二叉搜索树(BST树)的简单实现
#include <stdlib.h>
template<typename T>
class CBinSTree;
template <typename T>
class CTreeNode
{//树节点类
public:
CTreeNode(const T& item,CTreeNode<T>* lptr = NULL,CTreeNode<T>* rptr = NULL):data(item),left(lptr),right(rptr)
{
}
CTreeNode<T>* Left(void)
{
return left;
}
CTreeNode<T>* Right(void)
{
return right;
}
friend class CBinSTree<T>;
public:
T data;//数据
private:
CTreeNode<T>* left;//左子树
CTreeNode<T>* right;//右子树
};
template<typename T>
class CBinSTree
{//二叉搜索树类
public:
CBinSTree();
virtual ~CBinSTree();
CBinSTree(const CBinSTree<T>& tree);
CBinSTree<T>& operator = (const CBinSTree<T>& rhs);
CTreeNode<T>* FindNode(const T& item,CTreeNode<T>* &parent)const;//寻找节点
void PrintTree();//前序遍历树(非递归)
void ClearTree();//清空树
void Insert(const T& item);//插入数据
void Delete(const T& item);//删除数据
bool Contains(const T& item);//是否包含数据
CTreeNode<T>* FindMin()const;//找最小值
CTreeNode<T>* FindMax()const;//找最大值
protected:
//辅助函数区
CTreeNode<T>* GetTreeNode(const T& item,CTreeNode<T>* lptr=NULL,CTreeNode<T>* rptr=NULL);//分配树节点
void FreeTreeNode(CTreeNode<T>* p);//释放树节点
void DeleteTree(CTreeNode<T>* t);//删除树
CTreeNode<T>* CopyTree(CTreeNode<T>* t);//拷贝树
private:
CTreeNode<T> *root;//二叉搜索树树根
int size;//树节点个数
};
#include "stdafx.h"
#include "BinSTree.h"
#include <iostream>
#include <stack>
using namespace std;
//////////////////////////////////////////////////////////////////////
// Construction/Destruction
//////////////////////////////////////////////////////////////////////
template<typename T>
CBinSTree<T>::CBinSTree()
{
this->root = NULL;
this->size = 0;
}
template<typename T>
CBinSTree<T>::CBinSTree(const CBinSTree<T>& tree)
{
root = this->CopyTree(tree.root);
this->size = tree.size;
}
template<typename T>
CBinSTree<T>::~CBinSTree()
{
this->ClearTree();
}
template<typename T>
CBinSTree<T>& CBinSTree<T>::operator = (const CBinSTree<T>& rhs)
{
if(this==&rhs)
return *this;
this->ClearTree();
root = this->CopyTree(rhs.root);
size = rhs.size;
return *this;
}
template<typename T>
CTreeNode<T>* CBinSTree<T>::GetTreeNode(const T& item,CTreeNode<T>* lptr,CTreeNode<T>* rptr)
{
CTreeNode<T>* p;
p = new CTreeNode<T>(item,lptr,rptr);
if(p==NULL)
{
cerr<<"分配内存失败!"<<endl;
exit(1);
}
return p;
}
template<typename T>
CTreeNode<T>* CBinSTree<T>::FindMin()const
{
CTreeNode<T> *t = root;
while(t->left!=NULL)
{
t = t->left;
}
return t;
}
template<typename T>
CTreeNode<T>* CBinSTree<T>::FindMax()const
{
CTreeNode<T> *t = root;
while(t->right!=NULL)
{
t = t->right;
}
return t;
}
template<typename T>
bool CBinSTree<T>::Contains(const T& item)
{
CTreeNode<T> *p;
return (this->FindNode(item,p)!=NULL);
}
template<typename T>
CTreeNode<T>* CBinSTree<T>::CopyTree(CTreeNode<T>* t)
{
CTreeNode<T> *newnode,*newlptr,*newrptr;
if(t==NULL)
return NULL;
if(t->Left()!=NULL)
newlptr = CopyTree(t->Left());
else
newlptr = NULL;
if(t->Right()!=NULL)
newrptr = CopyTree(t->Right());
else
newrptr = NULL;
newnode = GetTreeNode(t->data,newlptr,newrptr);
return newnode;
}
template<typename T>
void CBinSTree<T>::FreeTreeNode(CTreeNode<T>* p)
{
delete p;
p = NULL;
}
template<typename T>
void CBinSTree<T>::DeleteTree(CTreeNode<T>* t)
{
if(t!=NULL)
{
DeleteTree(t->Left());
DeleteTree(t->Right());
FreeTreeNode(t);
}
}
template<typename T>
void CBinSTree<T>::ClearTree()
{
DeleteTree(root);
root = NULL;
}
template<typename T>
CTreeNode<T>* CBinSTree<T>::FindNode(const T& item,CTreeNode<T>* &parent)const
{
CTreeNode<T> *t = root;
parent = NULL;
while(t!=NULL)
{
if(item==t->data)
break;
else
{
parent = t;
if(item<t->data)
t = t->Left();
else
t = t->Right();
}
}
return t;
}
template<typename T>
void CBinSTree<T>::Insert(const T& item)
{
CTreeNode<T>* t = root,*parent = NULL,*newnode;
while(t!=NULL)
{
parent = t;
if(item<t->data)
t = t->Left();
else
