This looked like a clean OOP question until I started actually thinking through the edge cases.
Start by clarifying requirements and constraints (e.g., scale, timestamp precision, driver activity definition). Then design data structures and algorithms for each operation, focusing on efficient time-based queries and proration logic. Finally, discuss trade-offs and potential optimizations.
Pro tip: Emphasize the use of time-ordered data structures (like balanced BSTs or segment trees) for efficient range queries and updates, and clearly explain how you handle partial deliveries during payment marking.
Ask about expected scale (number of drivers, deliveries per day), timestamp granularity, definition of 'active driver' (e.g., during a delivery), and whether payments can be partial or must be for whole deliveries.
Propose structures: a map for driver rates, a list or tree of deliveries sorted by time, and a segment tree or interval tree for tracking driver activity to answer max concurrency queries.
Detail algorithms for registering drivers, recording deliveries (updating activity intervals), computing total cost (sum of rate * duration), and marking costs as paid up to a timestamp with proration for partial deliveries.
Explain how to efficiently find the maximum number of simultaneously active drivers in the past 24 hours using a sliding window or segment tree with lazy propagation.
Compare approaches (e.g., segment tree vs. sweep line), discuss time/space complexity, and suggest optimizations like caching or batch processing for high throughput.
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