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| Canonicalization of puzzles http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=11&t=71 |
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| Author: | enxio27 [ Tue May 20, 2008 4:20 am ] |
| Post subject: | Canonicalization of puzzles |
Ruud's Sudocue will canonicalize a collection of 81-character puzzle strings. Do I understand correctly that if two puzzle strings (as contrasted with solution strings) canonicalize to the same string, then they MUST be equivalent puzzles? If so, why would two canonically equivalent puzzles have different difficulty scores (as rated by Sudocue)? |
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| Author: | mhparker [ Thu May 29, 2008 8:18 am ] |
| Post subject: | Re: Canonicalization of puzzles |
enxio27 wrote: Do I understand correctly that if two puzzle strings (as contrasted with solution strings) canonicalize to the same string, then they MUST be equivalent puzzles? If so, why would two canonically equivalent puzzles have different difficulty scores (as rated by Sudocue)? I assume he means that 2 such puzzles are mathematically equivalent. The reason that 2 canonically equivalent puzzles can have different scores is most probably because nearly all automated solvers take the first move found that progresses the puzzle at every step, rather than collecting all available moves first and then taking the best one (whatever that means..). The first move found can thus be different in both cases. For example, 2 canonically equivalent puzzles may both have a naked subset available in one of the rows and another one in one of the columns. Regardless of whether an automated solver searches rows before columns or vice-versa, it will find and use one of the naked subsets for one of the two puzzles and the other naked subset for the other. This causes different solving paths to be taken, which in turn can lead to two different ratings. |
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