Validate binary tree symmetric
Last updated: October 12, 2025
Quick Overview
Given a binary tree, write a function to determine if it is symmetric around its center. A binary tree is considered symmetric if the left subtree is a mirror reflection of the right subtree. The function should take the root node of the binary tree as input and return a boolean value indicating whether the tree is symmetric.
Two Sigma
October 12, 202562
15
4,642 solved
Given a binary tree, write a function to determine if it is symmetric around its center. A binary tree is considered symmetric if the left subtree is a mirror reflection of the right subtree. The function should take the root node of the binary tree as input and return a boolean value indicating whether the tree is symmetric.
Two Sigma uses this problem in the Onsite to evaluate your algorithmic thinking. They expect you to discuss multiple approaches, analyze trade-offs between them, and implement the optimal solution with clean, readable code.
What the Interviewer Expects
- Recognize the underlying problem pattern (sliding window, two pointers, BFS/DFS, etc.)
- Discuss multiple approaches and trade-offs before coding
- Implement an optimal solution with clean, production-quality code
- Handle all edge cases including boundary conditions and invalid input
- Optimize both time and space complexity with clear justification
- Test your solution systematically with well-chosen examples
Key Topics to Cover
How to Approach This
- Clarify input constraints and edge cases before writing code.
- Walk through your approach verbally and confirm with the interviewer before coding.
- Start with a brute force solution, then optimize. Mention time and space complexity.
- Test your solution with examples, including edge cases like empty input or duplicates.
- Consider common patterns: sliding window, two pointers, hash map, BFS/DFS, dynamic programming.
Possible Follow-up Questions
- Can you optimize the space complexity of your solution?
- Can you solve this iteratively instead of recursively (or vice versa)?
- What happens if the input contains duplicates?
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Practice DSA ProblemsSample Answer
Problem Analysis
To determine if a binary tree is symmetric, we need to check if the left subtree is a mirror reflection of the right subtree. The specific pattern that applies here is Depth First Search (DFS) because...
Approach
- Define a recursive helper function
is_mirror(left, right)that checks if two nodes are mirrors of each other. - If both nodes are
None, they are mirrors, returnTrue. - If one node is `...
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