/**
         
 * Warranty & Liability
         
 * To the extent permitted by applicable law and unless explicitly
         
 * otherwise agreed upon, XLOG Technologies AG makes no warranties
         
 * regarding the provided information. XLOG Technologies AG assumes
         
 * no liability that any problems might be solved with the information
         
 * provided by XLOG Technologies AG.
         
 *
         
 * Rights & License
         
 * All industrial property rights regarding the information - copyright
         
 * and patent rights in particular - are the sole property of XLOG
         
 * Technologies AG. If the company was not the originator of some
         
 * excerpts, XLOG Technologies AG has at least obtained the right to
         
 * reproduce, change and translate the information.
         
 *
         
 * Reproduction is restricted to the whole unaltered document. Reproduction
         
 * of the information is only allowed for non-commercial uses. Selling,
         
 * giving away or letting of the execution of the library is prohibited.
         
 * The library can be distributed as part of your applications and libraries
         
 * for execution provided this comment remains unchanged.
         
 *
         
 * Restrictions
         
 * Only to be distributed with programs that add significant and primary
         
 * functionality to the library. Not to be distributed with additional
         
 * software intended to replace any components of the library.
         
 *
         
 * Trademarks
         
 * Jekejeke is a registered trademark of XLOG Technologies AG.
         
 */
         

         
:- ensure_loaded(library(edge/railgun)).
         

         
sudo :-
         
   between(1, 2, K),
         
   problem(K, M),
         
   sudoku(M),
         
   fail.
         
sudo.
         

         
/* 9 x 9 sudoku */
         

         
% sudoku(+Matrice)
         
sudoku(M) :-
         
   term_variables(M, L),
         
   L ins 1..9,
         
   maplist(all_different, M),
         
   transpose(M, H),
         
   maplist(all_different, H),
         
   groups(M),
         
   labeling([plausi], L).
         

         
% groups(+Matrice)
         
groups([]).
         
groups([As,Bs,Cs|L]) :- blocks(As, Bs, Cs), groups(L).
         

         
% blocks(+Vector, +Vector, +Vector)
         
blocks([], [], []).
         
blocks([N1,N2,N3|Ns1], [N4,N5,N6|Ns2], [N7,N8,N9|Ns3]) :-
         
   all_different([N1,N2,N3,N4,N5,N6,N7,N8,N9]),
         
   blocks(Ns1, Ns2, Ns3).
         

         
/* https://sudoku-puzzles.net/ */
         

         
/* Medium */
         
problem(1, [[_,_,_,1,_,_,_,3,_],
         
            [_,3,1,_,_,8,9,4,5],
         
            [_,_,2,_,9,_,1,_,_],
         
            [_,_,_,_,_,4,_,_,_],
         
            [_,9,5,_,3,_,2,7,_],
         
            [_,_,_,7,_,_,_,_,_],
         
            [_,_,3,_,6,_,5,_,_],
         
            [1,7,6,5,_,_,3,8,_],
         
            [_,5,_,_,_,9,_,_,_]]).
         

         
/* Medium 2 */
         
problem(2, [[_,2,8,_,_,_,_,5,_],
         
            [_,6,_,_,2,_,_,3,_],
         
            [_,_,_,1,8,3,_,_,_],
         
            [7,_,9,_,_,_,_,_,_],
         
            [_,_,4,_,_,_,2,_,_],
         
            [_,_,_,9,3,8,6,_,_],
         
            [_,_,_,_,_,_,1,_,7],
         
            [4,1,_,_,_,_,_,2,_],
         
            [_,_,_,6,_,5,_,_,9]]).
         

         
/***********************************************************/
         
/* Matrice Utility                                         */
         
/***********************************************************/
         

         
/**
         
 * Carlo Capelli, Stackoverflow, December 7, 2015
         
 */
         
% transpose(+Matrice, -Matrice)
         
transpose([], []).
         
transpose([U], B) :- !, sys_gen(U, B).
         
transpose([H|T], R) :- transpose(T, TC), sys_splash(H, TC, R).
         

         
% sys_gen(+List, -Matrice)
         
sys_gen([], []).
         
sys_gen([H|T], [[H]|RT]) :- sys_gen(T,RT).
         

         
% sys_splash(+List, +Matrice, -Matrice)
         
sys_splash([], [], []).
         
sys_splash([H|T], [R|K], [[H|R]|U]) :- sys_splash(T,K,U).