c++模板类递归实现二叉搜索树及其基本操作

二叉树搜索概念：http://baike.baidu.com/link?url=RK7ax6iDk2wiEzUxjKBfyOTcYKLgaDuAcyih0a6qjAewfYeK9PoIhWzjdSZl7ylwhkOdx-6ZCFhGuF0aIG1phG-X2sc9QP8KFWavC95c-ocAL9cs71wZhCOHVHsdRs3Ugr1Z85Iycv1zosbpZiRHea

.H:

//尾递归可以用一个while循环很轻易解决！template<class T>class BinarySearchTree{public:BinarySearchTree( ):_root(NULL){}~BinarySearchTree( ){MakeEmpty( );}const T& FindMin( ) const{Node* ret = _FindMin( _root );if ( NULL == ret )//这样写可以吗？调用T类型默认构造函数{return T( );}else{return ret->_data;}}const T& FindMax( ) const{Node* ret = _FindMax( _root );if ( NULL == ret )//这样写可以吗？调用T类型默认构造函数{return T( );}else{return ret->_data;}}bool IsEmpty( ) const{return (NULL == _root) ? true : false;}bool Contains( const T& x ) const{return _Contains( x, _root );}void PrintTree( )const//采用中序遍历打印树{_PrintTree( _root );}void MakeEmpty( ){_MakeEmpty( _root );}void Insert( const T& x ){_Insert( x, _root );}void Remove( const T& x ){_Remove( x, _root );}const BinarySearchTree& operator=( const BinarySearchTree& rhs ){if ( this != &rhs ){MakeEmpty( );_root = Clone( rhs._root );}return *this;}private:struct Node{T _data;Node* _leftChild;Node* _rightChild;Node( const T& x, Node* leftChild, Node* rightChild ):_data(x),_leftChild(leftChild),_rightChild(rightChild){}};//别忘了;Node* _root;void _Insert( const T& x, Node*& root )//想， 它是怎么链起来的， 因为下一个root是 它父亲的左或右孩子的引用， 如果传引用， new后，它的父亲的左右孩子就被链起来了。  否则的话， 临时变量，   孩子被new值赋予后不会影响到调用它的函数的值(父亲的左or右孩子的值){if ( NULL == root ){root = new Node( x, NULL, NULL );}else if ( x < root->_data ){_Insert( x, root->_leftChild );}else if ( x > root->_data ){_Insert( x, root->_rightChild );}else{;//相等，目前什么都不做，当然，也可以更新值什么的.}}void _Remove( const T& x, Node*& root )//注意此时指针为引用{if ( NULL == root ){return;}else if ( x < root->_data ){_Remove( x, root->_leftChild );}else if ( x > root->_data ){_Remove( x, root->_rightChild );}else if ( (NULL != root->_leftChild) && (NULL != root->_rightChild) )//两个孩子为一种情况{root->_data = _FindMin( root->_rightChild )->_data;_Remove( root->_data, root->_rightChild );}else{Node* oldNode = root;root = (NULL == root->_leftChild ? root->_rightChild : root->_leftChild);delete oldNode;}//一个孩子，或叶子节点  归为一种情况}Node* _FindMin( Node* root ) const{if ( NULL == root ){return NULL;}if ( NULL == root->_leftChild ){return root;}return _FindMin( root->_leftChild );}Node* _FindMax( Node* root ) const{if ( NULL != root ){while ( NULL != root->_rightChild ){root = root->_rightChild;}}return root;}bool _Contains( const T& x, Node* root ) const{if ( NULL == root ){return false;}else if ( x < root->_data ){return _Contains( x, root->_leftChild );}else if ( x > root->_data ){return _Contains( x, root->_rightChild );}else{return true;}//利用while循环代替尾递归(递归语句在结尾)//while ( NULL != root )//{//if ( x < root->_data )//{//root = root->_leftChild;//}//else if ( x > root->_data )//{//root = root->_rightChild;//}//else//{//return true;//}//}//return false;//只要跳出循环，肯定没找到}void _MakeEmpty( Node*& root ) const{if ( NULL == root ){;}else{_MakeEmpty( root->_leftChild );//后序删除_MakeEmpty( root->_rightChild );delete root;}root = NULL;//别忘了置NULL}void _PrintTree( Node* root ) const//中序{if ( NULL == root ){return;}_PrintTree( root->_leftChild );cout << root->_data << " ";_PrintTree( root->_rightChild );}Node* Clone( Node* root ) const{if ( NULL == root ){return NULL;}else{return ( new Node(root->_data, Clone(root->_leftChild), Clone(root->_rightChild)) );}}};

.cpp:

#include <iostream>#include <windows.h>using namespace std;#include "BinarySearchTree.h"void test( );int main( ){test( );system( "pause" );return 0;}void test( ){BinarySearchTree<int> t1;int a[] = { 5, 3, 4, 1, 7, 8, 2, 6, 0, 9 };for ( size_t i = 0; i < (sizeof(a) / sizeof(a[0])); ++i ){t1.Insert( a[i] );}t1.PrintTree( );cout << endl;cout << t1.FindMin( ) << " " << t1.FindMax( ) << " " << endl;/*t1.MakeEmpty( );cout << t1.FindMin( ) << " " << t1.FindMax( ) << " " << endl;*/cout << t1.IsEmpty( ) << endl;cout << t1.Contains( 77 ) << endl;cout << t1.Contains( 7 ) << endl;t1.Remove( 9 );t1.PrintTree( );cout << endl;t1.Remove( 5 );t1.PrintTree( );cout << endl;t1.Remove( 0 );t1.Remove( 7 );t1.Remove( 6 );t1.Remove( 4 );t1.Remove( 3 );t1.Remove( 2 );t1.Remove( 1 );t1.Remove( 8 );t1.PrintTree( );}