AVL树

#pragma once#ifndef _AVL_TREE#define _AVL_TREE#include<iomanip>#include<iostream>using namespace std;//节点类template<typename T>class AVLTreeNode {public:T key;    //关键字（键值）int height;  //高度AVLTreeNode *left;    //左孩子AVLTreeNode *right;   //右孩子AVLTreeNode(T value,AVLTreeNode *l,AVLTreeNode *r):key(value),height(0),left(l),right(r){}};//AVLTree是AVL树对应的类template<typename T>class AVLTree {private:AVLTreeNode<T> *root;    //根节点public:AVLTree() :root(NULL) {};~AVLTree() {destory(root)};//获取树的高度int height();//比较两个值的大小int max(int a, int b);void preOrder();   //前序遍历AVL树void inOrder();    //中序遍历AVL树void postOrder();  //后序遍历AVL树AVLTreeNode<T>* search(T key);              //递归实现查找AVL树中键值为key的节点AVLTreeNode<T>* iterativeSearch(T key);     //非递归实现查找AVL树中键值为key的节点T minimum();           //查找最小节点：返回最小节点的键值T maximum();           //查找最大节点：返回最大节点的键值void insert(T key);    //将节点插入到AVL树中void remove(T key);    //删除节点void destory();        //销毁AVL树void print();          //打印AVL树private:int height(AVLTreeNode<T> *tree);     //获取树的高度void preOrder(AVLTreeNode<T>* tree) const;  //前序遍历AVL树void inOrder(AVLTreeNode<T>* tree) const;   //中序遍历AVL树void postOrder(AVLTreeNode<T>* tree) const; //后序遍历AVL树AVLTreeNode<T>* search(AVLTreeNode<T> *x, T key) const;            //递归实现查找二叉树AVLTreeNode<T>* iterativeSearch(AVLTreeNode<T> *x, T key) const;   //非递归实现查找二叉树AVLTreeNode<T>* minimum(AVLTreeNode<T> *tree);    //查找最小节点，返回tree为根节点的AVL树的最小节点AVLTreeNode<T>* maximum(AVLTreeNode<T> *tree);    //查找最大节点，返回tree为根节点的AVL树的最大节点AVLTreeNode<T>* leftLeftRotation(AVLTreeNode<T> *k2);    //LL：左左对应的情况（左单旋转）AVLTreeNode<T>* rightRightRotation(AVLTreeNode<T> *k1);  //RR：右右对应的情况（右单旋转）AVLTreeNode<T>* leftRightRotation(AVLTreeNode<T> *k3);   //LR：左右对应的情侣（左双旋转）AVLTreeNode<T>* rightLeftRotation(AVLTreeNode<T> *k1);   //RL: 右左对应的情况（右双旋转）AVLTreeNode<T>* insert(AVLTreeNode<T>* &tree, T key);              //插入节点AVLTreeNode<T>* remove(AVLTreeNode<T>* &tree, AVLTreeNode<T> *z);  //删除节点void destory(AVLTreeNode<T>* &tree);     //销毁AVL树void print(AVLTreeNode<T> *tree, T key, int direction);   //打印AVL树};template <typename T>     //获取树的高度int AVLTree<T>::height(AVLTreeNode<T> *tree){if (tree != NULL)return tree->height;return 0;}template <typename T>   //获取树的高度的接口函数int AVLTree<T>::height(){return height(root);}template <typename T>int AVLTree<T>::max(int a, int b){return a > b ? a : b;}template<typename T>  //前序遍历void AVLTree<T>::preOrder(AVLTreeNode<T> *tree) const{if (tree != NULL){cout << tree->key << " ";preOrder(tree->left);preOrder(tree->right);}}template<typename T>  //前序遍历的接口函数void AVLTree<T>::preOrder(){preOrder(root);}template<typename T>   //中序遍历void AVLTree<T>::inOrder(AVLTreeNode<T> *tree) const{if (tree != NULL){inOrder(tree->left);cout << tree->key << " ";inOrder(tree->right);}}template<typename T>    //中序遍历的接口函数void AVLTree<T>::inOrder(){inOrder(root);}template<typename T>   //后序遍历void AVLTree<T>::postOrder(AVLTreeNode<T> *tree) const{if (tree != NULL){postOrder(tree->left);postOrder(tree->right);cout << tree->key << " ";}}template<typename T> //后序遍历的接口函数void AVLTree<T>::postOrder(){postOrder(root);}template<typename T>  //递归实现查找二叉树AVLTreeNode<T>* AVLTree<T>::search(AVLTreeNode<T> *x, T