Efficient Sliding Window Algorithm: O(n) Solution with Functional Queues

This article presents an efficient algorithm for solving sliding window problems using functional programming techniques. By constructing functional queues based on two stacks and leveraging the properties of monoids, the algorithm calculates various statistics of sliding windows, such as maximum, minimum, or sum, in O(n) time. The article details the implementation of monoidally-annotated stacks and queues, provides code examples, and concludes with several related algorithmic challenges.