package knights_tour
Solves the 'Knights Tour' and various 'Poyomino' puzzles
Install
dune-project
Dependency
Authors
Maintainers
Sources
knights_tour-0.0.6.tbz
sha256=770624ae4e35d5a58188a1f25e16730d186df8bc4397827fe9a798ea5ca574e3
sha512=b6c7b2473ddf321afaac6b668f9c6820fb8cc872abc494b69edfdff4101c6b660645837b04801e2917c38dd9f19f79bb0a7b029d59a58ddf1e3a235659bab099
doc/src/knights_tour.pentominos/pointSet.ml.html
Source file pointSet.ml
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(** A PointSet is a set of points in 2d space. Each point has int coordinates and represents a square on a chess-like game board (of unspecified/inifinite dimenions)*) open Knights_tour include Set.Make(Point) let of_string image = let lines = String.split_on_char '\n' image |> List.map String.trim in let points = ref empty in lines |> List.iteri (fun y line -> line |> String.iteri (fun x c -> match c with | '.' | ' ' -> () | _ -> points := add {x;y} !points ) ); !points let min_map selector points = fold (fun pt acc -> Int.min (selector pt) acc) points Int.max_int let max_map selector points = fold (fun pt acc -> Int.max (selector pt) acc) points Int.min_int let min_x = min_map (fun p -> p.x) let max_x = max_map (fun p -> p.x) let min_y = min_map (fun p -> p.y) let max_y = max_map (fun p -> p.y) let%expect_test "min max" = let points = of_string " . ...# ..## ...######### ..." in ( Format.printf "min_x = %d\n" (min_x points); Format.printf "max_x = %d\n" (max_x points); Format.printf "min_y = %d\n" (min_y points); Format.printf "max_y = %d\n" (max_y points); ) ;[%expect{| min_x = 2 max_x = 11 min_y = 2 max_y = 4 |}] let%expect_test "pointset parsed from string image" = of_string ( ".# ## .##" ) |> iter (fun {x;y} -> (Format.printf "(%d, %d)\n" x y)) ;[%expect{| (1, 0) (0, 1) (1, 1) (1, 2) (2, 2) |}] let to_string points = let image = Buffer.create 60 in for y = min_y points to max_y points do for x = min_x points to max_x points do Buffer.add_char image ( if mem {x;y} points then '#' else '.' ) done; Buffer.add_char image '\n' done; Buffer.contents image let%expect_test "to_string" = let points = of_string " . ...# ..## ...######### ..." in print_endline (to_string points) ;[%expect{| .#........ ##........ .######### |}] let neighbours Point.{x;y} = Point.[ { x = x - 1 ; y }; { x ; y = y - 1 }; { x = x + 1 ; y }; { x ; y = y + 1 } ] |> of_list let flatmap f points = fold (fun elt acc -> union (f elt) acc) points empty let adjacent points = let all_neighbours = points |> flatmap neighbours in diff all_neighbours points let%expect_test "adjacent" = let input = of_string " # # ## " in input |> adjacent |> (fun adjacent -> Printf.printf "org: (%d, %d)\n" (min_x input) (min_y input); Printf.printf "adj: (%d, %d)\n" (min_x adjacent) (min_y adjacent); Printf.printf "%s\n" (to_string adjacent) ) ;[%expect{| org: (0, 1) adj: (-1, 0) .#.. #.#. #.#. #..# .##. |}] let translate (delta : Point.t) = map (fun {x; y} -> { x = x + delta.x; y = y + delta.y }) let normalize_translation points = let min_x = points |> min_x in let min_y = points |> min_y in translate {x = -min_x; y = -min_y} points let rotate_point Point.{x;y} = Point.{x = -y; y = x} let mirror_point Point.{x;y} = Point.{y = x; x = y} let rotate points = map rotate_point points |> normalize_translation let mirror = map mirror_point module PointSetSet = Set.Make(struct type nonrec t = t let compare = compare end) let variants ini = let open Searchspace in ( int_range 0 1 |=> fun mirror_count -> int_range 0 3 |-> fun rot_count -> ini |> normalize_translation |> Fun.repeat rot_count rotate |> Fun.repeat mirror_count mirror ) |> Searchspace.to_seq |> PointSetSet.of_seq |> PointSetSet.to_seq |> List.of_seq let variants_with_transform shape = let open Searchspace in let transforms = int_range 0 1 |=> fun mirror_count -> int_range 0 3 |-> fun rot_count -> fun pts -> pts |> normalize_translation |> Fun.repeat rot_count rotate |> Fun.repeat mirror_count mirror in let seen = ref PointSetSet.empty in let results = ref [] in transforms |> to_seq |> Seq.iter (fun transform -> let transformed = transform shape |> normalize_translation in if not (PointSetSet.mem transformed !seen) then begin seen := PointSetSet.add transformed !seen; results := (transform, transformed) :: !results end ); List.rev !results let normalize points = points |> variants |> List.hd let%expect_test "variants assymetric" = of_string ".