最小生成树

来源：互联网发布：js div弹窗编辑：程序博客网时间：2024/06/05 13:33
#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;}