Topological Sort on interval list
Last updated: November 13, 2025
Quick Overview
Given a list of intervals, perform a topological sort to determine a valid ordering of the intervals such that no two overlapping intervals appear in the sorted order. The input will be a list of intervals represented as pairs of integers, and the output should be a list of intervals in a valid topological order. If no valid order exists, return an empty list.
xAI
November 13, 2025258
13
1,809 solved
Given a list of intervals, perform a topological sort to determine a valid ordering of the intervals such that no two overlapping intervals appear in the sorted order. The input will be a list of intervals represented as pairs of integers, and the output should be a list of intervals in a valid topological order. If no valid order exists, return an empty list.
xAI uses this problem in the Technical Screen 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 modify your solution to handle streaming input?
- How would you test this solution thoroughly?
- What if the input doesn't fit in memory?
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Problem Analysis
The problem requires us to perform a topological sort on a list of intervals such that no two overlapping intervals exist in the sorted order. This problem can be effectively approached using a graph-...
Approach
- Build a Graph: Create a graph where each interval is a node. For two intervals (A, B), if A ends before B starts, add a directed edge from A to B.
- Topological Sort: Use Kahn's algorithm...
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