Finding all combinations of well-formed brackets

Question

This came up while talking to a friend and I thought I\'d ask here since it\'s an interesting problem and would like to see other people\'s solutions.

The task is to

Answer 1

A simple F#/OCaml solution :

let total_bracket n =
    let rec aux acc = function
        | 0, 0 -> print_string (acc ^ "\n")
        | 0, n -> aux (acc ^ ")") (0, n-1)
        | n, 0 -> aux (acc ^ "(") (n-1, 1)
        | n, c ->
                aux (acc ^ "(") (n-1, c+1);
                aux (acc ^ ")") (n,   c-1)
    in
    aux "" (n, 0)