最小生成树算法(1)-----------prim

标签：mst   prim   数据结构   最小生成树   算法   

#include <iostream>
#include <iomanip>
using namespace std;				
#define MaxVertexNum 100				//最大顶点数
#define INFINTY 65535                 //最大值 

typedef char VertexType;				
typedef int AdjType;	

typedef struct {
	VertexType vertex[MaxVertexNum];					//顶点向量
	AdjType arcs[MaxVertexNum][MaxVertexNum];			//邻接矩阵
	int vexnum,arcnum;									//图的当前顶点数和弧数
}MGraph; 

//求最小生成树的辅助数组
typedef struct closedge{
	VertexType adjvex;             //记录最小边在U中的那个顶点
    int lowcost;                   //存储最小边的权重
}Closedge[MaxVertexNum];
Closedge closedge;

int LocateVex(MGraph *G,VertexType v);
void CreateUDN(MGraph *G);
void Prim(MGraph *G,VertexType u);
void display(MGraph *G);

int main()
{
	MGraph G;
    CreateUDN(&G);
    Prim(&G,'1');
	return 0;
}
/*
1 2 6
1 3 1
1 4 5
2 3 5
2 5 3
3 4 5
3 5 6
3 6 4
4 6 2
5 6 6
*/

//以无向带权图为例
void CreateUDN(MGraph *G)
{
    VertexType v1,v2;
    int weight; 
     
    //确定顶点数和弧数
    cout<<"请输入顶点数和边数："; 
    cin>>G->vexnum>>G->arcnum;

     //确定各个顶点的值
     cout<<"请输入各顶点的值：";     
     for(int i=0;i<G->vexnum;i++) 
        cin>>G->vertex[i];
    
    //初始化邻接矩阵
     for (int i = 0; i < G->vexnum; ++i)
     {
         for(int j=0;j< G->vexnum;j++)
            G->arcs[i][j] = INFINTY;
     } 
     
     //确定邻接矩阵
     cout<<"请输入"<<G->arcnum<<"对顶点和相应的权重：\n"; 
     for(int k=0; k<G->arcnum; k++)
     {
        cin>>v1>>v2>>weight;
        int i = LocateVex(G,v1);
        int j = LocateVex(G,v2);        
        if(i>=0 && j>=0)
        {
            G->arcs[i][j] = weight;
            G->arcs[j][i] = weight;
        }
            
     }     
    display(G);
}

//求顶点位置函数
int LocateVex(MGraph *G,VertexType v)
{
    int i;
    for(i=0;i<G->vexnum;i++)
    {
        if(G->vertex[i] == v)
            return i;
    }
    return -1;
}

int Min(MGraph *G)
{
    int k;
    int min = INFINTY;
    for(int i=0;i<G->vexnum;i++)
    {
        if(closedge[i].lowcost!=0 && closedge[i].lowcost<min)
        {
            min = closedge[i].lowcost;
            k = i;
        }
    }
    return k;
}

void Prim(MGraph *G,VertexType u)
{
    int m,s=0;
    VertexType v0,u0;
    int k = LocateVex(G,u);
    closedge[k].lowcost = 0;	//讲当前顶点加入生成树中 

    //初始化V-U中的顶点的辅助数组(即开始顶点到其他各顶点的距离） 
    for(int i=0;i<G->vexnum;i++)
    {
        if(i!=k)
        {
            closedge[i].adjvex = u;
            closedge[i].lowcost = G->arcs[k][i];
            //cout<<"----------"<<closedge[i].lowcost<<endl;
        }
    }

    //找n-1条边
	cout<<"最小生成树的边为："<<endl;; 
    for(int e=1;e<G->vexnum;e++)
    {
    	
    	m = Min(G);
        u0 = closedge[m].adjvex;
        v0 = G->vertex[m];          
        cout<<"("<<u0<<","<<v0<<")"<<endl;
       
		s+=closedge[m].lowcost;
		closedge[m].lowcost = 0;
		//在 v0顶点加入U中之后，更新closedge[i](即更新生成树到每一个非树顶点的距离） 
       	for (int i = 0; i < G->vexnum; i++)
       	{
           	if(G->arcs[m][i]<closedge[i].lowcost)
           	{
                closedge[i].lowcost = G->arcs[m][i];
                closedge[i].adjvex = v0;
           	}
       	}
    }
    cout<<"最小生成树的权重之和为："<<s<<endl;
}

void display(MGraph *G)
{
	cout<<"该图对应的临接矩阵为："<<endl; 
    for(int i=0;i<G->vexnum;i++)
    {
        for(int j=0;j<G->vexnum;j++)
        {
            cout<<setw(8)<<G->arcs[i][j];
        }
        cout<<endl;
    }  
       
}

最小生成树算法(1)-----------prim

标签：mst   prim   数据结构   最小生成树   算法   

原文地址：http://blog.csdn.net/huolang_vip/article/details/46537851