How do you check if a binary tree is symmetric?

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

**Target Audience:** Beginners preparing for coding interviews; you should know what a binary tree is. **Difficulty:** Easy **Language:** Python 3 > **How to read this doc:** Every idea is explained in plain language first, then tagged with `📌 Interview term:` so you also learn the exact words an interviewer expects. Every code block in this Python version was run, and the **Verified** section quotes the real output. ## 1. Why This Even Matters — A Story First Fold a sheet of paper in half, put a blob of paint on one side, and press the halves together. When you open it, the picture is perfectly symmetric: every blob on the left has a twin at the same height on the right, the same distance from the fold. A symmetric binary tree is that ink-blot picture. Draw a vertical line through the root; the left half must be the exact mirror image of the right half — same values, same shape, flipped. The trap is in the word "mirror". It is not enough for the two halves to look the same; the *

The problem

Question presented to candidate: "Given the root of a binary tree, write a Python function that returns True if the tree is a mirror of itself — symmetric around its centre — and False otherwise. Can you do it both recursively and iteratively?"

What a strong answer should cover:

Reduce the problem to a two-argument mirror check: is_mirror(root.left, root.right).
The four cases: both None, exactly one None, different values, then outer pair and inner pair.
An iterative version with a deque of node pairs (pairs containing None are fine).
O(n) time, O(h) recursion or O(w) queue space; why an inorder palindrome check is wrong.
Python specifics: compare values with ==, not is (is tests object identity and fails for larger ints built at runtime); and short-circuits; the recursion limit of 1000 limits the recursive version on deep trees.

Clarifying questions expected:

"Must the shape mirror as well as the values?"
"Should an empty tree count as symmetric?"

Code / implementation expected: Yes — a recursive Python helper on two nodes, and ideally an iterative queue-of-pairs version.

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 is. Difficulty: Easy Language: Python 3

How to read this doc: Every idea is explained in plain language first, then tagged with 📌 Interview term: so you also learn the exact words an interviewer expects. Every code block in this Python version was run, and the Verified section quotes the real output.

1. Why This Even Matters — A Story First

Fold a sheet of paper in half, put a blob of paint on one side, and press the halves together. When you open it, the picture is perfectly symmetric: every blob on the left has a twin at the same height on the right, the same distance from the fold.

A symmetric binary tree is that ink-blot picture. Draw a vertical line through the root; the left half must be the exact mirror image of the right half — same values, same shape, fl

The solution is hidden so you can try first

11 min read · 10 sections

Python code

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

PythonRecursive mirror check on six trees

Practice

PythonIterative queue of pairs, the wrong inorder-palindrome idea, and a 100001-node V tree