t = t->Right();
}
newnode = this->GetTreeNode(item);
if(parent==NULL)
root = newnode;
else if(item<parent->data)
parent->left = newnode;
else
parent->right = newnode;
size++;
}
template<typename T>
void CBinSTree<T>::Delete(const T& item)
{
CTreeNode<T> *pDNode,*pRNode,*pParNode;
if((pDNode = this->FindNode(item,pParNode))==NULL)
return;
if(pDNode->left==NULL)
pRNode = pDNode->right;
else if(pDNode->right==NULL)
pRNode = pDNode->left;
else
{
CTreeNode<T> *pParOfRNode = pDNode;
pRNode = pDNode->left;
while(pRNode->right!=NULL)
{
pParOfRNode = pRNode;
pRNode = pRNode->right;
}
if(pParOfRNode==pDNode)
{
pRNode->right = pDNode->right;
}
else
{
pParOfRNode->right = pRNode->left;
pRNode->left = pDNode->left;
pRNode->right = pDNode->right;
}
}
if(pParNode==NULL)
root = pRNode;
else if(pDNode->data<pParNode->data)
pParNode->left = pRNode;
else
pParNode->right = pRNode;
this->FreeTreeNode(pDNode);
this->size--;
}
template<typename T>
void CBinSTree<T>::PrintTree()
{
stack<CTreeNode<T>* > s;
CTreeNode<T>* p = root;
while (p!=NULL || !s.empty())
{
while (p!=NULL) //遍历左子树
{
cout<<p->data<<endl;
s.push(p);
p=p->Left();
}//endwhile
if (!s.empty())
{
p=s.top();
s.pop();
p=p->Right(); //通过下一次循环实现右子树遍历
}//endif
}
}
// test.cpp : Defines the entry point for the console application.
//
#include "stdafx.h"
#include "BinSTree.cpp"
#include <iostream>
using namespace std;
CBinSTree<int>* MakeSampleTree()
{//示例BST树
CBinSTree<int> *tree1 = new CBinSTree<int>();
int a = 5;
tree1->Insert(a);
tree1->Insert(30);
tree1->Insert(65);
tree1->Insert(25);
tree1->Insert(35);
tree1->Insert(50);
tree1->Insert(10);
tree1->Insert(28);
tree1->Insert(26);
tree1->Insert(33);
return tree1;
}
int main(int argc, char* argv[])
{
CBinSTree<int> *tree1 = MakeSampleTree();
tree1->PrintTree();
std::cout<<"删除节点30:"<<endl;
tree1->Delete(30);
tree1->PrintTree();
cout<<tree1->Contains(40)<<endl;
CTreeNode<int> *p = tree1->FindMin();
cout<<p->data<<endl;
return 0;
}
template<typename T>class CBinSTree;template <typename T>class CTreeNode{//树节点类
public: CTreeNode(const T& item,CTreeNode<T>* lptr = NULL,CTreeNode<T>* rptr = NULL):data(item),left(lptr),right(rptr) {
} CTreeNode<T>* Left(void) { return left; } CTreeNode<T>* Right(void) { return right; } friend class CBinSTree<T>;public: T data;//数据private: CTreeNode<T>* left;//左子树 CTreeNode<T>* right;//右子树};template<typename T>class CBinSTree {//二叉搜索树类public: CBinSTree(); virtual ~CBinSTree(); CBinSTree(const CBinSTree<T>& tree); CBinSTree<T>& operator = (const CBinSTree<T>& rhs); CTreeNode<T>* FindNode(const T& item,CTreeNode<T>* &parent)const;//寻找节点 void PrintTree();//前序遍历树(非递归) void ClearTree();//清空树 void Insert(const T& item);//插入数据 void Delete(const T& item);//删除数据 bool Contains(const T& item);//是否包含数据 CTreeNode<T>* FindMin()const;//找最小值 CTreeNode<T>* FindMax()const;//找最大值protected: //辅助函数区 CTreeNode<T>* GetTreeNode(const T& item,CTreeNode<T>* lptr=NULL,CTreeNode<T>* rptr=NULL);//分配树节点 void FreeTreeNode(CTreeNode<T>* p);//释放树节点 void DeleteTree(CTreeNode<T>* t);//删除树 CTreeNode<T>* CopyTree(CTreeNode<T>* t);//拷贝树private: CTreeNode<T> *root;//二叉搜索树树根 int size;//树节点个数};
#include "stdafx.h"#include "BinSTree.h"#include <iostream>#include <stack>using namespace std;//////////////////////////////////////////////////////////////////////// Construction/Destruction//////////////////////////////////////////////////////////////////////template<typename T>CBinSTree<T>::CBinSTree(){ this->root = NULL; this->size = 0;}template<typename T>CBinSTree<T>::CBinSTree(const CBinSTree<T>& tree){ root = this->CopyTree(tree.root); this->size = tree.size;}template<typename T>CBinSTree<T>::~CBinSTree(){ this->ClearTree();}template<typename T>CBinSTree<T>& CBinSTree<T>::operator = (const CBinSTree<T>& rhs){ if(this==&rhs) return *this; this->ClearTree(); root = this->CopyTree(rhs.root); size = rhs.size; return *this;}template<typename T>CTreeNode<T>* CBinSTree<T>::GetTreeNode(const T& item,CTreeNode<T>* lptr,CTreeNode<T>* rptr){ CTreeNode<T>* p; p = new CTreeNode<T>(item,lptr,rptr); if(p==NULL) { cerr<<"分配内存失败!"