代码:
// Minimum-Cost-Spanning-Tree.cpp : 定义控制台应用程序的入口点。
//
#include "stdafx.h"
#include<iostream>
#include<stdlib.h>//产生随机数组用
#include<time.h> //同上
#include <list>
#include "windows.h"
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_by_weight(const MyArc& arc);//边按权值插入队列中合适位置,
void insert_Graph(const Graph &graph);//将图的连通分量插入队列
void sort_by_number();//按照编号权值大小再次排列
MyArc pop();
MyArc pop_min(list<int> temp);// 对应节点的最小权值的边出队
};
MyArc MyQueues:: pop_min(list<int> temp)//顶点集合中到另一个集合权值最小的弧
{
int min = 0;
list<int>::iterator pos_vex = temp.begin();
list<MyArc>::iterator pos = m_list.begin();
list<MyArc>::iterator temp_pos;
MyArc arc ;
for(pos = m_list.begin(); pos != m_list.end(); pos++)
{
if(pos->m_beginVex == *pos_vex)
{
min = pos->m_weight;//找到第一个作为最小
break;
}
}
while(pos_vex!=temp.end())
{
pos = m_list.begin();
while(pos!=m_list.end())
{
if((pos->m_weight <=min)&&(pos->m_beginVex == *pos_vex||pos->m_endVex == *pos_vex) )//找到这顶点最小权值的边
{
arc = *pos;
min = pos->m_weight;
temp_pos = pos;
}
pos++;
}
pos_vex++;
}
m_list.erase(temp_pos);
return arc;
}
//边出队
MyArc MyQueues::pop()
{
MyArc arc=m_list.front();
m_list.pop_front();
return arc;
}
void MyQueues::sort_by_number()
{
int arcnum = m_list.size();
list<MyArc>::iterator pos=m_list.begin();
list<MyArc> templist;
int vexnum = 0;
for(int i=0;i<arcnum;i++)
{
pos = m_list.begin();
while(1)
{
//pos = m_list.begin();
while(pos != m_list.end())
{
if(pos->m_beginVex == vexnum) //从零开始
{
templist.push_back(*pos);
pos = m_list.erase(pos);
}
else
{
pos++;
}
}
if(pos == m_list.end())
{
vexnum++;
break;
}
}
}
m_list = templist;
}
//边按权值插入队列中合适位置,
void MyQueues::insert_by_weight(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::insert_Graph(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_by_weight(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.insert_Graph(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;
}
}
}
//prim算法
void prim(const Graph& graph,Graph& smtree)
{
MyQueues arcqueues;//保存从小到大排列的边
arcqueues.insert_Graph(graph);
arcqueues.sort_by_number();
MyArc myarc;//Arc表示边的类型
int vexnum = 0; //已经放入集合的顶点个数
int vex = 0; //初始顶点编号
list<int> vexList;//已经放入最小生成树的顶点的集合
vexList.push_back(vexnum);//先加入第0号节点
list<int>::iterator pos = vexList.begin();
int i = 1;
while(vexnum<graph.m_vexnum-1)
{
//cout<<"end"<<endl;
//if (vexnum==(graph.m_vexnum-1))
//{
//break;
//}
myarc = arcqueues.pop_min(vexList);
pos = vexList.begin();
for (pos = vexList.begin() ; pos != vexList.end();)
{
if ((myarc.m_endVex != *pos))
{
pos++;
}
else
break;
}
if(pos==vexList.end())//没有在已经的最小生成树的节点中
{
smtree.insert(myarc);
//cout<<"insert :"<<i++<<endl;
vexList.push_back(myarc.m_endVex);
vexnum++;
}
}
}
//输出最小生成树
void SmallestTreeOutput(const Graph& smtree)
{
cout<<"最小生成树:"<<endl;
int sum = 0;
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])
{
int temp = smtree.m_pmatrix[i*smtree.m_vexnum+j];
cout<<'('<<i<<','<<j<<','<<temp<<')'<<endl;
sum = sum + temp;
}
cout <<"最短距离为："<<sum<<endl;
}
/*
主函数
*/
int main()
{
int i;
while(1)
{
cout<<"请输入顶点数目:";
cin>>i;
int vex=i;
int *matrix=new int[vex*vex];
SetMatrix(vex,matrix);
Graph graph(vex,matrix) , smtree_kruskal(vex);
kruskal(graph,smtree_kruskal);
SmallestTreeOutput(smtree_kruskal);
Graph smtree_prim(vex);
prim(graph,smtree_prim);
SmallestTreeOutput(smtree_prim);
delete []matrix;
}
system("pause");
}