数据结构——邻接矩阵的最小生成树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_Prim

int 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;
}