Josephus — Optimized

The Dllist data structure doesn't keep track of the list's size, so Dllist.length ∈ Ο(n). We can speed up the function by tracking the size:

(* return number of survivor, size-tracking optimization *)
(* only twice as fast *)
let josephus n m =
  let rec j size circle =
    if size = 1
    then Dllist.get circle
    else j (size-1) (Dllist.drop (Dllist.skip circle (m-1)))
  in
  let dl = Dllist.of_list (1--n) in
    j (Dllist.length dl) dl