ImplementClaim probe

Tail at scale: bounded retry with jitter

Implement `run(attempt, base_ms, cap_ms)` returning the jittered backoff delay (ms) for retry `attempt` (0-indexed): exponential backoff base = base_ms * 2^attempt, capped at cap_ms, then apply FULL jitter: a uniformly random value in [0, capped]. For determinism, use a fixed pseudo-random sample: rand = ((attempt * 7919) % 1000) / 1000 (a value in [0,1)). Return the integer floor of rand * capped. Also return the raw capped backoff so the learner can see the bound.

python12 mindifficulty 2/4

From The Tail at Scale

Sample tests

run([0,100,2000])→{"backoff_ms":0,"capped_ms":100}
run([1,100,2000])→{"backoff_ms":183,"capped_ms":200}
run([2,100,2000])→{"backoff_ms":335,"capped_ms":400}

Hints

Exponential backoff grows by 2^attempt each retry — but without jitter, synchronized clients still collide.
Full jitter picks a uniform value in [0, capped], so retries spread out instead of thundering back together.
capped = min(base_ms * 2^attempt, cap_ms).
The deterministic rand = ((attempt * 7919) % 1000) / 1000 makes the result reproducible.

Hints

Code runs in an isolated sandbox on the OpenSandbox judge. No model key required.