Minimum Discards to Balance Inventory

Description

You are given two integers w and m, and an integer array arrivals, where arrivals[i] is the type of item arriving on day i (days are 1-indexed).

Items are managed according to the following rules:

- Each arrival may be kept or discarded; an item may only be discarded on its arrival day.

- For each day i, consider the window of days [max(1, i - w + 1), i] (the w most recent days up to day i):


- For any such window, each item type may appear at most m times among kept arrivals whose arrival day lies in that window.

- If keeping the arrival on day i would cause its type to appear more than m times in the window, that arrival must be discarded.





Return the minimum number of arrivals to be discarded so that every w-day window contains at most m occurrences of each type.