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

/**
 * File: avl_tree.dart
 * Created Time: 2023-04-04
 * Author: liuyuxin (gvenusleo@gmail.com)
 */

import 'dart:math';
import '../utils/print_util.dart';
import '../utils/tree_node.dart';

class AVLTree {
  TreeNode? root;

  /* Constructor */
  AVLTree() {
    root = null;
  }

  /* Get node height */
  int height(TreeNode? node) {
    // Empty node height is -1, leaf node height is 0
    return node == null ? -1 : node.height;
  }

  /* Update node height */
  void updateHeight(TreeNode? node) {
    // Node height equals the height of the tallest subtree + 1
    node!.height = max(height(node.left), height(node.right)) + 1;
  }

  /* Get balance factor */
  int balanceFactor(TreeNode? node) {
    // Empty node balance factor is 0
    if (node == null) return 0;
    // Node balance factor = left subtree height - right subtree height
    return height(node.left) - height(node.right);
  }

  /* Right rotation operation */
  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 node height
    updateHeight(node);
    updateHeight(child);
    // Return the root of the subtree after rotation
    return child;
  }

  /* Left rotation operation */
  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 node height
    updateHeight(node);
    updateHeight(child);
    // Return the root of the subtree after rotation
    return child;
  }

  /* Perform rotation operation to restore balance to the subtree */
  TreeNode? rotate(TreeNode? node) {
    // Get the balance factor of node
    int factor = balanceFactor(node);
    // Left-leaning tree
    if (factor > 1) {
      if (balanceFactor(node!.left) >= 0) {
        // Right rotation
        return rightRotate(node);
      } else {
        // First left rotation then right rotation
        node.left = leftRotate(node.left);
        return rightRotate(node);
      }
    }
    // Right-leaning tree
    if (factor < -1) {
      if (balanceFactor(node!.right) <= 0) {
        // Left rotation
        return leftRotate(node);
      } else {
        // First right rotation then left rotation
        node.right = rightRotate(node.right);
        return leftRotate(node);
      }
    }
    // Balanced tree, no rotation needed, return
    return node;
  }

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

  /* Recursively insert node (helper method) */
  TreeNode? insertHelper(TreeNode? node, int val) {
    if (node == null) return TreeNode(val);
    /* 1. Find insertion position and insert 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; // Do not insert duplicate nodes, return
    updateHeight(node); // Update node height
    /* 2. Perform rotation operation to restore balance to the subtree */
    node = rotate(node);
    // Return the root node of the subtree
    return node;
  }

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

  /* Recursively remove node (helper method) */
  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 ?? node.right;
        // Number of child nodes = 0, remove node and return
        if (child == null)
          return null;
        // Number of child nodes = 1, remove node
        else
          node = child;
      } else {
        // Number of child nodes = 2, remove the next node in in-order traversal and replace the current node with it
        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 node height
    /* 2. Perform rotation operation to restore balance to the subtree */
    node = rotate(node);
    // Return the root node of the subtree
    return node;
  }

  /* Search node */
  TreeNode? search(int val) {
    TreeNode? cur = root;
    // Loop find, break after passing leaf nodes
    while (cur != null) {
      // Target node is in cur's right subtree
      if (val < cur.val)
        cur = cur.left;
      // Target node is in cur's left subtree
      else if (val > cur.val)
        cur = cur.right;
      // Target node equals current node
      else
        break;
    }
    return cur;
  }
}

void testInsert(AVLTree tree, int val) {
  tree.insert(val);
  print("\nAfter inserting node $val, the AVL tree is");
  printTree(tree.root);
}

void testRemove(AVLTree tree, int val) {
  tree.remove(val);
  print("\nAfter removing node $val, the AVL tree is");
  printTree(tree.root);
}

/* Driver Code */
void main() {
  /* Initialize empty AVL tree */
  AVLTree avlTree = AVLTree();
  /* Insert node */
  // Notice how the AVL tree maintains balance after inserting nodes
  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 duplicate node */
  testInsert(avlTree, 7);

  /* Remove node */
  // Notice how the AVL tree maintains balance after removing nodes
  testRemove(avlTree, 8); // Remove node with degree 0
  testRemove(avlTree, 5); // Remove node with degree 1
  testRemove(avlTree, 4); // Remove node with degree 2

  /* Search node */
  TreeNode? node = avlTree.search(7);
  print("\nFound node object = $node, node value = ${node!.val}");
}