Re: [Bug-apl] ⎕DLX (2)

[Christian Robert]

Juergen,

replacing all [2..9] by 1
seams to work is is *lightning* *fast*.

      sortvn←{⍵[⍋⊃⍵]}

      Display 9 9 ⍴ {⍵[1+⎕io]} ¨ sortvn { ⎕io + (⌊⍵÷9) (9|⍵) } ¨ ⎕io-⍨ ⎕dlx z
┏━━━━┯━━━┯━━━━┳━━━━┯━━━┯━━━━┳━━━━┯━━━┯━━━━┓
┃  1 │ 2 │ 3  ┃  4 │ 5 │ 6  ┃  7 │ 8 │ 9  ┃
┠────┼───┼────╂────┼───┼────╂────┼───┼────┨
┃  7 │ 8 │ 9  ┃  1 │ 2 │ 3  ┃  4 │ 5 │ 6  ┃
┠────┼───┼────╂────┼───┼────╂────┼───┼────┨
┃  4 │ 5 │ 6  ┃  7 │ 8 │ 9  ┃  1 │ 2 │ 3  ┃
┣━━━━┿━━━┿━━━━╋━━━━┿━━━┿━━━━╋━━━━┿━━━┿━━━━┫
┃  3 │ 1 │ 2  ┃  8 │ 4 │ 5  ┃  9 │ 6 │ 7  ┃
┠────┼───┼────╂────┼───┼────╂────┼───┼────┨
┃  6 │ 9 │ 7  ┃  3 │ 1 │ 2  ┃  8 │ 4 │ 5  ┃
┠────┼───┼────╂────┼───┼────╂────┼───┼────┨
┃  8 │ 4 │ 5  ┃  6 │ 9 │ 7  ┃  3 │ 1 │ 2  ┃
┣━━━━┿━━━┿━━━━╋━━━━┿━━━┿━━━━╋━━━━┿━━━┿━━━━┫
┃  2 │ 3 │ 1  ┃  5 │ 7 │ 4  ┃  6 │ 9 │ 8  ┃
┠────┼───┼────╂────┼───┼────╂────┼───┼────┨
┃  9 │ 6 │ 8  ┃  2 │ 3 │ 1  ┃  5 │ 7 │ 4  ┃
┠────┼───┼────╂────┼───┼────╂────┼───┼────┨
┃  5 │ 7 │ 4  ┃  9 │ 6 │ 8  ┃  2 │ 3 │ 1  ┃
┗━━━━┷━━━┷━━━━┻━━━━┷━━━┷━━━━┻━━━━┷━━━┷━━━━┛

Now, I have to figure-out how to setup the initial constraints
with some predetermined values. eg, dynamically building the "z" matrix I 
suppose.

Can I just append a new set of constraints at the right side of the "z" matrix 
? (a 729x81 )

thanks,

Xtian.



On 2016-11-24 06:56, Juergen Sauermann wrote:
> Hi Xtian,
>
> the constraint matrix *B* for *⎕DLX B* should contain 0 1 or 2 (either
> as numbers or as characters (blank is also allowed and means 0)
> If the matrix contains other numbers or characters than you get a DOMAIN ERROR.
>
> Referring to Knuth's original paper, 1 stands for a primary constraint while 2 
> stands
> for a secondary constraint. A mix of 1 and 2 in the same column is not allowed.
> As far as I can see, in the sudoku case all constraints are primary, so z 
> should contain
> only 0s and 1s.
>
> I also believe that the number of rows (729 == 9×9×9) stated in one of your 
> links is correct,
> but the number of columns (9×9×4=324) is maybe not. I would suppose that it is 
> 9×(9+9+9+2)=171
> for 9 digits×(9 rows + 9 columns + 9 boxes + 2 main diagonals).
>
> If you have a matrix *z* with numbers indicating the digits for the different 
> constraints (which is
> easier to troubleshoot than a pure 0/1 matrix) , then instead of *⎕DLX z* you 
> can probably
> simply use *⎕DLX ∼z∈0 '0 '*to avoid the DOMAIN ERROR. This works, of course,
> only if there are no secondary constraints involved, like for sudokus.
>
> /// Jürgen