图的邻接矩阵以及深度优先遍历 + 广度优先遍历_邻接矩阵深度优先遍历和广度优先遍历

图的邻接矩阵表示法非常简单，一个定点数组，一个二维数组搞定，类似与这样

下面简单实现一个邻接矩阵表示的方法的图，以及遍历的两种方式。

Graph.h

#pragma once

#define MAX_SIZE 30
template<class T,class E>
class Graph
{
public:
    Graph(size_t size);
    virtual ~Graph();
    bool isEmpty()const {
        return verticleSize == 0;
    }
    int numberofVerticles(){
        return verticleSize ;
    }



protected:
    int maxVerticles=MAX_SIZE;
    int verticleSize;

    virtual T getValue(int i) = 0;                //获取值
    virtual E getWeight(int v1, int v2) = 0;      //根据两个定点获取边的权值
    virtual int getFirstNeighbor(int v) = 0;      //取顶点v的第一个邻接顶点  
    virtual int getNextNeighbor(int v, int w) = 0; //取邻接顶点w的下一个邻接顶点  
    virtual int getVertexPos(T vertex) = 0;      //由定点获取下标
    virtual T* getVerticles() = 0;              //获取定点数量

};

template<class T, class E>
 Graph<T, E>::Graph(size_t size):verticleSize(size)
{

}

 template<class T, class E>
 inline Graph<T, E>::~Graph()
 {
 }
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父类只是定义了一些基本方法，不再赘述。

遍历方式

我们按照深度遍历的顺序，假设从v1开始，那么数序是v1->v0->v4->v2->v3

同样从v1开始，顺序是v1->v0->v2->v4->v3

GraphMatrix.h

#pragma once
#include "Graph.h"
#include <iostream>
#include <stack>
#include <queue>

#define INF 0xffffff

using namespace std;

template<class T, class E>
class GraphMatrix :public Graph<T, E>
{
public:
    GraphMatrix(size_t size);
    ~GraphMatrix();
    static const int MAX_WEIGHT = INF;

    T getValue(int i) override;
    E getWeight(int v1, int v2)override;
    int getFirstNeighbor(int v) override;      //取顶点v的第一个邻接顶点  
    int getNextNeighbor(int v, int w)override; //取邻接顶点w的下一个邻接顶点  
    int getVertexPos(T vertex)override;
    T* getVerticles() override;
    E** getMatrix();
    void outputGraph();
    void bfsIndex(int i);           //广度优先搜索
    void bfs(int i);
    void dfsStack(int i);//深度优先搜索使用堆栈
    void dfsIndex(int i);
    void dfs(int i); //深度优先搜索使用递归
    int getUnVisitedVerticles(int i);
    int findNextUnVisitedVert(int i);



private:
    T* verticles;
    E** matrix;
    bool* visit;
};



template<class T, class E>
GraphMatrix<T, E>::GraphMatrix(size_t size) :Graph<T, E>(size)
{
    verticles = new T[size];
    matrix = new E*[size];

    for (int i = 0; i < this->verticleSize; i++) {
        matrix[i] = new E[size];
    }

    visit = new bool[size];
    for (int i = 0; i < size; i++) {
        visit[i] = false;
    }
}

template<class T, class E>
GraphMatrix<T, E>::~GraphMatrix()
{
    delete[] matrix;
    delete[] verticles;
}

template<class T, class E>
T GraphMatrix<T, E>::getValue(int i)
{
    if (i >= 0 && i < this->verticleSize)
        return verticles[i];
    else
        return NULL;
}

template<class T, class E>
E GraphMatrix<T, E>::getWeight(int v1, int v2)
{
    if (v1 >= 0 && v2 >= 0) {
        return matrix[v1][v2];
    }
    return -1;
}

template<class T, class E>
int GraphMatrix<T, E>::getFirstNeighbor(int v)
{
    for (int i = 0; i < this->verticleSize; i++) {
        if ((matrix[v][i]) != 0 && matrix[v][i] != MAX_WEIGHT) {
            return i;
        }
    }
    return MAX_WEIGHT;
}

  template<class T, class E>
   int GraphMatrix<T, E>::getNextNeighbor(int v, int w)
  {
       for (int i = w+1; i < this->verticleSize; i++) {
           if ((matrix[v][i]) != 0 && matrix[v][i] != MAX_WEIGHT) {
               return i;
           }
       }
       return MAX_WEIGHT;

  }

  template<class T, class E>
   int GraphMatrix<T, E>::getVertexPos(T vertex)
  {
       for (int i = 0; i < Graph<T,E>::verticleSize; i++) {
           if (verticles[i] == vertex) {
               return i;
           }
       }
      return -1;
  }

  template<class T, class E>
   T * GraphMatrix<T, E>::getVerticles()
  {
      return verticles;
  }

   template<class T, class E>
   E ** GraphMatrix<T, E>::getMatrix()
   {

       return matrix;
   }

   template<class T, class E>
    void GraphMatrix<T, E>::outputGraph()
    {
            //输出图的所有顶点和边信息  
            int i, j, n, m;
            T e1, e2;
            E weight;
            n = this->numberofVerticles();     //点数  
            cout << "顶点数的边数为：";
            cout << n   << endl;      //输出点数
            cout << "各边依次为：" << endl;
            for (i = 0; i<n; i++)
            {
                for (j = 0; j<n; j++)
                {
                    weight = this->getWeight(i, j);
                    if (weight>0 && weight< MAX_WEIGHT)
                    {
                        e1 = this->getValue(i);
                        e2 = this->getValue(j);
                        cout << "(" << e1 << "," << e2 << "," << weight << ")" << endl;
                    }
                }
            }

