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Task/N-queens-problem/Prolog/n-queens-problem-5.pro

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+% 8 queens problem.
+%  q(Row) represents a queen, allocated one per row. No rows ever clash.
+%  The columns are chosen iteratively from available columns held in a
+%  list, reduced with each allocation, so we need never check verticals.
+%  For diagonals, we check prior to allocation whether each newly placed
+%  queen will clash with any of the prior placements. This prevents
+%  most invalid permutations from ever being attempted.
+can_place(_, []) :- !.	   % success for empty board
+can_place(q(R,C),Board) :- % check diagonals against allocated queens
+	member(q(Ra,Ca), Board), abs(Ra-R) =:= abs(Ca-C), !, fail.
+can_place(_,_).            % succeed if no diagonals failed
+
+queens([], [], Board, Board).                            % found a solution
+queens([q(R)|Queens], Columns, Board, Solution) :-
+	nth0(_,Columns,C,Free), can_place(q(R,C),Board), % find all solutions
+	queens(Queens,Free,[q(R,C)|Board], Solution).    % recursively
+
+queens :-
+  findall(q(N), between(0,7,N), Queens), findall(N, between(0,7,N), Columns),
+  findall(B, queens(Queens, Columns, [], B), Boards),     % backtrack over all
+  length(Boards, Len), writef('%w solutions:\n', [Len]),  % Output solutions
+  member(R,Boards), reverse(R,Board), writef('  - %w\n', [Board]), fail.
+queens.