Listing all permutations of a string/integer

Question

A common task in programming interviews (not from my experience of interviews though) is to take a string or an integer and list every possible permutation.

Is there

Answer 1

Here's a purely functional F# implementation:

let factorial i =
    let rec fact n x =
        match n with
        | 0 -> 1
        | 1 -> x
        | _ -> fact (n-1) (x*n)
    fact i 1

let swap (arr:'a array) i j = [| for k in 0..(arr.Length-1) -> if k = i then arr.[j] elif k = j then arr.[i] else arr.[k] |]

let rec permutation (k:int,j:int) (r:'a array) =
    if j = (r.Length + 1) then r
    else permutation (k/j+1, j+1) (swap r (j-1) (k%j))

let permutations (source:'a array) = seq { for k = 0 to (source |> Array.length |> factorial) - 1 do yield permutation (k,2) source }

Performance can be greatly improved by changing swap to take advantage of the mutable nature of CLR arrays, but this implementation is thread safe with regards to the source array and that may be desirable in some contexts. Also, for arrays with more than 16 elements int must be replaced with types with greater/arbitrary precision as factorial 17 results in an int32 overflow.