Citadel·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Citadel software engineer interview with a pretty gnarly intervals problem. The naive approach won't cut it here, they clearly want you to think past brute force.

Questions Asked (1)

Given n employees with working time intervals, form the largest possible team where at least one 'core' employee's schedule overlaps with every other team member's schedule. What's the maximum team size?

Algorithms & Data Structures

Author's notes

My first instinct was to check every pair of intervals and build some kind of graph, which is O(n^2) and they basically told you upfront that won't pass.

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AI HintsAI Generated

Suggested Approach

Model each employee's interval as a point in a sweep-line problem, and for each candidate core employee, count how many other intervals overlap with theirs. The maximum count across all employees is the answer, but optimize by sorting endpoints and using a heap or two-pointer technique to avoid O(n^2) comparisons.

Pro tip: Clarify that the core employee must be part of the team and that overlaps are inclusive (touching endpoints count). Mention that if no core exists, the answer is 1 (the employee themselves), and handle edge cases like zero-duration intervals.

1. Clarify problem constraints

Confirm whether intervals are closed (inclusive endpoints), whether the core employee must be in the team, and if the team can be empty. Also ask about input size to determine expected complexity.

2. Brute-force baseline

For each employee as core, iterate through all others and count overlaps. This O(n^2) approach is simple and correct, but may be too slow for large n.

3. Optimize with sweep-line

Sort all start and end points. Use a sweep to maintain active intervals; for each interval, the number of overlaps is the active count minus 1 (excluding itself). Track the maximum.

4. Handle edge cases

Consider intervals that touch at endpoints (count as overlap), zero-length intervals, and the case where no overlaps exist (answer is 1).

5. Analyze complexity

The sweep-line approach runs in O(n log n) time due to sorting, with O(n) space. This is optimal for large n.

Key Points to Mention

Interval overlap condition: two intervals [a,b] and [c,d] overlap if max(a,c) <= min(b,d).
Sweep-line algorithm: sort events (start/end) and maintain a count of active intervals.
Core employee must be included in the team, so the team size is 1 + number of overlapping intervals.
Time complexity: O(n log n) with sorting, O(n^2) brute-force is acceptable for small n.
Edge cases: no overlaps (answer 1), all intervals overlap (answer n), zero-duration intervals.
Space complexity: O(n) for storing events or intervals.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.