Find the Minimum Delivery Processing Speed

Problem Description

DoorDash manages a batch of delivery orders that must be processed before the delivery hub closes. You are given a list of integers orders, where orders[i] represents the number of items in the i-th order, and an integer hours, representing the total time available in hours.

Because orders are indivisible, if a courier processes an order at a speed of k items per hour, and an order has n items, it will take ceil(n / k) hours to complete that specific order. You must process all orders one by one, and you cannot split a single order across multiple hours in a way that exceeds the capacity k per hour. Effectively, for a chosen speed k, the time taken for any order of size n is ceil(n / k) hours.

Find the minimum positive integer speed k such that the total time taken to process all orders is less than or equal to hours. If it is impossible to complete all orders within the given hours (e.g., if the number of orders exceeds the available hours), return -1.

Function Signature

def min_delivery_speed(orders: List[int], hours: int) -> int:

Examples

Example 1:

• Input: orders = [3, 6, 7, 11], hours = 8
• Output: 4
• Explanation: With speed 4, the times are ceil(3/4)=1, ceil(6/4)=2, ceil(7/4)=2, ceil(11/4)=3. Total hours: 1+2+2+3 = 8.

Example 2:

• Input: orders = [30, 11, 23, 4, 20], hours = 5
• Output: 30

Constraints

• 1 hours, it is impossible to process them because we must complete at least one order per hour. Return -1.