(* Lecture 1: Introduction *)
(* SGDM, Carsten Schuermann *)


datatype Pebble = White | Blue

(* Flipper *)

fun skip nil = nil
  | skip (White :: rest) = White :: (flip rest)
  | skip (Blue :: rest)  = Blue :: (flip rest)
 
and skip2 nil = nil
  | skip2 (White :: rest) = White :: (skip rest)
  | skip2 (Blue :: rest)  = Blue :: (skip rest)

and flip nil = nil
  | flip (White :: rest) = Blue :: (skip2 rest)
  | flip (Blue :: rest)  = White :: (skip rest)
 
(* Flipper end *)

fun toString nil = ""
  | toString (White :: rest) = "." ^ (toString rest)
  | toString (Blue :: rest) = "X" ^ (toString rest)

fun iterate f 0 C = nil
  | iterate f n C = 
     (print ((toString C) ^ "\n");
     iterate f (n-1) (f C))

val example1 = [White, White, White, White, White, White, Blue, Blue, Blue, Blue, Blue, Blue]
val example2 = [White, White, White]
val example3 = [White, White, White, White, Blue, Blue, Blue, Blue]

fun minimal f C =
  let fun minimal' n' C' = if C = C' then n' else minimal' (n' + 1) (f C')
  in 
    minimal' 1 (f C)
  end 

fun whites 0 = nil
  | whites n = White :: (whites (n - 1))

fun cycle f C =  iterate f (minimal f C) C