Data commit

Task/N-queens-problem/Erlang/n-queens-problem-1.erl

@@ -0,0 +1,83 @@
+-module( n_queens ).
+
+-export( [display/1, solve/1, task/0] ).
+
+display( Board ) ->
+	%% Queens are in the positions in the Board list.
+	%% Top left corner is {1, 1}, Bottom right is {N, N}. There is a queen in the max column.
+	N = lists:max( [X || {X, _Y} <- Board] ),
+	[display_row(Y, N, Board) || Y <- lists:seq(1, N)].
+
+solve( N ) ->
+    Positions = [{X, Y} || X <- lists:seq(1, N), Y <- lists:seq(1, N)],
+    try
+    bt( N, Positions, [] )
+
+    catch
+    _:{ok, Board} -> Board
+
+    end.
+
+task() ->
+    task( 4 ),
+    task( 8 ).
+
+
+
+bt( N, Positions, Board ) -> bt_reject( is_not_allowed_queen_placement(N, Board), N, Positions, Board ).
+
+bt_accept( true, _N, _Positions, Board ) -> erlang:throw( {ok, Board} );
+bt_accept( false, N, Positions, Board ) -> bt_loop( N, Positions, [], Board ).
+
+bt_loop( _N, [], _Rejects, _Board ) -> failed;
+bt_loop( N, [Position | T], Rejects, Board ) ->
+	bt( N, T ++ Rejects, [Position | Board] ),
+	bt_loop( N, T, [Position | Rejects], Board ).
+
+bt_reject( true, _N, _Positions, _Board ) -> backtrack;
+bt_reject( false, N, Positions, Board ) -> bt_accept( is_all_queens(N, Board), N, Positions, Board ).
+
+diagonals( N, {X, Y} ) ->
+	D1 = diagonals( N, X + 1, fun diagonals_add1/1, Y + 1, fun diagonals_add1/1 ),
+	D2 = diagonals( N, X + 1, fun diagonals_add1/1, Y - 1, fun diagonals_subtract1/1 ),
+	D3 = diagonals( N, X - 1, fun diagonals_subtract1/1, Y + 1, fun diagonals_add1/1 ),
+	D4 = diagonals( N, X - 1, fun diagonals_subtract1/1, Y - 1, fun diagonals_subtract1/1 ),
+	D1 ++ D2 ++ D3 ++ D4.
+
+diagonals( _N, 0, _Change_x, _Y, _Change_y ) -> [];
+diagonals( _N, _X, _Change_x, 0, _Change_y ) -> [];
+diagonals( N, X, _Change_x, _Y, _Change_y ) when X > N -> [];
+diagonals( N, _X, _Change_x, Y, _Change_y ) when Y > N -> [];
+diagonals( N, X, Change_x, Y, Change_y ) -> [{X, Y} | diagonals( N, Change_x(X), Change_x, Change_y(Y), Change_y )].
+
+diagonals_add1( N ) -> N + 1.
+
+diagonals_subtract1( N ) -> N - 1.
+
+display_row( Row, N, Board ) ->
+	[io:fwrite("~s", [display_queen(X, Row, Board)]) || X <- lists:seq(1, N)],
+	io:nl().
+
+display_queen( X, Y, Board ) -> display_queen( lists:member({X, Y}, Board) ).
+display_queen( true ) -> " Q";
+display_queen( false ) -> " .".
+
+is_all_queens( N, Board ) -> N =:= erlang:length( Board ).
+
+is_diagonal( _N, [] ) -> false;
+is_diagonal( N, [Position | T] ) ->
+	Diagonals = diagonals( N, Position ),
+	T =/= (T -- Diagonals)
+	orelse is_diagonal( N, T ).
+
+is_not_allowed_queen_placement( N, Board ) ->
+	Pieces = erlang:length( Board ),
+	{Xs, Ys} = lists:unzip( Board ),
+	Pieces =/= erlang:length( lists:usort(Xs) )
+	orelse Pieces =/= erlang:length( lists:usort(Ys) )
+	orelse is_diagonal( N, Board ).
+
+task( N ) ->
+    io:fwrite( "N = ~p. One solution.~n", [N] ),
+    Board = solve( N ),
+    display( Board ).

Task/N-queens-problem/Erlang/n-queens-problem-2.erl

@@ -0,0 +1,14 @@
+%%%For 8X8 chessboard with N queens.
+-module(queens).
+-export([queens/1]).
+
+queens(0) -> [[]];
+queens(N) ->
+     [[Row | Columns] || Columns <- queens(N-1),
+          Row <- [1,2,3,4,5,6,7,8] -- Columns,
+          safe(Row, Columns, 1)].
+
+safe(_Row, [], _N) -> true;
+safe(Row, [Column|Columns], N) ->
+     (Row /= Column + N) andalso (Row /= Column - N) andalso
+          safe(Row, Columns, (N+1)).