图的存储方式及实现

图的存储方式及实现

邻接矩阵法

• 图类的各元素

  class MGraph //有向图
  {
  private:
      int Ne;              //边数
      int N;               //结点数
      int Graph[Max][Max]; //二维矩阵
      char Node[Max];      //结点值
  public:
      MGraph(char a[], int n, int e);
      void display();
      void getOutNum(); //出度
      void getInNum();  //入度
  };
  

• 初始化图

  MGraph::MGraph(char a[], int n, int e)
  {
      Ne = e;
      N = n;
  
      //给结点赋值
      for (int i = 0; i < N; i++)
      {
          Node[i] = a[i];
      }
  
      //输入边并赋值
      memset(Graph, 0, sizeof(Graph));
      int i, j;
      for (int k = 0; k < e; k++)
      {
          cin >> i >> j;
          Graph[i][j] = 1; //有向图且无权值
          // Graph[j][i] = 1; //无向图
      }
  }
  

• 展示函数

  void MGraph::display()
  {
      cout << "输出各结点的值"
           << "\n";
      for (int i = 0; i < N; i++)
      {
          cout << Node[i] << " ";
      }
      cout << "\n"
           << "输出邻接矩阵"
           << "\n";
      for (int i = 0; i < N; i++)
      {
          for (int j = 0; j < N; j++)
          {
              cout << Graph[i][j] << " ";
          }
          cout << "\n";
      }
  }
  

• 入度及出度

void MGraph::getOutNum()
{
    cout << endl;
    for (int i = 0; i < N; i++)
    {
        int num = 0;
        for (int j = 0; j < N; j++)
        {
            if (Graph[i][j] != 0)
            {
                num++;
            }
        }
        cout << "第" << i << "个结点的出度为:" << num << endl;
    }
}

void MGraph::getInNum()
{
    cout << endl;
    for (int i = 0; i < N; i++)
    {
        int num = 0;
        for (int j = 0; j < N; j++)
        {
            if (Graph[j][i] != 0)
            {
                num++;
            }
        }
        cout << "第" << i << "个结点的入度为:" << num << endl;
    }
}

邻接表法

• 结点数组，数组中的任一元素指向一链表，表示指向的结点

  struct Edge		//链表的结点
  {
      Edge *next; //指向下一个结点
      int p;      //结点对应的下标
  };
  
  struct Node		//数组元素
  {
      char val;
      Edge *first; //每个结点串一条链表，为指出的
  };
  

• 图类各元素

  class LGraph
  {
  private:
      Node node[Max]; //头结点的数组
      int N, Ne;
  
  public:
      LGraph(char a[], int n, int e);
      void display();
      void getInNum();
      void getOutNum();
  };
  

• 初始化图

  LGraph::LGraph(char a[], int n, int e)
  {
      N = n;
      Ne = e;
  
      //结点赋值
      for (int i = 0; i < N; i++)
      {
          node[i].val = a[i];
          node[i].first = NULL;
      }
  
      //连接
      char z, b;
      for (int k = 0; k < Ne; k++)
      {
          cin >> z >> b;
          for (int i = 0; i < N; i++)
          {
              if (z == node[i].val)
              { //找到要插入的头
                  Edge *e = new Edge;
                  // e->p = k;
                  for (int j = 0; j < N; j++)
                  { //找到结点的值对应的下标
                      if (b == node[j].val)
                      {
                          e->p = j;
                          break;
                      }
                  }
                  e->next = node[i].first;
                  node[i].first = e;
                  break;
              }
          }
      }
  }
  

• 展示函数，需要注意的是，遍历时需要创建一个临时变量来代替first指针，否则first最终将指向链表最后一个元素的后面

  void LGraph::display()
  {
      cout << "输出各结点及其指向的其他结点"
           << "\n";
      for (int i = 0; i < N; i++)
      {
          Edge *o = node[i].first; //防止头指针被改变
          cout << node[i].val << " ";
          while (o != NULL)
          {
              cout << o->p << " ";
              o = o->next;
          }
          cout << endl;
      }
  }
  

• 入度及出度：first指针的处理同上

  void LGraph::getOutNum()
  {
      cout << endl;
      for (int i = 0; i < N; i++)
      {
          int num = 0;
          Edge *o = node[i].first; //防止头指针被改变
          while (o != NULL)
          {
              num++;
              o = o->next;
          }
          cout << node[i].val << "的结点的出度为:" << num << endl;
      }
  }
  
  void LGraph::getInNum()
  {
      cout << endl;
      int x[N]; //用以存储各结点的入度
      memset(x, 0, sizeof(x));
      for (int i = 0; i < N; i++)
      {
          while (node[i].first != NULL)
          {
              x[node[i].first->p]++;
              node[i].first = node[i].first->next;
          }
      }
      for (int i = 0; i < N; i++)
      {
          cout << node[i].val << "的结点的入度为:" << x[i] << endl;
      }
  }