AVL树前传

实现插入和记录平衡因子，不调整。

难点在尾递归，可能修改节点平衡因子

#include<iostream>
using namespace std;
template <class T> class AvlTree;
template <class T>
class AvlNode
{ 
   T data;  //关键码
	AvlNode *leftChild;
	AvlNode *rightChild;
	int balance;//平衡因子
 public:
	AvlNode():leftChild(NULL),rightChild(NULL),balance(0){};
	AvlNode(const T& e,AvlNode<T> *lt=NULL):
	    data(e),leftChild(lt),rightChild(lt),balance(0){};//默认缺省参数值
	
	int getBalance() const	{ return balance;}
	AvlNode<T>* getLeftChild() const{return leftChild;}
	AvlNode<T>* getrightChild() const{return rightChild;}
	T getData() const{return data;}
	bool Insert(T x);
	bool Insert(AvlNode<T> *&rt,T x,bool taller);
	
	friend class AvlTree<T>;
};
template <class T>
class AvlTree
{ AvlNode<T> *root;
	bool Insert(AvlNode<T> *& rt,T x,bool &taller);
	bool Remove(AvlNode<T> * &rt,T x ,bool &shorter);
	
	void RotateLeft(AvlNode<T> * &node);
	void RotateRight(AvlNode<T> *&node);
	void RightBalanceAfterInsert(AvlNode<T> * &sRoot,bool &taller);
	void LeftBalanceAfterDeltete(AvlNode<T> *&sRoot,bool &shorter);
	public:
		AvlTree():root(NULL)  {}
		AvlNode<T>* getRoot() const
	    	{return root;}
		bool Insert(T x)
			{ bool taller=false;
			   return Insert(root,x,taller);
			}
		bool Remove(T x)
			{ bool shorter=false;
				return Remove(root,x,shorter);
			}
		
		void DisplayTree(AvlNode<T> *t,int layer) const;
};
//关于 Insert，如果在本节点插入后，由平衡状态0变成+1或-1,
// 将对上一级的平衡产生影响，对应是+1或-1.
// 另一种情况是本级插入后由不平衡状态+1、-1变成平衡0，
//对上一级的平衡状态不产生影响。
template<typename T>
void AvlTree<T>::RotateLeft(AvlNode<T> * & node)
{ //这个左旋好复杂？？
	//原来的node节点的地址被上一级指向，不能更换，只能替换数据
	if((node==NULL)||(node->rightChild==NULL)) return ;
		AvlNode<T> * tmpNode=new AvlNode<T>(node->data);
		if(tmpNode==NULL) return;
		
		tmpNode->lefChild=node->leftChild;//新增的节点将替代node向Left下沉
		node->leftChild=tmpNode;
		tmpNode->rightChild=node->rightChild->leftChild;
		
		AvlNode<T> *toDelete=node->rightChild;
		node->data=toDelete->data;//node节点将被原来右子节点替代
		node->rightChild=toDelete->rightChild;
		
		delete toDelete;//删除原来的右子结点
}
template<typename T>
void AvlTree<T>::RotateRight(AvlNode<T> *& node)
{  if((node==NULL) || (node->leftChild==NULL)) return;
	AvlNode<T> *tmpNode=new AvlNode<T>(node->data);
	if( tmpNode==NULL) return;
	//新节点将替代node向Right下沉
	tmpNode->rightChild=node->rightChild;
	node->rightChild=tmpNode;
	tmpNode->leftChild=node->leftChild->rightChild;
	//原来的Node Left子节点转移（上升）到Node
	AvlNode<T> *toDelete=node->leftChild;
	node->data=toDelete->data;
	node->leftChild=toDelete->leftChild;
	
}

template<typename T>
bool  AvlTree<T>:: Insert(AvlNode<T> *& rt,T x,bool &taller)
{//递归插入，成功则返回True，若插入使树长高，taller为true.
     	bool success=false;
	if( rt==NULL ) //边界条件，插入节点
    { rt=new AvlNode<T>(x);
		taller=true;
		return true;
	}
	else
	{ if(x<=rt->data)
		{  if( success=Insert(rt->leftChild,x,taller) )
			{/* switch(rt->balance)//插入左边成功
				{case 1: 
					if(taller) {rt->balance=0;taller=false;}
					break;
				case 0:
					if(taller) rt->balance=-1;
					break;
				case -1:
					if(taller) rt->balance=-2;//此处要调整
					 break;  
                }*/
				if(taller) rt->balance--;
			if(rt->balance>=0) taller=false;
			}
		}
		
		else if(success=Insert(rt->rightChild,x,taller))
			     { /*   switch(rt->balance)//右插成功
						{  case 1:
							if(taller) rt->balance=2;//此处要调整
							break;
						  case 0:
							 if(taller) rt->balance=1;
					         break;
				          case -1:
							  if(taller) {rt->balance=0; taller=false;}
							  break;
						} */
				 if(taller)  rt->balance++;
					 if(rt->balance<=0)taller=false;
				}  
								     
	}
	return success;
	
}

template<typename T>
void AvlTree<T>::DisplayTree(AvlNode<T> *t,int layer) const
//深度优先，输出信息。
{  cout<<endl;
	if(t==NULL) return;
	cout<<"level---"<<layer<<endl;
	cout<<"       data:"<<t->data<<"     balance:"<<t->balance<<endl;
	DisplayTree(t->leftChild,layer+1);
	DisplayTree(t->rightChild,layer+1);
}
int main()
{  
	AvlTree<int> a;
	for(int i=1;i<=10;i++)
    {	int b;
		cin>>b;
		a.Insert(b);
	}
	AvlNode<int>* rt;
	rt=a.getRoot();
	a.DisplayTree(rt,1);
	return 0;
}