二叉搜索树和红黑树概述以及模板实现(1)

最近研究了一下算法导论里面关于二叉搜索树和红黑树的一章，对于红黑树的内容虽然还没有完全消化吸收，写一篇blog算是对所有内容的一个复习和反思吧。

1. 二叉搜索树

二叉搜索树是一颗二叉树，要求对于任何一个节点，它的左儿子内的数据要小于根节点数据，而右节点的数据要大于根节点内的数据。

例如

在搜索问题中，虽然哈希表在比较好的情况下可以提供O(1)的时间，但是对于数据分布不好，或者数据较少的时候会造成聚集或者空间浪费。但是用搜索树，在检索效率平均是lnN

下面用看《算法导论》实现的算法分析一些具体的操作，其实基本的操作和一般的二叉树一样，包括插入、删除、遍历等。只不过因为树结构的特殊，在操作后要做一些处理。

#ifndef BINARY_SEARCH_TREE_H#define BINARY_SEARCH_TREE_H#include <assert.h>#include <stack>#include <iostream>namespace DataStructure{

        //模板节点

template <typename T>class TreeNode{public:T data;TreeNode *left,*right;TreeNode *parent;TreeNode(){parent = left = right = NULL;}TreeNode(T _data){data = _data;parent = left = right = NULL;}};template<typename T>class BinarySearchTree{public:typedef TreeNode<T> NodeType;public:BinarySearchTree(){m_pRoot = NULL;}/** Add a element into tree*/TreeNode<T>* insert(T _element);/** Find a element*/TreeNode<T>* search(T _element) const;/** delete an element*/bool delete_element(TreeNode<T> *_pElement);/**search the element interactively*/TreeNode<T>* interative_search(T data);/**the minimum element of the tree*/TreeNode<T>* minimum_element(TreeNode<T> *)const;/**the maximum element*/TreeNode<T>* maximum_element(TreeNode<T> *)const;/**tree successor */TreeNode<T>* successor(TreeNode<T>* pElement) const;/**tree predecessor */TreeNode<T>* predecessor(TreeNode<T> *pElement)const;/**iterate all elements*/void print_ordered_elements()const;/*** delete one node from the tree*/private:TreeNode<T> * m_pRoot;};/** Add a element into tree*/template<typename T>TreeNode<T>* BinarySearchTree<T>::insert(T _element){if(m_pRoot == NULL){m_pRoot = new TreeNode<T>;m_pRoot->data = _element;m_pRoot->left = m_pRoot->right = NULL;return m_pRoot;}else{TreeNode<T> *pNode = m_pRoot;while(pNode != NULL){if( _element > pNode->data ){//insert into right subtree//pNode = pNode->right;//make the current element be the right son.if(pNode->right == NULL){TreeNode<T> *pNewElement = new TreeNode<T>;pNewElement->data = _element;pNewElement->left = NULL;pNewElement->right = NULL;pNewElement->parent = pNode;pNode->right = pNewElement;return pNewElement;}else{pNode = pNode->right;}}else if(_element < pNode->data ){//insert into left subtree//pNode = pNode->left;if(pNode->left == NULL){TreeNode<T> *pNewElement = new TreeNode<T>;pNewElement->data = _element;pNewElement->left = NULL;pNewElement->right = NULL;pNewElement->parent = pNode;pNode->left = pNewElement;return pNewElement;}else{pNode = pNode->left;}}else{return pNode;}}}return NULL;}/** Find an element* if there is no such element return NULL*/template<typename T>TreeNode<T>* BinarySearchTree<T>::search(T _element) const{TreeNode<T> *pElement = m_pRoot;while(pElement != NULL){//search the leftif(_element < pElement->data){pElement = pElement->left;}else if(_element > pElement->data){pElement = pElement->right;}else{return pElement;}}return NULL;}/** delete an element*/template<typename T>bool BinarySearchTree<T>::delete_element(TreeNode<T> *_pElement){//assert//assert(_pElement != NULL && m_pRoot != NULL);if(_pElement == NULL || m_pRoot == NULL){return false;}TreeNode<T> *realDelete = NULL;TreeNode<T> *pSon = NULL;if(_pElement ->left == NULL || _pElement->right == NULL){realDelete = _pElement;}else{realDelete = successor(_pElement);}if(realDelete->left != NULL){pSon = realDelete->left;}else{pSon = realDelete->right;}if(pSon != NULL){pSon->parent = realDelete->parent;}if(realDelete ->parent != NULL){if(realDelete->parent->left == realDelete){realDelete->parent->left = pSon;}else{realDelete->parent->right = pSon;}if(_pElement != realDelete){_pElement->data = realDelete->data;delete realDelete;}}else{delete m_pRoot;m_pRoot = NULL;}return true;//this is what age}/**the minimum element of the tree*/template<typename T>TreeNode<T>* BinarySearchTree<T>::minimum_element(TreeNode<T> *pCNode)const{TreeNode<T> *pNode = pCNode;while(pNode->left != NULL){pNode = pNode->left;}return pNode;}/**the maximum element*/template<typename T>TreeNode<T>* BinarySearchTree<T>::maximum_element(TreeNode<T> *pCNode)const{TreeNode<T> *pNode = pCNode;while(pNode->right != NULL){pNode = pNode->right;}return pNode;}//print template<typename T>void BinarySearchTree<T>::print_ordered_elements()const{std::stack<TreeNode<T>*> elements;TreeNode<T>* tmp = m_pRoot;elements.push(m_pRoot);std::cout<<"All Elements\n";while(!elements.empty()){while(tmp != NULL){tmp = tmp ->left;elements.push(tmp);}elements.pop();if(!elements.empty()){tmp = elements.top();elements.pop();std::cout<<tmp->data<<std::endl;tmp = tmp->right;elements.push(tmp);}}}/**tree successor */template<typename T>TreeNode<T>* BinarySearchTree<T>::successor(TreeNode<T>* pElement) const{if(pElement->right != NULL){return minimum_element(pElement->right);}TreeNode<T>* pNode = pElement->parent;while(pNode != NULL && pNode ->right == pElement){pElement = pNode;pNode = pNode->parent;}return pNode;}/**tree predecessor */template<typename T>TreeNode<T>* BinarySearchTree<T>::predecessor(TreeNode<T> *pElement)const{if(pElement->left != NULL){return maximum_element(pElement->left);}TreeNode<T>* pNode = pElement->parent;while(pNode != NULL && pNode ->left == pElement){pElement = pNode;pNode = pNode->parent;}return pNode;}}//namespace DataStructure#endif //BINARY_SEARCH_TREE_H