bool visited[MAX_V]; //全局变量记录访问结点 

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 Prim(MGraph *G)
{
    int LOW[G->v];
    int CLOSE[G->v];
    bool visited[G->v];
    
    int i,j,k,t;
    int min;
	
	for(i = 0; i < G->v; i++) // 记录所有结点为未访问 
    {
    	visited[i] = false;
    }
    
    
    for(i = 0; i < G->v; i++) //以0结点为初始结点 
    {
    	LOW[i] = G->weight[0][i];
    	CLOSE[i] = 0;
    }
    
    visited[0] = true;
    
    for(i = 1; i < G->v; i++)
    {
    	min = INF;//LOW[i];
    	//k = i;
    	for(j = 0; j < G->v; j++)
    	  if( visited[j] == false && LOW[j] != 0 )
    	  {
    	  	   if(LOW[j] < min)
    	  	   {
    	  	   	   min = LOW[j];
    	  	   	   k = j;
    	  	   }
    	  }
  	    cout << "(" << k << "," << CLOSE[k] << ")" << endl;
  	    	    
        visited[k] = true;
  	    
  	    for(j = 0; j < G->v; j++)
  	    {
  	    	if(visited[j] != true)
  	    	{
  	    		if(G->weight[k][j] < LOW[j] || LOW[j] == 0)
	            {
				    LOW[j] = G->weight[k][j];
  	    		    CLOSE[j] = k;
	            }
  	    	}
  	    }
    }
    
}




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