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/*
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* File: avl_tree.rs
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* Created Time: 2023-07-14
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* Author: night-cruise (2586447362@qq.com)
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*/
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use hello_algo_rust::include::{print_util, TreeNode};
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use std::cell::RefCell;
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use std::cmp::Ordering;
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use std::rc::Rc;
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type OptionTreeNodeRc = Option<Rc<RefCell<TreeNode>>>;
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/* AVL 树 */
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struct AVLTree {
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root: OptionTreeNodeRc, // 根节点
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}
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impl AVLTree {
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/* 构造方法 */
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fn new() -> Self {
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Self { root: None }
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}
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/* 获取节点高度 */
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fn height(node: OptionTreeNodeRc) -> i32 {
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// 空节点高度为 -1 ，叶节点高度为 0
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match node {
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Some(node) => node.borrow().height,
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None => -1,
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}
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}
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/* 更新节点高度 */
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fn update_height(node: OptionTreeNodeRc) {
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if let Some(node) = node {
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let left = node.borrow().left.clone();
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let right = node.borrow().right.clone();
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// 节点高度等于最高子树高度 + 1
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node.borrow_mut().height = std::cmp::max(Self::height(left), Self::height(right)) + 1;
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}
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}
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/* 获取平衡因子 */
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fn balance_factor(node: OptionTreeNodeRc) -> i32 {
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match node {
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// 空节点平衡因子为 0
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None => 0,
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// 节点平衡因子 = 左子树高度 - 右子树高度
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Some(node) => {
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Self::height(node.borrow().left.clone()) - Self::height(node.borrow().right.clone())
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}
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}
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}
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/* 右旋操作 */
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fn right_rotate(node: OptionTreeNodeRc) -> OptionTreeNodeRc {
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match node {
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Some(node) => {
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let child = node.borrow().left.clone().unwrap();
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let grand_child = child.borrow().right.clone();
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// 以 child 为原点，将 node 向右旋转
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child.borrow_mut().right = Some(node.clone());
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node.borrow_mut().left = grand_child;
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// 更新节点高度
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Self::update_height(Some(node));
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Self::update_height(Some(child.clone()));
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// 返回旋转后子树的根节点
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Some(child)
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}
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None => None,
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}
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}
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/* 左旋操作 */
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fn left_rotate(node: OptionTreeNodeRc) -> OptionTreeNodeRc {
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match node {
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Some(node) => {
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let child = node.borrow().right.clone().unwrap();
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let grand_child = child.borrow().left.clone();
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// 以 child 为原点，将 node 向左旋转
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child.borrow_mut().left = Some(node.clone());
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node.borrow_mut().right = grand_child;
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// 更新节点高度
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Self::update_height(Some(node));
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Self::update_height(Some(child.clone()));
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// 返回旋转后子树的根节点
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Some(child)
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}
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None => None,
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}
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}
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/* 执行旋转操作，使该子树重新恢复平衡 */
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fn rotate(node: OptionTreeNodeRc) -> OptionTreeNodeRc {
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// 获取节点 node 的平衡因子
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let balance_factor = Self::balance_factor(node.clone());
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// 左偏树
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if balance_factor > 1 {
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let node = node.unwrap();
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if Self::balance_factor(node.borrow().left.clone()) >= 0 {
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// 右旋
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Self::right_rotate(Some(node))
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} else {
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// 先左旋后右旋
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let left = node.borrow().left.clone();
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node.borrow_mut().left = Self::left_rotate(left);
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Self::right_rotate(Some(node))
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}
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}
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// 右偏树
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else if balance_factor < -1 {
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let node = node.unwrap();
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if Self::balance_factor(node.borrow().right.clone()) <= 0 {
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// 左旋
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Self::left_rotate(Some(node))
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} else {
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// 先右旋后左旋
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let right = node.borrow().right.clone();
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node.borrow_mut().right = Self::right_rotate(right);
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Self::left_rotate(Some(node))
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}
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} else {
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// 平衡树，无须旋转，直接返回
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node
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}
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}
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/* 插入节点 */
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fn insert(&mut self, val: i32) {
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self.root = Self::insert_helper(self.root.clone(), val);
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}
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/* 递归插入节点（辅助方法） */
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fn insert_helper(node: OptionTreeNodeRc, val: i32) -> OptionTreeNodeRc {
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match node {
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Some(mut node) => {
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/* 1. 查找插入位置并插入节点 */
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match {
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let node_val = node.borrow().val;
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node_val
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}
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.cmp(&val)
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{
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Ordering::Greater => {
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let left = node.borrow().left.clone();
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node.borrow_mut().left = Self::insert_helper(left, val);
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}
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Ordering::Less => {
