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Citadel·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say
May 2026

Summary

Citadel software engineer interview with a scheduling optimization problem that had a tricky discount mechanic baked in. The math side of it was more involved than I expected for what looked like a greedy problem at first glance.

Questions Asked (1)

Q1

You have n images, each with a daily processing cost and a fixed date range it must run. On any given day you can apply a discount exactly once, replacing the total cost of all running images that day with a flat discountPrice. Find the minimum total cost across all days, modulo 1,000,000,007.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

My first instinct was greedy, pick the days where the sum of active image costs is highest and apply the discount there.

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AI HintsAI Generated

Suggested Approach

Model the problem as choosing a single day to apply the discount, since it can be used at most once. For each candidate day, compute the total cost as the sum of costs of images not running that day plus the discount price if any images are running, and take the minimum over all days. Use a sweep line or difference array to efficiently compute daily totals.

Pro tip: Clarify with the interviewer whether the discount is mandatory or optional; if optional, you must also consider the case of not using it. Also, remember to apply modulo only at the end to avoid precision issues.

1. Understand the problem

Restate the problem to ensure you understand the constraints: n images, each with a cost and a date range, and a discount that can be applied exactly once on any day, replacing the total cost of running images that day with a flat discountPrice.

2. Define the objective

The goal is to minimize the total cost across all days. Since the discount is applied on exactly one day, the total cost is the sum of costs on all other days plus the discounted cost on the chosen day.

3. Compute daily costs efficiently

Use a difference array or sweep line to compute the total cost of running images for each day. For each image, add its cost to the start day and subtract it after the end day in the difference array, then prefix sum to get daily totals.

4. Evaluate each possible discount day

For each day, compute the total cost if the discount is applied that day: total cost of all days minus the daily cost of that day plus the discount price (if any images are running; otherwise, the discount might not apply). Take the minimum over all days.

5. Handle edge cases and modulo

Consider edge cases: no images running on a day, discount price higher than daily cost, and the possibility of not using the discount if it's optional. Finally, apply modulo 1,000,000,007 to the result.

Key Points to Mention

  • Difference array or sweep line for efficient daily cost computation
  • Time complexity: O(n + D) where D is the number of days, or O(n log n) if using events
  • Space complexity: O(D) for the difference array
  • Handling of days with no running images (discount may not apply)
  • Modulo operation at the end to prevent overflow
  • Clarify whether discount is mandatory or optional

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