package knights_tour
Solves the Knight's tour puzzle; and others
Install
dune-project
Dependency
Authors
Maintainers
Sources
knights_tour-0.0.2.tbz
sha256=8362f846492183e83e1901f73933d772c193c08b8a375480c28d0f23f0d29e11
sha512=5fe79ac95a3e5a2e01d429665fa7a8bfef422d9843758b35db2c8efc299c762c1d22974266f5e8802ee6f81e09223aa90476824d1fd93540c473cc8a357d38a3
doc/src/knights_tour.pentominos/puzzle.ml.html
Source file puzzle.ml
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(** board upon which to place the pieces *) board : Board.t; } let classic = { pieces = Polyomino.of_order 5; board = Board.classic; } let classic_no_symmetric_solutions = { classic with pieces = classic.pieces |> Polyomino.pin_symmetry } let lowest_point board = Board.vacant board |> PointSet.min_elt type placement = { piece: Polyomino.t; points: PointSet.t; } let move_to_target target points = let open Searchspace in Searchspace.of_seq (PointSet.to_seq points) |-> (fun point -> PointSet.translate (Point.diff target point) points) let place_one piece board target = let open Searchspace in Polyomino.variants piece |> Searchspace.of_list |=> move_to_target target |?> (fun points -> points |> PointSet.for_all (fun point -> Board.(get board point = Vacant)) ) |-> (fun points -> {points;piece}) let smallest measure xs = let keep_smallest (sx,x) (sy,y) = if Int.compare sx sy <= 0 then (sx, x) else (sy, y) in match List.map (fun x -> (measure x, x)) xs with | [] -> failwith "An empty list doesn't have a smallest element" | fst::rst -> List.fold_left keep_smallest fst rst |> snd let%expect_test "smallest string" = let cases = [ ["Hello"; "World"; "Very long"; "a"]; ["The"; "Quick"; "Brown fox"; "jumps"]; ["Short"; "in"; "the"; "middle"]; ["all"; "the"; "sam"] ] in cases |> List.iter (fun words -> words |> List.iter (Printf.printf "%s; "); smallest String.length words |> Printf.printf " => %s\n" ) ;[%expect{| Hello; World; Very long; a; => a The; Quick; Brown fox; jumps; => The Short; in; the; middle; => in all; the; sam; => all |}] (** Finds all valid placements for the most constrained target.*) let most_constrained_point {pieces; board} targets = let open Searchspace in let placements_per_target = targets |> PointSet.to_seq |> Seq.map (fun target -> pieces |> Searchspace.of_list |=> (fun piece -> place_one piece board target) |> Searchspace.to_seq |> List.of_seq ) |> List.of_seq in smallest List.length placements_per_target |> of_list let%expect_test "most_constrained_point" = let board = Board.of_string " ######## ######## ######## ###..### ###..### ######## #######. ######## " in let puzzle = {board; pieces=Polyomino.of_order 5} in let vacancies = Board.vacant board in let most_constrained = most_constrained_point puzzle vacancies in most_constrained |> Searchspace.to_seq |> Seq.iter (fun {piece;points} -> Board.put puzzle.board points piece |> Board.to_string |> Printf.printf "%s\n" ) ;[%expect{| ........ ........ ........ ...##... ...##... ........ .......# ...AAAAA ........ ........ ........ ...##... ...##... ........ ....B..# ....BBBB ........ ........ ........ ...##... ...##.B. ......B. ......B# ......BB ........ ........ ........ ...##... ...##... ........ .....C.# ....CCCC ........ ........ ........ ...##... ...##... ........ ......C# ....CCCC ........ ........ ........ ...##... ...##... ........ .....DD# .....DDD ........ ........ ........ ...##... ...##... ......EE ......E# ......EE ........ ........ ........ ...##... ...##... .....F.. .....F.# .....FFF ........ ........ ........ ...##... ...##... ......G. ......G# .....GGG ........ ........ ........ ...##... ...##... ........ ....HHH# ......HH ........ ........ ........ ...##... ...##... ........ ....HH.# .....HHH ........ ........ ........ ...##... ...##... ......I. .....II# ......II ........ ........ ........ ...##... ...