(* "n choose m" -- for nonnegative integers n, m with 0<=m<=n *)

(* NOTE: "n choose 0" = 1 for any non-negative n including 0 *)



fun choose (n, m) =
    let
        exception BadN and BadM
    in
        if n <= 0 then raise BadN
        else if m < 0 orelse m > n then raise BadM
        else if m = 0 orelse m = n then 1
        else choose (n-1, m) + choose (n-1, m-1)
    end
;

(* scanInt (L) converts a list of decimal digits to the integer that is the
   value of the string in reverse
*)

fun scanInt (nil) = 0
|   scanInt (h::t) = ord(h)-ord(#"0")+10*scanInt(t);

(* string2Int (s) converts a string s of decimal digits to its equivalent
   integer.
*)

fun string2Int (s) = scanInt (rev(explode(s)));

(* The following function prints (onto stdio) the decimal representation
   of an integer. Note that for negative integers a minus sign is used
   as opposed to the usual ML convention of using the character "~".
*)

fun printInt (n) =
        (* the following iterative function converts a non-negative integer
           into a list of decimal digits
        *)
    let fun prIntIter (n, L) =
            if n = 0 then
               if null (L) then [#"0"]
               else L
            else prIntIter (n div 10, chr((n mod 10) + ord (#"0"))::L)
        ;
        val L = prIntIter (abs(n), []);
    in  if  n<0 then print (implode(#"-"::L))
        else print(implode (L))
    end
;

fun comb ([n,m]) = (printInt (choose (string2Int(n), string2Int(m)));
                        print ("\n"));

(* SMLofNJ.exportML "combinations";  *)

SMLofNJ.exportFn ("combfile", ("comb" ["5", "4"]));