Generate All Subsets of N

(* In this scripte, we will write a function to generate all the subset of {1,2,...,n} 
 * The basic idea is to use the bit array of 1, 2, ..., n to represent the subset.
 *)

let rec int_power x n =
  let xf = float_of_int x
  and nf = float_of_int n in
  int_of_float (xf ** nf) ;;


let generate_subset n =
  let arr = Array.init n (fun x -> x + 1)in
  let rec generate_set result index k =
    match k with
    | 0 -> result
    | k ->
      if k land 1 = 1 then
        let elem = arr.(index) in
        generate_set (elem::result) (index + 1) (k lsr 1)
      else
        generate_set result (index + 1) (k lsr 1)
  in
    let rec generate_allset result k limit =
      match k < limit with
      | false -> result
      | true ->
        let res = generate_set [] 0 k in
        generate_allset (res::result) (k + 1) limit
    in
    let num_iter = int_power 2 n in
    let final_result = generate_allset [] 0 num_iter in
    final_result ;;


generate_subset 1 ;;
generate_subset 2 ;;
generate_subset 3 ;;
generate_subset 4 ;;