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

F#:

Here is a solution that, unlike my previous solution, I believe may be correct. Also, it is more efficient.

#light

let brackets2 n =
    let result = new System.Collections.Generic.List<_>()
    let a = Array.create (n*2) '_'
    let rec helper l r diff i =
        if l=0 && r=0 then
            result.Add(new string(a))
        else
            if l > 0 then
                a.[i] <- '('
                helper (l-1) r (diff+1) (i+1)
            if diff > 0 then
                a.[i] <- ')'
                helper l (r-1) (diff-1) (i+1)
    helper n n 0 0
    result

Example:

(brackets2 4) |> Seq.iter (printfn "%s")

(*
(((())))
((()()))
((())())
((()))()
(()(()))
(()()())
(()())()
(())(())
(())()()
()((()))
()(()())
()(())()
()()(())
()()()()
*)