C++实现二叉树基本操作详解

树是一种重要的非线性数据结构，二叉树是树型结构的一种重要类型。本学年论文介绍了二叉树的定义，二叉树的存储结构，二叉树的相关术语，以此引入二叉树这一概念，为展开二叉树的基本操作做好理论铺垫。二叉树的基本操作主要包含以下几个模块：二叉树的遍历方法，计算二叉树的结点个数，计算二叉树的叶子结点个数，二叉树深度的求解等内容。

前序遍历（递归&非递归）

• 访问根节点
• 前序访问左子树
• 前序访问右子树
  

//前序非递归
  void PrevOrder()
  {
    stack<Node*> s;
    Node *cur = _root;

    while (cur || !s.empty())
    {
      while (cur)
      {
        cout << cur->_data << " ";
        s.push(cur);
        cur = cur->_left;
      }
      //此时当前节点的左子树已遍历完毕
      Node *tmp = s.top();
      s.pop();
      cur = tmp->_right;
    }
    cout << endl;
  }

  //前序递归
  void PrevOrderR()
  {
    _PrevOrder(_root);

    cout << endl;
  }

  void _PrevOrder(Node *root)
  {
    if (root == NULL) //必须有递归出口！！！
      return;

    cout << root->_data << " ";
    _PrevOrder(root->_left);
    _PrevOrder(root->_right);
  }

中序遍历（递归&非递归）

• 中序访问左子树
• 访问根节点
• 中序访问右子树
  

//中序非递归
  void InOrder()
  {
    stack<Node*> s;
    Node *cur = _root;

    while (cur || !s.empty())
    {
      while (cur)
      {
        s.push(cur);
        cur = cur->_left;
      }
      //此时当前节点的左子树已遍历完毕
      Node *tmp = s.top();
      cout << tmp->_data << " ";
      s.pop();
      cur = tmp->_right;
    }
    cout << endl;
  }

  //中序递归
  void InOrderR()
  {
    _InOrder(_root);

    cout << endl;
  }

  void _InOrder(Node *root)
  {
    if (root == NULL)
      return;

    _InOrder(root->_left);
    cout << root->_data << " ";
    _InOrder(root->_right);
  }

后序遍历（递归&非递归）

  //后序非递归
  //后序遍历可能会出现死循环，所以要记录下前一个访问的节点
  void PostOrder()
  {
    stack<Node*> s;
    Node *cur = _root;
    Node *prev = NULL;

    while (cur || !s.empty())
    {
      while (cur)
      {
        s.push(cur);
        cur = cur->_left;
      }
      Node *tmp = s.top();
      if (tmp->_right && tmp->_right != prev)
      {
        cur = tmp->_right;
      }
      else
      {
        cout << tmp->_data << " ";
        prev = tmp;
        s.pop();
      }
    }
    cout << endl;
  }

  //后序递归
  void PostOrderR()
  {
    _PostOrder(_root);

    cout << endl;
  }

  void _PostOrder(Node *root)
  {
    if (root == NULL)
      return;

    _PostOrder(root->_left);
    _PostOrder(root->_right);
    cout << root->_data << " ";
  }

层序遍历

从根节点开始，依次访问每层结点。
利用队列先进先出的特性，把每层结点从左至右依次放入队列。

 void LevelOrder() //利用队列！！！
  {
    queue<Node*> q;
    Node *front = NULL;

    //1.push根节点
    if (_root)
    {
      q.push(_root);
    }
    //2.遍历当前节点，push当前节点的左右孩子，pop当前节点
    //3.遍历当前节点的左孩子，再遍历右孩子，循环直至队列为空
    while (!q.empty())
    {

      front = q.front();
      cout << front->_data << " ";

      if (front->_left)
        q.push(front->_left);
      if (front->_right)
        q.push(front->_right);

      q.pop();
    }

    cout << endl;
  }

求二叉树的高度

  size_t Depth()
  {
    return _Depth(_root);
  }

  size_t _Depth(Node *root)
  {
    if (root == NULL)
      return 0;
    else if (root->_left == NULL && root->_right == NULL)
      return 1;
    else
    {
      size_t leftDepth = _Depth(root->_left) + 1;
      size_t rightDepth = _Depth(root->_right) + 1;
      return leftDepth > rightDepth ? leftDepth : rightDepth;
    }
  }

