C++模板实现二叉树

       二叉树是每个节点最多有两个子树的树结构。通常子树被称作“左子树”（left subtree）和“右子树”（right subtree）。二叉树常被用于实现二叉查找树和二叉堆。
      二叉树的每个结点至多只有二棵子树(不存在度大于2的结点)，二叉树的子树有左右之分，次序不能颠倒。二叉树的第i层至多有2^{i-1}个结点；深度为k的二叉树至多有2^k-1个结点；对任何一棵二叉树T，如果其终端结点数为n_0，度为2的结点数为n_2，则n_0=n_2+1。

      一棵深度为k，且有2^k-1个节点称之为满二叉树；深度为k，有n个节点的二叉树，当且仅当其每一个节点都与深度为k的满二叉树中，序号为1至n的节点对应时，称之为完全二叉树。

      下面我们使用模板实现一颗简单二叉树：

BinTreeNode.h

template<typename Type> class BinaryTree;template<typename Type> class BinTreeNode{public:friend class BinaryTree<Type>;BinTreeNode():m_pleft(NULL),m_pright(NULL){}BinTreeNode(Type item,BinTreeNode<Type> *left=NULL,BinTreeNode<Type> *right=NULL):m_data(item),m_pleft(left),m_pright(right){}Type GetData() const;//get thd dataBinTreeNode<Type> *GetLeft() const;//get the left nodeBinTreeNode<Type> *GetRight() const;//get the right nodevoid SetData(const Type data);//change the datavoid SetLeft(const BinTreeNode<Type> *left);//change thd left nodevoid SetRight(const BinTreeNode<Type> *right);//change the right nodevoid InOrder();//inorder the tree with the root of the nodevoid PreOrder();//perorder the tree with the root of the nodevoid PostOrder();//postoder the tree with the root of the nodeint Size();//get sizeint Height();//get heightBinTreeNode<Type> *Copy(const BinTreeNode<Type> *copy);//copy the nodevoid Destroy(){//destroy the tree with the root of the nodeif(this!=NULL){this->m_pleft->Destroy();this->m_pright->Destroy();delete this;}}friend bool equal<Type>(const BinTreeNode<Type> *s,const BinTreeNode<Type> *t);//is equal?private:BinTreeNode<Type> *m_pleft,*m_pright;Type m_data;};template<typename Type> Type BinTreeNode<Type>::GetData() const{return this!=NULL?m_data:-1;}template<typename Type> BinTreeNode<Type>* BinTreeNode<Type>::GetLeft() const{return this!=NULL?m_pleft:NULL;}template<typename Type> BinTreeNode<Type>* BinTreeNode<Type>::GetRight() const{return this!=NULL?m_pright:NULL;}template<typename Type> void BinTreeNode<Type>::SetData(const Type data){if(this!=NULL){m_data=data;}}template<typename Type> void BinTreeNode<Type>::SetLeft(const BinTreeNode<Type> *left){if(this!=NULL){m_pleft=left;}}template<typename Type> void BinTreeNode<Type>::SetRight(const BinTreeNode<Type> *right){if(this!=NULL){m_pright=right;}}template<typename Type> BinTreeNode<Type>* BinTreeNode<Type>::Copy(const BinTreeNode<Type> *copy){if(copy==NULL){return NULL;}BinTreeNode<Type> *temp=new BinTreeNode<Type>(copy->m_data);temp->m_pleft=Copy(copy->m_pleft);temp->m_pright=Copy(copy->m_pright);return temp;}template<typename Type> bool equal(const BinTreeNode<Type> *s,const BinTreeNode<Type> *t){if(s==NULL&&t==NULL){return 1;}if(s&&t&&s->m_data==t->m_data&&equal(s->m_pleft,t->m_pleft)&&equal(s->m_pright,t->m_pright)){return 1;}return 0;}template<typename Type> void BinTreeNode<Type>::InOrder(){if(this!=NULL){this->m_pleft->InOrder();cout<<"--->"<<this->m_data;this->m_pright->InOrder();}}template<typename Type> void BinTreeNode<Type>::PreOrder(){if(this!=NULL){cout<<"--->"<<this->m_data;this->m_pleft->PreOrder();this->m_pright->PreOrder();}}template<typename Type> void BinTreeNode<Type>::PostOrder(){if(this!=NULL){this->m_pleft->PostOrder();this->m_pright->PostOrder();cout<<"--->"<<this->m_data;}}template<typename Type> int BinTreeNode<Type>::Size(){if(this==NULL){return 0;}return 1+this->m_pleft->Size()+this->m_pright->Size();}template<typename Type> int BinTreeNode<Type>::Height(){if(this==NULL){return -1;}int lheight,rheight;lheight=this->m_pleft->Height();rheight=this->m_pright->Height();return 1+(lheight>rheight?lheight:rheight);}

