最小生成树算法(1)-----------prim

#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;
}

}