# ## .# .#" |> variants |> List.map to_string |> List.iter (Format.printf "-------------\n%s") ;[%expect{| ------------- #### .#.. ------------- #### ..#. ------------- #. ## #. #. ------------- #. #. ## #. ------------- .#.. #### ------------- .# ## .# .# ------------- .# .# ## .# ------------- ..#. #### |}] let%expect_test "variants symmetric" = of_string ".# ### .#" |> variants |> List.map to_string |> List.iter (Format.printf "-------------\n%s") ;[%expect{| ------------- .#. ### .#. |}] let%expect_test "normalized rep of variants are equal to one another" = let open Printf in let vars = of_string ".# ## .# .#" |> variants |> Array.of_list in vars |> Array.iteri (fun i1 v1 -> printf "%d: " i1; vars |> Array.iter (fun v2 -> printf "%b " ((compare (normalize v1) (normalize v2)) = 0) ); printf "\n" ) ; [%expect{| 0: true true true true true true true true 1: true true true true true true true true 2: true true true true true true true true 3: true true true true true true true true 4: true true true true true true true true 5: true true true true true true true true 6: true true true true true true true true 7: true true true true true true true true |}] let%expect_test "rotate and normalize translation" = let points = of_string ( ".# ## .# .#" ) in for i = 0 to 3 do Fun.repeat i rotate points |> (fun points -> Printf.printf "=======================\n%!"; Printf.printf "min_x : %d min_y : %d\n%!" (min_x points) (min_y points); Printf.printf "=======================\n%!"; Printf.printf "%s\n%!" (to_string points) ) done ; [%expect{| ======================= min_x : 0 min_y : 0 ======================= .# ## .# .# ======================= min_x : 0 min_y : 0 ======================= ..#. #### ======================= min_x : 0 min_y : 0 ======================= #. #. ## #. ======================= min_x : 0 min_y : 0 ======================= #### .#.. |}] let%expect_test "variants_with_transform" = let input_shapes = List.map of_string [ "## ##" ; "## ## ## ##" ; "#. ##" ; "# ##" ; "# # ##" ] in let test_shape = of_string ( ".# ## .# .#" ) in input_shapes |> List.iter (fun shape -> Printf.printf "Shape:\n%s\n" (to_string shape); let syms = variants_with_transform shape in Printf.printf "Symmetries: %d\n" (List.length syms); List.iteri (fun i (transform, b) -> ( Printf.printf "Symmetry %d:\n" i; Printf.printf "%s\n" (to_string b); Printf.printf "Transformed shape:\n"; Printf.printf "%s\n" (test_shape |> transform |> to_string); Printf.printf "---\n" )) syms; Printf.printf "========================\n" ); [%expect{| Shape: ## ## Symmetries: 1 Symmetry 0: ## ## Transformed shape: .# ## .# .# --- ======================== Shape: ## ## ## ## Symmetries: 2 Symmetry 0: ## ## ## ## Transformed shape: .# ## .# .# --- Symmetry 1: #### #### Transformed shape: ..#. #### --- ======================== Shape: #. ## Symmetries: 4 Symmetry 0: #. ## Transformed shape: .# ## .# .# --- Symmetry 1: ## #. Transformed shape: ..#. #### --- Symmetry 2: ## .# Transformed shape: #. #. ## #. --- Symmetry 3: .# ## Transformed shape: #### .#.. --- ======================== Shape: #. ## Symmetries: 4 Symmetry 0: #. ## Transformed shape: .# ## .# .# --- Symmetry 1: ## #. Transformed shape: ..#. #### --- Symmetry 2: ## .# Transformed shape: #. #. ## #. --- Symmetry 3: .# ## Transformed shape: #### .#.. --- ======================== Shape: #. #. ## Symmetries: 8 Symmetry 0: #. #. ## Transformed shape: .# ## .# .# --- Symmetry 1: ### #.. Transformed shape: ..#. #### --- Symmetry 2: ## .# .# Transformed shape: #. #. ## #. --- Symmetry 3: ..# ### Transformed shape: #### .#.. --- Symmetry 4: ### ..# Transformed shape: .#.. #### --- Symmetry 5: ## #. #. Transformed shape: .# .# ## .# --- Symmetry 6: #.. ### Transformed shape: #### ..#. --- Symmetry 7: .# .# ## Transformed shape: #. ## #. #. --- ======================== |}]
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