findMax.sml

(* Recursive definition *)
fun max3 (x, y, z) = Int.max(x, Int.max(y, z))
fun min3 (x, y, z) = Int.min(x, Int.min(y, z))

fun findMax 0 = 0
  | findMax 1 = 1
  | findMax 2 = 2
  | findMax 3 = 0
  | findMax 4 = 1
  | findMax n = max3 (findMin (n-5), findMin (n-4), findMin (n-3))

and findMin 0 = 0
  | findMin 1 = 1
  | findMin 2 = 2
  | findMin 3 = 0
  | findMin 4 = 0
  | findMin n = min3 (findMax (n-5), findMax (n-4), findMax (n-3))

(* Closed form *)
fun findMax 0 = 0
  | findMax 1 = 1
  | findMax 2 = 2
  | findMax n =
    case (n mod 8) of
        3 => 0
      | 4 => 1
      | 5 => 2
      | 6 => 2
      | 7 => 2
      | 0 => 0
      | 1 => 0
      | 2 => 0
      | _ => raise Fail "(n mod 8) > 7?"