Problem Solving on Paper

What they ask

Same round as the SQL questions: the engineering manager hands you a printed sheet and you solve on paper, talking through your approach. The problems are general problem solving rather than a specific framework, sized to fit in a few minutes each.

A representative one:

You get a list of order timestamps (Unix seconds) for one warehouse in a day, unsorted. Return the start of the busiest 60-minute window, meaning the window containing the most orders. On ties, return the earliest start.

Examples

• [100, 200, 3700, 3800, 3900], window 3600 seconds: the window starting at 3700 holds 3700, 3800, 3900 (3 orders), so return 3700. The window starting at 200 only holds 200, 3700.
• [0, 1000, 5000, 6000]: two windows tie with 2 orders each, return the earlier start, 0.

Constraints

• Up to 10^5 timestamps, values fit in 64-bit integers.
• A window is inclusive at the start and exclusive at the end: [start, start + 3600).
• A window may start at an order timestamp; that is sufficient, and you should be able to argue why.

What they look for

• A correct brute force first, stated clearly, then the sorted two-pointer improvement.
• Handwritten code that would actually run: an off-by-one on the window boundary is the usual mistake.
• Complexity you can defend: O(n log n) for the sort, O(n) for the sweep.
• Clarifying questions before writing, for example whether timestamps can repeat.

You will not have a compiler, so walk through your code on the first example line by line.