seven languages in seven weeks prolog day 3

sudoku.pl

% The valid methods valdiates that every elements (that should be a list) contains only different numbers.
% this is copied from the book.
valid([]).
valid([Head|Tail]) :- 
    fd_all_different(Head), 
    valid(Tail).


% Splits a list in to mutliple lists of length N. 
split_head_tail(_,[],[],[]).
split_head_tail(0,Tail,[],Tail).
split_head_tail(N,[Head|Tail],[Head|Y],Z):-
    N1 is N-1,
    split_head_tail(N1,Tail,Y,Z),
    !.

split_in_to_rows(N, [], []).
split_in_to_rows(N, List, [List]) :-
    length(List, N).
split_in_to_rows(N, List, Result) :-
    split_head_tail(N, List, Row, Rest),
    split_in_to_rows(N, Rest, Rows),
    append([Row], Rows, Result),
    !.
    
% takes the n-th column from the rows.
col_row([Row], ColNumber, [Element]) :-
    nth(ColNumber, Row, Element), !.
 
col_row([First|Rest], ColNumber, [Element|Column]) :-
    nth(ColNumber, First, Element),
    col_row(Rest, ColNumber, Column),!.
 
col_rows(Rows, Columns) :-
    length(Rows, NumberOfRows),
    col_rows(NumberOfRows, Rows, Columns).
 
% splits rows into columns
col_rows(0, _, []).
 
col_rows(NumberOfRows, Rows, Result) :-
    NumberOfRows > 0,
    col_row(Rows, NumberOfRows, Column),
    Number is (NumberOfRows - 1),
    col_rows(Number, Rows, Columns),
    append(Columns, [Column], Result),
    !.     


% solves the 4x4 Sudoku
sudoku4(Puzzle, Solution) :-
        Solution = Puzzle,
        Puzzle = [S11, S12, S13, S14, 
                  S21, S22, S23, S24, 
                  S31, S32, S33, S34, 
                  S41, S42, S43, S44], 
        
        Square1 = [S11, S12, S21, S22],
        Square2 = [S13, S14, S23, S24],
        Square3 = [S31, S32, S41, S42],
        Square4 = [S33, S34, S43, S44], 
        
        solveSudoku(4, [Square1, Square2, Square3, Square4], Puzzle, Solution).
        

% solves the 6x6 sudoku
sudoku6(Puzzle, Solution) :-
        Solution = Puzzle,
        Puzzle = [S11, S12, S13, S14, S15, S16, 
                  S21, S22, S23, S24, S25, S26,
                  S31, S32, S33, S34, S35, S36, 
                  S41, S42, S43, S44, S45, S46,
                  S51, S52, S53, S54, S55, S56,
                  S61, S62, S63, S64, S65, S66
                  ], 
        Square1 = [S11, S12, S13, S21, S22, S23],
        Square2 = [S14, S15, S16, S24, S25, S26],

        Square3 = [S31, S32, S33, S41, S42, S43],
        Square4 = [S34, S35, S36, S44, S45, S46],

        Square5 = [S51, S52, S53, S61, S62, S63],
        Square6 = [S54, S55, S56, S64, S65, S66],
	
	solveSudoku(6,  [Square1, Square2, Square3, Square4, Square5, Square6], Puzzle, Solution).

% solves a sudoku of Number X Number
solveSudoku(Number, Squares, Puzzle, Solution) :-
	fd_domain(Solution, 1, Number),
        split_in_to_rows(Number, Puzzle, Rows),
        col_rows(Rows, Columns),
	append(Rows, Columns, RowsAndCols),
        append(RowsAndCols, Squares, Validatables),
        valid(Validatables),
        write_list(Rows).
	


write_list([]).
write_list([Head|Tail]) :-
    nl,
    write(Head),
    write_list(Tail).