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[Med] Bracket Match Generation (self.challenges)

submitted 1 year ago* (last edited 1 year ago) by Ategon to c/challenges

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Bracket Inc. wants to ship out new products using their excess brackets. They have tasked you with generating every possible assortment of brackets for some n brackets where the brackets will match

A bracket match is an opening and closing version of the same kind of bracket beside each other ()
If a bracket matches then outer brackets can also match (())
n will be an even number
The valid brackets are ()[]{}

For example for n = 4 the options are

()()
(())
[][]
[[]]
{}{}
{{}}
[]()
()[]
(){}
{}()
[]{}
{}[]
({})
{()}
([])
[()]
{[]}
[{}]

You must accept n as a command line argument (entered when your app is ran) and print out all of the matches, one per line

(It will be called like node main.js 4 or however else to run apps in your language)

You can use the solution tester in this post to test you followed the correct format https://programming.dev/post/1805174

Any programming language may be used. 2 points will be given if you pass all the test cases with 1 bonus point going to whoevers performs the quickest and 1 for whoever can get the least amount of characters

To submit put the code and the language you used below

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[–] oessessnex 2 points 1 year ago* (last edited 1 year ago)

That was pretty fun :)

My solution is in OCaml. I generate the Dyck language directly (which is basically what this is).

type color = P | B | C
type dyck = Fork of color * dyck * dyck | Nil

let fork c i n = Fork (c, i, n)

let colors = List.to_seq [P; B; C]

let color_open = function P -> "(" | B -> "[" | C -> "{"

let color_close = function P -> ")" | B -> "]" | C -> "}"

let rec to_string = function
  | Fork (c, i, n) -> color_open c ^ to_string i ^ color_close c ^ to_string n
  | Nil -> ""

let memo f =
  let t = Hashtbl.create 10 in
  let rec g x =
    try Hashtbl.find t x with
    | Not_found ->
      let y = f g x in
      Hashtbl.add t x y;
      y
  in g

let ( let* ) x f = Seq.flat_map f x

let generate' recur = function
  | 0 -> Seq.return Nil
  | n ->
    Seq.memoize @@
    let* d = Seq.take n @@ Seq.ints 1 in
    let* c = colors in
    Seq.map_product (fork c) (recur (d - 1)) (recur (n - d))

let generate = memo generate'

let () =
  let n = (int_of_string Sys.argv.(1)) / 2 in
  Seq.iter (fun d -> print_endline (to_string d)) (generate n)