/* 

  "Boring Sudoku" in Picat.

  From comp.lang.prolog:
  https://groups.google.com/forum/#!topic/comp.lang.prolog/lnDbm04jrfg

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/


% import util.
import cp.


main => go.


go ?=>
  Vars=[[2,_,_,6,7,_,_,_,_],
       [_,_,6,_,_,_,2,_,1],
       [4,_,_,_,_,_,8,_,_],
       [5,_,_,_,_,9,3,_,_],
       [_,3,_,_,_,_,_,5,_],
       [_,_,2,8,_,_,_,_,7],
       [_,_,1,_,_,_,_,_,4],
       [7,_,8,_,_,_,6,_,_],
       [_,_,_,_,5,3,_,_,8]],

  sudoku(Vars),
  foreach(Row in Vars) println(Row) end,

  % solve(Vars), % No need for solve with this problem instance.

  % println(after=Vars),
  fail,
  nl.

go => true.


sudoku(Vars) =>

    Vars = [
        [A11, A12, A13, A14, A15, A16, A17, A18, A19],
        [A21, A22, A23, A24, A25, A26, A27, A28, A29],
        [A31, A32, A33, A34, A35, A36, A37, A38, A39],
        [A41, A42, A43, A44, A45, A46, A47, A48, A49],
        [A51, A52, A53, A54, A55, A56, A57, A58, A59],
        [A61, A62, A63, A64, A65, A66, A67, A68, A69],
        [A71, A72, A73, A74, A75, A76, A77, A78, A79],
        [A81, A82, A83, A84, A85, A86, A87, A88, A89],
        [A91, A92, A93, A94, A95, A96, A97, A98, A99]],

    Vars :: 1..9,

    all_distinct([A11, A12, A13, A14, A15, A16, A17, A18, A19]),
    all_distinct([A21, A22, A23, A24, A25, A26, A27, A28, A29]),
    all_distinct([A31, A32, A33, A34, A35, A36, A37, A38, A39]),
    all_distinct([A41, A42, A43, A44, A45, A46, A47, A48, A49]),
    all_distinct([A51, A52, A53, A54, A55, A56, A57, A58, A59]),
    all_distinct([A61, A62, A63, A64, A65, A66, A67, A68, A69]),
    all_distinct([A71, A72, A73, A74, A75, A76, A77, A78, A79]),
    all_distinct([A81, A82, A83, A84, A85, A86, A87, A88, A89]),
    all_distinct([A91, A92, A93, A94, A95, A96, A97, A98, A99]),

    all_distinct([A11, A21, A31, A41, A51, A61, A71, A81, A91]),
    all_distinct([A12, A22, A32, A42, A52, A62, A72, A82, A92]),
    all_distinct([A13, A23, A33, A43, A53, A63, A73, A83, A93]),
    all_distinct([A14, A24, A34, A44, A54, A64, A74, A84, A94]),
    all_distinct([A15, A25, A35, A45, A55, A65, A75, A85, A95]),
    all_distinct([A16, A26, A36, A46, A56, A66, A76, A86, A96]),
    all_distinct([A17, A27, A37, A47, A57, A67, A77, A87, A97]),
    all_distinct([A18, A28, A38, A48, A58, A68, A78, A88, A98]),
    all_distinct([A19, A29, A39, A49, A59, A69, A79, A89, A99]),

    all_distinct([A11, A21, A31, A12, A22, A32, A13, A23, A33]),
    all_distinct([A41, A51, A61, A42, A52, A62, A43, A53, A63]),
    all_distinct([A71, A81, A91, A72, A82, A92, A73, A83, A93]),
    all_distinct([A14, A24, A34, A15, A25, A35, A16, A26, A36]),
    all_distinct([A44, A54, A64, A45, A55, A65, A46, A56, A66]),
    all_distinct([A74, A84, A94, A75, A85, A95, A76, A86, A96]),
    all_distinct([A17, A27, A37, A18, A28, A38, A19, A29, A39]),
    all_distinct([A47, A57, A67, A48, A58, A68, A49, A59, A69]),
    all_distinct([A77, A87, A97, A78, A88, A98, A79, A89, A99]).