二叉树

二叉树:   二叉树是一棵特殊的树，二叉树每个节点最多有两个孩子结点，分别称为左孩子和右孩子。

满二叉树:    高度为N的满二叉树有2^N - 1个节点的二叉树。

完全二叉树:  若设二叉树的深度为h，除第 h 层外，其它各层 (1～h-1) 的结点数都达到最大个数，第 h 层所有的结点都连续集中在最左边，这就是完全二叉树。

前序遍历(先根遍历):（1）：先访问根节点；（2）：前序访问左子树；（3）：前序访问右子树；  

中序遍历:          （1）：中序访问左子树；（2）：访问根节点；    （3）：中序访问右子树；  

后序遍历(后根遍历):（1）：后序访问左子树；（2）：后序访问右子树；（3）：访问根节点；    

层序遍历：         （1）：一层层节点依次遍历。                                           

#include <iostream>using namespace std;#include <queue>#include<stack>template<class T>struct BinaryTreeNode{T _data;BinaryTreeNode<T>* _left;BinaryTreeNode<T>* _right;BinaryTreeNode(const T& x):_data(x), _left(NULL), _right(NULL){}};template<class T>class BinaryTree{public:BinaryTree():_root(NULL){}BinaryTree(const T* a, size_t size){size_t index = 0;_root = _CreatTree(a, size, index);}BinaryTree(const BinaryTree<T>& t){_root = _Copy(t._root);}BinaryTree<T>& operator=(const BinaryTree<T>& t){if (_root != t._root){this->_delete(_root);_root = _Copy(t._root);}return *this;}BinaryTreeNode<T>* find(const T& x){return _find(_root, x);}void PrevOrder(){_PrevOrder(_root);cout << endl;}void InOrder(){_InOrder(_root);cout << endl;}void PostOrder(){_PostOrder(_root);cout << endl;}void PrevOrder_NOR(){_PrevOrder_NOR(_root);}void InOrder_NOR(){_InOrder_NOR(_root);}void PostOrder_NOR(){_PostOrder_NOR(_root);}void LevelOrder(){_LevelOrder(_root);cout << endl;}int depth(){return _depth(_root);}int size(){return _size(_root);}~BinaryTree(){if (_root != NULL){_delete(_root);}}protected:BinaryTreeNode<T>* _CreatTree(const T* a, size_t size, size_t& index){BinaryTreeNode<T>* root = NULL;if (index < size){if ('#' != a[index]){root = new BinaryTreeNode<T>(a[index]);root->_left = _CreatTree(a, size, ++index);root->_right = _CreatTree(a, size, ++index);}}return root;}BinaryTreeNode<T>* _Copy(BinaryTreeNode<T>* root){if (root == NULL){return NULL;}BinaryTreeNode<T>* _root = new BinaryTreeNode<T>(root->_data);if (root->_left != NULL){_root->_left = _Copy(root->_left);}if (root->_right != NULL){_root->_right = _Copy(root->_right);}return _root;}BinaryTreeNode<T>* _find(BinaryTreeNode<T>* root, const T& x){BinaryTreeNode<T>* bt = NULL;if (root == NULL){return NULL;}if (root->_data == x){return root;}if (root->_left != NULL){bt = _find(root->_left, x);if (bt != NULL){return bt;}}if (root->_right != NULL){bt = _find(root->_right, x);if (bt != NULL){return bt;}}return NULL;}void _PrevOrder(BinaryTreeNode<T>* root){if (root == NULL){return;}cout << root->_data << " ";_PrevOrder(root->_left);_PrevOrder(root->_right);}void _PrevOrder_NOR(BinaryTreeNode<T>* root){if (root == NULL){return;}stack<BinaryTreeNode<T>*> s;s.push(root);while (!s.empty()){BinaryTreeNode<T>* ret = s.top();s.pop();cout << ret->_data << " ";if (ret->_right != NULL){s.push(ret->_right);}if (ret->_left != NULL){s.push(ret->_left);}}cout << endl;}void _InOrder(BinaryTreeNode<T>* root){if (root == NULL){return;}_InOrder(root->_left);cout << root->_data << " ";_InOrder(root->_right);}void _InOrder_NOR(BinaryTreeNode<T>* root){if (root == NULL){return;}stack<BinaryTreeNode<T>*> s;BinaryTreeNode<T>* ret = root;while (ret || !s.empty()){while (ret){s.push(ret);ret = ret->_left;}if (!s.empty()){ret = s.top();cout << ret->_data << " ";s.pop();ret = ret->_right;}}cout << endl;}void _PostOrder(BinaryTreeNode<T>* root){if (root == NULL){return;}_PostOrder(root->_left);_PostOrder(root->_right);cout << root->_data << " ";}void _PostOrder_NOR(BinaryTreeNode<T> *root){if (root == NULL){return;}stack<BinaryTreeNode<T>*> s;BinaryTreeNode<T> *cur = root;BinaryTreeNode<T> *PreVisited = NULL;while (cur){s.push(cur);cur = cur->_left;}while (!s.empty()){cur = s.top();s.pop();if (cur->_right == NULL || cur->_right == PreVisited){cout << cur->_data << " ";PreVisited = cur;}else{s.push(cur);cur = cur->_right;while (cur){s.push(cur);cur = cur->_left;}}}cout << endl;}void _LevelOrder(BinaryTreeNode<T>* root){if (root == NULL){return;}queue<BinaryTreeNode<T>*> q1;q1.push(root);while (!q1.empty()){BinaryTreeNode<T>* b1 = q1.front();q1.pop();cout << b1->_data << " ";if (b1->_left != NULL){q1.push(b1->_left);}if (b1->_right != NULL){q1.push(b1->_right);}}}int _size(BinaryTreeNode<T>* root){if (root == NULL){return 0;}return _size(root->_left) + _size(root->_right) + 1;} int _depth(BinaryTreeNode<T>* root){if (root == NULL){return 0;}int ldepth = _depth(root->_left);int rdepth = _depth(root->_right);return ldepth > rdepth ? ldepth+1 :rdepth + 1;}void _delete(BinaryTreeNode<T>* root){if (root == NULL){return;}_delete(root->_left);_delete(root->_right);delete root;root = NULL;}private:BinaryTreeNode<T>* _root;};int main(){int a[10] = { 1, 2, 3, '#', '#', 4, '#', '#', 5, 6 };BinaryTree<int> t1(a, 10);t1.PrevOrder();t1.InOrder();t1.PostOrder();t1.LevelOrder();BinaryTree<int> t2(t1);t2 = t1;cout<<t1.size()<<endl;cout << t1.depth() << endl;cout << t1.find(4)->_data << endl; t1.PrevOrder_NOR();t1.InOrder_NOR(); t1.PostOrder_NOR();return 0;}