Find cycle in matrix
Last updated: December 4, 2025
Quick Overview
Given a 2D matrix filled with integers, write a function to determine if there is a cycle in the matrix. A cycle is defined as a path that starts and ends at the same cell, moving only in four possible directions (up, down, left, right) without revisiting any cell. The function should return true if a cycle exists and false otherwise.
Brex
December 4, 20255
14
1,479 solved
Given a 2D matrix filled with integers, write a function to determine if there is a cycle in the matrix. A cycle is defined as a path that starts and ends at the same cell, moving only in four possible directions (up, down, left, right) without revisiting any cell. The function should return true if a cycle exists and false otherwise.
This coding problem is frequently asked during Phone Screen at Brex. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Brex expects candidates to write production-quality code, not just solve the puzzle.
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 solve this iteratively instead of recursively (or vice versa)?
- How would you parallelize this solution?
- Can you solve this in a single pass?
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Practice DSA ProblemsSample Answer
Problem Analysis
To determine if there is a cycle in a 2D matrix, we can recognize that this problem can be modeled as a graph traversal problem, where each cell in the matrix is a node. The possible movements (up, do...
Approach
- Define a DFS function that will take the current cell coordinates, the previous cell coordinates (to avoid immediately going back), and a visited matrix.
- For each cell, check all four possible d...
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