110. Balanced Binary Tree

Problem Statement:
Given a binary tree, determine if it is
height-balanced.

Example 1:
Input: root = [3,9,20,null,null,15,7]
Output: true

Example 2:
Input: root = [1,2,2,3,3,null,null,4,4]
Output: false

Example 3:
Input: root = []
Output: true

Constraints:

• The number of nodes in the tree is in the range [0, 5000].
• -104 <= Node.val <= 104

Solution:

Algorithm:

1. If the root is null, return true.
2. Create a variable leftHeight to store the height of the left subtree.
3. Create a variable rightHeight to store the height of the right subtree.
4. Return true if the absolute difference between leftHeight and rightHeight is less than or equal to 1 and the left subtree is balanced and the right subtree is balanced, otherwise return false.

Code:

public class Solution {
    public boolean isBalanced(TreeNode root) {
        if (root == null) {
            return true;
        }
        int leftHeight = height(root.left);
        int rightHeight = height(root.right);
        return Math.abs(leftHeight - rightHeight) <= 1 && isBalanced(root.left) && isBalanced(root.right);
    }

    private int height(TreeNode root) {
        if (root == null) {
            return 0;
        }
        return 1 + Math.max(height(root.left), height(root.right));
    }

}

Time Complexity:
O(n^2) where n is the number of nodes in the tree.
Space Complexity:
O(n) where n is the number of nodes in the tree.