Implement Courier Delivery Cost Tracking

Problem Statement

You are tasked with building a billing tracker for an on-demand courier platform. Couriers are paid based on hourly rates that can change over time. Each delivery is logged as a half-open time interval [start_time, end_time) in seconds.

Implement the CourierDeliveryTracker class with the following methods:

• set_rate(courier_id: str, timestamp: int, hourly_rate_cents: int) -> None Sets the courier's hourly rate (in cents) starting from timestamp (inclusive). This rate remains in effect until a later rate is set for that courier. Timestamps for a given courier may not necessarily arrive in chronological order.

• record_delivery(delivery_id: str, courier_id: str, start_time: int, end_time: int) -> None Records a delivery completed by courier_id during [start_time, end_time) where start_time int Calculates the total cost (in cents) for the specified delivery. If the delivery spans multiple rate periods, prorate the pay according to the time spent in each rate period. The exact prorated cost for d seconds at rate r cents/hour is d * r / 3600. Sum all unrounded segment costs, then round half up to the nearest cent: math.floor(total + 0.5).

• get_courier_payout(courier_id: str, start_time: int, end_time: int) -> int Returns the total earnings for courier_id across all deliveries that overlap with the query window [start_time, end_time). For deliveries that only partially overlap with the query window, only count the overlapping portion. Deliveries for a single courier do not overlap with each other.

Example

tracker = CourierDeliveryTracker()

# Courier C1 starts at $18.00/hr (1800 cents/hr) at t = 0
tracker.set_rate("C1", 0, 1800)

# Courier C1 gets a raise to $24.00/hr (2400 cents/hr) at t = 3600
tracker.set_rate("C1", 3600, 2400)

# Delivery D1 spans t = 1800 to t = 5400 (1 hour under 1800, 0.5 hours under 2400)
tracker.record_delivery("D1", "C1", 1800, 5400)

# Cost: (1800s * 1800 / 3600) + (1800s * 2400 / 3600) = 900 + 1200 = 2100 cents
print(tracker.get_delivery_cost("D1")) # Output: 2100

# Payout for window [3600, 7200)
# Overlap with D1 is [3600, 5400) (1800s at 2400 cents/hr = 1200 cents)
print(tracker.get_courier_payout("C1", 3600, 7200)) # Output: 1200

Constraints

• Timestamps are non-negative integers: 0 = 0
• For every delivery, start_time >= min(timestamp) among all rate changes for that courier.
• Up to 10^4 calls across all methods.
• Each delivery_id is unique.