最小生成树

#include<iostream>
#include<stdlib.h>//产生随机数组用
#include<time.h> //同上

using namespace std;


class MyArc
{
public:
    int m_beginVex;
    int m_endVex;
    int m_weight;
    MyArc(int beginVex,int endVex,int weight);
    MyArc(){}
    bool operator < (const MyArc& arc)
    {
        return m_weight<arc.m_weight;
    }
    bool operator == (const MyArc& arc)
    {
        return m_weight==arc.m_weight;
    }
    bool operator > (const MyArc& arc)
    {
        return m_weight>arc.m_weight;
    }
};

MyArc::MyArc(int beginVex,int endVex,int weight):m_beginVex(beginVex),m_endVex(endVex),m_weight(weight)
{

}

class Graph
{
public:
    int m_vexnum;//顶点数
    int m_arcnum;//弧数目
    int *m_pmatrix;
public:
    ~Graph();
    Graph(int vexnum);
    Graph(int vexnum,int *pmatrix);
    void insert(MyArc arc);//按权值大小排序插入
    bool bound(int x);   //判断顶点x是否已与其它顶点连通

};

//构造函数
Graph::Graph(int vexnum)
{
    m_pmatrix=new int[vexnum*vexnum];
    m_vexnum=vexnum;
    m_arcnum=0;
    for(int i=0;i<vexnum*vexnum;++i)
    {
        m_pmatrix[i]=0; //初始化邻接矩阵
    }


}

//构造函数
Graph::Graph(int vexnum,int *pmatrix)
{
    m_vexnum=vexnum;
    // m_arcnum=arcnum;
    m_pmatrix=new int[m_vexnum*m_vexnum];
    for(int i=0;i<m_vexnum*m_vexnum;++i)
    {
        m_pmatrix[i]=pmatrix[i];
    }
}

//测试 顶点x是否已与其他点连通
bool Graph::bound(int x)
{
    for(int i=0;i<m_vexnum;++i) if(m_pmatrix[x+i*m_vexnum]!=0) return true;
    return false;
}

//在邻接表中连通 arc表示的边，并且设置权
void Graph::insert(MyArc arc)
{
    m_pmatrix[arc.m_beginVex*m_vexnum+arc.m_endVex]=arc.m_weight;
    m_pmatrix[arc.m_endVex*m_vexnum+arc.m_beginVex]=arc.m_weight;
    ++m_arcnum;
}
//析构
Graph::~Graph()
{
    delete[] m_pmatrix;
    m_pmatrix = NULL;
}

class MyQueues
{
public:
    list<MyArc> m_list;
    MyQueues(){}
    void insert(const MyArc& arc);//边按权值插入队列中合适位置,
    void InsertGraph(const Graph &graph);//将图的连通分量插入队列
    MyArc pop();
};
//边出队
MyArc MyQueues::pop()
{
    MyArc arc=m_list.front();
    m_list.pop_front();
    return arc;
}
//边按权值插入队列中合适位置,
void MyQueues::insert(const MyArc& arc)
{
    list<MyArc>::iterator pos=m_list.begin();
    while(pos!=m_list.end())
    {
        if(*pos>arc) break;
        else
            ++pos;
    }
    m_list.insert(pos,arc);
}
//将图的连通分量插入队列
void MyQueues::InsertGraph(const Graph &graph)
{
    for(int i=0;i<graph.m_vexnum;++i)
    {
        for(int j=i+1;j<graph.m_vexnum;++j)//上三角矩阵的联通分量
              {
                if(graph.m_pmatrix[i*graph.m_vexnum+j])
                    insert(MyArc(i,j,graph.m_pmatrix[i*graph.m_vexnum+j]));
              }
    }
}
//用随机数组初始化matrix数组并且打印
void SetMatrix(int vexnum,int *pmatrix)
{
    srand((unsigned)time(NULL));
    for(int i=0;i<vexnum;++i)//产生随机权值矩阵
    {
        for(int j=i;j<vexnum;++j)
        {
              if(j==i)
              {
                  pmatrix[i*vexnum+j]=0;
                  continue;
              }
              int rnum=rand();
              rnum%=99;
              rnum++;//产生1~99的随机整数作为边的权值
              pmatrix[i*vexnum+j]=rnum;//先填写上三角矩阵
              pmatrix[j*vexnum+i]=rnum;//后填写下三角矩阵
        }
    }
    cout<<"***随机产生的各边权值矩阵 [顶点数为 "<<vexnum<<"] ****\n";
  for(int i=0;i<vexnum;++i)//输出随机权值矩阵
    {
        for(int j=0;j<vexnum;++j)
        {
              cout<<pmatrix[i*vexnum+j]<<"\t";
        }
        cout<<endl;
    }

}


//判断连通边arc后 图graph 是否存在回路
bool IsCycle(Graph& graph, MyArc& arc)
{
    list<int> mylist;
    mylist.push_back(arc.m_beginVex);
    int *ps=new int[graph.m_vexnum];
    for(int i=0;i<graph.m_vexnum;++i)
        ps[i]=0;
    while(!mylist.empty())
    {
        int x=mylist.front();
        ps[x]=1;
        mylist.pop_front();
        for(int i=0;i<graph.m_vexnum;++i)
        {
              if(graph.m_pmatrix[i+x*graph.m_vexnum]!=0)
              {
                  if(i==arc.m_endVex) return true;
                  if(ps[i]!=1) mylist.push_back(i);
              }
        }
    }
    delete[] ps;
    return false;//遍历完成没有环
}

//克鲁斯卡尔算法
void kruskal(const Graph& graph,Graph& smtree)
{
    MyQueues arcqueues;//保存从小到大排列的边
    arcqueues.InsertGraph(graph);
    MyArc myarc;//Arc表示边的类型
    int arcnum=0; //边的个数
    while(arcnum<graph.m_vexnum-1)//此处的含义为边的数目正好为顶点数目减一，注意与prim算法表达式相同但是含义不同
    {
        myarc=arcqueues.pop();
        if(!IsCycle(smtree,myarc))
        {
              smtree.insert(myarc);
              ++arcnum;
        }
    }
}

//输出最小生成树
void SmallestTreeOutput(const Graph& smtree)
{
    cout<<"最小生成树:"<<endl;
    for(int i=0;i<smtree.m_vexnum;++i)//输出最小树
        for(int j=i+1;j<smtree.m_vexnum;++j)
              if(smtree.m_pmatrix[i*smtree.m_vexnum+j])
                  cout<<'('<<i<<','<<j<<','<<smtree.m_pmatrix[i*smtree.m_vexnum+j]<<')'<<endl;
}


/*
主函数
*/

int main()
{
    int i;
    cout<<"请输入顶点数目:";
    cin>>i;
    int vex=i;
    int *matrix=new int[vex*vex];
    cout<<endl;
    SetMatrix(vex,matrix);
    Graph graph(vex,matrix),smtree(vex);
    kruskal(graph,smtree);
    SmallestTreeOutput(smtree);
    delete []matrix;
}