> For the complete documentation index, see [llms.txt](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/tree/110.-balanced-binary-tree.md).

# 110. Balanced Binary Tree

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]`:

```
    3
   / \
  9  20
    /  \
   15   7
```

Return true.\
\
**Example 2:**

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

```
       1
      / \
     2   2
    / \
   3   3
  / \
 4   4
```

Return false.

```cpp
// Top-Down Recursion
int helper(TreeNode* node) {
    if (!node) return 0;
    return max(helper(node->left), helper(node->right)) + 1;
}
bool isBalanced(TreeNode* root) { // time: O(n^2); space: O(n)
    if (!root) return true;
    int left = helper(root->left);
    int right = helper(root->right);
    return abs(left - right) <= 1 && isBalanced(root->left) && isBalanced(root->right);
}
```

```cpp
// Bottom-Up Recursion
int helper(TreeNode* node) {
    if (!node) return 0;
    int left = helper(node->left);
    if (left == -1) return -1;
    int right = helper(node->right);
    if (right == -1) return -1;
    if (abs(left - right) > 1) return -1;
    return max(left, right) + 1;
}
bool isBalanced(TreeNode* root) { // time: O(n); space: O(n)
    return helper(root) != -1;
}
```