(* CS421 - Fall 2009
 * MP2 
 *
 *)

(* Problem 1 *)
let reverse_pair (x, y) = (y, x)

(* Problem 2 *)
let add_times ((x, y), (a, b)) = x * y + a * b

(* Problem 3 *)
let rev_first_two l =
  match l with
    x::x'::xs -> x'::x::xs
  | _         -> l

(* Problem 4 *)
let rec concat l =
  match l with
    []    -> ""
  | s::ss -> s ^ concat ss

(* Problem 5 *)
let rec add_sub l =
  match l with
    x::x'::xs -> x - x' + add_sub xs
  | x::[]     -> x
  | []        -> 0
  
(* Problem 6 *)
let rec accumulate_aux l n =
  match l with
    []    -> []
  | x::xs -> (x + n)::accumulate_aux xs (x + n)

let accumulate l = accumulate_aux l 0

(* Problem 7 *)
let rec fixpoint f n = 
   let n' = f n in if n = n' then n else fixpoint f n'

(* Problem 8 *)
let rec count l a =
  match l with
    []    -> 0
  | x::xs -> if x = a then 1 + count xs a else count xs a 

(* Problem 9 *)
let rec all p l =
  match l with
    []    -> true
  | x::xs -> p x && all p xs 

(* Problem 10 *)
let rec filter p l =
  match l with
    []    -> []
  | x::xs -> if p x then x::filter p xs else filter p xs 

(* Problem 11 *)
let rec riffle_aux l1 l2 l2_orig =
  match l2 with
       [] -> riffle_aux l1 l2_orig l2_orig
  | y::ys ->
    match l1 with
      x::x'::xs -> x::y::riffle_aux (x'::xs) ys l2_orig
    | _         -> l1

let riffle l1 l2 =
  match l2 with
    [] -> l1
  | _  -> riffle_aux l1 l2 l2