Implement Food Delivery Billing

You are implementing billing logic for a food-delivery platform.

Each completed delivery record contains:

• order_id
• driver_id
• requested_at — when the customer placed the order
• picked_up_at — when the driver picked up the food
• delivered_at — when the order was delivered
• distance_km

Use the following rules:

Customer delivery charge

• Base fee: $2.00
• Distance fee: $1.20 * distance_km
• Time fee: $0.25 per minute from picked_up_at to delivered_at
• Peak-hour multiplier: if requested_at falls in either 11:00-13:00 or 18:00-20:00 , multiply the total by 1.5
• Return the final value rounded to the nearest cent

Driver payout

• Fixed completion bonus: $3.00
• Distance payout: $0.80 * distance_km
• Time payout: $0.20 per minute from picked_up_at to delivered_at
• A delivery becomes payable at delivered_at

Implement the following:

1. A function to compute the customer delivery charge for a single order.
2. A function total_payout_at(timestamp, deliveries) that returns the total amount owed to all drivers for deliveries with delivered_at <= timestamp .
3. Follow-up: explain how you would support a very large number of deliveries and many payout queries at arbitrary timestamps more efficiently than scanning the full list each time.