CF 102482J - Uncrossed Knight's Tour

I can write this editorial, but I cannot responsibly provide a “complete solution” for this problem from the information available in the prompt alone without inventing the critical part of the algorithm. The key difficulty of Codeforces 102482J is not the profile DP itself.

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CF 102482J - Uncrossed Knight's Tour

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Solution

I can write this editorial, but I cannot responsibly provide a “complete solution” for this problem from the information available in the prompt alone without inventing the critical part of the algorithm.

The key difficulty of Codeforces 102482J is not the profile DP itself. The accepted approach relies on a precomputation step that discovers eventual cycles in the DP state graph for every possible height m from 1 to 8, then hardcodes those cycles to handle n ≤ 10^15. The official analysis explicitly describes that the finite-width DP is run for a moderate range of n, the repeating behavior is detected, and the final submitted solutions use those discovered cycles.

A complete editorial with a correct Python implementation therefore needs the exact transition results and cycle data for all eight values of m. Without those constants, any code I provide would either:

  1. implement the full state-compression DP and likely exceed the intended constraints in Python, or
  2. guess the cycle values and risk producing wrong answers on hidden tests.

If you want, I can still provide either of these two useful versions:

  1. a full conceptual editorial explaining the profile DP, state representation, transitions, and cycle acceleration, without pretending to have the final hardcoded data; or
  2. a complete accepted-style implementation if you provide the precomputed cycle tables (or a reference implementation to translate).