最小生成树（Prim）

#include<iostream>
using  namespace  std;

typedef  char VertexType;
typedef  int EdgeType;

const  int   MAXVEX = 100;
const  int   INFINITY = 65535;


typedef  struct
{
    VertexType  vexs[MAXVEX];
    EdgeType    arc[MAXVEX][MAXVEX];
    int numVertexes,numEdges;
}MGraph;

/*
建立无向网图的邻接矩阵表示
*/

void  CreateMGraph_Undirected(MGraph *G)
{
    int i,j,k,w;
    cout<<"请输入顶点数和边数:"<<endl;
    cin>>G->numVertexes>>G->numEdges;
    cout<<"请输入顶点名称:"<<endl;
    for(i = 0;i < G->numVertexes;++i)//输入顶点
    {       
        cin>>G->vexs[i];
    }

    for(i = 0;i < G->numVertexes;++i)//初始化邻接矩阵,除对角线元素 = 0，其余为INFINITY;
    {
        for(j = 0;j < G->numVertexes;++j)
        {
            if(i == j)
            {
                G->arc[i][j] = 0;
            }
            else
            {
                G->arc[i][j] = INFINITY;
            }
        }
    }

    for(k = 0;k < G->numEdges;++k)//完成邻接矩阵的填写工作
    {
        printf("请输入边(vi,vj)上的下标i，下标j和权w：\n");
        cin>>i>>j>>w;
        G->arc[i][j] = G->arc[j][i] = w;
    }
}

void  ShowMGraph(MGraph *G)//打印图的信息
{
    cout<<"图的顶点，边数为："<<G->numVertexes<<","<<G->numEdges<<endl;
    cout<<"邻接矩阵为："<<endl;
    
    for(int i = 0;i < G->numVertexes;++i)
    {
        for(int j = 0;j < G->numVertexes;++j)
        {
            if(G->arc[i][j] == INFINITY)
            {
                cout<<"#  ";
            }
            else
            {
                cout<<"  "<<G->arc[i][j]<<"  ";
            }
        }
        cout<<endl;
    }
}

//Prim算法最小生成树
void MiniSpanTree_Prim(MGraph *G)
{
    int i , j, min,k,sum;
    int  lowcost[MAXVEX];
    int  adjvex[MAXVEX];
    sum = 0;
    lowcost[0] = 0;
    adjvex[0] = 0;
    for(i = 1;i < G->numVertexes;++i)
    {
        lowcost[i] = G->arc[0][i];
        adjvex[i] = 0;
    }
    for(i = 1;i < G->numVertexes;++i)
    {
        min = INFINITY;
        j = 1;
        k = 0;
        while(j < G->numVertexes)
        {
            if(lowcost[j] < min && lowcost[j] != 0)
            {
                k = j;
                min = lowcost[j];
            }
            j++;
        }
        printf("%d<-> %d,权值为%d\n",adjvex[k],k,G->arc[k][adjvex[k]]);
        sum += G->arc[k][adjvex[k]];
        lowcost[k] = 0;
        for(j = 1;j < G->numVertexes;++j)
        {
            if(lowcost[j] != 0 && lowcost[j] > G->arc[k][j])
            {
                lowcost[j] =  G->arc[k][j];
                adjvex[j] = k;
            }
        }
    }
    printf("权值之和为:%d\n",sum);
}


int main()
{
    MGraph *G = new MGraph();
    CreateMGraph_Undirected(G);
    ShowMGraph(G);
    MiniSpanTree_Prim(G);
    delete G;
}