How do you compute the diameter of a binary tree? | Interview Question

Q: How do you compute the diameter of a binary tree?

**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 Imagine a family of hikers spread over a network of mountain trails that never form a loop — every trail splits into at most two smaller trails as it goes downhill. Two friends want to stand as far apart as possible *along the trails* so they can test their walkie-talkies. Where should they stand? Your first guess might be "one at the very top, one

The problem

Question presented to candidate: "Given the root of a binary tree, write a Python function that returns the length of its diameter: the number of edges on the longest path between any two nodes. The path does not have to pass through the root."

What a strong answer should cover:

Every path has a highest (bend) node; the longest path bending at a node has height(left) + height(right) edges.
The answer is the maximum over all nodes, so a root-only computation is wrong when the longest path sits inside one subtree.
One post-order pass: return the height to the parent, record the best left + right on the side — O(n) time, O(h) space.
Why recomputing heights at every node is O(n · h), O(n²) on a chain.
Python details: a nested helper with nonlocal best (or a one-element list) instead of a global, and the 1000-frame recursion limit for deep chains.
Edges vs nodes: a single node has diameter 0.

Clarifying questions expected:

Is the length measured in edges or in nodes?
Must the path go through the root?

Code / implementation expected: Yes — a nested height(node) helper inside diameter(root), in Python 3.

trees
recursion

Try it yourself

Sketch your approach before you read the solution. That is what the interview tests.

Stuck? Get a hint.

A short nudge toward the approach. It will not give the answer away.

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

Imagine a family of hikers spread over a network of mountain trails that never form a loop — every trail splits into at most two smaller trails as it goes downhill. Two friends want to stand as far apart as possible along the trails so they can test

The solution is hidden so you can try first

12 min read · 11 sections

Python code

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

PythonOne post-order pass: return height, record L + R (5 trees)

Practice

PythonReconstruct the longest path; brute force vs one pass

Practice

Discussion

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