% 9-queens program




:- module queens.


:- interface.

:- import_module list, int, io, printlist.

:- pred main1(list(int)).
:- mode main1(out) is nondet.

:- pred main3(list(int), io__state, io__state).
:- mode main3(out, di, uo) is nondet.

:- implementation.

main1(Out) :-	
	data(Data),
	queen(Data, Out).

main3(Out) -->
	{ data(Data), queen(Data, Out) },
	print_list(Out).

:- pred data(list(int)).
:- mode data(out) is det.

:- pred queen(list(int), list(int)).
:- mode queen(in, out) is nondet.



:- pred qperm(list(int), list(int)).
:- mode qperm(in, out) is nondet.

:- pred qdelete(int, list(int), list(int)).
:- mode qdelete(out, in, out) is nondet.

:- pred safe(list(int)).
:- mode safe(in) is semidet.

:- pred nodiag(int, int, list(int)).
:- mode nodiag(in, in, in) is semidet.





data([1,2,3,4,5,6,7,8,9]).



queen(Data, Out) :-
	qperm(Data, Out),
	safe(Out).



qperm([], []).
qperm([X|Y], K) :-
	qdelete(U, [X|Y], Z),
	K = [U|V],
	qperm(Z, V).



	% gives performance of about 8.7
qdelete(A, [A|L], L).
qdelete(X, [A|Z], [A|R]) :-
	qdelete(X, Z, R).







safe([]).
safe([N|L]) :-
	nodiag(N, 1, L),
	safe(L).






nodiag(_, _, []).
nodiag(B, D, [N|L]) :-
	NmB is N - B,
	BmN is B - N,
	( D = NmB ->
		fail
	; D = BmN ->
		fail
	;
		true
	),
	D1 is D + 1,
	nodiag(B, D1, L).