[LeetCode] 110. Balanced Binary Tree

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Problem

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

For this problem, a height-balanced binary tree is defined as:

a binary tree in which the depth of the two subtrees of every node never differ by more than 1.

Example 1:

Given the following tree [3,9,20,null,null,15,7]:

1
2
3
4
5
    3
   / \
  9  20
    /  \
   15   7

Return true.

Example 2:

Given the following tree [1,2,2,3,3,null,null,4,4]:

1
2
3
4
5
6
7
       1
      / \
     2   2
    / \
   3   3
  / \
 4   4

Return false.

Explanation

  1. We use recursion method to solve most of the tree problem. There are 3 conditon to check if the root is a balanced binary tree.

    1. The difference between left subtree’s height and right subtree’s height is no more than 1.
    2. Left subtree is already a balanced binary tree.
    3. Right subtree is already a balanced binary tree.

  2. The base case of the getHeight helper funtion is if the root is NULL, we can return its height to be zero.

Solution

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/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    int getHeight(TreeNode root) {
        if (root == null) return 0;
        return 1+Math.max(getHeight(root.left), getHeight(root.right));
    }
    public boolean isBalanced(TreeNode root) {
        if (root == null) return true;
        return isBalanced(root.left) && isBalanced(root.right) && Math.abs(getHeight(root.left)-getHeight(root.right)) <= 1;
    }
}