/* 

  Sudoku using maplist/2 in Picat.

  Inspired by the Prolog model htps://rosettacode.org/wiki/Sudoku#Prolog
  The same example is here:
  - http://swish.swi-prolog.org/example/clpfd_sudoku.pl
  - https://www.swi-prolog.org/pldoc/man?section=clpfd-sudoku

  From https://www.swi-prolog.org/pldoc/man?section=clpfd-sudoku
  """ 
  In this concrete case, the constraint solver is strong enough to find the 
  unique solution without any search. 
  """

  It's true for this Picat model as well when using all_distinct/1, 
  though I added solve/1 since I want it slightly more general.

  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 ?=>
  problem(1,Rows),
  sudoku(Rows),  
  foreach(Row in Rows)
    println(Row)
  end,
  fail, % ensure unique solution
  nl.

go => true.


sudoku(Rows) =>
  Rows :: 1..9,
  maplist(all_distinct, Rows), % don't need solve/1
  % maplist(all_different, Rows), % all_different/1 need solve/1
  maplist(all_distinct, Rows.transpose()),
  Rows = [A,B,C,D,E,F,G,H,I],
  blocks(A,B,C), blocks(D,E,F), blocks(G,H,I),
  solve(Rows).
 

blocks([], [], []) => true.
blocks([A,B,C|Bs1], [D,E,F|Bs2], [G,H,I|Bs3]) =>
        all_distinct([A,B,C,D,E,F,G,H,I]),
        blocks(Bs1, Bs2, Bs3).
 
problem(1, Rows) => 
  Rows = 
  [[_,_,_,_,_,_,_,_,_],
   [_,_,_,_,_,3,_,8,5],
   [_,_,1,_,2,_,_,_,_],
   [_,_,_,5,_,7,_,_,_],
   [_,_,4,_,_,_,1,_,_],
   [_,9,_,_,_,_,_,_,_],
   [5,_,_,_,_,_,_,7,3],
   [_,_,2,_,1,_,_,_,_],
   [_,_,_,_,4,_,_,_,9]].


maplist(Goal, List) =>
  maplist_(List, Goal).
maplist_([], _) ?=> true.
maplist_([Elem|Tail], Goal) => 
  call(Goal, Elem),
  maplist_(Tail, Goal).