hello-algo/en/codes/java/chapter_tree/avl_tree.java

/**
 * File: avl_tree.java
 * Created Time: 2022-12-10
 * Author: krahets (krahets@163.com)
 */

package chapter_tree;

import utils.*;

/* AVL tree */
class AVLTree {
    TreeNode root; // Root node

    /* Get the node height */
    public int height(TreeNode node) {
        // A null node has height -1; a leaf has height 0
        return node == null ? -1 : node.height;
    }

    /* Update the node height */
    private void updateHeight(TreeNode node) {
        // The node height equals the height of its taller subtree + 1
        node.height = Math.max(height(node.left), height(node.right)) + 1;
    }

    /* Get the balance factor */
    public int balanceFactor(TreeNode node) {
        // A null node has balance factor 0
        if (node == null)
            return 0;
        // Node balance factor = left subtree height - right subtree height
        return height(node.left) - height(node.right);
    }

    /* Right rotation */
    private TreeNode rightRotate(TreeNode node) {
        TreeNode child = node.left;
        TreeNode grandChild = child.right;
        // Rotate node to the right around child
        child.right = node;
        node.left = grandChild;
        // Update the node height
        updateHeight(node);
        updateHeight(child);
        // Return the root of the rotated subtree
        return child;
    }

    /* Left rotation */
    private TreeNode leftRotate(TreeNode node) {
        TreeNode child = node.right;
        TreeNode grandChild = child.left;
        // Rotate node to the left around child
        child.left = node;
        node.right = grandChild;
        // Update the node height
        updateHeight(node);
        updateHeight(child);
        // Return the root of the rotated subtree
        return child;
    }

    /* Perform rotations to restore balance in this subtree */
    private TreeNode rotate(TreeNode node) {
        // Get the balance factor of node
        int balanceFactor = balanceFactor(node);
        // Left-heavy tree
        if (balanceFactor > 1) {
            if (balanceFactor(node.left) >= 0) {
                // Rotate right
                return rightRotate(node);
            } else {
                // Rotate left, then right
                node.left = leftRotate(node.left);
                return rightRotate(node);
            }
        }
        // Right-heavy tree
        if (balanceFactor < -1) {
            if (balanceFactor(node.right) <= 0) {
                // Rotate left
                return leftRotate(node);
            } else {
                // Rotate right, then left
                node.right = rightRotate(node.right);
                return leftRotate(node);
            }
        }
        // The tree is balanced; return without rotating
        return node;
    }

    /* Insert a node */
    public void insert(int val) {
        root = insertHelper(root, val);
    }

    /* Insert a node recursively (helper method) */
    private TreeNode insertHelper(TreeNode node, int val) {
        if (node == null)
            return new TreeNode(val);
        /* 1. Find the insertion position and insert the node */
        if (val < node.val)
            node.left = insertHelper(node.left, val);
        else if (val > node.val)
            node.right = insertHelper(node.right, val);
        else
            return node; // Return without inserting a duplicate node
        updateHeight(node); // Update the node height
        /* 2. Perform rotations to restore balance in this subtree */
        node = rotate(node);
        // Return the subtree root
        return node;
    }

    /* Remove a node */
    public void remove(int val) {
        root = removeHelper(root, val);
    }

    /* Remove a node recursively (helper method) */
    private TreeNode removeHelper(TreeNode node, int val) {
        if (node == null)
            return null;
        /* 1. Find and remove the node */
        if (val < node.val)
            node.left = removeHelper(node.left, val);
        else if (val > node.val)
            node.right = removeHelper(node.right, val);
        else {
            if (node.left == null || node.right == null) {
                TreeNode child = node.left != null ? node.left : node.right;
                // Number of children = 0: remove node and return
                if (child == null)
                    return null;
                // Number of children = 1: remove node directly
                else
                    node = child;
            } else {
                // Number of children = 2: remove the inorder successor and use its value to replace the current node value
                TreeNode temp = node.right;
                while (temp.left != null) {
                    temp = temp.left;
                }
                node.right = removeHelper(node.right, temp.val);
                node.val = temp.val;
            }
        }
        updateHeight(node); // Update the node height
        /* 2. Perform rotations to restore balance in this subtree */
        node = rotate(node);
        // Return the subtree root
        return node;
    }

    /* Find a node */
    public TreeNode search(int val) {
        TreeNode cur = root;
        // Search in a loop until reaching a null reference beyond a leaf
        while (cur != null) {
            // The target node lies in the right subtree of cur
            if (cur.val < val)
                cur = cur.right;
            // The target node lies in the left subtree of cur
            else if (cur.val > val)
                cur = cur.left;
            // The target node was found; exit the loop
            else
                break;
        }
        // Return the target node
        return cur;
    }
}

public class avl_tree {
    static void testInsert(AVLTree tree, int val) {
        tree.insert(val);
        System.out.println("\nAfter inserting node " + val + " the AVL tree is:");
        PrintUtil.printTree(tree.root);
    }

    static void testRemove(AVLTree tree, int val) {
        tree.remove(val);
        System.out.println("\nAfter removing node " + val + " the AVL tree is:");
        PrintUtil.printTree(tree.root);
    }

    public static void main(String[] args) {
        /* Initialize an empty AVL tree */
        AVLTree avlTree = new AVLTree();

        /* Insert a node */
        // Observe how the AVL tree maintains balance after a node is inserted
        testInsert(avlTree, 1);
        testInsert(avlTree, 2);
        testInsert(avlTree, 3);
        testInsert(avlTree, 4);
        testInsert(avlTree, 5);
        testInsert(avlTree, 8);
        testInsert(avlTree, 7);
        testInsert(avlTree, 9);
        testInsert(avlTree, 10);
        testInsert(avlTree, 6);

        /* Insert a duplicate node */
        testInsert(avlTree, 7);

        /* Remove a node */
        // Observe how the AVL tree maintains balance after a node is removed
        testRemove(avlTree, 8); // Remove a node with 0 children
        testRemove(avlTree, 5); // Remove a node with 1 child
        testRemove(avlTree, 4); // Remove a node with 2 children

        /* Look up a node */
        TreeNode node = avlTree.search(7);
        System.out.println("\nFound node object: " + node + ", node value = " + node.val);
    }
}