299 lines
10 KiB
Rust
299 lines
10 KiB
Rust
/*
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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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include!("../include/include.rs");
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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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use tree_node::TreeNode;
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type OptionTreeNodeRc = Option<Rc<RefCell<TreeNode>>>;
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/* AVL tree */
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struct AVLTree {
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root: OptionTreeNodeRc, // Root node
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}
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impl AVLTree {
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/* Constructor */
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fn new() -> Self {
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Self { root: None }
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}
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/* Get node height */
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fn height(node: OptionTreeNodeRc) -> i32 {
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// Empty node height is -1, leaf node height is 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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/* Update node height */
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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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// Node height equals the height of the tallest subtree + 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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/* Get balance factor */
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fn balance_factor(node: OptionTreeNodeRc) -> i32 {
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match node {
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// Empty node balance factor is 0
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None => 0,
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// Node balance factor = left subtree height - right subtree height
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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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/* Right rotation operation */
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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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// Rotate node to the right around child
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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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// Update node height
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Self::update_height(Some(node));
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Self::update_height(Some(child.clone()));
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// Return the root of the subtree after rotation
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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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/* Left rotation operation */
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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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// Rotate node to the left around child
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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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// Update node height
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Self::update_height(Some(node));
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Self::update_height(Some(child.clone()));
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// Return the root of the subtree after rotation
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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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/* Perform rotation operation to restore balance to the subtree */
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fn rotate(node: OptionTreeNodeRc) -> OptionTreeNodeRc {
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// Get the balance factor of node
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let balance_factor = Self::balance_factor(node.clone());
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// Left-leaning tree
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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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// Right rotation
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Self::right_rotate(Some(node))
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} else {
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// First left rotation then right rotation
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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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// Right-leaning tree
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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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// Left rotation
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Self::left_rotate(Some(node))
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} else {
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// First right rotation then left rotation
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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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// Balanced tree, no rotation needed, return
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node
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}
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}
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/* Insert node */
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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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/* Recursively insert node (helper method) */
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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. Find insertion position and insert node */
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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); // Do not insert duplicate nodes, return
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}
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}
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Self::update_height(Some(node.clone())); // Update node height
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/* 2. Perform rotation operation to restore balance to the subtree */
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node = Self::rotate(Some(node)).unwrap();
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// Return the root node of the subtree
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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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/* Remove node */
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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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/* Recursively remove node (helper method) */
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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. Find and remove the node */
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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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// Number of child nodes = 0, remove node and return
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None => {
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return None;
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}
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// Number of child nodes = 1, remove node
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Some(child) => node = child,
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}
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} else {
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// Number of child nodes = 2, remove the next node in in-order traversal and replace the current node with it
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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())); // Update node height
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/* 2. Perform rotation operation to restore balance to the subtree */
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node = Self::rotate(Some(node)).unwrap();
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// Return the root node of the subtree
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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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/* Search node */
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fn search(&self, val: i32) -> OptionTreeNodeRc {
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let mut cur = self.root.clone();
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// Loop find, break after passing leaf nodes
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while let Some(current) = cur.clone() {
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match current.borrow().val.cmp(&val) {
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// Target node is in cur's right subtree
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Ordering::Less => {
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cur = current.borrow().right.clone();
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}
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// Target node is in cur's left subtree
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Ordering::Greater => {
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cur = current.borrow().left.clone();
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}
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// Found target node, break loop
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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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// Return target node
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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!("\nInsert node {} after, AVL tree is", 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!("\nRemove node {} after, AVL tree is", val);
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print_util::print_tree(&tree.root.clone().unwrap());
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}
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/* Initialize empty AVL tree */
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let mut avl_tree = AVLTree::new();
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/* Insert node */
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// Notice how the AVL tree maintains balance after inserting nodes
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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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/* Insert duplicate node */
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test_insert(&mut avl_tree, 7);
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/* Remove node */
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// Notice how the AVL tree maintains balance after removing nodes
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test_remove(&mut avl_tree, 8); // Remove node with degree 0
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test_remove(&mut avl_tree, 5); // Remove node with degree 1
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test_remove(&mut avl_tree, 4); // Remove node with degree 2
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/* Search node */
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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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"\nThe found node object is {:?}, node value = {}",
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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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