AVLTree - 二叉平衡树的实现之二(C++)

      此AVLTree的实现 比上一篇的实现，从代码的观赏性和简洁性来看，更加棒，更加好看，不过效率上没有上一个实现快,初学者看这个实现更容易理解AVLTree两个关键性操作的实现

template<class E, class K>class AVLtree2{private: AVLNode<E,K>* root; void LeftSingleRotate(AVLNode<E,K>*& p ); //左单旋转 void LeftDoubleRotate(AVLNode<E,K>*& p ); //左双旋转 void RightSingleRotate(AVLNode<E,K>*& p ); //右单旋转 void RightDoubleRotate(AVLNode<E,K>*& p ); //右双旋转 void InOutput(const AVLNode<E,K> *p);void PostOutput(const AVLNode<E,K> *p);inline int Height(const AVLNode<E,K>* p) const;inline void Rotate_Help( AVLNode<E,K>*& p ); AVLtree2<E,K>& Insert_Help(AVLNode<E,K>*& p, const E& e ); AVLtree2<E,K>& Delete_Help(AVLNode<E,K>*& p, const K& k, E& e );public: AVLtree2(){ root = 0; } void Ascend() {InOutput(root); cout << endl;} void PostOut() {PostOutput(root); cout << endl;} AVLtree2<E,K>& Insert( const E& e ); AVLtree2<E,K>& Delete( const K& k, E& e );};//=================================// 7 5 // / ==> / /// 5 3 7// / // 3 //=================================//左单旋转实现template<class E, class K>void AVLtree2<E,K>::LeftSingleRotate(AVLNode<E,K>*& p ){AVLNode<E,K>* tmp = p->LeftChild; p->LeftChild = tmp->RightChild;p->height = max( Height(p->LeftChild), Height(p->RightChild) ) + 1; tmp->RightChild = p; p = tmp; p->height = max( Height(p->LeftChild), Height(p->RightChild) ) + 1;}//=================================// 7 8 // / ==> / /// 8 7 9// / // 9//=================================//右单旋转实现 template<class E, class K>void AVLtree2<E,K>::RightSingleRotate(AVLNode<E,K>*& p ){ AVLNode<E,K>* tmp = p->RightChild; p->RightChild = tmp->LeftChild; p->height = max( Height(p->LeftChild), Height(p->RightChild) ) + 1;tmp->LeftChild = p; p = tmp; p->height = max( Height(p->LeftChild), Height(p->RightChild) ) + 1;}//=================================// 4 4 3// / / / /// 2 ==> 3 ==> 2 4// / /// 3 2//=================================// 左双旋转实现template<class E, class K>void AVLtree2<E,K>::LeftDoubleRotate(AVLNode<E,K>*& p ){ RightSingleRotate(p->LeftChild ); LeftSingleRotate(p );}//=================================// 7 7 8// / / / /// 9 ==> 8 ==> 7 9// / /// 8 9//=================================// 右双旋转实现template<class E, class K>void AVLtree2<E,K>::RightDoubleRotate(AVLNode<E,K>*& p ){ LeftSingleRotate(p->RightChild ); RightSingleRotate(p );}template<class E, class K>inline int AVLtree2<E,K>::Height(const AVLNode<E,K>* p) const{ if (0 == p) return -1; return p->height;}template<class E, class K>AVLtree2<E,K>& AVLtree2<E,K>::Insert_Help(AVLNode<E,K>*& p, const E& e ){ if( p == 0 ){p = new AVLNode<E,K> (e);return *this; }if (e < p->data) Insert_Help(p->LeftChild, e ); else //e > p->data Insert_Help(p->RightChild, e ); // 调整根结点的高度，因为增加结点后，高度可能增加 p->height= max( Height(p->LeftChild), Height(p->RightChild))+ 1; // 检测左子树是否平衡 if( p->LeftChild ) Rotate_Help( p->LeftChild ); // 检测右子树是否平衡 if( p->RightChild ) Rotate_Help( p->RightChild ); // 检测此节点并调整 Rotate_Help( p );return *this;}template<class E, class K>AVLtree2<E,K>& AVLtree2<E,K>::Insert( const E& e ){return Insert_Help( root, e ); } template<class E, class K>void AVLtree2<E,K>::Rotate_Help( AVLNode<E,K>*& p ){//右子树高度比左子树高度大2if( Height(p->RightChild) - Height(p->LeftChild) == 2 ){if( Height(p->RightChild->LeftChild) <= Height(p->RightChild->RightChild) )RightSingleRotate( p );else RightDoubleRotate( p );}//左子树高度比右子树高度大2 else if( Height(p->RightChild) - Height(p->LeftChild) == -2 ){if( Height(p->LeftChild->RightChild) <= Height(p->LeftChild->LeftChild) )LeftSingleRotate( p );else LeftDoubleRotate( p );}} template<class E, class K>AVLtree2<E,K>& AVLtree2<E,K>::Delete_Help(AVLNode<E,K>*& p, const K& k, E& e ){ if( p == 0 ) return *this; if( k == p->data ){e = p->data; if( p->RightChild == 0 ){ AVLNode<E,K>* tmp = p; p = p->LeftChild; delete tmp; } else { AVLNode<E,K>* tmp = p->RightChild; while( tmp->LeftChild != 0 )tmp = tmp->LeftChild; p->data = tmp->data;Delete_Help( p->RightChild, tmp->data, e ); p->height= max( Height(p->LeftChild), Height(p->RightChild)) + 1; } return *this; } else if( k < p->data ) {Delete_Help( p->LeftChild, k, e );} else{Delete_Help( p->RightChild, k, e );} // 调整高度 p->height = max( Height(p->LeftChild), Height(p->RightChild)) + 1; // 检测左子树是否平衡 if( p->LeftChild ) Rotate_Help( p->LeftChild ); // 检测右子树是否平衡 if( p->RightChild ) Rotate_Help( p->RightChild ); // 检测此节点并调整 Rotate_Help( p );return *this; }template<class E, class K>AVLtree2<E,K>& AVLtree2<E,K>::Delete( const K& k, E& e ){ return Delete_Help( root, k, e ); }template<class E, class K>void AVLtree2<E,K>::InOutput(const AVLNode<E,K> *p){if(p) {InOutput(p->LeftChild);cout << p->data << " ";InOutput(p->RightChild);}}template<class E, class K>void AVLtree2<E,K>::PostOutput(const AVLNode<E,K> *p){if(p) {PostOutput(p->LeftChild);PostOutput(p->RightChild);cout << p->data << " ";}}

 

#ifndef AVLNode_#define AVLNode_template <class E, class K> class AVLtree;template <class E, class K> class AVLtree2;template <class E, class K> class DAVLtree;template <class E, class K>class AVLNode {friend AVLtree<E,K>;friend AVLtree2<E,K>;friend DAVLtree<E,K>;public:AVLNode() {LeftChild = RightChild = 0;}AVLNode(const E& e){data = e; bf = 0; LeftChild = RightChild = 0; height = 0; }private:E data;int bf;int height;AVLNode<E,K> *LeftChild, *RightChild;};#endif