AIroot - universal solving technique

ArtoI

Hello,

I have just invented universal technique AIroot, which solves all puzzles (at least have solved so far). It is based on the fact that, there can arrive three types on conflicts, when solving.

1. basic conflicts - there are only N-1 different candidates in N cell in the area
2. fish conflicts - when eliminating number from N rows/columns, it will disappear also from N+1 columns/rows.
3. unique conflicts - this pattern means multiple solutions

When all candidates, which cause conflict immediately, have been eliminated (AIroot link 1), it is time to start linking. Linking take into account all candidates, which cause any type of conflict immediately in the new situation. If any of the conflicts appear in second link, the number can be eliminated by some AIroot link 2 technique. So, the AIroot method is some kind of enlargement of the Trebor's Tabling, because it takes into account all conflict types.

All other techniques can be also be converted to the AIroot. For example: single = AIroot link 1 technique. In normal single all candidates, which can be seen by single cell, can be eliminated. In the AIroot the way of thinking is opposite, illegal candidate cause basic conflict (empty cell), so it can be eliminated. Respectively all fish like and UR techniques are AIroot link 1 techniques.

XY-wings and Bowman Bingo are AIroot link 2 techniques and so on.

Regards,
ArtoI

Ruud · Site Admin

It is not clear from your description how this works.

Can you explain it with an example?

Ruud
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ArtoI · Posted: Thu Oct 05, 2006 1:34 pm Post subject:

Procedure of using AIroot is quite simple.

1. put candidate to its' cell
2. check if any of the conflict appear
3. eliminate all candidates, which cause conflict in the new situation
4. repeat 2 and 3 until conflict appear of eliminations are not possible
5. if you want to find out the minimum number of links needed to solve puzzle, eliminate only these candidates, which can be eliminated with the minimum steps in each situation

gsf · Posted: Thu Oct 05, 2006 4:51 pm Post subject:

ArtoI · Posted: Wed Oct 11, 2006 1:38 pm Post subject:

Correct conclusion. The benefit of my sover is, that it finds out the shortest number of links needed to make next elimination. This feature is useful, when comparing the hardest sudokus, because it is possible to make scoring, which is independent from the subjective scoring of different solving techniques and also independent from application order of the different solving techniques.

All backtrack solvers I have seen before use only limited set of conflicts. AIroot method includes them all.

So, improvements are small but usefull.