:- use_module(library('clp/bounds')).
:- use_module(library('lists')).

% Our general constraint is that each set of 9 (row, column or 3x3 grid) is made
% up from the numbers 1-9, and each number is not repeated.
valid(L) :- L in 1..9, all_different(L).

% Transpose function from Worksheet 16 of 'Clause and Effect'
transpose([[]|_],[]).
transpose(R,[H|C]) :- chopcol(R,H,T), transpose(T,C).
chopcol([],[],[]).
chopcol([[H|T]|R],[H|Hs],[T|Ts]) :- chopcol(R,Hs,Ts).

% Describe 3 grids in terms of 3 rows
% TODO: There must be a better way to do this.
grids([E11,E12,E13,E14,E15,E16,E17,E18,E19],
      [E21,E22,E23,E24,E25,E26,E27,E28,E29],
      [E31,E32,E33,E34,E35,E36,E37,E38,E39],
      [E11,E12,E13,E21,E22,E23,E31,E32,E33],
      [E14,E15,E16,E24,E25,E26,E34,E35,E36],
      [E17,E18,E19,E27,E28,E29,E37,E38,E39]).

% Print a board
print_board([]).
print_board([H|T]) :- write(H), nl, print_board(T).

% Sudoku solving function. 
%
% Input is nine lists of nine integers
sudoku(Board) :-
  % Break the board down into rows
  Board = [R1, R2, R3, R4, R5, R6, R7, R8, R9],
  % Transpose the board to get the columns
  transpose(Board, [C1, C2, C3, C4, C5, C6, C7, C8, C9]),
  % Cut up the rows into 3x3 grids
  grids(R1,R2,R3,G1,G2,G3),
  grids(R4,R5,R6,G4,G5,G6),
  grids(R7,R8,R9,G7,G8,G9),
  % Each row contains unique entries
  valid(R1), valid(R2), valid(R3),
  valid(R4), valid(R5), valid(R6),
  valid(R7), valid(R8), valid(R9),
  % Each column contains unique entries
  valid(C1), valid(C2), valid(C3),
  valid(C4), valid(C5), valid(C6),
  valid(C7), valid(C8), valid(C9),
  % Each grid contains unique entries
  valid(G1), valid(G2), valid(G3),
  valid(G4), valid(G5), valid(G6),
  valid(G7), valid(G8), valid(G9),
  % Turn the board into a list of 81 variables
  flatten(Board, Elements),
  %sign a value to each variable
  label(Elements).