Topological Sort on array
Last updated: July 28, 2025
Quick Overview
Given a directed acyclic graph (DAG) represented as an array of edges, implement a function to perform a topological sort and return an array of vertices in a linear order that respects the dependencies defined by the edges. The function should handle cases where the graph is empty or has no valid topological ordering, returning an empty array in such cases.
Twilio
July 28, 202538
14
3,163 solved
Given a directed acyclic graph (DAG) represented as an array of edges, implement a function to perform a topological sort and return an array of vertices in a linear order that respects the dependencies defined by the edges. The function should handle cases where the graph is empty or has no valid topological ordering, returning an empty array in such cases.
Coding interviews at Twilio 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
- Quickly identify the optimal approach and its theoretical basis
- Handle complex algorithm design with multiple interacting components
- Write concise, elegant code under time pressure
- Prove correctness of your approach and discuss alternative solutions
- Optimize beyond the obvious: discuss constant factor improvements
- Address follow-up variations and explain how the solution generalizes
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 test this solution thoroughly?
- Can you optimize the space complexity of your solution?
- What happens if the input contains duplicates?
- Can you solve this iteratively instead of recursively (or vice versa)?
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Practice DSA ProblemsSample Answer
Problem Analysis
To solve the topological sort problem, we recognize that it involves a directed acyclic graph (DAG). The challenge is to return a linear ordering of its vertices such that for every directed edge u ->...
Approach
- Build the Graph: Convert the list of edges into an adjacency list representation and calculate the in-degrees for each vertex.
- Example: Given edges [(1, 0), (2, 1), (3, 1)], the adjacency ...
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