BinaryTree.h

#include "BinTreeNode.h"template<typename Type> class BinaryTree{public:BinaryTree():m_proot(NULL){}BinaryTree(const Type stop):m_stop(stop),m_proot(NULL){}BinaryTree(BinaryTree<Type>& copy);virtual ~BinaryTree(){m_proot->Destroy();}virtual bool IsEmpty(){//is empty?return m_proot==NULL;}virtual BinTreeNode<Type> *GetLeft(BinTreeNode<Type> *current);//get the left nodevirtual BinTreeNode<Type> *GetRight(BinTreeNode<Type> *current);//get the right nodevirtual BinTreeNode<Type> *GetParent(BinTreeNode<Type> *current);//ghe thd parentconst BinTreeNode<Type> *GetRoot() const;//get rootvirtual bool Insert(const Type item);//insert a new nodevirtual BinTreeNode<Type> *Find(const Type item) const;//find thd node with the datavoid InOrder();void PreOrder();void PostOrder();int Size();//get sizeint Height();//get heightBinaryTree<Type>& operator=(const BinaryTree<Type> copy);//evaluate nodefriend bool operator== <Type>(const BinaryTree<Type> s,const BinaryTree<Type> t);//is equal?friend ostream& operator<< <Type>(ostream& ,BinaryTree<Type>&);//output the datafriend istream& operator>> <Type>(istream& ,BinaryTree<Type>&);//input the dataprivate:Type m_stop;//just using for input the data;BinTreeNode<Type> *m_proot;//find the parent of current in the tree with the root of startBinTreeNode<Type> *GetParent(BinTreeNode<Type> *start,BinTreeNode<Type> *current);void Print(BinTreeNode<Type> *start,int n=0);//print the tree with the root of start};template<typename Type> BinaryTree<Type>::BinaryTree(BinaryTree<Type>& copy){if(copy.m_proot){this->m_stop=copy.m_stop;}m_proot=m_proot->Copy(copy.m_proot);}template<typename Type> BinTreeNode<Type>* BinaryTree<Type>::GetLeft(BinTreeNode<Type> *current){return m_proot&¤t?current->m_pleft:NULL;}template<typename Type> BinTreeNode<Type>* BinaryTree<Type>::GetRight(BinTreeNode<Type> *current){return m_proot&¤t?current->m_pright:NULL;}template<typename Type> const BinTreeNode<Type>* BinaryTree<Type>::GetRoot() const{return m_proot;}template<typename Type> BinTreeNode<Type>* BinaryTree<Type>::GetParent(BinTreeNode<Type> *start, BinTreeNode<Type> *current){if(start==NULL||current==NULL){return NULL;}if(start->m_pleft==current||start->m_pright==current){return start;}BinTreeNode<Type> *pmove;if((pmove=GetParent(start->m_pleft,current))!=NULL){//find the parent in the left subtreereturn pmove;}else{return GetParent(start->m_pright,current);//find the parent in the right subtree}}template<typename Type> BinTreeNode<Type>* BinaryTree<Type>::GetParent(BinTreeNode<Type> *current){return m_proot==NULL||current==m_proot?NULL:GetParent(m_proot,current);}template<typename Type> bool BinaryTree<Type>::Insert(const Type item){BinTreeNode<Type> *pstart=m_proot,*newnode=new BinTreeNode<Type>(item);if(m_proot==NULL){m_proot=newnode;return 1;}while(1){if(item==pstart->m_data){cout<<"The item "<<item<<" is exist!"