Minimize batches and allocate riders by time

Coding prompts (same interview round)

1) Minimum number of batches for time points

You are given a list of event time points (integers), e.g. [1, 3, 5, ...].

You need to group all events into batches under these constraints:

• Each batch can contain at most B events (capacity).
• Let t0 be the earliest time in a batch. Then every event time t in that batch must satisfy:
  • t - t0 <= W (i.e., all events lie within a window of size W starting at the earliest event in the batch).

Goal: return the minimum number of batches needed to include all events.

Input:

• times : array of integers (not guaranteed sorted)
• integers B (capacity), W (window)

Output:

• minimum number of batches

Notes:

• You may assume B >= 1 , W >= 0 .
• The implementation should be runnable and include self-chosen test cases.

2) Follow-up: minimum number of riders (Meeting Rooms II variant)

In a delivery setting, each order occupies a rider for an interval of time [start, end) (or [start, end]—clarify your convention).

Given a list of order time intervals, compute the minimum number of riders needed so that no rider is assigned overlapping orders.

Input: list of intervals (start, end)

Output: minimum number of riders required

(Expect a sweep-line / min-heap style solution.)