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13. Balanced Binary Tree

easyAsked at Vercel

Determine if a binary tree is height-balanced (left and right subtrees of every node differ in height by at most 1). Vercel asks this for the early-exit recursive pattern — a small twist on max-depth that catches sloppy candidates.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Source citations

Public interview reports confirming this problem appears in Vercel loops.

  • Glassdoor (2025-12)— Vercel screen; the early-exit version is the bonus signal.
  • Blind (2026-Q1)— Mentioned in Vercel onsite recap.

Problem

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

Constraints

  • The number of nodes in the tree is in the range [0, 5000].
  • -10^4 <= Node.val <= 10^4

Examples

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

Approaches

1. Compute height at every node

For every node, compute height of left and right; compare. Recurse into both children.

Time
O(n^2) worst case
Space
O(h)
function isBalanced(root) {
  if (!root) return true;
  const height = (n) => !n ? 0 : 1 + Math.max(height(n.left), height(n.right));
  return Math.abs(height(root.left) - height(root.right)) <= 1
      && isBalanced(root.left)
      && isBalanced(root.right);
}

Tradeoff: Quadratic because height() recurses fully at every node. Easy to write but slow.

2. Single-pass with early-exit sentinel (optimal)

Return height if balanced, -1 if not. As soon as any subtree is unbalanced, the -1 propagates up and short-circuits.

Time
O(n)
Space
O(h)
function isBalanced(root) {
  function check(node) {
    if (!node) return 0;
    const l = check(node.left);
    if (l === -1) return -1;
    const r = check(node.right);
    if (r === -1) return -1;
    if (Math.abs(l - r) > 1) return -1;
    return 1 + Math.max(l, r);
  }
  return check(root) !== -1;
}

Tradeoff: O(n) single pass. The sentinel value (-1) lets one return value carry both 'height' and 'this subtree is bad' — a common interview pattern.

Vercel-specific tips

Vercel grades for the early-exit pattern. Writing the O(n^2) version first is fine — say 'this is the naive approach, let me show you how to fold it into one pass.' Bonus signal: explaining why -1 is a safe sentinel (heights are non-negative).

Common mistakes

  • Returning the height with no sentinel — forces you back to the O(n^2) approach.
  • Forgetting to check both children's sentinels before computing the local height.
  • Confusing 'balanced' with 'complete' or 'perfect' — those are different definitions.

Follow-up questions

An interviewer at Vercel may pivot to one of these next:

  • Self-balancing tree insertion (AVL or red-black).
  • Convert sorted array to balanced BST (LC 108).
  • Maximum depth (LC 104) — base case for this problem.

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Output

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FAQ

Why is -1 a safe sentinel?

Heights are >= 0 by definition. Using -1 as 'this subtree is unbalanced' carves out an unreachable value that's cheap to test for.

What's the difference between balanced and complete?

Balanced is about height: every node's subtrees differ by at most 1. Complete is about shape: every level except possibly the last is full, and the last is filled left-to-right. They're orthogonal.

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