Topological Sort on array
Last updated: April 23, 2026
Quick Overview
Given a directed acyclic graph (DAG) represented by an array of edges, implement a function to perform a topological sort and return an array representing the linear ordering of its vertices. The function should handle cases where the graph has multiple valid topological sorts and ensure that the output is consistent with the provided input edges.
Amazon
April 23, 202628
9
422 solved
Given a directed acyclic graph (DAG) represented by an array of edges, implement a function to perform a topological sort and return an array representing the linear ordering of its vertices. The function should handle cases where the graph has multiple valid topological sorts and ensure that the output is consistent with the provided input edges.
This coding problem is frequently asked during Phone Screen at Amazon. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Amazon expects candidates to write production-quality code, not just solve the puzzle.
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
- Can you solve this iteratively instead of recursively (or vice versa)?
- What happens if the input contains duplicates?
- How would you modify your solution to handle streaming input?
- How would you test this solution thoroughly?
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Practice DSA ProblemsSample Answer
Problem Analysis
To solve the problem of performing a topological sort on a directed acyclic graph (DAG) represented by an array of edges, we need to recognize that this is a graph traversal problem where we must esta...
Approach
- Build the graph: Create an adjacency list to represent the graph from the edges array. Also, maintain an array to count in-degrees of each vertex.
- Initialize the queue: Start with all ve...
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