Simple coloring

SarC · Posted: Mon Dec 05, 2005 7:04 pm Post subject: Simple coloring

I have tried to implement simple coloring into my solver. It seems to work fine but I was wondering if there was any rules that I haven't coded ('cause I don't know 'em).

So here is a run-down of what I have made so far:

1) Color the board.

2) Check if there is two of the same letter in a house, for instance two A's. If that is true I remove the candidate from all cells that occupy that letter.

3) See if there are a conjugate pair in a house, for instance a 'b' and a 'B'. If true, remove the candidate from all non-colored cells in that house.

4) Then I check all non-colored cells and see if one share a house with a conjugate pair. If true, I remove the candidate from that non-colored cell.

5) Lastly I loop through all letter-cells and see what other letters they have in common, in regard to row, column and box. For instance, 'A' can be in the same house as 'b' and 'B'. I store all these pairs in an array 'Ab', 'AB' etc. I then reverse-case the array, so 'A' becomes 'a', 'B' becomes 'b' etc. Then I loop through all letter-cells again, this time looking for a cell that shares one of the pairs, previously collected. If this is true, I remove the candidate from this cell.

I am unsure if I need 3), since I also implement locked candidates, and that rule is used before coloring. I haven't found a test case, where the rule can be applied, after testing for locked candidates.

In 5), is it possible to exclude candidates from non-colored cells? In all my test, I have only come across exclusions in letter-cells.

Any help will be appriciated Wink

Ruud · Site Admin

SarC · Posted: Mon Dec 05, 2005 11:16 pm Post subject:

Thanks for your reply, Ruud. The rule of combining exclusions seems very interesting so I went investigation for an example where I could apply it.

Ruud · Site Admin

Never reverse before combining the rules. When you reverse, do not use the ! symbol. This symbol means "excludes" and that is no longer true when you reversed the case.

Your example analyzed:

SarC · Posted: Tue Dec 06, 2005 10:12 pm Post subject:

I've added the A!c + a!c = c!c (eliminate c) rule to my solver, so it produces output like this:

Ruud · Site Admin

View this topic for a good testset by Lummox JR: http://www.setbb.com/phpbb/viewtopic.php?t=320&mforum=sudoku

This sample (from the same topic) uses the transitivity you want to test:

SarC · Posted: Thu Dec 08, 2005 12:32 am Post subject:

Now I got the transitive test coded as well. Thanks for the link to the excellent post by Lummox JR and for all your help in my coloring quest.