(* CS421 - Summer 2007
 * MP1 Solution
 *
 * Please keep in mind that there may be more than one
 * way to solve a problem.
 *)

(* Problem 1 *)
let sum4 x y z t = x +. y +. z +. t

(* Problem 2 *)
let fst (x,y) = x

(* Problem 3 *)
let max3 x y z =
  let max_xy = if x > y then x else y
  in
    if max_xy > z then max_xy else z

(* Problem 4 *)
let cube_sum x y z =
  let sum = x + y + z
  in
    sum * sum * sum

(* Problem 5 *)
let twicehead lst =
  match lst with
      []    -> 0
    | x::xs -> 2 * x

(* Problem 6 *)
let replacehead a lst =
  match lst with
      []    -> []
   |  x::xs -> a::xs

(* Problem 7 *)
let birthday name num =
  print_string name;
  print_string " is ";
  print_int num;
  print_string " years old today.\n"

(* Problem 8 *)
let divide x y =
  if y = 0 then (false, 0) else (true, x / y)


(* Mapping recursion *)
(* Problem 9 *)
let rec square_lst lst =
  match lst with
      []    -> []
    | x::xs -> x * x::square_lst xs

(* Problem 10 *)
let rec map_lst f lst =
  match lst with
      []    -> []
    | x::xs -> f x::map_lst f xs

(* Folding recursion *)
(* Problem 11 *)
let rec dropneg_lst lst =
  match lst with
      []    -> []
    | x::xs -> if x < 0 then dropneg_lst xs else x::dropneg_lst xs

(* Tail recursion *)
(* Problem 12 *)
let concat_rev_lst lst =
  let rec aux lst res =
    match lst with
       []    -> res
     | x::xs -> aux xs (x ^ res)
  in
    aux lst ""

(* Problem 13 *)
let sumf_lst f lst =
  let rec aux lst res =
    match lst with
	[]    -> res
      | x::xs -> aux xs (if f x then x + res else res)
  in
    aux lst 0


(* Extra credit *)
(* Problem 14 *)
let rec repeat_item n item =
  if n <= 0 then []
  else item::(repeat_item (n-1) item)

let repeat_lst lst =
  let rec aux n lst =
    match lst with
        []    -> []
      | x::xs -> repeat_item n x::aux (n+1) xs
  in
    aux 1 lst