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13. Balanced Binary Tree

easyAsked at Etsy

Decide whether a tree is height-balanced — Etsy uses it to test pruning vs. naive double-recursion.

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

Problem

Given a binary tree, determine if it is height-balanced — every node's two subtrees differ in height by at most 1.

Constraints

  • Node count in [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 heights at each node

For each node, recompute left and right heights — recomputes a lot.

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

Tradeoff:

2. Bottom-up with sentinel

Return height up the tree; return -1 to short-circuit imbalance.

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

Tradeoff:

Etsy-specific tips

Etsy will reward the O(n) bottom-up solution explicitly — show you noticed the quadratic trap before they hint at it.

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Output

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