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# 0110. Balanced Binary Tree

<https://leetcode.com/problems/balanced-binary-tree>

## Description

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 left and right subtrees of *every* node differ in height by no more than 1.

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/10/06/balance_1.jpg)

```
**Input:** root = [3,9,20,null,null,15,7]
**Output:** true
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/10/06/balance_2.jpg)

```
**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`

## ac

O(n), traversal is always O(n)

```java
/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public boolean isBalanced(TreeNode root) {
        if (root == null) return true;
        return height(root) != -1;
    }

    private int height(TreeNode node) {
        if (node == null) return 0;

        int left = height(node.left);
        int right = height(node.right);

        if (left == -1 || right == -1 || Math.abs(left - right) > 1) return -1;

        return left > right ? 1 + left : 1 + right;
    }
}
```