Delivering Boxes from Storage to Ports

Given an ordered list of boxes (port, weight) and ship limits on maxBoxes and maxWeight, partition the sequence into contiguous delivery batches (respecting capacity) to minimize total trips, where each batch’s cost depends on the number of port switches inside it plus return trips. The core challenge is an optimization over contiguous segments — typically solved with dynamic programming combined with prefix sums and a sliding-window/monotonic-queue optimization to account for port-change costs efficiently.