Count cycle in binary tree
Last updated: December 14, 2025
Quick Overview
Given a binary tree, write a function to count the number of distinct cycles present in the tree's structure. A cycle is defined as a path that starts and ends at the same node without retracing any edge. Your function should take the root of the binary tree as input and return an integer representing the count of cycles.
Airbnb
December 14, 2025224
11
1,783 solved
Given a binary tree, write a function to count the number of distinct cycles present in the tree's structure. A cycle is defined as a path that starts and ends at the same node without retracing any edge. Your function should take the root of the binary tree as input and return an integer representing the count of cycles.
Airbnb uses this problem in the Take-home Project 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
- How would you parallelize this solution?
- What if the input doesn't fit in memory?
- Can you solve this iteratively instead of recursively (or vice versa)?
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Practice DSA ProblemsSample Answer
Problem Analysis
To solve the problem of counting distinct cycles in a binary tree, we need to recognize that a cycle is defined as a path that starts and ends at the same node without retracing any edge. This indicat...
Approach
- Initialize a Set: Start with an empty set to keep track of visited nodes. This will help in identifying cycles.
- DFS Function: Create a recursive DFS function that takes a node, the par...
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