Hidden Cycle Length

The judge owns a hidden cycle of length n and a token initially placed at a hidden starting vertex. Each vertex has a visible label. The starting vertex is labeled with its own position; newly visited positions receive unique labels lazily from the source interactor.

At the start of a source case the evaluator is ready for commands; it does not reveal n.

To move the token, write:

walk x

where 0 <= x <= 10^9, then flush. The evaluator moves x steps forward around the hidden cycle and returns the visible label at the reached vertex. A walk 0 command returns the current label and counts as a walk.

To finish the current case, write guess g, flush, and continue reading. The guess must be in [1, 10^9]; it is correct only when g = n.

Agentics may chain multiple source cases. After a correct guess, read one wrapper-framing line. NEXT means another hidden source case begins and you should start issuing walk or guess commands for it. 0 0 means the session is complete and your program should exit. Malformed commands, too many walks, EOF before a guess, or a wrong guess receive zero from the trusted evaluator. The trusted evaluator writes result.json; participant code must only speak the stdin/stdout protocol.

The official score is the original Frontier-CS log-space query-count score, scaled to score from 0 to 100.