   }

    template<class T, class E>
     void GraphMatrix<T, E>::bfsIndex(int i)
    {

         for (int j = 0; j < this->verticleSize; j++) {
             visit[j] = false;
         }
         for (int j = i; j < this->verticleSize; j++) {
             if (!visit[j]) {
                 bfs(j);
             }
         }
         for (int j = 0; j < i; j++) {
             if (!visit[j]) {
                 bfs(j);
             }
         }

    }

    template<class T, class E>
    void GraphMatrix<T, E>::bfs(int i)
    {
        if (!visit[i]) {
            cout << i << ",";
            visit[i] = true;
        }
         if (getFirstNeighbor(i) == MAX_WEIGHT) {
             return;
         }
         queue<int> q;
         int v = getFirstNeighbor(i);
         while (v!=MAX_WEIGHT)
         {
             if (!visit[v]) {

                 q.push(v);
                 visit[v] = true;
                 cout << v << ",";
             }
             v = getNextNeighbor(i, v);
         }
         while (!q.empty())
         {
             int vert = q.front();
             q.pop();
             bfs(vert);

         }





    }


    template<class T, class E>
     void GraphMatrix<T, E>::dfsStack(int i)
    {
         stack<int> s;
         visit[i] = true;
         cout << i<<",";
         s.push(i);
        while (!s.empty())
         {
             int vert = getUnVisitedVerticles(s.top());
             if (vert != MAX_WEIGHT) {
                 visit[vert] = true;
                 cout << vert << ",";
                 s.push(vert);

             }
             else {
                 int top = s.top();
                 s.pop();
                 if (s.empty()) {
                     int un = findNextUnVisitedVert(top);
                     if (un != MAX_WEIGHT) {
                         s.push(un);
                         cout << un << ",";
                         visit[un] = true;

                     }
                 }
             }

         }


    }

     template<class T, class E>
      void GraphMatrix<T, E>::dfsIndex(int i)
     {

          for (int j = 0; j < this->verticleSize; j++) {
              visit[j] = false;
          }
          for (int j = i; j < this->verticleSize; j++) {
              if (!visit[j]) {
                  dfs(j);
              }
          }
          for (int j = 0; j < i; j++) {
              if (!visit[j]) {
                  dfs(j);
              }
          }
     }

     template<class T, class E>
      void GraphMatrix<T, E>::dfs(int i)
     {
          visit[i] = true;
          cout << i << ",";
          int vert = getFirstNeighbor(i);

          while (vert!=MAX_WEIGHT)
          {
             if(!visit[vert])
              dfs(vert);
              vert = getNextNeighbor(i, vert);
          }
     }

     template<class T, class E>
      int GraphMatrix<T, E>::getUnVisitedVerticles(int i)
     {
         for (int j = 0; j < this->verticleSize; j++) {
             if (matrix[i][j] > 0 && matrix[i][j] < MAX_WEIGHT && !visit[j]) {
                 return j;
             }
         }

         return MAX_WEIGHT;
     }

      template<class T, class E>
      inline int GraphMatrix<T, E>::findNextUnVisitedVert(int i)
      {
          for (int j = i+1; j < this->verticleSize; j++) {
              if (!visit[j]) {
                  return j;
              }
          }
          for (int j = 0; j < i; j++) {
              if (!visit[j]) {
                  return j;
              }
          }
          return MAX_WEIGHT;
      }
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测试代码

#include "GraphMatrix.h"
#define varName(x) #x  
int main() {
    GraphMatrix<string, int> m(5);
    int * v0 = new int[5]{0,INF,INF,INF,6};
    int * v1 = new int[5]{ 9,0,3,INF,INF };
    int * v2 = new int[5]{ 2,INF,0,5,INF };
    int * v3 = new int[5]{ INF,INF,INF,0,1 };
    int * v4 = new int[5]{ INF,INF,INF,INF,0 };
    m.getMatrix()[0] = v0;
    m.getMatrix()[1] = v1;
    m.getMatrix()[2] = v2;
    m.getMatrix()[3] = v3;
    m.getMatrix()[4] = v4;

    m.getVerticles()[0] = varName(v0);
    m.getVerticles()[1] = varName(v1);
    m.getVerticles()[2] = varName(v2);
    m.getVerticles()[3] = varName(v3);
    m.getVerticles()[4] = varName(v4);

    m.outputGraph();


    m.dfsIndex(1);
    cout << endl;
    m.bfsIndex(1);

    system("pause");
}
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