求叶子节点的个数

size_t LeafSize()
  {
    return _LeafSize(_root);
  }

  size_t _LeafSize(Node *root)
  {
    if (root == NULL)
      return 0;
    else if (root->_left == NULL && root->_right == NULL)
      return 1;
    else
      return _LeafSize(root->_left) + _LeafSize(root->_right);
  }

求二叉树第k层的节点个数

size_t GetKLevel(int k)
  {
    return _GetKLevel(_root, k);
  }

  size_t _GetKLevel(Node *root, int k)
  {
    if (root == NULL)
      return 0;
    else if (k == 1)
      return 1;
    else
      return _GetKLevel(root->_left, k - 1) + _GetKLevel(root->_right, k - 1);
  }

完整代码如下：

template<class T>
struct BinaryTreeNode
{
  T _data;
  BinaryTreeNode *_left;
  BinaryTreeNode *_right;

  BinaryTreeNode(const T& d)
    :_data(d)
    , _left(NULL)
    , _right(NULL)
  {}
};

template<class T>
class BinaryTree
{
public:
  typedef BinaryTreeNode<T> Node;

  BinaryTree()
    :_root(NULL)
  {}

  BinaryTree(T *arr, size_t n, const T& invalid)
  {
    size_t index = 0;
    _root = _CreateBinaryTree(arr, n, invalid, index);
  }

  BinaryTree(const BinaryTree<T>& t)
    :_root(NULL)
  {
    _root = _CopyTree(t._root);
  }

  BinaryTree<T>& operator=(const BinaryTree<T>& t)
  {
    if (this != t)
    {
      Node *tmp = new Node(t._root);
      if (tmp != NULL)
      {
        delete _root;
        _root = tmp;
      }
    }
    return *this;
  }

  ~BinaryTree()
  {
    _DestroyTree(_root);
    cout << endl;
  }

  //前序非递归
  void PrevOrder()
  {
    stack<Node*> s;
    Node *cur = _root;

    while (cur || !s.empty())
    {
      while (cur)
      {
        cout << cur->_data << " ";
        s.push(cur);
        cur = cur->_left;
      }
      //此时当前节点的左子树已遍历完毕
      Node *tmp = s.top();
      s.pop();
      cur = tmp->_right;
    }
    cout << endl;
  }

  //前序递归
  void PrevOrderR()
  {
    _PrevOrder(_root);

    cout << endl;
  }

  //中序非递归
  void InOrder()
  {
    stack<Node*> s;
    Node *cur = _root;

    while (cur || !s.empty())
    {
      while (cur)
      {
        s.push(cur);
        cur = cur->_left;
      }
      //此时当前节点的左子树已遍历完毕
      Node *tmp = s.top();
      cout << tmp->_data << " ";
      s.pop();
      cur = tmp->_right;
    }
    cout << endl;
  }

  //中序递归
  void InOrderR()
  {
    _InOrder(_root);

    cout << endl;
  }

  //后序非递归
  //后序遍历可能会出现死循环，所以要记录下前一个访问的节点
  void PostOrder()
  {
    stack<Node*> s;
    Node *cur = _root;
    Node *prev = NULL;

    while (cur || !s.empty())
    {
      while (cur)
      {
        s.push(cur);
        cur = cur->_left;
      }
      Node *tmp = s.top();
      if (tmp->_right && tmp->_right != prev)
      {
        cur = tmp->_right;
      }
      else
      {
        cout << tmp->_data << " ";
        prev = tmp;
        s.pop();
      }
    }
    cout << endl;
  }

