Seven Languages in Seven Weeks: Prolog, Day 3

slice.prolog

slice([Head | Tail], Slice, Size, Type, I) :-
  slice_position(Type, Size, I, X, Y), 
  insert_into_slice(Head, Slice, X, Y),
  I1 is I + 1,
  slice(Tail, Slice, Size, Type, I1).

slice_position_row.prolog

slice_position('row', Size, I, X, Y) :-   
  X is I // Size,
  Y is I mod Size.

slice_position_square.prolog

slice_position('square', Size, I, X, Y) :- 
  Size_Sqrt is floor(sqrt(Size)),
  X is (I mod Size // Size_Sqrt) + (Size_Sqrt * (I // (Size * Size_Sqrt))),
  Y is (I mod Size_Sqrt) + (Size_Sqrt * ((I mod (Size * Size_Sqrt)) // Size)).

sudoku.prolog

sudoku(Puzzle, Solution) :-
  length(Puzzle, L),
  Size is floor(sqrt(L)),

  Solution = Puzzle,
  fd_domain(Solution, 1, Size),
    
  slice(Puzzle, Rows, Size, 'row'),
  slice(Puzzle, Cols, Size, 'col'),
  slice(Puzzle, Squares, Size, 'square'),
  
  valid(Rows),
  valid(Cols),
  valid(Squares),
        
  pretty_print(Rows).

valid([]).
valid([Head | Tail]) :- fd_all_different(Head), valid(Tail).

sublist_length([], _).
sublist_length([Head | Tail], Length) :- length(Head, Length), sublist_length(Tail, Length).

nth0(I, List, Out) :- I1 is I + 1, nth(I1, List, Out).

insert_into_slice(Item, Values, X, Y) :-
  nth0(X, Values, Bucket),
  nth0(Y, Bucket, Item).

slice_position('row', Size, I, X, Y) :-   
  X is I // Size,
  Y is I mod Size.

slice_position('col', Size, I, X, Y) :- 
  X is I mod Size,
  Y is I // Size.
  
slice_position('square', Size, I, X, Y) :- 
  Size_Sqrt is floor(sqrt(Size)),
  X is (I mod Size // Size_Sqrt) + (Size_Sqrt * (I // (Size * Size_Sqrt))),
  Y is (I mod Size_Sqrt) + (Size_Sqrt * ((I mod (Size * Size_Sqrt)) // Size)).

slice(Puzzle, Slice, Size, Type) :- slice(Puzzle, Slice, Size, Type, 0).
slice(_, Slice, Size, _, I) :- I is Size * Size, length(Slice, Size), sublist_length(Slice, Size).
slice([Head | Tail], Slice, Size, Type, I) :-
  slice_position(Type, Size, I, X, Y), 
  insert_into_slice(Head, Slice, X, Y),
  I1 is I + 1,
  slice(Tail, Slice, Size, Type, I1).

pretty_print([Head | Tail]) :-
  print(Head),
  print('\n'),
  pretty_print(Tail).

sudoku4.prolog

sudoku(Puzzle, Solution) :-
  Solution = Puzzle,
  
  Puzzle = [S11, S12, S13, S14,
            S21, S22, S23, S24,
            S31, S32, S33, S34,
            S41, S42, S43, S44],
  
  fd_domain(Solution, 1, 4),
  
  Row1 = [S11, S12, S13, S14],
  Row2 = [S21, S22, S23, S24],
  Row3 = [S31, S32, S33, S34],
  Row4 = [S41, S42, S43, S44],      
  
  Col1 = [S11, S21, S31, S41],
  Col2 = [S12, S22, S32, S42],
  Col3 = [S13, S23, S33, S43],
  Col4 = [S14, S24, S34, S44],      
  
  Square1 = [S11, S12, S21, S22],
  Square2 = [S13, S14, S23, S24],
  Square3 = [S31, S32, S41, S42],
  Square4 = [S33, S34, S43, S44],      
  
  valid([Row1, Row2, Row3, Row4,
         Col1, Col2, Col3, Col4,
         Square1, Square2, Square3, Square4]).

valid([]).
valid([Head | Tail]) :- fd_all_different(Head), valid(Tail).

sudoku4_output.txt

| ?- sudoku([_, _, 2, 3,
             _, _, _, _,
             _, _, _, _,
             3, 4, _, _],
             Solution).


S = [4,1,2,3,2,3,4,1,1,2,3,4,3,4,1,2]

sudoku6.prolog

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],
  
  fd_domain(Solution, 1, 6),
  
  Row1 = [S11, S12, S13, S14, S15, S16],
  Row2 = [S21, S22, S23, S24, S25, S26],
  Row3 = [S31, S32, S33, S34, S35, S36],
  Row4 = [S41, S42, S43, S44, S45, S46],      
  Row5 = [S51, S52, S53, S54, S55, S56],
  Row6 = [S61, S62, S63, S64, S65, S66],
  
  Col1 = [S11, S21, S31, S41, S51, S61],
  Col2 = [S12, S22, S32, S42, S52, S62],
  Col3 = [S13, S23, S33, S43, S53, S63],
  Col4 = [S14, S24, S34, S44, S54, S64],      
  Col5 = [S15, S25, S35, S45, S55, S65],      
  Col6 = [S16, S26, S36, S46, S56, 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],
  
  valid([Row1, Row2, Row3, Row4, Row5, Row6, 
         Col1, Col2, Col3, Col4, Col5, Col6,
         Square1, Square2, Square3, Square4, Square5, Square6]),
  
  pretty_print([Row1, Row2, Row3, Row4, Row5, Row6]).

valid([]).
valid([Head | Tail]) :- fd_all_different(Head), valid(Tail).
  
pretty_print([Head | Tail]) :-
 print(Head),
 print('\n'),
 pretty_print(Tail).

sudoku6_output.txt

| ?- sudoku6([1, _, _, _, _, _,
              _, 5, _, 2, _, _,
              _, 1, 6, _, 5, _, 
              _, 3, _, 6, 2, _, 
              _, _, 1, _, 3, _, 
              _, _, _, _, _, 5],
              Solution).

[1,2,3,5,4,6]
[6,5,4,2,1,3]
[2,1,6,3,5,4]
[4,3,5,6,2,1]
[5,6,1,4,3,2]
[3,4,2,1,6,5]

sudoku_output.txt

| ?- sudoku([_, _, 2, 3,
             _, _, _, _,
             _, _, _, _,
             3, 4, _, _],
             Solution).

[4,1,2,3]
[2,3,4,1]
[1,2,3,4]
[3,4,1,2]

| ?- sudoku([5, 3, _, _, 7, _, _, _, _, 
             6, _, _, 1, 9, 5, _, _, _, 
             _, 9, 8, _, _, _, _, 6, _, 
             8, _, _, _, 6, _, _, _, 3,
             4, _, _, 8, _, 3, _, _, 1,
             7, _, _, _, 2, _, _, _, 6,
             _, 6, _, _, _, _, 2, 8, _,
             _, _, _, 4, 1, 9, _, _, 5,
             _, _, _, _, 8, _, _, 7, 9], 
             Solution).

[5,3,4,6,7,8,9,1,2]
[6,7,2,1,9,5,3,4,8]
[1,9,8,3,4,2,5,6,7]
[8,5,9,7,6,1,4,2,3]
[4,2,6,8,5,3,7,9,1]
[7,1,3,9,2,4,8,5,6]
[9,6,1,5,3,7,2,8,4]
[2,8,7,4,1,9,6,3,5]
[3,4,5,2,8,6,1,7,9]

See Seven Languages in Seven Weeks: Prolog, Day 3 for more information.