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14. Balanced Binary Tree

easyAsked at Reddit

Determine if a binary tree is height-balanced. Reddit uses this to test bottom-up recursion — the same insight that lets them detect comment subtrees that have grown pathologically deep on one side (a fingerprint of bot reply chains).

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

Source citations

Public interview reports confirming this problem appears in Reddit loops.

  • Glassdoor (2026-Q1)— Reddit phone screen, common before fraud-detection follow-ups.

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 differs by more than one.

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

Example 3

Input
root = []
Output
true

Approaches

1. Top-down (recompute depth per node)

For each node, compute left depth and right depth via maxDepth; check difference.

Time
O(n^2)
Space
O(h)
function maxDepth(n) {
  if (!n) return 0;
  return 1 + Math.max(maxDepth(n.left), maxDepth(n.right));
}
function isBalanced(root) {
  if (!root) return true;
  const l = maxDepth(root.left), r = maxDepth(root.right);
  if (Math.abs(l - r) > 1) return false;
  return isBalanced(root.left) && isBalanced(root.right);
}

Tradeoff: Recomputes depths repeatedly. O(n^2) in the worst case (a left-leaning chain).

2. Bottom-up height with sentinel (optimal)

Return -1 from any unbalanced subtree to short-circuit. Otherwise return the actual height.

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

Tradeoff: Linear time, single pass. The -1 sentinel encodes 'unbalanced' so we don't need a second return value.

Reddit-specific tips

Reddit interviewers grade on whether you avoid the O(n^2) top-down trap. Bonus signal: connect this to detecting one-sided reply chains — bot accounts often spawn deep one-sided subtrees that trip a height-balance heuristic in their abuse pipeline.

Common mistakes

  • Recomputing depth at every node (O(n^2) trap).
  • Forgetting to propagate the -1 sentinel up.
  • Returning false instead of -1 inside the helper — loses the type contract.

Follow-up questions

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

  • Diameter of binary tree (LC 543) — same bottom-up pattern.
  • Binary tree maximum path sum (LC 124) — extends the pattern with a global accumulator.
  • What if 'balanced' means weight (size) instead of height?

Solve it now

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Output

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FAQ

Why return -1 instead of throwing?

Throws are expensive in JS and obscure control flow. -1 as a sentinel is idiomatic for 'height can't be negative'.

Does this work for n-ary trees?

Generalize the height function to take max over children[]. Same -1 short-circuit applies.

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