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% ?- queens(4, Qs).
% produces
% Qs = [3,1,4,2] ;
% Qs = [2,4,1,3]
% queens +int -[int]
module queens.
%spy X :- $print start X, X, $print ok X.
%spy X :- $print ko X, fail.
plus zero X X.
plus (s X) Y (s S) :- plus X Y S.
less zero (s _).
less (s X) (s Y) :- less X Y.
neq zero (s _).
neq (s _) zero.
neq (s X) (s Y) :- neq X Y.
queens N Qs :- range (s zero) N Ns, queens_aux Ns xnil Qs.
queens_aux xnil Qs Qs.
queens_aux UnplacedQs SafeQs Qs :-
select UnplacedQs UnplacedQs1 Q,
not_attack SafeQs Q (s zero),
queens_aux UnplacedQs1 (xcons Q SafeQs) Qs.
not_attack_aux Xs X :- not_attack Xs X (s zero).
not_attack xnil DUMMY1 DUMMY2 :- !.
not_attack (xcons Y Ys) X N :- plus Y N S1, neq X S1,
plus X N S2, neq Y S2,
N1 = (s N),
not_attack Ys X N1.
%select A B C :- $print first_clause (select A B C), fail.
select (xcons X Xs) Xs X.
%select A B C :- $print backtrack (select A B C), fail.
select (xcons Y Ys) (xcons Y Zs) X :- select Ys Zs X.
%select A B C :- $print no_more_chances (select A B C), fail.
range N N (xcons N xnil) :- !.
range M N (xcons M Ns) :- less M N, M1 = (s M), range M1 N Ns.
once :- queens (s (s (s (s zero)))) L, xxx L.
xxx (xcons (s (s zero)) (xcons (s (s (s (s zero)))) (xcons (s zero) (xcons (s (s (s zero))) xnil)))).
q L :- queens (s (s (s (s zero)))) L.
iter zero X.
iter (s N) X :- X, iter N X.
mult zero X zero.
mult (s X) Y Z :- mult X Y K, plus Y K Z.
exp zero X (s zero).
exp (s X) Y Z :- exp X Y K, mult Y K Z.
main :-
TEN = s (s (s (s (s (s (s (s (s (s zero))))))))),
exp (s (s (s (s zero)))) TEN TENTHOUSAND,
iter TENTHOUSAND once.
% ----------------------------------------------------------
%queens(N,Qs) :- range(1,N,Ns), queens(Ns,[],Qs).
%queens([],Qs,Qs).
%queens(UnplacedQs,SafeQs,Qs) :- select(UnplacedQs,UnplacedQs1,Q),
% not_attack(SafeQs,Q), queens(UnplacedQs1,[Q|SafeQs],Qs).
%not_attack(Xs,X) :- not_attack(Xs,X,1).
%not_attack([],_,_) :- !.
%not_attack([Y|Ys],X,N) :-X =\= Y+N,X =\= Y-N,N1 is N+1,not_attack(Ys,X,N1).
%select([X|Xs],Xs,X).
%select([Y|Ys],[Y|Zs],X) :- select(Ys,Zs,X).
%range(N,N,[N]) :- !.
%range(M,N,[M|Ns]) :- M < N, M1 is M+1, range(M1,N,Ns).
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