%implementation of the final step of ACC '98
%differs slightly from the original model (constraints #7 and mirroring).
timetable(X, Home, Away, Bye):-
	get_pattern_sets(PatternSet), 

	Schedule = [S1,S2,S3,S4,S5,S6,S7,S8,S9],
	make_schedule(S1),
	make_schedule(S2),
	make_schedule(S3),
	make_schedule(S4),
	make_schedule(S5),
	make_schedule(S6),
	make_schedule(S7),
	make_schedule(S8),
	make_schedule(S9),

	%1. all teams playing on a specific date are different (columns of Schedule)
	transpose(Schedule, ScheduleT), 
	all_rows_different(ScheduleT),

	%2. the schedule of two opposing teams must relate (Schedule[i,w] = j <=> Schedule[j,w] = i)
	numlist(1,9,TeamIndex),
	foreach(TeamIndex, foreach(TeamIndex, relate_schedule(ScheduleT))),

	%3. and  4.  each team must meet all other teams exactly 2 times and does not play itself
	count_games(Schedule),

	%5. The byes in the schedule correspond to the byes in the Bye pattern.
	numlist(1,18,WeekIndex),
	foreach(TeamIndex, foreach(WeekIndex, relate_byes(Schedule, Bye))),

	%6. if schedule[i,w] = j that must be reflected into the Home / Away patterns
	foreach(TeamIndex, foreach(TeamIndex, relate_games(ScheduleT, Home, Away))),

	%7.  may not be needed.
	%MIRRORING
	mirroring(ScheduleT, 1,8),
	mirroring(ScheduleT, 2,9),
	mirroring(ScheduleT, 3,12),
	mirroring(ScheduleT, 4,13),
	mirroring(ScheduleT, 5,14),
	mirroring(ScheduleT, 6,15),
	mirroring(ScheduleT, 7,16),
	mirroring(ScheduleT, 10,17),
	mirroring(ScheduleT, 11,18),
	
	%8. 
	constraint8(Schedule, 1, 4),
	constraint8(Schedule, 2, 6),
	constraint8(Schedule, 5, 8),
	constraint8(Schedule, 7, 9),
	constraint8(Schedule, 4, 1),
	constraint8(Schedule, 6, 2),
	constraint8(Schedule, 8, 5),
	constraint8(Schedule, 9, 7),

	%9
	constraint9(Schedule, 2, 4),
	constraint9(Schedule, 2, 9),
	constraint9(Schedule, 4, 6),
	constraint9(Schedule, 6, 9),

	%10
	numlist(1,17,WeekIndex1),
	foreach(TeamIndex, foreach(WeekIndex1, constraint10a(Schedule, Away))),

	numlist(1,16,WeekIndex2),
	foreach(TeamIndex, foreach(WeekIndex2, constraint10b(Schedule))),

	%11
	get_matrix_ij(Schedule, 6, 11, 2), 
	get_matrix_ij(Schedule, 6, 18, 2), 
	get_matrix_ij(Schedule, 6, 2, 1), 

	get_pattern_constraints(PatternSet, Home, Away, Bye),

	flatten(Schedule, LabelThis),
	labeling(LabelThis),
	%writeln(Home),
	%writeln(Away),
	%writeln(Bye),
	X = Schedule.

mirroring(ScheduleT, I, J):-
	nth(I, ScheduleT, Column_i), 
	nth(J, ScheduleT, Column_j),   
	equal(Column_i, Column_j).

get_pattern_constraints(PatternSet, HomeP, AwayP, ByeP):-

	PatternSet = [HomePattern, AwayPattern, ByePattern],
	get_matrix_ij(Bye, 2, 16, 1), 
	get_matrix_ij(Bye, 9, 1, 1), 
	get_matrix_ij(Bye, 3, 18, 0), 
	get_matrix_ij(Bye, 7, 18, 0), 
	get_matrix_ij(Bye, 6, 1, 0), 
	get_matrix_ij(Away, 1, 18, 0), 
	get_matrix_ij(Away, 2, 18, 0), 
	get_matrix_ij(Away, 5, 18, 0), 
	get_matrix_ij(Away, 9, 18, 0), 
	get_matrix_ij(Away, 1, 1, 0), 
	get_matrix_ij(Away, 3, 1, 0), 
	get_matrix_ij(Away, 4, 1, 0), 
	get_matrix_ij(Away, 9, 1, 0), 
	get_matrix_ij(Home, 9, 17, 0),

	P = [_, _, _, _, _, _, _, _, _],
	P in [1..9],
	all_different(P),
	
	get_pattern(AwayPattern, P, Away),
	%writeln(away),
	get_pattern(HomePattern, P, Home),
	%writeln(home),
	get_pattern(ByePattern, P, Bye),
	%writeln(bye),
	

	labeling(P), 
	%writeln(P),
	
	ByeP = Bye,
	HomeP = Home, 
	AwayP = Away.

%Out is a matrix formed from Pattern by taking rows in the order defined by P
get_pattern(Pattern, P, Out):-
	get_pattern(Pattern, P, Out, []).
get_pattern(_, [], Out, Out).
get_pattern(Pattern, [P|Ps], Out, Acc):-
	nth(P, Pattern, Row),
	RowList = [Row], 
	append(Acc, RowList, Acc1),

	get_pattern(Pattern, Ps, Out, Acc1).

