Calculate Courier Earnings

Design a function to calculate total courier pay from a set of delivery orders.

Assume time is represented as integer minutes, and intervals are half-open: an order active from minute start to minute end contributes on [start, end).

Base version

Each order has:

• accepted_at
• delivered_at

There is a global rate paid per minute.

For any minute in which an order is active, that order earns rate * k, where k is the number of orders active in that same minute. In other words, if k orders overlap during a minute, the total pay contributed by that minute is k * k * rate.

Implement a function that returns the total pay across all orders.

The interviewer may ask you to define reasonable input/output structures yourself, explain your chosen data structures, analyze time and space complexity, and write meaningful test cases.

Follow-up 1

Now each order may also include:

• arrived_at
• picked_up_at

The interval [arrived_at, picked_up_at) is store-wait time. A store-wait minute is paid only for that order itself:

• it must not increase the multiplier for any other order
• other orders must not increase its multiplier

Update the design to support this rule.

Follow-up 2

During configurable peak-hour intervals, the per-minute rate is doubled.

Explain how you would extend your solution to support this efficiently.