Sliding-Window Rate Limiter / Abuse IP Detection

Maintain per-user or per-IP activity within a `t`-second window. One version returns allow/deny for each request; another returns IPs that appear more than `k` times in any window. Requirements Rate-limiter version: Input: userId[i], time[i], k, and t. Output: an integer array where 1 means request i is allowed and 0 means denied. A request is allowed only if the user has made fewer than k accepted requests in the previous t seconds. If a request is denied, it is not counted for future rate-limit decisions. Abuse-IP version: Input: arrays of IP addresses and timestamps, plus threshold k and window length t. Output: every IP address that appears more than k times within any t-second window; return an empty array if none qualify. Examples ip = [1, 2, 1] timestamp = [6, 10, 15] k = 1 t = 10 Output: [1] IP 1 appears twice within a 10-second window. Notes Maintain a deque of recent accepted timestamps per user/IP. Before evaluating the current event, pop timestamps outside the active window. For the allow/deny variant, append the current timestamp only when the request is accepted. For the IP-detection variant, append every timestamp, and mark the IP when the deque size exceeds k. Preparation Code the per-key deque version and explicitly decide whether the window is [time - t, time] or (time - t, time]; this determines the pop condition. Practise the distributed follow-up: Redis sorted sets or lists for per-key state, TTL cleanup, and a Lua/scripted atomic update to avoid read-modify-write races.