DFS on interval list
Last updated: November 30, 2025
Quick Overview
Given a list of intervals, implement a Depth-First Search (DFS) algorithm to determine if there is a valid path that covers all intervals without any overlaps. The input will be a list of intervals represented as pairs of integers, and the output should be a boolean indicating whether such a path exists.
Coinbase
November 30, 20253
9
4,247 solved
Given a list of intervals, implement a Depth-First Search (DFS) algorithm to determine if there is a valid path that covers all intervals without any overlaps. The input will be a list of intervals represented as pairs of integers, and the output should be a boolean indicating whether such a path exists.
This coding problem is frequently asked during Take-home Project at Coinbase. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Coinbase 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
- Can you optimize the space complexity of your solution?
- How would you parallelize this solution?
- What happens if the input contains duplicates?
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Practice DSA ProblemsSample Answer
Problem Analysis
The problem requires us to determine if there exists a valid path through a list of intervals without any overlaps. This can be understood as a graph traversal problem where each interval can be thoug...
Approach
- Construct the Graph: First, we will represent the intervals as nodes. For each interval, we will create edges to other intervals that do not overlap (i.e., the end of one interval is less than ...
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