/*
 * 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
 * ], What).
 * 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 ], What).
 * puzzle input from wikipedia
 * */
:- use_module(library(clpfd)).

 sudoku(Input, Solution) :-
	 Solution = Input,
	 Input = [ S11, S12, S13, S14, S15, S16, S17, S18, S19,
		   S21, S22, S23, S24, S25, S26, S27, S28, S29,
		   S31, S32, S33, S34, S35, S36, S37, S38, S39,
		   S41, S42, S43, S44, S45, S46, S47, S48, S49,
		   S51, S52, S53, S54, S55, S56, S57, S58, S59,
		   S61, S62, S63, S64, S65, S66, S67, S68, S69,
		   S71, S72, S73, S74, S75, S76, S77, S78, S79,
		   S81, S82, S83, S84, S85, S86, S87, S88, S89,
		   S91, S92, S93, S94, S95, S96, S97, S98, S99 
		],

	Solution ins 1..9,
	Row1 = [S11, S12, S13, S14, S15, S16, S17, S18, S19],
	Row2 = [S21, S22, S23, S24, S25, S26, S27, S28, S29],
	Row3 = [S31, S32, S33, S34, S35, S36, S37, S38, S39],
	Row4 = [S41, S42, S43, S44, S45, S46, S47, S48, S49],
	Row5 = [S51, S52, S53, S54, S55, S56, S57, S58, S59],
	Row6 = [S61, S62, S63, S64, S65, S66, S67, S68, S69],
	Row7 = [S71, S72, S73, S74, S75, S76, S77, S78, S79],
	Row8 = [S81, S82, S83, S84, S85, S86, S87, S88, S89],
	Row9 = [S91, S92, S93, S94, S95, S96, S97, S98, S99],
	Rows = [Row1, Row2, Row3, Row4, Row5, Row6, Row7, Row8, Row9],
	Col1 = [S11, S21, S31, S41, S51, S61, S71, S81, S91],
	Col2 = [S12, S22, S32, S42, S52, S62, S72, S82, S92],
	Col3 = [S13, S23, S33, S43, S53, S63, S73, S83, S93],
	Col4 = [S14, S24, S34, S44, S54, S64, S74, S84, S94],
	Col5 = [S15, S25, S35, S45, S55, S65, S75, S85, S95],
	Col6 = [S16, S26, S36, S46, S56, S66, S76, S86, S96],
	Col7 = [S17, S27, S37, S47, S57, S67, S77, S87, S97],
	Col8 = [S18, S28, S38, S48, S58, S68, S78, S88, S98],
	Col9 = [S19, S29, S39, S49, S59, S69, S79, S89, S99],
	Cols = [Col1, Col2, Col3, Col4, Col5, Col6, Col7, Col8, Col9],
	Sqr1 = [S11, S12, S13, S21, S22, S23, S31, S32, S33],
	Sqr2 = [S14, S15, S16, S24, S25, S26, S34, S35, S36],
	Sqr3 = [S17, S18, S19, S27, S28, S29, S37, S38, S39],
	Sqr4 = [S41, S42, S43, S51, S52, S53, S61, S62, S63],
	Sqr5 = [S44, S45, S46, S54, S55, S56, S64, S65, S66],
	Sqr6 = [S47, S48, S49, S57, S58, S59, S67, S68, S69],
	Sqr7 = [S71, S72, S73, S81, S82, S83, S91, S92, S93],
	Sqr8 = [S74, S75, S76, S84, S85, S86, S94, S95, S96],
	Sqr9 = [S77, S78, S79, S87, S88, S89, S97, S98, S99],
	Squares = [Sqr1, Sqr2, Sqr3, Sqr4, Sqr5, Sqr6, Sqr7, Sqr8, Sqr9],

	valid(Squares),
	valid(Rows),
	valid(Cols),

	show(Solution).

sudoku4(Input, Solution) :-
	Solution = Input,
	Input = [ S11, S12, S13, S14,
		  S21, S22, S23, S24,
		  S31, S32, S33, S34,
		  S41, S42, S43, S44
		],
	Solution ins 1..4,
	Squares = [[S11, S12, S21, S22], [S13, S14, S23, S24], [S31, S32, S41, S42], [S33, S34, S43, S44]],
	Rows = [[S11, S12, S13, S14], [S21, S22, S23, S24], [S31, S32, S33, S34], [S41, S42, S43, S44]],
	Cols = [[S11, S21, S31, S41], [S12, S22, S32, S42], [S13, S23, S33, S43], [S14, S24, S34, S44]],
	valid(Squares),
	valid(Rows),
	valid(Cols).

valid([]).
valid([H|T]) :-
	all_distinct(H),
	valid(T).

show([S1, S2, S3, S4, S5, S6, S7, S8, S9 | T]) :-
	write(S1),
	write(" | "),
	write(S2),
	write(" | "),
	write(S3),
	write(" | "),
	write(S4),
	write(" | "),
	write(S5),
	write(" | "),
	write(S6),
	write(" | "),
	write(S7),
	write(" | "),
	write(S8),
	write(" | "),
	write(S9),
	nl,
	show(T).