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let right = node.borrow().right.clone();
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node.borrow_mut().right = Self::insert_helper(right, val);
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}
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Ordering::Equal => {
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return Some(node); // 重复节点不插入，直接返回
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}
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}
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Self::update_height(Some(node.clone())); // 更新节点高度
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/* 2. 执行旋转操作，使该子树重新恢复平衡 */
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node = Self::rotate(Some(node)).unwrap();
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// 返回子树的根节点
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Some(node)
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}
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None => Some(TreeNode::new(val)),
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}
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}
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/* 删除节点 */
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fn remove(&self, val: i32) {
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Self::remove_helper(self.root.clone(), val);
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}
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/* 递归删除节点（辅助方法） */
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fn remove_helper(node: OptionTreeNodeRc, val: i32) -> OptionTreeNodeRc {
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match node {
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Some(mut node) => {
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/* 1. 查找节点并删除 */
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if val < node.borrow().val {
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let left = node.borrow().left.clone();
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node.borrow_mut().left = Self::remove_helper(left, val);
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} else if val > node.borrow().val {
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let right = node.borrow().right.clone();
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node.borrow_mut().right = Self::remove_helper(right, val);
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} else if node.borrow().left.is_none() || node.borrow().right.is_none() {
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let child = if node.borrow().left.is_some() {
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node.borrow().left.clone()
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} else {
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node.borrow().right.clone()
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};
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match child {
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// 子节点数量 = 0 ，直接删除 node 并返回
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None => {
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return None;
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}
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// 子节点数量 = 1 ，直接删除 node
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Some(child) => node = child,
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}
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} else {
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// 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点
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let mut temp = node.borrow().right.clone().unwrap();
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loop {
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let temp_left = temp.borrow().left.clone();
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if temp_left.is_none() {
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break;
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}
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temp = temp_left.unwrap();
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}
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let right = node.borrow().right.clone();
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node.borrow_mut().right = Self::remove_helper(right, temp.borrow().val);
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node.borrow_mut().val = temp.borrow().val;
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}
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Self::update_height(Some(node.clone())); // 更新节点高度
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/* 2. 执行旋转操作，使该子树重新恢复平衡 */
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node = Self::rotate(Some(node)).unwrap();
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// 返回子树的根节点
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Some(node)
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}
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None => None,
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}
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}
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/* 查找节点 */
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fn search(&self, val: i32) -> OptionTreeNodeRc {
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let mut cur = self.root.clone();
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// 循环查找，越过叶节点后跳出
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while let Some(current) = cur.clone() {
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match current.borrow().val.cmp(&val) {
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// 目标节点在 cur 的右子树中
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Ordering::Less => {
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cur = current.borrow().right.clone();
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}
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// 目标节点在 cur 的左子树中
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Ordering::Greater => {
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cur = current.borrow().left.clone();
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}
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// 找到目标节点，跳出循环
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Ordering::Equal => {
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break;
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}
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}
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}
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// 返回目标节点
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cur
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}
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}
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/* Driver Code */
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fn main() {
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fn test_insert(tree: &mut AVLTree, val: i32) {
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tree.insert(val);
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println!("\n插入节点 {} 后，AVL 树为", val);
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print_util::print_tree(&tree.root.clone().unwrap());
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}
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fn test_remove(tree: &mut AVLTree, val: i32) {
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tree.remove(val);
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println!("\n删除节点 {} 后，AVL 树为", val);
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print_util::print_tree(&tree.root.clone().unwrap());
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}
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/* 初始化空 AVL 树 */
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let mut avl_tree = AVLTree::new();
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/* 插入节点 */
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// 请关注插入节点后，AVL 树是如何保持平衡的
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test_insert(&mut avl_tree, 1);
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test_insert(&mut avl_tree, 2);
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test_insert(&mut avl_tree, 3);
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test_insert(&mut avl_tree, 4);
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test_insert(&mut avl_tree, 5);
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test_insert(&mut avl_tree, 8);
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test_insert(&mut avl_tree, 7);
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test_insert(&mut avl_tree, 9);
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test_insert(&mut avl_tree, 10);
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test_insert(&mut avl_tree, 6);
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/* 插入重复节点 */
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test_insert(&mut avl_tree, 7);
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/* 删除节点 */
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// 请关注删除节点后，AVL 树是如何保持平衡的
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test_remove(&mut avl_tree, 8); // 删除度为 0 的节点
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test_remove(&mut avl_tree, 5); // 删除度为 1 的节点
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test_remove(&mut avl_tree, 4); // 删除度为 2 的节点
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/* 查询节点 */
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let node = avl_tree.search(7);
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if let Some(node) = node {
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println!(
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"\n查找到的节点对象为 {:?}，节点值 = {}",
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&*node.borrow(),
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node.borrow().val
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);
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}
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}
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