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13. Balanced Binary Tree

easyAsked at Canva

Decide whether a binary tree is height-balanced — Canva uses this to test bottom-up recursion versus naive top-down recomputation.

By Sam K., Founder, InterviewChamp.AI · Last verified

Problem

Given a binary tree, determine if it is height-balanced: for every node the heights of the two subtrees differ by no more than 1.

Constraints

  • 0 <= nodes <= 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. Top-down depth

At each node compute depth of both children; recomputes work.

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

Tradeoff:

2. Bottom-up depth with short-circuit

Return -1 from a subtree once imbalance found; otherwise return height. Single O(n) pass.

Time
O(n)
Space
O(h)
function isBalanced(root) {
  const 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:

Canva-specific tips

Canva interviewers like the early-exit sentinel pattern because it mirrors how their renderer aborts traversal at the first invalid layer.

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Output

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