#+TITLE: 99 Ocaml Problems
#+Author: Joseph Ferano

https://ocaml.org/problems

*** #1 - Tail of a list

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

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

**** Solution
#+begin_src ocaml
let rec last = function
  | []    -> None
  | [x]   -> Some x
  | _::xs -> last xs 
#+end_src

*** #2 - Last two elements of a list

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

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

**** Solution
#+begin_src ocaml
let rec last_two = function
  | [] | [_] -> None
  | [x;y] -> Some (x,y)
  | _::xs -> last_two xs
#+end_src

*** #3 - N'th element of a list

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.

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

**** Solution
#+begin_src ocaml
let rec nth index = function
  | [] -> failwith "nth"
  | x::xs -> if index = 0 then x else nth (index - 1) xs
#+end_src

*** #4 Find the number of elements of a list.

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

#+begin_src ocaml
# length ["a"; "b"; "c"];;
- : int = 3
# length [];;
- : int = 0
#+end_src

**** Solution
#+begin_src ocaml

#+end_src