key) const{if (x == NULL || x->key == key)return x;if (key < x->key)return search(x->left, key);elsereturn search(x->right, key);}template<typename T>   //递归实现查找二叉树的接口函数AVLTreeNode<T>* AVLTree<T>::search(T key){return search(root, key);}template<typename T>   //非递归实现查找二叉树AVLTreeNode<T>* AVLTree<T>::iterativeSearch(AVLTreeNode<T> *x,T key) const{while ((x != NULL) && (x->key != key)){if (key < x->key)x = x->left;elsex = x->right;}return x;}template<typename T>   //非递归实现查找二叉树的接口函数AVLTreeNode<T>* AVLTree<T>::iterativeSearch(T key){return iterativeSearch(root, key);}template<typename T> //查找最小节点，返回tree为根节点的AVL树的最小节点AVLTreeNode<T>* AVLTree<T>::minimum(AVLTreeNode<T> *tree){if (tree == NULL)return NULL;while (tree->left != NULL)tree = tree->left;return tree;}template<typename T>  //接口T AVLTree<T>::minimum(){AVLTreeNode<T> *p = minimum(root);if (p != NULL)return p->key;return (T)NULL;}template<typename T>  //查找最大节点：返回tree为根节点的AVL树的最大节点AVLTreeNode<T>* AVLTree<T>::maximum(AVLTreeNode<T> *tree){if (tree == NULL)return NULL;while (tree->right != NULL)tree = tree->right;return tree;}template<typename T>  //接口T AVLTree<T>::maximum(){AVLTreeNode<T> *p = maximum(root);if (p != NULL)return p->key;return (T)NULL;}template<typename T>  //LL：左左对应的情况（左单旋转）  返回值：旋转后的根节点AVLTreeNode<T>* AVLTree<T>::leftLeftRotation(AVLTreeNode<T> *k2){AVLTreeNode<T> *k1;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), k2->height) + 1;return k1;}template<typename T>  //RR：右右对应的情况（右单旋转） 返回值：旋转后的跟节点AVLTreeNode<T>* AVLTree<T>::rightRightRotation(AVLTreeNode<T> *k1){AVLTreeNode<T> *k2;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->right), k1->height) + 1;return k2;}template<typename T>  //LR：左右对应的情况（左双旋转） 返回值：旋转后的根节点AVLTreeNode<T>* AVLTree<T>::leftRightRotation(AVLTreeNode<T> *k3){k3->left = rightRightRotation(k3->left);return leftLeftRotation(k3);}template<typename T>  //RL：右左对应的情况（右双旋转）  返回值：旋转后的根节点AVLTreeNode<T>* AVLTree<T>::rightLeftRotation(AVLTreeNode<T> *k1){k1->right = leftLeftRotation(k1->right);return rightRightRotation(k1);}template<typename T>  //将节点插入到AVL树中，并返回根节点AVLTreeNode<T>* AVLTree<T>::insert(AVLTreeNode<T>* &tree, T key){if (tree == NULL){//新建节点tree = new AVLTreeNode<T>(key, NULL, NULL);if (tree == NULL){cout << "ERROR: create avltree node failed!" << endl;return NULL;}}else if (key < tree->key)  //应该将key插入到tree的左子树的情况{tree->left = insert(tree->left, key);//插入节点后，若AVL树失去平衡，则进行相应的调节。if (height(tree->left) - height(tree->right) == 2){if (key < tree->left->key)tree = leftLeftRotation(tree);elsetree = leftRightRotation(tree);}}else if (key > tree->key)  //应该将key插入到tree的右子树的情况{tree->right = insert(tree->right, key);//插入节点后，若AVL树失去平衡，则进行相应的调节if (height(tree->right) - height(tree->left) == 2){if (key > tree->right->key)tree = rightRightRotation(tree);elsetree = rightLeftRotation(tree);}}else   //key==tree->key{cout << "添加失败：不允许添加相同的节点！" << endl;}tree->height = max(height(tree->left), height(tree->right)) + 1;return tree;}template<typename T>  //插入操作的接口函数void AVLTree<T>::insert(T key){insert(root, key);}template<typename T>   //删除节点，返回根节点AVLTreeNode<T>* AVLTree<T>::remove(AVLTreeNode<T>* &tree, AVLTreeNode<T> *z){//根为空或者没有要删除的节点，直接返回NULLif (tree == NULL || z == NULL)return NULL;if (z->key < tree->key)  //待删除的节点再左子树中{tree->left = remove(tree->left, z);//删除节点后，若AVL树失去平衡，则进行相应的调节if (height(tree->right) - height(tree->left) == 2){AVLTreeNode<T> *r = tree->right;if (height(r->left) > height(r->right))tree = rightLeftRotation(tree);elsetree = rightRightRotation(tree);}}else if (z->key > tree->key)  //待删除的节点在右子树中{tree->right = remove(tree->right, z);//删除节点后，若AVL树失去平衡，则进行相应的调节if (height(tree->left) - height(tree->right) == 2){AVLTreeNode<T> *l = tree->left;if (height(l->right) > height(l->left))tree = leftRightRotation(tree);elsetree = leftLeftRotation(tree);}}else   //tree是对应要删除的节点{//tree的左右孩子都非空if ((tree->left != NULL) && (tree->right != NULL)){if (height(tree->left) > height(tree->right)){//如果tree的左子树比右子树高；//则01找出tree的左子树的最大节点//02将该最大节点的值赋给tree//03删除改最大的节点//这类似与用tree的左子树中最大节点做tree的替身//采用这种方法的好处式：删除tree的左子树中最大节点之后，AVL树仍然式平衡的AVLTreeNode<T> *max = maximum(tree->left);tree->key = max->key;tree->left = remove(tree->left, max);}else{//如果tree的左子树不比右子树高（即它们相等，或右子树比左子树高1//则01找出tree的右子树中的最小节点//02将该最小节点的值赋给tree//03删除该最小节点//这类似于用tree的右子树中最小节点做tree的替身//采用这种方式的好处式：删除tree的右子树中最小节点之后AVL树仍然式平衡的AVLTreeNode<T> *min = maximum(tree->right);tree->key = min->key;tree->right = remove(tree->right, min);}}else{AVLTreeNode<T> *tmp = tree;tree = (tree->left != NULL) ? tree->left : tree->right;delete tmp;}}return tree;}template<typename T>  //删除的接口函数void AVLTree<T>::remove(T key){AVLTreeNode<T> *z;if ((z = search(root, key)) != NULL)root = remove(root, z);}template<typename T>  //销毁AVL树void AVLTree<T>::destory(AVLTreeNode<T>* &tree){if (tree == NULL)return;if (tree->left != NULL)destory(tree->left);if (tree->right != NULL)destory(tree->right);delete tree;}template<typename T>  //销毁AVL树的接口函数void AVLTree<T>::destory(){destory(root);}template<typename T>  //打印AVL树void AVLTree<T>::print(AVLTreeNode<T> *tree, T key, int direction){if (tree!= NULL){if (direction == 0)   //tree是根节点cout << setw(2) << tree->key << " is root " << endl;elsecout << setw(2) << tree->key << " is " << setw(2) << key << "'s "<<setw(12) << (direction == 1 ? "right chilid" : "left child" )<< endl;print(tree->left, tree->key, -1);print(tree->right, tree->key, 1);}}template<typename T>  //打印AVL树的接口函数void AVLTree<T>::print(){if (root != NULL)print(root, root->key, 0);}#endif // !_AVL_TREE

#include<iostream>#include"AVLTree.h"using namespace std;static int arr[] = { 3,2,1,4,5,6,7,16,15,14,13,12,11,10,8,9 };#define TBL_SIZE(a)((sizeof(a))/(sizeof(a[0])))int main(){int i, ilen;AVLTree<int> *tree = new AVLTree<int>();cout << "==依次添加：";ilen = TBL_SIZE(arr);for (i = 0; i < ilen; i++){cout << arr[i] << " ";tree->insert(arr[i]);}cout << "\n==前序遍历";tree->preOrder();cout << "\n==中序遍历";tree->inOrder();cout << "\n==后序遍历";tree->postOrder();cout << endl;cout << "==高度" << tree->height() << endl;cout << "最小值" << tree->minimum() << endl;cout << "最大值" << tree->maximum() << endl;cout << "树的详细信息" << endl;tree->print();i = 8;cout << "\n==删除根节点" << i;tree->remove(i);cout << "\n==中序遍历";tree->inOrder();cout << "\n==树的详细信息" << endl;tree->print();//销毁AVL树tree->destory();return 0;}