(* 
 * CS 334
 * Stephen Freund
 * Tail Recursion Examples
 *)



(* Sum squares from 1 up to n*n. *)
fun sumSq n =
  if n <= 0 then 0 else n*n + sumSq(n-1);

(* Sum squares using tail-recursive helper
   function that requires O(1) space. *)
fun sumSq n =
  let fun sumSqTail(0,t) = t
        | sumSqTail(n,t) = sumSqTail(n-1, t + n*n)
  in
    sumSqTail(n,0)
  end;

sumSq 10;


(****************************************************)


(* An O(n^2) function to reverse a list *)
fun rev nil = nil
  | rev (x::xs) = (rev xs) @ [x];

(* 
   A tail-recursive version that runs in O(n) time
   and uses only O(1) space. 
*)
fun rev l = 
  let fun revTail(nil,r) = r
        | revTail(x::xs,r) = revTail(xs,x::r)
  in
    revTail(l,nil)
  end;

rev [1,2,3,4,5];