	

make_schedule(Schedule):-
	Schedule = [_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_],
	Schedule in [0..9].



%(Schedule[i,w] = j <=> Schedule[j,w] = i)  or (ScheduleT[w,i] = j <=> ScheudleT[w,j] = i for any w in [1..18])
relate_schedule([], _, _).
relate_schedule([Row|ScheduleT], I, J):-
	(I = J, !;
	nth(I, Row, Swi),
	nth(J, Row, Swj),
	
	%writeln((Swi #= J) #<=> (Swj #= I)),
	(Swi #= J) #<=> (Swj #= I),

	relate_schedule(ScheduleT, I, J)).

%make sure that each team plays with all other exactly 2 times and does not meet itself.
count_games(Schedule):-
	count_games(Schedule, 1).
count_games([], _).
count_games([S|Schedule], Index):-
	exactly(2,S,0),
	(Index = 1, !, exactly(0,S,1) ; exactly(2,S,1)),
	(Index = 2, !, exactly(0,S,2) ; exactly(2,S,2)),
	(Index = 3, !, exactly(0,S,3) ; exactly(2,S,3)),
	(Index = 4, !, exactly(0,S,4) ; exactly(2,S,4)),
	(Index = 5, !, exactly(0,S,5) ; exactly(2,S,5)),
	(Index = 6, !, exactly(0,S,6) ; exactly(2,S,6)),
	(Index = 7, !, exactly(0,S,7) ; exactly(2,S,7)),
	(Index = 8, !, exactly(0,S,8) ; exactly(2,S,8)),
	(Index = 9, !, exactly(0,S,9) ; exactly(2,S,9)),

	Index1 is Index + 1,
	count_games(Schedule, Index1).

%make sure that Schedule corresponds to the pattern in byes
relate_byes(Schedule, Bye, I,W):-
       get_matrix_ij(Schedule, I, W, Game), 
       get_matrix_ij(Bye, I, W, B),
       ((Game #= 0) #<=> (B #= 1)).	

%make sure that Schedule corresponds to the pattern
relate_games(Schedule, Home, Away, I, J):-
	(I = J, !; 
	relate_games(Schedule, Home, Away, I, J, 1)).
relate_games([], _, _, _, _, _).
relate_games([S|Schedule], Home, Away, I, J, W):-
	nth(I, S, Oponent_i), 
	get_matrix_ij(Home, I, W, H1),
	get_matrix_ij(Away, I, W, A1), 
	get_matrix_ij(Home, J, W, H2),
	get_matrix_ij(Away, J, W, A2), 
	(Oponent_i #= J) #=> ( ((H1 #= 1) #/\ (A2 #= 1)) #\/ ((H2 #= 1) #/\ (A1 #= 1))),
	
	W1 is W + 1,
	relate_games(Schedule, Home, Away, I, J, W1).

constraint8(Schedule, I, J):-
	get_matrix_ij(Schedule, I, 18, X), 

	(X #= J) #\/ (X#=3) #\/ (X#=0).
	
constraint9(Schedule, I, J):-
	get_matrix_ij(Schedule, I, 11, X1), 
	get_matrix_ij(Schedule, I, 12, X2), 
	get_matrix_ij(Schedule, I, 13, X3), 
	get_matrix_ij(Schedule, I, 14, X4), 
	get_matrix_ij(Schedule, I, 15, X5), 
	get_matrix_ij(Schedule, I, 16, X6), 
	get_matrix_ij(Schedule, I, 17, X7), 
	get_matrix_ij(Schedule, I, 18, X8), 


	(X1 #= J) #= B1, 
	(X2 #= J) #= B2, 
	(X3 #= J) #= B3, 
	(X4 #= J) #= B4, 
	(X5 #= J) #= B5, 
	(X6 #= J) #= B6, 
	(X7 #= J) #= B7, 
	(X8 #= J) #= B8, 

	at_least_one([B1, B2, B3, B4, B5, B6, B7, B8]).
	
constraint10a(Schedule, Away, I, W):-
	get_matrix_ij(Schedule, I, W, X1), 
	get_matrix_ij(Away, I, W, X3), 
	W1 is W + 1,
	get_matrix_ij(Schedule, I, W1, X2),
	get_matrix_ij(Away, I, W, X4), 

	B1 #= ((X1 #= 2) #\/ (X1 #= 6)),
	B2 #= ((X2 #= 2) #\/ (X2 #= 6)),
	
	X3 + X4 + B1 + B2 #< 4.

constraint10b(Schedule, I, W):-
	get_matrix_ij(Schedule, I, W, X1), 
	W1 is W + 1,
	get_matrix_ij(Schedule, I, W1, X2),
	W2 is W + 2,
	get_matrix_ij(Schedule, I, W2, X3),

	B1 #= ((X1 #= 2) #\/ (X1 #= 6) #\/ (X1 #= 9)),
	B2 #= ((X2 #= 2) #\/ (X2 #= 6) #\/ (X2 #= 9)),
	B3 #= ((X3 #= 3) #\/ (X3 #= 6) #\/ (X3 #= 9)),
	
	B1 + B2 + B3 #< 3.