##... .....J.. .....JJ# ......JJ ........ ........ ........ ...##... ...##... .....KK. ......K# ......KK |}] let rec solve_aux ~report_progress puzzle targets = let open Searchspace in if PointSet.is_empty targets then ( report_progress "Solved" puzzle; return puzzle.board ) else most_constrained_point puzzle targets |=> (fun {piece; points} -> let puzzle = { board=Board.put puzzle.board points piece; pieces=List.filter (fun p -> Polyomino.compare p piece <> 0) puzzle.pieces; } in report_progress "Placed a piece" puzzle; let targets = PointSet.union targets (PointSet.adjacent points) |> PointSet.filter (fun pt -> (Board.get puzzle.board pt) = Vacant) in solve_aux ~report_progress puzzle targets ) let solve ?(report_progress = fun _ _ -> ()) puzzle = solve_aux ~report_progress puzzle (PointSet.singleton (lowest_point puzzle.board)) let%expect_test "Placements of a polyomino on a target" = let puzzle = classic in let pentos = puzzle.pieces in let piece = List.hd pentos in let board = puzzle.board in let target = Point.{x=1;y=2} in Printf.printf "===============\nPlacing @ (%d, %d):\n%s" target.x target.y (Polyomino.to_string piece); place_one piece board target |> Searchspace.to_seq |> Seq.iter (fun placement -> Board.put board placement.points placement.piece |> Board.to_string |> Printf.printf "\n%s" ) ; [%expect{| =============== Placing @ (1, 2): ##### ........ ........ .AAAAA.. ...##... ...##... ........ ........ ........ ........ ........ AAAAA... ...##... ...##... ........ ........ ........ ........ ........ .A...... .A.##... .A.##... .A...... .A...... ........ ........ .A...... .A...... .A.##... .A.##... .A...... ........ ........ .A...... .A...... .A...... .A.##... .A.##... ........ ........ ........ |}] let%expect_test "Placements of all tetro-minos @(0,0)" = let pentos = Polyomino.of_order 4 in let board = Board.classic in let target = Point.{x=0;y=0} in pentos |> List.iter (fun piece -> Printf.printf "===============\nPlacing @ (%d, %d):\n%s" target.x target.y (Polyomino.to_string piece); place_one piece board target |> Searchspace.to_seq |> Seq.iter (fun placement -> Board.put board placement.points placement.piece |> Board.to_string |> Printf.printf "\n%s" ) ) ; [%expect{| =============== Placing @ (0, 0): #### AAAA.... ........ ........ ...##... ...##... ........ ........ ........ A....... A....... A....... A..##... ...##... ........ ........ ........ =============== Placing @ (0, 0): ### #.. BBB..... B....... ........ ...##... ...##... ........ ........ ........ BBB..... ..B..... ........ ...##... ...##... ........ ........ ........ BB...... B....... B....... ...##... ...##... ........ ........ ........ BB...... .B...... .B...... ...##... ...##... ........ ........ ........ B....... BBB..... ........ ...##... ...##... ........ ........ ........ B....... B....... BB...... ...##... ...##... ........ ........ ........ =============== Placing @ (0, 0): ### .#. CCC..... .C...... ........ ...##... ...##... ........ ........ ........ C....... CC...... C....... ...##... ...##... ........ ........ ........ =============== Placing @ (0, 0): ## ## DD...... DD...... ........ ...##... ...##... ........ ........ ........ =============== Placing @ (0, 0): ##. .## EE...... .EE..... ........ ...##... ...##... ........ ........ ........ E....... EE...... .E...... ...##... ...##... ........ ........ ........ |}] let%expect_test "solve classic pentos" = let puzzle = classic in solve puzzle |> Searchspace.to_seq |> Seq.take 4 |> Seq.map Board.to_string |> Seq.iter print_endline ;[%expect{| AAAAAFFF BBBBHHIF BLHHHIIF LLL##KII CLG##KKK CCGGGJJK CEGEDDJJ CEEEDDDJ AAAAAFFF BBBBHHIF BLHHHIIF LLL##KII CLG##KKK CCGGGJJK CEGEJJDD CEEEJDDD AAAAAJJD BBBBJJDD EEEBJGDD EHE##GGG HHL##GKK HLLLIIKF HCLIIKKF CCCCIFFF AAAAADDD BBCCCCDD BGGGCEEE BHG##ELE BHG##LLL HHJKKILF HJJKIIIF JJKKIFFF |}]