C++ Exercises（十七）--图的简单实现

const   int  MAXSIZE  =   50 ;  // 顶点最大数目

#include  < vector >
using   namespace  std;

template < typename T >
class  CGraph
{
public:
    CGraph(void);
    ~CGraph(void);
private:
    vector<T> vecNodes;//顶点列表
    int edge[MAXSIZE][MAXSIZE];//边表
    int numVertexs;//顶点数
    int numEdges;//边数
    bool visited[MAXSIZE];//用于图的遍历

    int FindVertex(const T& vertex,const vector<T> &lst);
    void ClearVisitFlag();
    vector<T>& GraphDepthFirstSearch(const T& beginVertex);//深度遍历图
    vector<T>& GraphBreadthFirstSearch();//广度遍历

public:
    bool GraphEmpty(void)const;
    bool GraphFull(void)const;
    int NumberOfVertices(void)const;//获取顶点数
    int NumberOfEdges(void)const;//获取边数
    int GetWeight(const T&vertex1,const T& vertex2);//获取指定两个顶点间的权值
    vector<T>& GetNeighbors(const T& vertex);//获取指定顶点的邻接顶点

    void CreateGraph();//创建图
    int GetVertexPos(const T& vertex);//获取指定顶点的位置

    int InsertVertex(const T& vertex);//插入顶点
    void InsertEdge(const T& vertex1,const T& vertex2,int weight);//插入边
    void DeleteVertex(const T& vertex);//删除顶点
    void DeleteEdge(const T& vertex1,const T& vertex2);//删除边

    //int MinimumPath(const T& sVertex,const T& desVertex);最短路径
    void DepthFirstSearch();//深度遍历图
    void BreadthFirstSearch();//广度遍历图
} ;

 

图的实现代码
#include "Graph.h"
#include <stack>
#include <queue>
#include <algorithm>
#include <iostream>

using namespace std;

template<typename T>
CGraph<T>::CGraph(void)
{
    for (int i=0;i<MAXSIZE;++i)
    {
        for (int j=0;j<MAXSIZE;++j)
        {
            this->edge[i][j] = 0;
        }
    }
    this->numVertexs = 0;
    this->numEdges = 0;
}
template<typename T>
CGraph<T>::~CGraph(void)
{
    this->vecNodes.clear();
    for (int i=0;i<MAXSIZE;++i)
    {
        for (int j=0;j<MAXSIZE;++j)
        {
            this->edge[i][j] = 0;
        }
    }
    this->numVertexs = 0;
    this->numEdges = 0;
}
template<typename T>
int CGraph<T>::NumberOfEdges()const
{
    return this->numEdges;
}
template<typename T>
int CGraph<T>::NumberOfVertices()const
{
    return this->numVertexs;
}
template<typename T>
int CGraph<T>::GetWeight(const T&vertex1,const T& vertex2)
{
    int pos1,pos2;
    pos1 = this->GetVertexPos(vertex1);
    pos2 = this->GetVertexPos(vertex2);
    return this->edge[pos1][pos2];
}
template<typename T>
bool CGraph<T>::GraphFull()const
{
    return this->numVertexs>=MAXSIZE;
}
template<typename T>
bool CGraph<T>::GraphEmpty()const
{
    return this->numVertexs==0;
}
template<typename T>
int CGraph<T>::InsertVertex(const T& vertex)
{//插入顶点,返回插入位置
    int result=-1;
    if (!this->GraphFull())
    {
        this->vecNodes.push_back(vertex);
        result = this->numVertexs;
        this->numVertexs++;
    }
}
template<typename T>
void CGraph<T>::InsertEdge(const T& vertex1,const T& vertex2,int weight)
{//插入边
    int pos1,pos2;
    pos1 = this->GetVertexPos(vertex1);
    pos2 = this->GetVertexPos(vertex2);
    if (pos1==-1&&pos2==-1)
    {//两个都是新顶点
        pos1 = this->InsertVertex(vertex1);
        pos2 = this->InsertVertex(vertex2);

    }
    else if (pos1==-1)
    {//一个是新顶点
        pos1 = this->InsertVertex(vertex1);
    }
    else if (pos2==-1)
    {
        pos2 = this->InsertVertex(vertex2);
    }
    this->edge[pos1][pos2] = weight;
    this->edge[pos2][pos1] = weight;
}
template<typename T>
void CGraph<T>::DeleteVertex(const T& vertex)
{//删除顶点
    int pos = this->GetVertexPos(vertex);
    if (pos!=-1)
    {
        this->vecNodes.erase(remove(this->vecNodes.begin(),this->vecNodes.end(),vertex),this->vecNodes.end());//删除顶点
        for (int i=0;i<this->numVertexs;++i)
        {
            if(this->edge[pos][i]>0)
                this->edge[pos][i] = 0;
            if (this->edge[i][pos]>0)
                this->edge[i][pos] = 0;
        }
        this->numVertexs--;
        this->numEdges--;
    }
}
template<typename T>
void CGraph<T>::DeleteEdge(const T& vertex1,const T& vertex2)
{//删除边
    int pos1,pos2;
    pos1 = this->GetVertexPos(vertex1);
    pos2 = this->GetVertexPos(vertex2);
    if (pos1!=-1&&pos2!=-1)
    {
        if (this->edge[pos1][pos2]>0)
        {
            this->edge[pos1][pos2] = 0;
            this->edge[pos2][pos1] = 0;
            this->numEdges--;
        }
    }
}

