How do you check if a binary tree is balanced? | Interview Question

Q: How do you check if a binary tree is balanced?

**Target Audience:** Beginners preparing for coding interviews — you should know what a binary tree and a recursive function are; everything else is explained. **Difficulty:** Medium **Language:** Python 3 > **How to read this doc:** every idea is explained in plain words first. When a word appears that an interviewer will expect you to know, it is tagged `📌 Interview term:` with a one-line definition, and every tagged term is collected in the Quick Glossary at the end. Every program on this page was actually run, and the output you see in the **Verified** section is copied from that run. ## 1. Why This Even Matters — A Story First Picture a mobile hanging over a baby's cot: a stick, with a string at each end, and on each string either a toy or another, smaller stick with its own two strings. It only hangs nicely if **every** stick is roughly level. A mobile where the top stick is perfectly level but one of the lower sticks droops badly still looks broken. A binary tree is the

The problem

Question presented to candidate: "You are given the root of a binary tree, a tree of Node objects with val, left and right. Write a Python function that returns true if the tree is height-balanced — meaning that at every node, the heights of the left and right subtrees differ by at most one — and false otherwise."

What a strong answer should cover:

The definition applies at every node, not just the root, and an empty tree is balanced.
The naive top-down approach (compute both heights at every node) and why it repeats work: O(n · h), so O(n log n) on a balanced tree.
The bottom-up post-order approach: return the height, or a sentinel such as -1 as soon as a subtree fails, so the whole check is O(n).
Space is the recursion stack, O(h): O(log n) when balanced, O(n) for a chain.
Python details: compare the sentinel with == -1 (height 0 is falsy), and the default recursion limit of 1000 for skewed trees.
Why balance matters: search trees stay O(log n) only while their height is small.

Clarifying questions expected:

Is "balanced" the height-gap-at-most-one definition, and is an empty tree balanced?
Can the tree be very deep (risk of stack overflow)?

Code / implementation expected: Yes — check_height(node) returning an int, plus is_balanced(root), in Python 3.

trees
balanced

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Solution

Target Audience: Beginners preparing for coding interviews — you should know what a binary tree and a recursive function are; everything else is explained.
Difficulty: Medium
Language: Python 3

How to read this doc: every idea is explained in plain words first. When a word appears that an interviewer will expect you to know, it is tagged 📌 Interview term: with a one-line definition, and every tagged term is collected in the Quick Glossary at the end. Every program on this page was actually run, and the output you see in the Verified section is copied from that run.

1. Why This Even Matters — A Story First

Picture a mobile hanging over a baby's cot: a stick, with a string at each end, and on each string either a toy or another, smaller stick with its own two strings. It only hangs nicely if every stick is roughly level. A mobile where the top stick i

The solution is hidden so you can try first

14 min read · 11 sections

Python code

Edit the code and run it here. Each printed line with an expected value becomes a test.

PythonBottom-up check with a -1 sentinel (7 trees)

Practice

PythonTop-down vs bottom-up: nodes touched

Practice

Discussion

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