Count connected components in interval list
Last updated: November 2, 2025
Quick Overview
Given a list of intervals, write a function to count the number of connected components formed by overlapping intervals. Two intervals are considered connected if they overlap or touch each other. The function should take a list of intervals as input and return an integer representing the number of connected components.
Datadog
November 2, 2025136
12
2,995 solved
Given a list of intervals, write a function to count the number of connected components formed by overlapping intervals. Two intervals are considered connected if they overlap or touch each other. The function should take a list of intervals as input and return an integer representing the number of connected components.
Datadog 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
- Quickly identify the optimal approach and its theoretical basis
- Handle complex algorithm design with multiple interacting components
- Write concise, elegant code under time pressure
- Prove correctness of your approach and discuss alternative solutions
- Optimize beyond the obvious: discuss constant factor improvements
- Address follow-up variations and explain how the solution generalizes
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?
- How would you test this solution thoroughly?
- What if the input doesn't fit in memory?
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Problem Analysis
To solve the problem of counting connected components in a list of intervals, we can utilize the sorting technique. Two intervals are considered connected if they overlap or touch each other. This...
Approach
- Sort the Intervals: Start by sorting the list of intervals based on their starting points. For instance, given intervals
[[1, 3], [2, 4], [6, 8], [7, 9]], sorting yields `[[1, 3], [2, 4], [6,...
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