kruskal 最小生成树

#include<iostream>
#include<stdlib.h>//产生随机数组用
#include<time.h> //同上
#include<list>
using namespace std;


// 1) 带权边的类MyArc:

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)
{}


//2) 表示图的邻接矩阵类Graph:
class Graph
{
public:
int m_vexnum;
int m_arcnum;
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;

}

//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;
}
//3) 按权存储边的有序队列类MyQueues:

//边按权值插入队列中合适位置,
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;
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)
if(graph.m_pmatrix[i*graph.m_vexnum+j]) insert(MyArc(i,j,graph.m_pmatrix[i*graph.m_vexnum+j]));
}
}

//5)判断是否有回路的IsCycle函数：
bool IsCycle(Graph& graph, MyArc& arc)
{
list<int> my_list;
my_list.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(!my_list.empty())
{
int x=my_list.front();
ps[x]=1; //表明顶点x已经被访问过了
my_list.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) my_list.push_back(i);
}
}
}
delete[] ps;
return false;
}
//4) kruskal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)
{
myarc=arcqueues.pop();
if(!IsCycle(smtree,myarc))
{
smtree.insert(myarc);
++arcnum;
}
}
}


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;
pmatrix[j*vexnum+i]=rnum;
}
}
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;
}

}

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;
}



void main()
{
int vex; //---顶点数目
cout<<"请输入顶点数目:";
cin>>vex;


int *matrix=new int[vex*vex];
cout<<endl;
SetMatrix(vex,matrix); //---产生随机矩阵
Graph graph(vex,matrix),smtree(vex);
kruskal(graph,smtree);
SmallestTreeOutput(smtree);
delete []matrix;
}