Code Craft: Batch with Capacity & Time Window (MLE)

MLE PhD intern coding round. Given timepoints `1, 3, 5, ...` and per-batch constraints `(capacity B, window W)`, group timepoints into the minimum number of batches such that each batch holds at most B items and the latest item in a batch is within W time units of the earliest. Follow-up extends to a meeting-room-2 style sweep-line variant. Requirements Input: a sorted list of timepoints, a batch capacity B, a window length W. Group timepoints into batches such that: Each batch holds ≤ B timepoints. For each batch, max(batch) − min(batch) ≤ W. Output: minimum number of batches. Follow-up: rebrand as "riders picking up orders" — given pickup intervals, compute the minimum number of riders / batches needed using a sweep-line / meeting-room-2 pattern. Notes Greedy works because the input is sorted: open a batch starting at the earliest unbatched timepoint, fill with as many subsequent timepoints as possible up to capacity B, closing when the next timepoint would exceed the window or capacity. Equivalent to interval-cover by capped-size windows. Time complexity O(n) after the input is sorted; if not sorted, O(n log n). The candidate is also asked to author test cases and run them — keep a 3-test scaffold ready (small / boundary / capacity-exceeded). The follow-up extension ("riders picking up orders") is classic LC 253 "Meeting Rooms II" — sweep with a min-heap of active end-times. Different objective (concurrent rooms vs batch grouping) so don't conflate the two algorithms. Preparation Drill the greedy + window pattern on sorted data. Drill LC 253 separately for the sweep-line follow-up. Practice writing self-authored test cases — interviewers explicitly grade this.