BFS on interval list
Last updated: November 6, 2025
Quick Overview
Given a list of intervals, implement a Breadth-First Search (BFS) algorithm to find the maximum number of non-overlapping intervals that can be selected. The input will be a list of intervals represented as pairs of integers, where each pair denotes the start and end of an interval. The output should be an integer representing the count of the maximum non-overlapping intervals.
Scale AI
November 6, 2025140
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3,911 solved
Given a list of intervals, implement a Breadth-First Search (BFS) algorithm to find the maximum number of non-overlapping intervals that can be selected. The input will be a list of intervals represented as pairs of integers, where each pair denotes the start and end of an interval. The output should be an integer representing the count of the maximum non-overlapping intervals.
This coding problem is frequently asked during Technical Screen at Scale AI. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Scale AI expects candidates to write production-quality code, not just solve the puzzle.
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?
- Can you optimize the space complexity of your solution?
- Can you solve this iteratively instead of recursively (or vice versa)?
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Problem Analysis
This problem is best approached using a Greedy algorithm rather than a traditional BFS. The goal is to select the maximum number of non-overlapping intervals from a list, which aligns with the concept...
Approach
- Sort the Intervals: Begin by sorting the list of intervals based on their end times. For example, given intervals
[(1, 3), (2, 4), (3, 5)], sorting will yield[(1, 3), (2, 4), (3, 5)].
2....
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