<<endl; exit(1); } return p;}template<typename T>CTreeNode<T>* CBinSTree<T>::FindMin()const{ CTreeNode<T> *t = root; while(t->left!=NULL) { t = t->left; } return t;}template<typename T>CTreeNode<T>* CBinSTree<T>::FindMax()const{ CTreeNode<T> *t = root; while(t->right!=NULL) { t = t->right; } return t;}template<typename T>bool CBinSTree<T>::Contains(const T& item){ CTreeNode<T> *p; return (this->FindNode(item,p)!=NULL);}template<typename T>CTreeNode<T>* CBinSTree<T>::CopyTree(CTreeNode<T>* t){ CTreeNode<T> *newnode,*newlptr,*newrptr; if(t==NULL) return NULL; if(t->Left()!=NULL) newlptr = CopyTree(t->Left()); else newlptr = NULL; if(t->Right()!=NULL) newrptr = CopyTree(t->Right()); else newrptr = NULL; newnode = GetTreeNode(t->data,newlptr,newrptr); return newnode;}template<typename T>void CBinSTree<T>::FreeTreeNode(CTreeNode<T>* p){ delete p; p = NULL;}template<typename T>void CBinSTree<T>::DeleteTree(CTreeNode<T>* t){ if(t!=NULL) { DeleteTree(t->Left()); DeleteTree(t->Right()); FreeTreeNode(t); }}template<typename T>void CBinSTree<T>::ClearTree(){ DeleteTree(root); root = NULL;}template<typename T>CTreeNode<T>* CBinSTree<T>::FindNode(const T& item,CTreeNode<T>* &parent)const{ CTreeNode<T> *t = root; parent = NULL; while(t!=NULL) { if(item==t->data) break; else { parent = t; if(item<t->data) t = t->Left(); else t = t->Right(); } } return t;}template<typename T>void CBinSTree<T>::Insert(const T& item){ CTreeNode<T>* t = root,*parent = NULL,*newnode; while(t!=NULL) { parent = t; if(item<t->data) t = t->Left(); else t = t->Right(); } newnode = this->GetTreeNode(item); if(parent==NULL) root = newnode; else if(item<parent->data) parent->left = newnode; else parent->right = newnode; size++;}template<typename T>void CBinSTree<T>::Delete(const T& item){ CTreeNode<T> *pDNode,*pRNode,*pParNode; if((pDNode = this->FindNode(item,pParNode))==NULL) return; if(pDNode->left==NULL) pRNode = pDNode->right; else if(pDNode->right==NULL) pRNode = pDNode->left; else { CTreeNode<T> *pParOfRNode = pDNode; pRNode = pDNode->left; while(pRNode->right!=NULL) { pParOfRNode = pRNode; pRNode = pRNode->right; } if(pParOfRNode==pDNode) { pRNode->right = pDNode->right; } else { pParOfRNode->right = pRNode->left; pRNode->left = pDNode->left; pRNode->right = pDNode->right; } } if(pParNode==NULL) root = pRNode; else if(pDNode->data<pParNode->data) pParNode->left = pRNode; else pParNode->right = pRNode; this->FreeTreeNode(pDNode); this->size--;}template<typename T>void CBinSTree<T>::PrintTree(){ stack<CTreeNode<T>* > s; CTreeNode<T>* p = root; while (p!=NULL || !s.empty()) { while (p!=NULL) //遍历左子树 { cout<<p->data<<endl; s.push(p); p=p->Left(); }//endwhile if (!s.empty()) { p=s.top(); s.pop(); p=p->Right(); //通过下一次循环实现右子树遍历 }//endif }}
// test.cpp : Defines the entry point for the console application.//#include "stdafx.h"#include "BinSTree.cpp"#include <iostream>using namespace std;CBinSTree<int>* MakeSampleTree(){//示例BST树 CBinSTree<int> *tree1 = new CBinSTree<int>(); int a = 5; tree1->Insert(a); tree1->Insert(30); tree1->Insert(65); tree1->Insert(25); tree1->Insert(35); tree1->Insert(50); tree1->Insert(10); tree1->Insert(28); tree1->Insert(26); tree1->Insert(33); return tree1;}int main(int argc, char* argv[]){ CBinSTree<int> *tree1 = MakeSampleTree(); tree1->PrintTree(); std::cout<<"删除节点30:"<<endl; tree1->Delete(30); tree1->PrintTree(); cout<<tree1->Contains(40)<<endl; CTreeNode<int> *p = tree1->FindMin(); cout<<p->data<<endl; return 0;}