AVL樹

//修改自《算法之美》，更易理解（自認爲）
#include<iostream>
using namespace std;
template <class T> class AvlTree;
template <class T>
class AvlNode
{ 
   T data;  //關鍵碼
	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){};//默認缺省參數值
	
	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;
			void DisplayTree2(AvlNode<T> *t,int layer) const;
};
//關於 Insert，如果在本節點插入後，由平衡狀態0變成+1或-1,
// 將對上一級的平衡產生影響，對應是+1或-1.
// 另一種情況是本級插入後由不平衡狀態+1、-1變成平衡0，
//對上一級的平衡狀態不產生影響。
template<typename T>
void AvlTree<T>::RotateLeft(AvlNode<T> * & node)
{ //這個左旋好複雜？？
	//原來的node節點的地址被上一級指向，不能更換，只能替換數據
	if((node==NULL)||(node->rightChild==NULL)) return ;
		AvlNode<T> * tmpNode=new AvlNode<T>(node->data);
		if(tmpNode==NULL) return;
		
		tmpNode->leftChild=node->leftChild;//新增的節點將替代node向Left下沉
		node->leftChild=tmpNode;
		tmpNode->rightChild=node->rightChild->leftChild;
		
		AvlNode<T> *toDelete=node->rightChild;
		node->data=toDelete->data;//node節點將被原來右子節點替代
		node->rightChild=toDelete->rightChild;
		
		delete toDelete;//刪除原來的右子結點
}
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;
	//新節點將替代node向Right下沉
	tmpNode->rightChild=node->rightChild;
	node->rightChild=tmpNode;
	tmpNode->leftChild=node->leftChild->rightChild;
	//原來的Node Left子節點轉移（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)
{//遞歸插入，成功則返回True，若插入使樹長高，taller爲true.
     	bool success=false;
	if( rt==NULL ) //邊界條件，插入節點
    { rt=new AvlNode<T>(x);
		taller=true;
		return true;
	}
	else
	{ if(x<=rt->data)
		{  if( success=Insert(rt->leftChild,x,taller) )
			{ switch(rt->balance)//插入左邊成功
				{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;//此處要調整
					else break;
					if(rt->leftChild->balance==-1) 
					{
					   RotateRight(rt);
					   rt->balance=0;
					   rt->rightChild->balance=0;
					}else{ RotateLeft(rt->leftChild);
						         RotateRight(rt);
						         if(rt->balance==-1)
								   { rt->leftChild->balance=0;
									  rt->rightChild->balance=1;
						           }
								  else{  rt->leftChild->balance=-1;
									          rt->rightChild->balance=0;
								         }
								  rt->balance=0;
								}
					taller=false;
					 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;//此處要調整
							else break;
							if(rt->rightChild->balance==1)
							{  RotateLeft(rt);
								rt->leftChild->balance=0;
								rt->balance=0;
							}
							else{ RotateRight(rt->rightChild);
								       RotateLeft(rt);
								       if(rt->balance==-1)
									   { rt->leftChild->balance=0;
										   rt->rightChild->balance=1;
										}
										else{ rt->leftChild->balance=-1;
											       rt->rightChild->balance=0;
											   }
									  rt->balance=0;
								   }
							taller=false;
							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
//深度優先，輸出信息。
{  if(t==NULL)  return;
    cout<<t->data<<"["<<t->balance<<"]  ";
	if(t->leftChild!=NULL) cout<<"left: "<<t->leftChild->data;
	if(t->rightChild!=NULL) cout<<"  right: "<<t->rightChild->data;
	cout<<"**"<<endl;
	DisplayTree(t->leftChild,layer+1);
	DisplayTree(t->rightChild,layer+1);
}
template<typename T>
void AvlTree<T>::DisplayTree2(AvlNode<T> *t,int layer) const
//深度優先，輸出信息。
{  if(t==NULL)  return;
	cout<<t->data<<"["<<t->balance<<"]";
    cout<<"(";
	DisplayTree(t->leftChild,layer+1);
	cout<<")";
	cout<<"(";
	DisplayTree(t->rightChild,layer+1);
	cout<<")";
	return;
}
int main()
{  
	AvlTree<int> a;
	for(int i=1;i<=15;i++)
    {	int b;
		cin>>b;
		a.Insert(b);
	}
	AvlNode<int>* rt;
	rt=a.getRoot();
	a.DisplayTree(rt,1);

	return 0;
}