二叉树：每个节点最多两个孩子节点。

二叉树的结构：         struct TreeNode

{

DataType _value;     //节点值

TreeNode*  _left;    //左孩子

TreeNode*  _ridht;   //右孩子

};

二叉树的基础：        构造、拷贝构造、析构、赋值运算符的重载

二叉树的知识点：      高度、节点的个数、子节点的个数

二叉树的遍历：        前序、中序、后序遍历(递归及非递归)

遍历顺序：            前序——根左右          中序——左根右          后序——左右根

注意: 递归遍历时，应该注意不要出现栈溢出现象。

因为++index返回对象，index++返回临时变量，所以传引用做参数时有++index。

#pragma once#include<queue>
#include<stack>//二叉树的结构
template<class T>
struct BinaryTreeNode
{BinaryTreeNode<T>* _left;BinaryTreeNode<T>* _right;T _data;//构造函数BinaryTreeNode(const T& x):_left(NULL), _right(NULL), _data(x){}
};
template<class T>
class BinaryTree
{typedef BinaryTreeNode<T> Node;  public://构造BinaryTree():_root(NULL){}// a--树的节点前序遍历的数组  size--数组中元素个数  invaild--无效值即节点为空BinaryTree(const T* a,size_t size,const T& invalid){size_t index = 0;_root = _CreateTree(a, size,invalid,index);}//析构~BinaryTree(){_Destory(_root);_root = NULL;}//拷贝  BinaryTree(const BinaryTree<T>& t){_root = _Copy(t._root);}//赋值重载(传统)//BinaryTree<T>& operator=(const BinaryTree<T>& t)//{//  if (this != &t)//  {//     Node* tmp = _Copy(t._root);//      _Destory(_root);//      _root = tmp;// }// return *this;//}//赋值重载(现代)BinaryTree<T>& operator=(BinaryTree<T> t){swap(_root, t._root);return *this;}T& operator->(){return _root;}public:void PrevOrder()//前序{_PrevOrder(_root);cout << endl;}void InOrder()//中序{_InOrder(_root);cout << endl;}void PostOrder()//后序{_PostOrder(_root);cout << endl;}size_t Size()  //节点个数{return _Size(_root);}size_t Depth()  //树的深度{return _Depth(_root);}size_t LeafSize()  //叶子节点个数{return _LeafSize(_root);}//层次遍历void LevelOrder(){queue<Node*> q;if (_root){q.push(_root);}while (!q.empty()){Node* front = q.front();cout << front->_data << " ";q.pop();if (front->_left){q.push(front->_left);}if (front->_right){q.push(front->_right);}}cout << endl;}
public://非递归的前中后序遍历（栈）void PrevOrder_NonR(){stack<Node*> s;if (_root)s.push(_root);while (!s.empty()){Node* top = s.top();cout << top->_data << " ";s.pop();//栈后进先出  ，所以 右先进，左先出if (top->_right)s.push(top->_right);if (top->_left)s.push(top->_left);}cout << endl;}void InOrder_NonR(){//压左树//取出一个节点即它的左路走完了，在访问右树（看作子问题）stack<Node*> s;Node* cur = _root;while (cur || !s.empty()){//压树的左路节点直至最左段节点while (cur){s.push(cur);cur = cur->_left;}if (!s.empty()){Node* top = s.top();s.pop();cout << top->_data << " ";cur=top->_right;}}cout << endl;}void PostOrder_NonR(){Node* prev = NULL;Node* cur = _root;stack<Node*> s;while (cur || !s.empty()){//压树的左路节点直至最左段节点while (cur){s.push(cur);cur = cur->_left;}Node* top = s.top();if (top->_right == NULL || top->_right == prev){cout << top->_data << " ";s.pop();prev = top;}else{cur = top->_right;}}cout << endl;}protected://注意 此处index要用引用传参Node* _CreateTree(const T* a, size_t size, const T& invalid, size_t& index) {Node* root = NULL;if ((index < size) && (a[index] != invalid)){root = new Node(a[index]);//注意下面只能用++index。此处传的是引用 //因为++index返回对象，index++返回临时变量。root->_left = _CreateTree(a, size, invalid, ++index);root->_right = _CreateTree(a, size, invalid, ++index);}return root;}void _Destory(Node* root){if (root == NULL)return;_Destroy(root->_left);_Destroy(root->_right);delete root;}Node* _Copy(Node* root){if (root == NULL)return NULL;NOde* newRoot = new Node(root->_data);newRoot->_left = _Copy(root->_left);newRoot->_right = _Copy(root->_right);return newRoot;}//void _PrevOrder(Node* root){if (root == NULL)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;return (_Size(root->_left) + _Size(root->_right) + 1);}size_t _Depth(Node* root){if (root == NULL)return 0;size_t LeftDepth = _Depth(root->_left);size_t RightDepth = _Depth(root->_right);return (LeftDepth > RightDepth) ? (LeftDepth + 1) : (RightDepth + 1);}size_t _LeafSize(Node* root){if (root == NULL)return 0;if ((root->_left == NULL) && (root->_right == NULL))return 1;return (_LeafSize(root->_left) + _LeafSize(root->_right));}
private:Node *_root;
};