The concurrency part is where I got turned around.
Model each order as a set of time intervals: active intervals (accept to deliver) and wait intervals (restaurant wait). Use a sweep-line algorithm over all interval endpoints to compute, for each minute, the number of orders whose active intervals cover that minute but whose wait intervals do not. Then multiply the per-minute rate by that count and sum to get total pay.
Pro tip: Clarify edge cases upfront—like whether wait windows are inclusive, how to handle overlapping wait and active periods, and whether pay is computed per minute or per second—to avoid incorrect assumptions and demonstrate attention to detail.
Ask about time granularity (minute vs second), inclusivity of intervals, and how wait windows interact with active periods. Confirm that wait time is excluded from concurrency for other orders but still counts for the order itself.
For each order, create two types of intervals: active (accept to deliver) and wait (restaurant wait start to end). Convert these into events: +1 for active start, -1 for active end, and similarly for wait intervals, but note that wait intervals should not contribute to concurrency.
Collect all event timestamps, sort them, and sweep through time. Maintain a running count of active orders, adjusting for starts and ends. At each minute, compute the concurrency count as the number of orders whose active interval covers that minute and whose wait interval does not.
For each minute, multiply the concurrency count by the per-minute rate (which may scale with concurrency). Sum these products to get total pay. If the rate is a function of concurrency, apply it accordingly.
Discuss time complexity: O(n log n) due to sorting events, where n is the number of orders. Space complexity O(n). Mention potential optimizations like bucketing if time range is small.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This follow-up is where things got messy for me.
First, clarify the pricing model: base rate, peak-hour multiplier, concurrent-order multiplier, and wait pause. Then, propose a modular design where each factor is applied in a defined order, and discuss how to handle interactions (e.g., whether peak-hour multiplier applies before or after concurrent multiplier). Finally, outline the algorithm and data structures to compute the final price efficiently.
Pro tip: Mention that you would make the peak-hour windows configurable via a data structure like an interval tree or a sorted list of time ranges, and discuss how to handle overlapping or adjacent windows. Also, emphasize the importance of defining the order of operations clearly to avoid ambiguity in pricing.
Ask clarifying questions: Are peak hours defined per restaurant or globally? Can they overlap? Does the wait pause apply before or after peak multiplier? Confirm the order of applying multipliers.
Propose a formula: final_price = (base_rate * peak_multiplier * concurrent_multiplier) * (active_minutes) - wait_pause_adjustment, or similar. Specify the order: e.g., apply peak multiplier to base rate first, then concurrent multiplier, then subtract paused time.
Suggest storing peak windows as a list of intervals (start, end) and using binary search or interval tree for efficient lookup. Mention handling of overlapping windows by merging or taking union.
Explain how to modify the existing algorithm: for each minute, check if it falls in a peak window; if so, apply double rate. Then apply concurrent multiplier and subtract wait time. Discuss time complexity.
Address trade-offs: precomputing peak minutes vs. on-the-fly lookup; handling timezone changes; overlapping windows; and ensuring the wait pause does not double-count. Mention testing strategies.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.