<<endl;return 0;}if(item<pstart->m_data){if(pstart->m_pleft==NULL){pstart->m_pleft=newnode;return 1;}pstart=pstart->m_pleft;//if less than the node then insert to the left subtree}else{if(pstart->m_pright==NULL){pstart->m_pright=newnode;return 1;}pstart=pstart->m_pright;//if more than the node then insert to the right subtree}}}template<typename Type> BinTreeNode<Type>* BinaryTree<Type>::Find(const Type item) const{BinTreeNode<Type> *pstart=m_proot;while(pstart){if(item==pstart->m_data){return pstart;}if(item<pstart->m_data){pstart=pstart->m_pleft;//if less than the node then find in the left subtree}else{pstart=pstart->m_pright;//if more than the node then find in the right subtree}}return NULL;}template<typename Type> void BinaryTree<Type>::Print(BinTreeNode<Type> *start, int n){if(start==NULL){for(int i=0;i<n;i++){cout<<"     ";}cout<<"NULL"<<endl;return;}Print(start->m_pright,n+1);//print the right subtreefor(int i=0;i<n;i++){//print blanks with the height of the nodecout<<"     ";}if(n>=0){cout<<start->m_data<<"--->"<<endl;//print the node}Print(start->m_pleft,n+1);//print the left subtree}template<typename Type> BinaryTree<Type>& BinaryTree<Type>::operator=(const BinaryTree<Type> copy){if(copy.m_proot){this->m_stop=copy.m_stop;}m_proot=m_proot->Copy(copy.m_proot);    return *this;}template<typename Type> ostream& operator<<(ostream& os,BinaryTree<Type>& out){out.Print(out.m_proot);return os;}template<typename Type> istream& operator>>(istream& is,BinaryTree<Type>& in){Type item;cout<<"initialize the tree:"<<endl<<"Input data(end with "<<in.m_stop<<"!):";is>>item;while(item!=in.m_stop){//m_stop is the end of inputin.Insert(item);is>>item;}return is;}template<typename Type> bool operator==(const BinaryTree<Type> s,const BinaryTree<Type> t){return equal(s.m_proot,t.m_proot);}template<typename Type> void BinaryTree<Type>::InOrder(){this->m_proot->InOrder();}template<typename Type> void BinaryTree<Type>::PreOrder(){this->m_proot->PreOrder();}template<typename Type> void BinaryTree<Type>::PostOrder(){this->m_proot->PostOrder();}template<typename Type> int BinaryTree<Type>::Size(){return this->m_proot->Size();}template<typename Type> int BinaryTree<Type>::Height(){return this->m_proot->Height();}

Main.cpp

#include <iostream>using namespace std;#include "BinaryTree.h"int main(){BinaryTree<int> tree(-1);//int init[10]={3,6,0,2,8,4,9,1,5,7};int init[30]={17,6,22,29,14,0,21,13,27,18,2,28,8,26,3,12,20,4,9,23,15,1,11,5,19,24,16,7,10,25};for(int i=0;i<30;i++){tree.Insert(init[i]);}//cin>>tree;cout<<tree<<endl;cout<<tree.GetParent(tree.Find(20))->GetData()<<endl;cout<<tree.Find(15)->GetRight()->GetData()<<endl;cout<<"size="<<tree.Size()<<endl;cout<<"height="<<tree.Height()<<endl;tree.InOrder();cout<<endl<<endl;tree.PreOrder();cout<<endl<<endl;tree.PostOrder();cout<<endl<<endl;BinaryTree<int> tree2=tree;cout<<tree2<<endl;cout<<tree2.GetParent(tree2.Find(20))->GetData()<<endl;cout<<tree2.Find(15)->GetRight()->GetData()<<endl;cout<<(tree==tree2)<<endl;return 0;}