DFS on interval list
Last updated: October 12, 2025
Quick Overview
Given a list of intervals, implement a Depth-First Search (DFS) algorithm to find all possible combinations of non-overlapping intervals. The input will be a list of intervals represented as pairs of integers, and the output should be a list of lists, where each sublist contains a combination of non-overlapping intervals. Ensure that your solution efficiently handles overlapping intervals and returns all unique combinations.
Palo Alto Networks
October 12, 2025522
12
4,030 solved
Given a list of intervals, implement a Depth-First Search (DFS) algorithm to find all possible combinations of non-overlapping intervals. The input will be a list of intervals represented as pairs of integers, and the output should be a list of lists, where each sublist contains a combination of non-overlapping intervals. Ensure that your solution efficiently handles overlapping intervals and returns all unique combinations.
Palo Alto Networks 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
- 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
- What happens if the input contains duplicates?
- How would you modify your solution to handle streaming input?
- What is the worst-case input for your solution?
- Can you solve this in a single pass?
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Problem Analysis
This problem can be effectively solved using a Depth-First Search (DFS) approach, as we need to explore all possible combinations of non-overlapping intervals. The intervals can be viewed as nodes in ...
Approach
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Sort the Intervals: Start by sorting the list of intervals based on their start times. This helps in easily determining overlapping intervals later.
Example: Given intervals `[[1, 3], [2...
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