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13. Balanced Binary Tree

easyAsked at Tesla

Determine if a binary tree is height-balanced.

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

Problem

Given the root of a binary tree, return true if it is height-balanced — for every node, the heights of left and right subtrees differ by at most 1.

Constraints

  • 0 <= node count <= 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 height recomputed

Compute height at every node, recurse.

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 single pass

Return height or -1 sentinel; bail when any subtree is unbalanced.

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:

Tesla-specific tips

Tesla wants the bottom-up sentinel that avoids the O(n^2) trap — same idea as bailing on a planner branch the instant a subtree fails its real-time deadline.

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Output

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