Design rolling-window conversation score tracker

Design a class that tracks conversation scores over a rolling time window. ## Requirements You are given a window size `W` (in seconds) at initialization time. Each conversation event has: - `conversation_id` (string/int, unique) - `timestamp` (integer seconds) - `score` (integer in `[1, 5]`) Implement the following operations: 1. `record(conversation_id, timestamp, score)` - Records a new conversation score. - Assume calls to `record` arrive with **non-decreasing** `timestamp`. 2. `get_average(now)` - Returns the average score of all conversations with timestamps in the **active window**: - `(now - W, now]` (i.e., strictly greater than `now-W` and up to `now`, inclusive). - If there are no active conversations, return `0` (or specify a reasonable alternative). 3. `update(conversation_id, new_score, now)` - Updates the score for `conversation_id` **only if** that conversation is currently in the active window at time `now`. - If the conversation is not active (expired or missing), ignore or return an error indicator (define your choice). 4. `get_top_percentile_nth_score(p, n, now)` - Consider only active-window conversations at time `now`. - Let `m` be the number of active conversations. - Define the **top `p` percentile** as the highest-scoring `k = ceil(p/100 * m)` conversations. - Sort active conversations by `(score DESC, timestamp ASC, conversation_id ASC)`. - Return the **score** of the `n`-th conversation (1-indexed) within that top-percentile subset. - If `m = 0` or `n > k`, return `null` (or a sentinel). ## Constraints (for design purposes) - Up to ~`2e5` total operations. - `W` can be large. - Scores are integers in `[1,5]`. Explain any additional assumptions you make and discuss expected time/space complexity for each operation.