Validate graph symmetric
Last updated: November 23, 2025
Quick Overview
Given an undirected graph represented as an adjacency matrix, write a function to determine if the graph is symmetric. The function should return `true` if the graph is symmetric (i.e., for every edge from vertex A to vertex B, there is an edge from vertex B to vertex A) and `false` otherwise. The input will be a square matrix of size n x n, where n is the number of vertices in the graph.
Redfin
November 23, 2025453
8
645 solved
Given an undirected graph represented as an adjacency matrix, write a function to determine if the graph is symmetric. The function should return `true` if the graph is symmetric (i.e., for every edge from vertex A to vertex B, there is an edge from vertex B to vertex A) and `false` otherwise. The input will be a square matrix of size n x n, where n is the number of vertices in the graph.
Redfin 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?
- Can you optimize the space complexity of your solution?
- What if the input doesn't fit in memory?
- How would you test this solution thoroughly?
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Problem Analysis
The problem requires us to check whether an undirected graph is symmetric based on its adjacency matrix representation. A graph is symmetric if for every edge from vertex A to vertex B, there exists a...
Approach
- Input Validation: First, check if the input is a square matrix (n x n). If not, return false.
- Matrix Comparison: Use a nested loop to iterate through the upper triangle of the matrix (...
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