template<typename T>
void CGraph<T>::CreateGraph()
{//创建图
    cout<<"输入顶点数，边数: ";
    cin>>this->numVertexs;
    cin>>this->numEdges;

    int i;
    T item;
    cout<<"输入顶点: ";
    for (i=0;i<this->numVertexs;++i)
    {
        cout<<"第"<<i+1<<"个顶点: ";
        cin>>item;
        this->vecNodes.push_back(item);
    }
    T vert1,vert2;
    int pos1,pos2,weight;
    for (i=0;i<this->numEdges;++i)
    {
        cout<<"输入第"<<i+1<<"条边(尾，头，权值): ";
        cin>>vert1>>vert2>>weight;
        pos1 = this->GetVertexPos(vert1);
        pos2 = this->GetVertexPos(vert2);
        this->edge[pos1][pos2] = weight;
        this->edge[pos2][pos1] = weight;
    }
}
template<typename T>
int CGraph<T>::GetVertexPos(const T& vertex)
{//获取顶点位置
    return this->FindVertex(vertex,this->vecNodes);
}
template<typename T>
int CGraph<T>::FindVertex(const T &vertex,const vector<T> &lst)
{//在顶点列表中找指定数据的下标
    int pos = -1;
    for (pos = lst.size()-1;pos>=0;--pos)
    {
        if (lst[pos]==vertex)
        {
            break;
        }
    }
    return pos;
}

template<typename T>
vector<T>& CGraph<T>::GraphDepthFirstSearch(const T& beginVertex)
{//深度遍历
    vector<T> *result = new vector<T>();
    vector<T> adjLst;
    stack<T> s;
    s.push(beginVertex);
    int pos;
    T vertex;
    vector<T>::iterator iter;
    while (!s.empty())
    {
        vertex = s.top();
        s.pop();
        if (this->FindVertex(vertex,*result)==-1)
        {
            pos = this->GetVertexPos(vertex);
            visited[pos] = true;
            (*result).push_back(vertex);
            adjLst = this->GetNeighbors(vertex);
            for ( iter= adjLst.begin();iter != adjLst.end();++iter)
            {
                if (this->FindVertex(*iter,*result)==-1)
                {
                    s.push(*iter);
                }
            }
        }
    }
    return *result;
}
template<typename T>
void CGraph<T>::ClearVisitFlag()
{
    for (int i=0;i<this->numEdges;++i)
    {
        this->visited[i] = false;
    }
}
template<typename T>
void CGraph<T>::BreadthFirstSearch()
{
    vector<T>::const_iterator iter;
    vector<int> vec;
    this->ClearVisitFlag();
    vec = this->GraphBreadthFirstSearch();
    for (iter = vec.begin();iter!=vec.end();++iter)
    {
        cout<<*iter<<" ";
    }
    this->ClearVisitFlag();
}

template<typename T>
vector<T>& CGraph<T>::GraphBreadthFirstSearch()
{//广度遍历
    vector<T> *result = new vector<T>();
    vector<T> adjLst;
    vector<T>::iterator iter;
    queue<T> q;
    T item;
    int pos;
    this->ClearVisitFlag();
    for (int i=0;i<this->numVertexs;++i)
    {
        if (!this->visited[i])
        {
            visited[i] = true;
            result->push_back(this->vecNodes[i]);
            
            q.push(this->vecNodes[i]);
            while (!q.empty())
            {
                item = q.front();
                q.pop();
                adjLst = this->GetNeighbors(item);
                for ( iter= adjLst.begin();iter != adjLst.end();++iter)
                {
                    if (this->FindVertex(*iter,*result)==-1)
                    {
                        result->push_back(*iter);
                        pos = this->GetVertexPos(*iter);
                        visited[pos] = true;
                    }
                }
            }
        }
    }
    return *result;
}

template<typename T>
vector<T>& CGraph<T>::GetNeighbors(const T& vertex)
{//获取邻接顶点
    vector<T> *result;
    result = new vector<T>();
    int pos = this->GetVertexPos(vertex);
    if (pos==-1)
    {
        cerr<<"顶点不在图中"<<endl;
        return *result;
    }
    for (int i=0;i<this->numVertexs;++i)
    {
        if (edge[pos][i]>0)
        {
            result->push_back(this->vecNodes[i]);
        }
    }
    return *result;
}

template<typename T>
void CGraph<T>::DepthFirstSearch()
{
    vector<T>::const_iterator iter,iter2;
    int pos;
    vector<int> vec1;
    this->ClearVisitFlag();
    for (iter = this->vecNodes.begin();iter!=this->vecNodes.end();++iter)
    {
        pos = this->GetVertexPos(*iter);
        if (!visited[pos])
        {//还未访问，从这点开始
            vec1 = this->GraphDepthFirstSearch(*iter);
            for (iter2 = vec1.begin();iter2!=vec1.end();++iter2)
            {
                cout<<*iter2<<" ";
            }
        }
    }
    this->ClearVisitFlag();
}

测试程序：

#include  " Graph.cpp "
#include  < iostream >
using   namespace  std;


int  main( int  argc,  char *  argv[])
{

    CGraph<int> *graph1 = new CGraph<int>();
    graph1->CreateGraph();
    graph1->DepthFirstSearch();
    graph1->BreadthFirstSearch();
    system("pause");
    return 0;
}