prolog: nqueens.pl + nqueens.sx (N=1..5), 6 tests

lib/prolog/tests/programs/nqueens.pl

@@ -0,0 +1,27 @@
+%% nqueens — permutation-and-test formulation.
+%% Caller passes the row list [1..N]; queens/2 finds N column placements
+%% s.t. no two queens attack on a diagonal. Same-column attacks are
+%% structurally impossible — Qs is a permutation, all distinct.
+%%
+%% No `>/2` `</2` `=</2` built-ins yet, so range/3 is omitted; tests pass
+%; the literal range list. Once the operator table lands and arithmetic
+%% comparison built-ins are in, range/3 can be added.
+queens(L, Qs) :- permute(L, Qs), safe(Qs).
+
+permute([], []).
+permute(L, [H|T]) :- select(H, L, R), permute(R, T).
+
+select(X, [X|T], T).
+select(X, [H|T], [H|R]) :- select(X, T, R).
+
+safe([]).
+safe([Q|Qs]) :- safe(Qs), no_attack(Q, Qs, 1).
+
+no_attack(_, [], _).
+no_attack(Q, [Q1|Qs], D) :-
+  is(D2, +(Q, D)),
+  \=(D2, Q1),
+  is(D3, -(Q, D)),
+  \=(D3, Q1),
+  is(D1, +(D, 1)),
+  no_attack(Q, Qs, D1).