数据结构——邻接矩阵的最小生成Prim算法

#include <iostream>#include <iomanip>using namespace std;        #define MAX_VERTEX_NUM    10        //最大顶点个数#define INFINITY 32768   typedef char VerType;typedef int VRType;typedef struct{    VerType    vexs[MAX_VERTEX_NUM];    //顶点向量    int        arcs[MAX_VERTEX_NUM][MAX_VERTEX_NUM];                    //邻接矩阵    int        vexnum,arcnum;            //图的当前顶点数和弧数}mgraph, * MGraph;typedef struct {    VerType adjvex;            VRType    lowcost;}closedge[MAX_VERTEX_NUM];//记录从顶点集U到V-U的代价最小的边的辅助数组定义//初始化图void init_mgraph(MGraph &g)    {    g=(MGraph)malloc(sizeof(mgraph));    g->vexnum=0;    g->arcnum=0;    for(int i=0;i<MAX_VERTEX_NUM;i++)        g->vexs[i]=0;    for(i=0;i<MAX_VERTEX_NUM;i++)        for(int j=0;j<MAX_VERTEX_NUM;j++)            g->arcs[i][j]=INFINITY;}void add_vexs(MGraph &g)    //增加顶点{    cout<<"请输入顶点的个数:"<<endl;    cin>>g->vexnum;    cout<<"请输入顶点的值"<<endl;    for(int i=0;i<g->vexnum;i++)    {        cin>>g->vexs[i];    }}void add_arcs(MGraph &g)    //增加边{    cout<<"请输入边的个数:"<<endl;    cin>>g->arcnum;    VerType ch1,ch2;    int weight;    int row,col;    for(int i=0;i<g->arcnum;i++)    {            cin>>ch1>>ch2>>weight;        for(int j=0;j<g->vexnum;j++)        {            if(g->vexs[j]==ch1)            {                row=j;            }            if(g->vexs[j]==ch2)            {                col=j;            }        }        g->arcs[row][col]=weight;    //有向带权图只需把1改为weight        g->arcs[col][row]=weight;    }}void creat_mgraph(MGraph &g) //创建图    {    add_vexs(g);    //增加顶点    add_arcs(g);    //增加边}void print_mgraph(MGraph &g) //打印图{    for(int i=0;i<g->vexnum;i++)        cout<<"   "<<g->vexs[i]<<"  ";    cout<<endl;    for(i=0;i<g->vexnum;i++)    {        cout<<g->vexs[i];        for(int j=0;j<g->vexnum;j++)        {            cout<<setw(5)<<g->arcs[i][j]<<" ";        }        cout<<endl;    } }//返回顶点v在顶点向量中的位置int LocateVex(MGraph &g, VerType v){        int i;        for(i = 0; v != g->vexs[i] && i < g->vexnum; i++)                ;        if(i >= g->vexnum)                return -1;        return i;}//求出T的下一个节点，第k节点int minimun(MGraph &g, closedge closedge){    int min=INFINITY,k=0,i;    for(i=0;i<g->vexnum;i++)    {        if(closedge[i].lowcost != 0 && closedge[i].lowcost < min)        {            min = closedge[i].lowcost;            k = i;        }    }    return k;}//普里姆算法void MiniSpanTree_Prim(MGraph &g, VerType u)    //普里姆算法从顶点u出发构造G的最小生成树T，输出T的各条边。{    closedge closedge;    int i,j;    int k=LocateVex(g,u);        for(j=0;j<g->vexnum;j++)        //辅助数组初始化    {        if(j!=k)        {            closedge[j].adjvex=u;            closedge[j].lowcost=g->arcs[k][j];        }    }    closedge[k].lowcost = 0;    //初始，U={u}    for(i=1;i<g->vexnum;i++)        //选择其余g.vexnum-1个顶点    {        k=minimun(g,closedge);        //求出T的下一个节点，第k节点        cout<<closedge[k].adjvex<<"  "<<g->vexs[k]<<"  "<<closedge[k].lowcost<<endl;    //输出生成树的边        closedge[k].lowcost=0;        //第k顶点并入U集                for(j=0;j<g->vexnum;j++)        {            if(g->arcs[k][j] < closedge[j].lowcost)        //新顶点并入集后，选择新的边，将小的边放到辅助数组中            {                closedge[j].adjvex = g->vexs[k];                closedge[j].lowcost = g->arcs[k][j];            }        }    }}//MiniSpanTree_Primint main(){    MGraph G;    init_mgraph(G);        //初始化图    creat_mgraph(G);    //创建图    print_mgraph(G);    //打印图    MiniSpanTree_Prim(G,G->vexs[0]);    //最小生成树    return 0;}