First 3 problems

README.org

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