Topological Sort on matrix
Last updated: April 19, 2026
Quick Overview
Given a directed acyclic graph (DAG) represented as an adjacency matrix, implement a topological sort algorithm to return a linear ordering of its vertices. The output should be a list of vertices such that for every directed edge from vertex A to vertex B, A appears before B in the ordering. If the graph contains cycles, return an empty list.
Morgan Stanley
April 19, 20269
12
4,138 solved
Given a directed acyclic graph (DAG) represented as an adjacency matrix, implement a topological sort algorithm to return a linear ordering of its vertices. The output should be a list of vertices such that for every directed edge from vertex A to vertex B, A appears before B in the ordering. If the graph contains cycles, return an empty list.
Coding interviews at Morgan Stanley focus on problem-solving approach as much as the final solution. The interviewer wants to see you break down the problem, consider edge cases, and optimize iteratively. Communication throughout the process is key.
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?
- What happens if the input contains duplicates?
- Can you solve this in a single pass?
Sharpen Your Skills on Codemia
Practice similar problems with our interactive workspace, get AI feedback, and track your progress.
Practice DSA ProblemsSample Answer
Problem Analysis
The problem requires us to perform a topological sort on a directed acyclic graph (DAG) represented by an adjacency matrix. The topological sort algorithm is applicable here because it allows us to or...
Approach
- Initialize: Create an array to store the in-degree of each vertex based on the adjacency matrix. The in-degree of a vertex represents how many edges point to it. Also, create a queue to store v...
Submit Your Answer
