图的最小生成树之普里姆Prim算法

源代码如下：

#include<iostream>
using namespace std;
#define MAX_VERTEX_NUM 20
#define infinity 9
typedef int QElemType;
typedef int EdgeData;
typedef char VertexData;
typedef struct
{
    VertexData verlist[MAX_VERTEX_NUM];            //顶点表
     EdgeData edge[MAX_VERTEX_NUM][MAX_VERTEX_NUM]; //邻接矩阵--可试为边之间的关系
     int vexnum,edgenum;                          //顶点数和边数
}MTGraph;

void printMTGragh(MTGraph *G){
	int i,j;
	for (i = 1 ; i <= G->vexnum ; i++){
		for (j = 1 ; j <= G->vexnum ; j++)
			cout<<G->edge[i][j]<<" ";
		cout<<endl;
	}
//	Prim(G,G->edge);
}

void Prim(MTGraph *G){             //集合V-U的顶点尚未加入最小生成树中，集合U则已加入
	int lowcost[MAX_VERTEX_NUM+1]; //用来保存集合V-U中各顶点与集合U中顶点最短边的权值，
								   // lowcost[v] = infinity 表示顶点V已加入了最小生成树中 

	int closest[MAX_VERTEX_NUM+1]; //用来保存依附于该边的在集合U的顶点
									// 该边：集合V-U中各顶点与集合U中顶点最短边
	int i,j,k,h,min;
//	printMTGragh(G);
	for(i = 2;i<=G->vexnum;i++){
		lowcost[i] = G->edge[1][i];
		closest[i] = 1;  //将定点1加入集合U中
	}
	for(i = 2;i<=G->vexnum;i++){
		min = 9 ;
		k = i;
		for(j=2;j<=G->vexnum;j++)
			if(lowcost[j] < min && lowcost[j]!=0){
				min = lowcost[j]; //在 lowcost中取最小边
				k = j;
			}
		cout<<"将第"<<i<<"个元素放入集合U中时，Lowcost原序列：";
		for(h = 2;h<=G->vexnum;h++)
			cout<<lowcost[h]<<" ";
		cout<<endl;
		cout<<"("<<k<<","<<closest[k]<<")"<<endl; //输出顶点K与之对应的权值
		cout<<"取出的顶点为:"<<k<<"将顶点"<<k<<"与顶点"<<closest[k]<<"相连"<<endl;
		lowcost[k] = 0;  //将顶点K置于集合U中 

		for(j=2;j<=G->vexnum;j++) //调整数组lowcost和 cloest
			if(G->edge[k][j]<lowcost[j]){
				lowcost[j] = G->edge[k][j];
				closest[j] = k;
			}
		cout<<"将第"<<i<<"个元素放入集合U中时，Lowcost更新后的序列：";
		for(h = 2;h<=G->vexnum;h++)
			cout<<lowcost[h]<<" ";
		cout<<endl;
	}
}  //时间复杂度O(n^2)
//建立图的邻接矩阵
void createMTGraph(MTGraph *G){
	int i,j,k,w;
	cout<<"输入顶点数和边数如（5 7）"<<endl;
	cin>>G->vexnum>>G->edgenum;
	cout<<"输入顶点信息,如（A B C D...）"<<endl;
	for(i = 0 ; i<G->vexnum;i++)
		cin>>G->verlist[i];
	for(i = 0 ; i<=G->vexnum;i++)
		for(j = 0 ; j<=G->vexnum;j++)
			G->edge[i][j] = infinity;

	cout<<"输入边(i,j)上的权值w,如(i j w)"<<endl;
	 for(k=0;k<G->edgenum;k++){
	 	cin>>i>>j>>w;
	 	G->edge[i][j] = w;
	 	G->edge[j][i] = w;
	 }
}

main(){
	MTGraph *G ;
	G = new MTGraph();
	createMTGraph(G);
	printMTGragh(G);
	Prim(G);
	system("pause");
}

程序运行后的结果

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