AVLTree - 二叉平衡树的实现之一(C++)

 

 

template<class E, class K>class AVLtree {public:AVLtree() {root = 0;}~AVLtree() {Erase(root);}bool Search(const K& k, E& e) const;AVLtree<E,K>& Insert(const E& e);AVLtree<E,K>& Delete(const K& k, E& e);void Ascend() {InOutput(root); cout << endl;}void PostOut() {PostOutput(root); cout << endl;}private:AVLNode<E,K> *root;void Erase(AVLNode<E,K> *t);void InOutput(AVLNode<E,K> *t);void PostOutput(AVLNode<E,K> *t);void FixBF(AVLNode<E,K> *, AVLNode<E,K>*, const E&);void RRrotate(AVLNode<E,K> *, AVLNode<E,K>*, AVLNode<E,K> *);void LLrotate(AVLNode<E,K> *, AVLNode<E,K>*, AVLNode<E,K> *);void RLrotate(AVLNode<E,K> *, AVLNode<E,K>*, AVLNode<E,K> *);void LRrotate(AVLNode<E,K> *, AVLNode<E,K>*, AVLNode<E,K> *);};template<class E, class K>void AVLtree<E,K>::Erase(AVLNode<E,K> *t){//用前序遍历的方式删除所有节点if (t) {Erase(t->LeftChild);Erase(t->RightChild);delete t;}}template<class E, class K>bool AVLtree<E,K>::Search(const K& k, E &e) const{AVLNode<E,K> *p = root;while (p){if (k < p->data) p = p->LeftChild;else if (k > p->data) p = p->RightChild;else {e = p->data;return true;}}return false;}template<class E, class K>void AVLtree<E,K>::FixBF(AVLNode<E,K> *q, AVLNode<E,K> *r, const E &e){//从q到r的平衡因子通常为0//根据实际情况改变成 +1 或 -1while (q != r){if (e < q->data) {q->bf = 1;q = q->LeftChild;}else {q->bf = -1;q = q->RightChild;}}}template<class E, class K>void AVLtree<E,K>::LLrotate(AVLNode<E,K> *PA, AVLNode<E,K> *A, AVLNode<E,K> *B){//LL型的旋转A->LeftChild = B->RightChild;B->RightChild = A;if (PA) // A 是否有父节点{if (A == PA->LeftChild)PA->LeftChild = B;else PA->RightChild = B;}else{root = B;}//设置平衡因子A->bf = B->bf = 0;}template<class E, class K>void AVLtree<E,K>::RRrotate(AVLNode<E,K> *PA, AVLNode<E,K> *A, AVLNode<E,K> *B){//RR型的旋转A->RightChild = B->LeftChild;B->LeftChild = A;if (PA) // A 是否有父节点{if (A == PA->LeftChild)PA->LeftChild = B;else PA->RightChild = B;}else{root = B;}//设置平衡因子A->bf = B->bf = 0;}template<class E, class K>void AVLtree<E,K>::LRrotate(AVLNode<E,K> *PA, AVLNode<E,K> *A, AVLNode<E,K> *B){//LR型的旋转AVLNode<E,K> *C = B->RightChild;A->LeftChild = C->RightChild;B->RightChild = C->LeftChild;C->LeftChild = B;C->RightChild = A;if (PA) // A 是否有父节点{if (A == PA->LeftChild)PA->LeftChild = C;elsePA->RightChild = C;}else {root = C;}//设置平衡因子int b = C->bf;if (b == 1) {B->bf = 0;A->bf = -1;}else if (b == -1) {B->bf = 1;A->bf = 0;}else // b = 0{B->bf = A->bf = 0;}C->bf = 0;}template<class E, class K>void AVLtree<E,K>::RLrotate(AVLNode<E,K> *PA, AVLNode<E,K> *A, AVLNode<E,K> *B){//RL型的旋转AVLNode<E,K> *C = B->LeftChild;A->RightChild = C->LeftChild;B->LeftChild = C->RightChild;C->LeftChild = A;C->RightChild = B;if (PA) // A 是否有父节点{if (A == PA->LeftChild)PA->LeftChild = C;else PA->RightChild = C;}else{root = C;}//设置平衡因子int b = C->bf;if (b == 1){B->bf = -1;A->bf = 0;}else if (b == -1) {B->bf = 0;A->bf = 1;}else // b = 0{B->bf = A->bf = 0;}C->bf = 0;}template<class E, class K>AVLtree<E,K>& AVLtree<E,K>::Insert(const E& e){AVLNode<E,K> *p = root, *pp = 0, // p的父节点 *A = 0, // 平衡因子不为0 的最后一个节点 *PA; // A的父节点//找到可以插入的地方//同时记录最后一个平衡因子不为0的节点及其父节点while (p) {if (p->bf) {A = p;PA = pp;}pp = p;// 将p移向子节点if (e < p->data) p = p->LeftChild;else if (e > p->data) p = p->RightChild;else throw BadInput();/*if(e <= p->data) p = p->LeftChild;elsep = p->RightChild;*/}AVLNode<E,K> *r = new AVLNode<E,K> (e);if (root) {if (e < pp->data) pp->LeftChild = r;else pp->RightChild = r;}else {root = r;return *this;}//查看是否需要再平衡，还是只是简单的刷新下平衡因子if(A){if (A->bf < 0) // bf = -1 在插入前{if (e < A->data){//插入到A的左子树,左子树高度加1//A新的平衡因子等于0, 不需要再平衡A->bf = 0;//刷新下从A到r的平衡因子FixBF(A->LeftChild,r,e);}else {//插入到A的右子树//A的平衡因子为-2, 需要再平衡AVLNode<E,K> *B = A->RightChild;if (e > B->data) {// RR型FixBF(B->RightChild,r,e);RRrotate(PA,A,B);}else {// RL型FixBF(B->LeftChild,r,e);RLrotate(PA,A,B);}}}else // bf = +1 在插入前{if (e > A->data){//插入到A的右子树,右子树高度加1//A新的平衡因子等于0, 不需要再平衡A->bf = 0;//刷新下从A到r的平衡因子FixBF(A->RightChild,r,e);}else {//插入到A的左子树//A的平衡因子为+2, 需要再平衡AVLNode<E,K> *B = A->LeftChild;if (e < B->data) {// LL型FixBF(B->LeftChild,r,e);LLrotate(PA,A,B);}else {// LR型FixBF(B->RightChild,r,e);LRrotate(PA,A,B);}}}}else // A一直为0, 不需要再平衡{//刷新下从root到r的平衡因子FixBF(root,r,e);}return *this;}template<class E, class K>AVLtree<E,K>& AVLtree<E,K>::Delete(const K& k, E& e){// 如果元素数量超过2^60, S栈将会溢出Stack<AVLNode<E,K>*> S(100);AVLNode<E,K> *p = root;while (p && p->data != k){S.Add(p);if (k < p->data) p = p->LeftChild;else p = p->RightChild;}if (!p) throw BadInput();e = p->data; //p有两个子树的情况if (p->LeftChild && p->RightChild) {//查找p左子树里元素值最大的节点S.Add(p);AVLNode<E,K> *s = p->LeftChild;while (s->RightChild) {S.Add(s);s = s->RightChild;}//将p左子树里元素值最大的节点等于pp->data = s->data;p = s;}//只有一个子树的情况AVLNode<E,K> *c;if (p->LeftChild) c = p->LeftChild;else c = p->RightChild;if (p == root){ root = c;}else {if (p == S.Top()->LeftChild)S.Top()->LeftChild = c;else S.Top()->RightChild = c;}E f = p->data; //f也许不等于edelete p;AVLNode<E,K> *q;try { S.Delete(q);}catch (OutOfBounds){//根节点被删除了return *this;}while (q){if (f <= q->data) {//从q的左子树删除的q->bf--;//高度并未发生改变, 不需要再做什么if (q->bf == -1) return *this;if (q->bf == -2){//树变得不平衡了, 需要旋转AVLNode<E,K> *B = q->RightChild, *PA; // q就是A节点 // PA是A的父节点try {S.Delete(PA);}catch (OutOfBounds){//说明A是根节点PA = 0;}switch (B->bf) {case 0: // L0型RRrotate(PA,q,B);B->bf = 1;q->bf = -1;return *this;case 1: // L1型RLrotate(PA,q,B);break;case -1:// L-1型RRrotate(PA,q,B);break;}q = PA;}else // q->bf == 0{try {S.Delete(q);}catch (OutOfBounds){return *this;}}} else {//从q的右子树删除的q->bf++;//高度并未发生改变, 不需要再做什么if (q->bf == 1) return *this;if (q->bf == 2) {//树变得不平衡了, 需要旋转AVLNode<E,K> *B = q->LeftChild, *PA; // q就是A节点 // PA是A的父节点try {S.Delete(PA);}catch (OutOfBounds){//说明A是根节点PA = 0;} switch (B->bf) {case 0: // R0型LLrotate(PA,q,B);B->bf = -1;q->bf = 1;return *this;case 1: // R1型LLrotate(PA,q,B);break;case -1: // R-1 型LRrotate(PA,q,B);break;}q = PA;}else // q->bf == 0{try{S.Delete(q);}catch (OutOfBounds){return *this;}}}}return *this;}template<class E, class K>void AVLtree<E,K>::InOutput(AVLNode<E,K> *t){if(t) {InOutput(t->LeftChild);cout << t->data << " ";InOutput(t->RightChild);}}template<class E, class K>void AVLtree<E,K>::PostOutput(AVLNode<E,K> *t){if(t) {PostOutput(t->LeftChild);PostOutput(t->RightChild);cout << t->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

 

stack:

template<class T>class Stack {public:Stack(int MaxStackSize = 10);~Stack() {delete [] stack;}bool IsEmpty() const {return top == -1;}bool IsFull() const {return top == MaxTop;}T Top() const;Stack<T>& Add(const T& x);Stack<T>& Delete(T& x);private:int top;int MaxTop;T *stack;};template<class T>Stack<T>::Stack(int MaxStackSize){MaxTop = MaxStackSize - 1;stack = new T[MaxStackSize];top = -1;}template<class T>T Stack<T>::Top() const{if (IsEmpty()) throw OutOfBounds();return stack[top];}template<class T>Stack<T>& Stack<T>::Add(const T& x){if (IsFull()) throw NoMem();stack[++top] = x;return *this;}template<class T>Stack<T>& Stack<T>::Delete(T& x){ if (IsEmpty()) throw OutOfBounds(); x = stack[top--]; return *this;}