c++类实现二叉查找树的抽象数据结构

说明：

1.0  二叉查找树可以看成是改进的二分查找法:  不需要依赖有序的数组

1.1 对于二叉查找树的前缀/后缀的查找，可能需要改变二叉树的类型，增加parent指针

1.2 对于插入/删除/查找（二分，最值之类）的操作，不需要考虑parent指针的问题

1.3  二叉查找树的平衡度可能很差，可能的解决办法:1.随机读取数组中的数据； 2.重新构建一颗AVL树

<pre name="code" class="cpp">#ifndef BINARYTREE_H#define BINARYTREE_H#include<iostream>using namespace std;typedef struct linknode {int data;struct linknode *left;struct linknode *right;struct linknode *parent;}*ptree,tree;class BINARYTREE{public:BINARYTREE(){};~BINARYTREE(){};void insertTree(ptree _tree, ptree treeNode) const ;  //插入ptree createTree(int arr[],int size) ;void middleOrder(ptree _tree) const ;      void preOrder(ptree _tree) const;int BSTsearch(ptree _tree, int value);                //查找int BSTsearch2(ptree _tree, int value) ;ptree MAX(ptree _tree);                               //查找最大值ptree MIN(ptree _tree);int DELETE(ptree &valueNode);                         //删除节点int deleteNode(ptree &_tree, int value);};void BINARYTREE::insertTree(ptree _tree, ptree treeNode) const {if(_tree->data>=treeNode->data ) {if(NULL == _tree->left) {_tree->left=treeNode;treeNode->parent=_tree;}else {insertTree(_tree->left,treeNode);}}if(_tree->data<treeNode->data  ) {if(NULL==_tree->right) {_tree->right = treeNode;treeNode->parent = _tree;}else {insertTree(_tree->right,treeNode);}}}ptree BINARYTREE::createTree(int arr[], int size) {int i;ptree _tree = new tree;_tree->data=arr[0];_tree->left=NULL;_tree->right=NULL;_tree->parent=NULL;for( i=1; i<size; ++i ) {ptree treeTmp = new tree;treeTmp->data=arr[i];treeTmp->left=NULL;treeTmp->right=NULL;treeTmp->parent=NULL;insertTree(_tree,treeTmp);}return _tree;}void BINARYTREE::middleOrder(ptree _tree) const {if(NULL==_tree) {return;}middleOrder(_tree->left);cout<<_tree->data<<"  ";middleOrder(_tree->right);}void BINARYTREE::preOrder(ptree _tree) const {if(NULL==_tree) {return;}cout<<_tree->data<<"  ";preOrder(_tree->left);preOrder(_tree->right);}int BINARYTREE::BSTsearch(ptree _tree, int value) {if(NULL==_tree) {return -1;}if(value>_tree->data) {return BSTsearch(_tree->right,value);}if(value<_tree->data) {return BSTsearch(_tree->left,value);}if(value==_tree->data) {return 1;}return -1;}int BINARYTREE::BSTsearch2(ptree _tree, int value) {if(NULL == _tree) {return -1;}while( NULL != _tree && value!=_tree->data) {_tree=(value<_tree->data?_tree->left:_tree->right);}if( NULL != _tree ) {return 1;}return -1;}ptree BINARYTREE::MAX(ptree _tree) {if(NULL == _tree ) {return NULL;}while( NULL != _tree->right ) {_tree=_tree->right;} return _tree;}int BINARYTREE::DELETE(ptree &valueNode){//显然此时不存在节点是空的情况//1.是叶子节点，直接删除//2.只有左/右子树，删除蜕化成单链表的删除（特殊在于，知道该节点的地址，所以只用保留后继即可删除）//3.有左+右节点。问题转化成：//3.1寻找该节点的前继（该节点的左子树的最大值（左子树的最右边值）,同时记录最大值的上一个状态）;//3.2前继覆盖此节点(模拟删除);//3.3删除前继节点：2种情况，见代码if(NULL==valueNode->left) {ptree tmp = valueNode;valueNode=valueNode->right;delete tmp;tmp=NULL;}else if(NULL == valueNode->right) {ptree tmp= valueNode->left;delete valueNode;valueNode=tmp;}else if(NULL!=valueNode->left && NULL!=valueNode->left) {ptree parentNode=valueNode;ptree tmp = valueNode->left;while(tmp->right) {parentNode = tmp;tmp=tmp->right;}valueNode->data=tmp->data;if(parentNode!=valueNode) {parentNode->right=tmp->left;}else {valueNode->left=NULL;}delete tmp;tmp=NULL;}return 1;}int BINARYTREE::deleteNode(ptree &_tree, int value) {if(NULL==_tree) {return -1;}if(value == _tree->data) {return DELETE(_tree);}if(value<_tree->data) {return deleteNode(_tree->left,value);}if(value>_tree->data) {return deleteNode(_tree->right,value);}return 1;}#endif

#include"search.h"#include"binaryTree.h"int main() {int arr[]={1,2,3,4,5,6};int arr1[]={1,4,5,2,3,6};int size=sizeof(arr)/sizeof(int);int value=4;BINARYTREE * _binarytree = new BINARYTREE;ptree _tree = _binarytree->createTree(arr1,size);ptree maxNode = _binarytree->MAX(_tree);cout<<"max number in tree is : " <<maxNode->data<<endl;_binarytree->middleOrder(_tree);cout<<""<<endl;_binarytree->preOrder(_tree);cout<<""<<endl;_binarytree->deleteNode(_tree,4);_binarytree->middleOrder(_tree);cout<<""<<endl;//_binarytree->preOrder(_tree);SEARCH * _search = new SEARCH;if(1 == _search->binarySearch1(arr,size,value)) {cout<<value<<" in arrary!"<<endl;}if(1 == _search->binarySearch2(arr,0,size-1,value)) {cout<<value<<" in arrary!"<<endl;}if(1 == _binarytree->BSTsearch(_tree,value)) {cout<<value<<" in arrary!"<<endl;}else {cout<<value<<" not in arrary!"<<endl;}    cout<<_binarytree->BSTsearch2(_tree,value)<<endl;system("pause");return 1;<p>}</p><p></p><p></p><p>参考：http://songlee24.github.io/2015/01/13/binary-search-tree/参考：http://songlee24.github.io/2015/01/13/binary-search-tree/</p>