(*
  A Polymorphic QuickSort function for any list.
  Stephen Freund
  cs334
*)

(* Always include these at the top of your SML files so 
   large datatype values and lists will print fully *)
Control.Print.printDepth := 100;
Control.Print.printLength := 100;

(* 
  partition: (('a * 'a -> bool) * 'a * 'a list) 
              -> ('a list * 'a list)
  In this version, you must supply a lessThan fuction for
  comparing values.
*)
fun partition (lessThan, pivot, nil) = (nil, nil)
  | partition (lessThan, pivot, x::xs) =
      let val (smaller, bigger) = partition(lessThan, pivot, xs) 
      in
	if lessThan(x,pivot) then (x::smaller, bigger) 
	       	     else (smaller, x::bigger)
      end;

(* qsort: ('a * 'a -> bool) * 'a list -> 'a list *)
fun qsort (lessThan, nil) = nil
  | qsort (lessThan, p::rest) = 
      let val (smaller, bigger) = partition(lessThan, p,rest)
      in
	qsort (lessThan, smaller) @ [p] @ qsort(lessThan, bigger)
      end;



qsort (op<, [6,23,6,3,78,23,12,6,7,34,7]);

qsort ((fn (x,y) => (abs x) < (abs y)), [~3, 5, 2, ~1]);

qsort (op<, ["moo", "purple", "cow", "wombat"]);