Topological Sort on array
Last updated: May 11, 2026
Quick Overview
Given a directed acyclic graph (DAG) represented as an array of edges, implement a function to perform a topological sort on the graph. The function should return an array of vertices in a linear order such that for every directed edge from vertex A to vertex B, A comes before B in the output array. If the graph contains cycles, the function should return an empty array.
Grafana Labs
May 11, 2026467
13
3,135 solved
Given a directed acyclic graph (DAG) represented as an array of edges, implement a function to perform a topological sort on the graph. The function should return an array of vertices in a linear order such that for every directed edge from vertex A to vertex B, A comes before B in the output array. If the graph contains cycles, the function should return an empty array.
Grafana Labs 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
- Identify the correct data structure and algorithm for the problem
- Write clean, bug-free code with proper variable naming
- Analyze time and space complexity correctly
- Handle basic edge cases (empty input, single element)
- Communicate your thought process while coding
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 your solution change if the input was sorted?
- Can you solve this in a single pass?
- Can you solve this iteratively instead of recursively (or vice versa)?
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Problem Analysis
To solve the problem of performing a topological sort on a directed acyclic graph (DAG) represented as an array of edges, we can use the Kahn's Algorithm or a Depth-First Search (DFS) approach...
Approach
- Construct the Graph: We will create an adjacency list and an in-degree count for each vertex based on the edges provided. For example, if the edges are [(0, 1), (0, 2), (1, 2)], the adjacency l...
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