/*-------------------------------------------------------------------------*/
/* Benchmark (Boolean)                                                     */
/*                                                                         */
/* Name           : bschur.pl                                              */
/* Title          : Schur's lemma                                          */
/* Original Source: Giovanna Dore - Italy                                  */
/* Adapted by     : Daniel Diaz for GNU Prolog                             */
/* Date           : January 1993                                           */
/*                                                                         */
/* Color the integers 1,2...,N with 3 colors so that there is no monochrome*/
/* triplets (x,y,z) where x+y=z. Solution iff N<=13.                       */
/* The solution is a list [ [Int11,Int12,Int13],..., [IntN1,IntN2,IntN3] ] */
/* where Intij is 1 if the integer i is colored with the color j.          */
/*                                                                         */
/* Solution:                                                               */
/* N=4  [[0,0,1],[0,1,0],[0,0,1],[1,0,0]]                                  */
/*      [[0,0,1],[0,1,0],[0,1,0],[0,0,1]]                                  */
/*        ...                                                              */
/* N=13 [[0,0,1],[0,1,0],[0,1,0],[0,0,1],[1,0,0],[1,0,0],[0,0,1],[1,0,0],  */
/*       [1,0,0],[0,0,1],[0,1,0],[0,1,0],[0,0,1]] (first solution)         */
/*-------------------------------------------------------------------------*/

q:-	write('N ?'), read_integer(N),
	statistics(runtime,_),
	(schur(N,A),
	 write(A), nl, 
	 fail 
	   ;
	 write('No more solutions'), nl),
	statistics(runtime,[_,Y]),
	write('time : '), write(Y), nl.




schur(N,A):-
	create_array(N,3,A),
	for_each_line(A,only1),
	pair_constraints(A,A),
	!,
	array_labeling(A).




pair_constraints([],_):-
	!.

pair_constraints([_],_):-
	!.

pair_constraints([_,[K1,K2,K3]|A2],[[I1,I2,I3]|A1]):-
	#\ (I1 #/\ K1),
	#\ (I2 #/\ K2),
	#\ (I3 #/\ K3),
	triplet_constraints(A2,A1,[I1,I2,I3]),
	pair_constraints(A2,A1).




triplet_constraints([],_,_).

triplet_constraints([[K1,K2,K3]|A2],[[J1,J2,J3]|A1],[I1,I2,I3]):-
	#\ (I1 #/\ J1 #/\ K1),
	#\ (I2 #/\ J2 #/\ K2),
	#\ (I3 #/\ J3 #/\ K3),
	triplet_constraints(A2,A1,[I1,I2,I3]).



:- include(array).

% interface with for_each_... procedures

array_prog(only1,L):-
	fd_only_one(L).



:- initialization(q).