  //后序递归
  void PostOrderR()
  {
    _PostOrder(_root);

    cout << endl;
  }

  void LevelOrder() //利用队列！！！
  {
    queue<Node*> q;
    Node *front = NULL;

    //1.push根节点
    if (_root)
    {
      q.push(_root);
    }
    //2.遍历当前节点，push当前节点的左右孩子，pop当前节点
    //3.遍历当前节点的左孩子，再遍历右孩子，循环直至队列为空
    while (!q.empty())
    {

      front = q.front();
      cout << front->_data << " ";

      if (front->_left)
        q.push(front->_left);
      if (front->_right)
        q.push(front->_right);

      q.pop();
    }

    cout << endl;
  }

  size_t Size()
  {
    return _Size(_root);
  }

  size_t LeafSize()
  {
    return _LeafSize(_root);
  }

  size_t GetKLevel(int k)
  {
    return _GetKLevel(_root, k);
  }

  size_t Depth()
  {
    return _Depth(_root);
  }

  Node* Find(const T& d)
  {
    return _Find(_root, d);
  }

protected:
  Node* _CreateBinaryTree(T *arr, size_t n, const T& invalid, size_t& index)
  {
    Node *root = NULL;
    if (index < n && arr[index] != invalid)
    {
      root = new Node(arr[index]);
      index++;
      root->_left = _CreateBinaryTree(arr, n, invalid, index);
      index++;
      root->_right = _CreateBinaryTree(arr, n, invalid, index);
    }
    return root;
  }

  Node* _CopyTree(Node *root)
  {
    Node *newRoot = NULL;

    if (root)
    {
      newRoot = new Node(root->_data);
      newRoot->_left = _CopyTree(root->_left);
      newRoot->_right = _CopyTree(root->_right);
    }

    return newRoot;
  }

  void _DestroyTree(Node *root)
  {
    if (root)
    {
      _Destroy(root->_left);
      _Destroy(root->_right);
      delete root;
    }
  }

  void _PrevOrder(Node *root)
  {
    if (root == NULL) //必须有递归出口！！！
      return;

    cout << root->_data << " ";
    _PrevOrder(root->_left);
    _PrevOrder(root->_right);
  }

  void _InOrder(Node *root)
  {
    if (root == NULL)
      return;

    _InOrder(root->_left);
    cout << root->_data << " ";
    _InOrder(root->_right);
  }

  void _PostOrder(Node *root)
  {
    if (root == NULL)
      return;

    _PostOrder(root->_left);
    _PostOrder(root->_right);
    cout << root->_data << " ";
  }

  size_t _Size(Node *root)
  {
    if (root == NULL)
      return 0;
    else
      return _Size(root->_left) + _Size(root->_right) + 1;
  }

  size_t _LeafSize(Node *root)
  {
    if (root == NULL)
      return 0;
    else if (root->_left == NULL && root->_right == NULL)
      return 1;
    else
      return _LeafSize(root->_left) + _LeafSize(root->_right);
  }

  size_t _GetKLevel(Node *root, int k)
  {
    if (root == NULL)
      return 0;
    else if (k == 1)
      return 1;
    else
      return _GetKLevel(root->_left, k - 1) + _GetKLevel(root->_right, k - 1);
  }

  size_t _Depth(Node *root)
  {
    if (root == NULL)
      return 0;
    else if (root->_left == NULL && root->_right == NULL)
      return 1;
    else
    {
      size_t leftDepth = _Depth(root->_left) + 1;
      size_t rightDepth = _Depth(root->_right) + 1;
      return leftDepth > rightDepth ? leftDepth : rightDepth;
    }
  }

  Node* _Find(Node *root, const T& d)
  {
    if (root == NULL)
      return NULL;
    else if (root->_data == d)
      return root;
    else if (Node *ret = _Find(root->_left, d))
      return ret;
    else
      _Find(root->_right, d);
  }

protected:
  Node *_root;
};

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