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28 lines
856 B
Prolog
28 lines
856 B
Prolog
%% nqueens — permutation-and-test formulation.
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%% Caller passes the row list [1..N]; queens/2 finds N column placements
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%% s.t. no two queens attack on a diagonal. Same-column attacks are
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%% structurally impossible — Qs is a permutation, all distinct.
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%%
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%% No `>/2` `</2` `=</2` built-ins yet, so range/3 is omitted; tests pass
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%; the literal range list. Once the operator table lands and arithmetic
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%% comparison built-ins are in, range/3 can be added.
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queens(L, Qs) :- permute(L, Qs), safe(Qs).
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permute([], []).
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permute(L, [H|T]) :- select(H, L, R), permute(R, T).
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select(X, [X|T], T).
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select(X, [H|T], [H|R]) :- select(X, T, R).
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safe([]).
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safe([Q|Qs]) :- safe(Qs), no_attack(Q, Qs, 1).
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no_attack(_, [], _).
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no_attack(Q, [Q1|Qs], D) :-
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is(D2, +(Q, D)),
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\=(D2, Q1),
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is(D3, -(Q, D)),
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\=(D3, Q1),
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is(D1, +(D, 1)),
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no_attack(Q, Qs, D1).
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