图的最小生成树——Prim算法

Prim算法的基本思想用伪代码描述如下：

1. 初始化：U = {v0}； TE={ }； 
2. 重复下述操作直到U = V： 
    2.1 在E中寻找最短边(u，v)，且满足u∈U，v∈V-U；
    2.2 U = U + {v}；

    2.3 TE = TE + {(u，v)}；

源码：

#include<iostream>
#include<vector>
#include<queue>
#include<iomanip>
#include<algorithm>
using namespace std;
#define INF 0x3f3f3f3f
#define VertexData unsigned int//顶点序号类型
#define UINT unsigned int
#define vexCounts 6//顶点数据
char vextex[]={ 'A', 'B', 'C', 'D', 'E', 'F' };
struct node
{
    VertexData data;
    unsigned int lowestcost;
}closedge[vexCounts];//辅助信息

void GetAdjMat(unsigned int adjMat[][vexCounts])//初始化邻接矩阵
{
    for(int i=0;i<vexCounts;i++)
         for(int j=0;j<vexCounts;j++)
    {
        if(i==j)    adjMat[i][j]=0;
        else adjMat[i][j]=INF;
    }
    adjMat[0][1] = 6; adjMat[0][2] = 1; adjMat[0][3] = 5;
    adjMat[1][0] = 6; adjMat[1][2] = 5; adjMat[1][4] = 3;
    adjMat[2][0] = 1; adjMat[2][1] = 5; adjMat[2][3] = 5; adjMat[2][4] = 6; adjMat[2][5] = 4;
    adjMat[3][0] = 5; adjMat[3][2] = 5; adjMat[3][5] = 2;
    adjMat[4][1] = 3; adjMat[4][2] = 6; adjMat[4][5] = 6;
    adjMat[5][2] = 4; adjMat[5][3] = 2; adjMat[5][4] = 6;

}

int Minmum(struct node* closedge)//获取最小边序号
{
    int min=INF;
    int index=-1;
    for(int i=0;i<vexCounts;i++)
    {
        if(closedge[i].lowestcost<min&&closedge[i].lowestcost!=0)
        {
            min=closedge[i].lowestcost;
            index=i;
        }
    }
    return index;
}

void MiniSpanTree_Prim(unsigned int adjMat[][vexCounts],VertexData s)
{
    for(int i=0;i<vexCounts;i++)//初始
    {
        closedge[i].lowestcost=INF;
    }
    closedge[s].data=s;//从顶点s开始
    closedge[s].lowestcost=0;
    for(int i=0;i<vexCounts;i++)//初始辅助数组
    {
        if(i!=s)
        {
            closedge[i].data=s;
            closedge[i].lowestcost=adjMat[s][i];
        }
    }
    for(int e=1;e<vexCounts;e++)//n-1条边时退出
    {
        int k=Minmum(closedge);//选择最小代价边
        cout<<vextex[closedge[k].data]<<"---"<<vextex[k]<<endl;//加入到最小生成树
        closedge[k].lowestcost=0;//代价置为0
        for(int i=0;i<vexCounts;i++)//更新v中顶点最小代价边信息
        {
            if(adjMat[k][i]<closedge[i].lowestcost)
            {
                closedge[i].data=k;
                closedge[i].lowestcost=adjMat[k][i];
            }
        }
    }
}

int main()
{
    unsigned int adjMat[vexCounts][vexCounts]={0};
    GetAdjMat(adjMat);
    cout<<"打印顶点："<<endl;
    for(int i=0;i<vexCounts;i++) cout<<vextex[i]<<" ";
    cout<<endl<<"打印邻接矩阵："<<endl;
    for(int i=0;i<vexCounts;i++)
        for(int j=0;j<vexCounts;j++)
        {
            if(adjMat[i][j]==INF) cout<<setw(5)<<"INF";
            else cout<<setw(5)<<adjMat[i][j];
            if(j==vexCounts-1) cout<<endl;
        }
        cout<<"---------------Prim--------------------"<<endl;
        MiniSpanTree_Prim(adjMat,0);
        return 0;
}

截图：