Thread-safe Token Bucket Rate Limiter

Problem: Thread-safe Token Bucket Rate Limiter Design and implement a thread-safe rate limiter using the Token Bucket algorithm. Requirements Use the Token Bucket algorithm. Support concurrent calls from multiple threads and guarantee atomic token accounting and distribution. Discuss how to reduce lock contention under high concurrency. API Implement: allow(now: float, cost: int = 1) -> bool Meaning: at time now, try to consume cost tokens. Return True if enough tokens are available; otherwise return False. Input Format For deterministic judging, logical time is provided: First line: capacity refill_rate, where capacity is bucket capacity and refill_rate is tokens added per second. Second line: integer m, number of operations. Next m lines: ALLOW now cost Output Format For each ALLOW, print one line: true or false. Constraints 1 <= capacity <= 10^9 0 < refill_rate <= 10^9 1 <= m <= 200000 now is non-decreasing. Example Input 5 1 6 ALLOW 0 1 ALLOW 0 1 ALLOW 0 1 ALLOW 0 1 ALLOW 0 1 ALLOW 0 1 Output true true true true true false