Citadel·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026

Summary

Citadel SWE interview with a calendar scheduling problem that sounds straightforward until you actually have to handle all the edge cases they throw at you. Solid algorithmic question with a system design flavor baked in.

Questions Asked (1)

Given K participants' calendars, each containing sorted non-overlapping busy intervals within a working window, and a required meeting duration, find the earliest available time slot that fits within all participants' working hours and avoids all busy intervals. Also discuss time and space complexity, and how you'd handle unsorted or overlapping inputs and large K.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

The core merge logic wasn't too bad once I realized you just sweep through all busy intervals across calendars and find gaps.

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AI HintsAI Generated

Suggested Approach

Clarify assumptions (working hours, interval inclusivity, K size), then present a solution that merges all busy intervals into a single sorted list, scans for gaps between consecutive busy intervals within the working window, and returns the earliest gap that fits the meeting duration. Follow with complexity analysis and discuss handling unsorted/overlapping inputs and large K via streaming or divide-and-conquer.

Pro tip: Mention that you'd validate inputs and handle edge cases (e.g., no available slot, meeting duration exceeds working window) before coding, and explicitly state that you'd confirm whether intervals are half-open or closed—this shows attention to detail and prevents off-by-one errors.

1. Clarify requirements and assumptions

Ask about working hours (same for all?), interval inclusivity, K size, and whether inputs are guaranteed sorted and non-overlapping. Confirm the expected output format (start time or interval).

2. Outline the core algorithm

Explain that you'll merge all busy intervals into a single sorted list (using a min-heap or K-way merge if K is large), then scan for gaps between consecutive intervals and the working window boundaries to find the earliest slot of at least the required duration.

3. Analyze time and space complexity

State that merging K sorted lists of total size N takes O(N log K) time with a heap, and scanning takes O(N). Space is O(N) for the merged list, or O(K) if using a heap and processing on the fly.

4. Discuss handling unsorted or overlapping inputs

If inputs are unsorted, sort each list first (O(N log N) total) or use a global sort; if overlapping, merge intervals during the scan. Mention that overlapping within a single participant's calendar can be merged first.

5. Address large K and scalability

For very large K, avoid storing all intervals; use a streaming approach with a min-heap to merge on the fly, or divide-and-conquer. Discuss trade-offs between memory and time, and potential parallelization.

Key Points to Mention

Merge all busy intervals into a single sorted list using a min-heap for efficiency when K is large.
Scan for gaps between consecutive busy intervals and the working window boundaries, checking if gap length >= meeting duration.
Time complexity: O(N log K) for merging, O(N) for scanning; space complexity: O(N) or O(K) with streaming.
Handle unsorted inputs by sorting each list first (O(N log N)) or using a global sort; handle overlapping intervals by merging them during the scan.
For large K, consider streaming with a heap to avoid storing all intervals, or divide-and-conquer to parallelize.
Edge cases: no available slot, meeting duration exceeds working window, intervals touching boundaries, and inclusivity of endpoints.

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