99 Ocaml Problems

Write a function last : 'a list -> 'a option that returns the last element of a list

# last ["a" ; "b" ; "c" ; "d"];;
- : string option = Some "d"
                      # last [];;
- : 'a option = None

let rec last = function
  | []    -> None
  | [x]   -> Some x
  | _::xs -> last xs

Find the last but one (last and penultimate) elements of a list.

# last_two ["a"; "b"; "c"; "d"];;
- : (string * string) option = Some ("c", "d")
# last_two ["a"];;
- : (string * string) option = None

let rec last_two = function
  | [] | [_] -> None
  | [x;y] -> Some (x,y)
  | _::xs -> last_two xs

Find the N'th element of a list.

REMARK: OCaml has List.nth which numbers elements from 0 and raises an exception if the index is out of bounds.

# List.nth ["a"; "b"; "c"; "d"; "e"] 2;;
- : string = "c"
# List.nth ["a"] 2;;
Exception: Failure "nth".

let rec nth index = function
  | [] -> failwith "nth"
  | x::xs -> if index = 0 then x else nth (index - 1) xs

OCaml standard library has List.length but we ask that you reimplement it. Bonus for a tail recursive solution.

# length ["a"; "b"; "c"];;
- : int = 3
# length [];;
- : int = 0