Design a Windowed Hit Counter with Fixed Buckets and Concurrency

Design a hit counter and discuss three follow-ups: many hits at the same timestamp, reducing storage and operation cost with two fixed-size arrays, and thread safety with attention to contention. ### Constraints and Clarifications The source names problem362 but does not reproduce its window or boundary contract; its official statement is access-gated. For a self-contained design, choose integer-second timestamps, a fixed window W, nondecreasing operation timestamps, and queries counting hits in(t-W,t]. These are explicit practice assumptions, not imported numeric limits. Clarify whether concurrent callers use processing time or may submit late event timestamps. ### What a Strong Answer Covers Aggregate identical timestamps, store bucket timestamps and counts in a ring, explain stale-slot reuse, and state complexity in terms of W. Define a consistency model for concurrent hits and queries rather than assuming atomic increments alone are sufficient. ### Follow-up Questions - Why is O(W) scanning called constant time only when W is treated as a fixed configured constant? - What changes if events arrive out of order?