avl树的C++实现

这里给出了C++代码的实现。关于AVL树的C语言的实现参见《AVL树（Adelson-Velskii-Landis tree）》

//3avl_tree_c++.h#ifndef AVL_TREE_cplusplus_H#define AVL_TREE_cplusplus_H#include <iostream>using namespace std;template <typename Comparable>class AvlTree{public:AvlTree():root(NULL) {}AvlTree(const AvlTree &rhs): root(NULL) {*this = rhs;}~AvlTree() {makeEmpty();}const Comparable &findMin() const {if (isEmpty())cout << "树为空" << endl;return findMin(root)->element;}const Comparable &findMax() const {if (isEmpty())cout << "树为空" << endl;return findMax(root)->element;}bool contains(const Comparable &x) const {return contains(x, root);}bool isEmpty() const {return root == NULL;}void printTree() const {if (isEmpty())cout << "Empty tree." << endl;else {cout << "先序：";printTreePreOrder(root);cout << endl << "中序：";printTreeInOrder(root);cout << endl << "后序：";printTreePostOrder(root);}cout << endl;}void makeEmpty() {makeEmpty(root);}void insert(const Comparable &x) {insert(x, root);}void remove(const Comparable &x) {remove(x, root);}const AvlTree &operator=(const AvlTree &rhs) {if (this != &rhs) {makeEmpty();root = clone(rhs.root);}return this;}private:struct AvlNode {Comparable element;AvlNode *left;AvlNode *right;int height;AvlNode(const Comparable &theElement, AvlNode *l, AvlNode *r, int h = 0): element(theElement), left(l), right(r), height(h) {}};AvlNode *root;void insert(const Comparable &x, AvlNode* &t) {if (t == NULL)t = new AvlNode(x, NULL, NULL);else if (x < t->element) {insert(x, t->left);if (height(t->left) - height(t->right) == 2)if (x < t->left->element)rotateWithLeftChild(t);elsedoubleWithLeftChild(t);}else if (x > t->element) {insert(x, t->right);if (height(t->right) - height(t->left) == 2)if (t->right->element < x)rotateWithRightChild(t);elsedoubleWithRightChild(t);}else; //要往树中插入已经存在的元素，什么也不做t->height = max(height(t->left), height(t->right)) + 1;}void remove(const Comparable &x, AvlNode* &t) {if (t == NULL)return;if (x < t->element) {remove(x, t->left);if (height(t->right) - height(t->left) == 2) {if (height(t->right->left) > height(t->right->right))doubleWithRightChild(t);elserotateWithRightChild(t);}}else if (x > t->element) {if (height(t->left) - height(t->right) == 2) {if (height(t->left->right) > height(t->left->left))doubleWithLeftChild(t);elserotateWithLeftChild(t);}}else if (t->left && t->right) { //找到要删除的位置，t有两个孩子t->element = findMin(t->right)->element;remove(t->element, t->right);t->height = max(height(t->left), height(t->right)) + 1;}else {AvlNode *oldNode = t;t = (t->left == NULL) ? t->right : t->left;delete oldNode;}if (t != NULL)t->height = max(height(t->left), height(t->right)) + 1;}AvlNode *findMin(AvlNode *t) const {if (t == NULL)return NULL;if (t->left == NULL)return t;return findMin(t->left);}AvlNode  *findMax(AvlNode *t) const {//注释部分为递归//if (t == NULL)//return NULL;//if (t->right == NULL)//return t;//return findMax(t->right);//非递归形式if (t != NULL)while (t->right != NULL)t = t->right;return t;}bool contains(const Comparable &x, AvlNode *t) const {if (t == NULL)return false;else if (x < t->element)return contains(x, t->left);else if (x > t->element)return contains(x, t->right);elsereturn true;}/*//非迭代操作bool contains(const Comparable &x, AvlNode *t) {while (t != NULL) {if (x < t->element)t = t->left;else if (x > t->element)t = t->right;elsereturn true;}return false;}*/void makeEmpty(AvlNode* &t) {if (t != NULL) {makeEmpty(t->left);makeEmpty(t->right);delete t;}t = NULL;}void printTreePreOrder(AvlNode *t) const {if (t != NULL) {cout << t->element << " ";printTreePreOrder(t->left);printTreePreOrder(t->right);}}void printTreeInOrder(AvlNode * t) const {if (t != NULL) {printTreeInOrder(t->left);cout << t->element << " ";printTreeInOrder(t->right);}}void printTreePostOrder(AvlNode * t) const {if (t != NULL) {printTreePostOrder(t->left);printTreePostOrder(t->right);cout << t->element << " ";}}AvlNode *clone(AvlNode *t) const {if (t == NULL)return NULL;return new AvlNode(t->element, clone(t->left), clone(t->right));}int height(AvlNode *t) const {return t == NULL ? -1 : t->height;}int max(int lhs, int rhs) {return lhs > rhs ? lhs : rhs;}//单旋转，左-左void rotateWithLeftChild(AvlNode * & k2) {AvlNode *k1 = k2->left;k2->left = k1->right;k1->right = k2;k2->height = max(height(k2->left), height(k2->right)) + 1;k1->height = max(height(k1->left), height(k1->right)) + 1;k2 = k1; }//单旋转，右-右void rotateWithRightChild(AvlNode * & k1) {AvlNode *k2 = k1->right;k1->right = k2->left;k2->left = k1;k1->height = max(height(k1->left), height(k1->right)) + 1;k2->height = max(height(k2->left), height(k2->right)) + 1;k1 = k2;}//双旋转，左-右void doubleWithLeftChild(AvlNode * & k3) {rotateWithRightChild(k3->left);rotateWithLeftChild(k3);}//双旋转，右-左void doubleWithRightChild(AvlNode * & k3) {rotateWithLeftChild(k3->right);rotateWithRightChild(k3);}};#endif

测试代码：

#include "3avl_tree_c++.h"int main() {AvlTree<int> tree;int i = 0;while (i != 9) {tree.insert(i++);}tree.printTree();cout << endl << "删除11但11不存在：" << endl;tree.remove(11);tree.printTree();    cout << endl << "删除 5和8：" << endl;tree.remove(5);tree.remove(8);tree.printTree();return 0;}