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% naive queens
queensn(ShowResult) :-
q10(R),
( ShowResult = true ->
write(R), nl
; true).
q8(R) :-
q([1,2,3,4,5,6,7,8], R).
q10(R) :-
q([1,2,3,4,5,6,7,8,9,10], R).
q(L,C):-
perm(L,P),
pair(L,P,C),
safe([],C).
perm([],[]).
perm(Xs,[Z|Zs]):-
sel(Z,Xs,Ys),
perm(Ys,Zs).
sel(X,[X|Xs],Xs).
sel(X,[Y|Ys],[Y|Zs]):-
sel(X,Ys,Zs).
pair([],[],[]).
pair([X|Y],[U|V],[p(X,U)|W]):-
pair(Y,V,W).
safe(_X,[]).
safe(X,[Q|R]):-
test(X,Q),
safe([Q|X],R).
test([],_X).
test([R|S],Q):-
test(S,Q),
nd(R,Q).
nd(p(C1,R1),p(C2,R2)):-
C is C1-C2,
R is R1-R2, C=\=R,
NR is R2-R1, C=\=NR.
% benchmark interface
benchmark(ShowResult) :-
queensn(ShowResult).
:- include(common).
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