156 lines
3.0 KiB
Org Mode
156 lines
3.0 KiB
Org Mode
#+TITLE: 99 Ocaml Problems
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#+Author: Joseph Ferano
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https://ocaml.org/problems
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*** #1 Tail of a list
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Write a function ~last : 'a list -> 'a option~ that returns the last element of a
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list
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#+begin_src ocaml
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# last ["a" ; "b" ; "c" ; "d"];;
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- : string option = Some "d"
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# last [];;
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- : 'a option = None
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#+end_src
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**** Solution
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#+begin_src ocaml
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let rec last = function
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| [] -> None
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| [x] -> Some x
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| _::xs -> last xs
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#+end_src
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*** #2 Last two elements of a list
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Find the last but one (last and penultimate) elements of a list.
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#+begin_src ocaml
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# last_two ["a"; "b"; "c"; "d"];;
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- : (string * string) option = Some ("c", "d")
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# last_two ["a"];;
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- : (string * string) option = None
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#+end_src
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**** Solution
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#+begin_src ocaml
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let rec last_two = function
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| [] | [_] -> None
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| [x;y] -> Some (x,y)
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| _::xs -> last_two xs
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#+end_src
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*** #3 N'th element of a list
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Find the N'th element of a list.
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REMARK: OCaml has List.nth which numbers elements from 0 and raises an exception
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if the index is out of bounds.
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#+begin_src ocaml
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# List.nth ["a"; "b"; "c"; "d"; "e"] 2;;
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- : string = "c"
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# List.nth ["a"] 2;;
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Exception: Failure "nth".
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#+end_src
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**** Solution
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#+begin_src ocaml
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let rec nth index = function
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| [] -> failwith "nth"
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| x::xs -> if index = 0 then x else nth (index - 1) xs
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#+end_src
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*** #4 Find the number of elements of a list.
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OCaml standard library has List.length but we ask that you reimplement it. Bonus for a tail
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recursive solution.
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#+begin_src ocaml
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# length ["a"; "b"; "c"];;
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- : int = 3
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# length [];;
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- : int = 0
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#+end_src
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**** Solution
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#+begin_src ocaml
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let length list =
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let rec length_rec acc = function
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| [] -> acc
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| _::xs -> length_rec (acc + 1) xs
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in length_rec 0 list
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#+end_src
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*** #5 Reverse a list.
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OCaml standard library has List.rev but we ask that you reimplement it.
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#+begin_src ocaml
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# rev ["a"; "b"; "c"];;
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- : string list = ["c"; "b"; "a"]
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#+end_src
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**** Solution
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#+begin_src ocaml
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let rev (list: int list) =
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let rec rev acc = function
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| [] -> acc
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| x::xs -> rev (x::acc) xs
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in rev [] list
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#+end_src
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*** #6 Palindrome
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Find out whether a list is a palindrome.
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HINT: a palindrome is its own reverse.
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#+begin_src ocaml
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# is_palindrome ["x"; "a"; "m"; "a"; "x"];;
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- : bool = true
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# not (is_palindrome ["a"; "b"]);;
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- : bool = true
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#+end_src
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**** Solution
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#+begin_src ocaml
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let is_palindrome list = list = List.rev list
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#+end_src
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*** #7 Flatten a list
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Flatten a nested list structure.
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#+begin_src ocaml
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type 'a node =
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| One of 'a
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| Many of 'a node list
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# flatten [One "a"; Many [One "b"; Many [One "c" ;One "d"]; One "e"]];;
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- : string list = ["a"; "b"; "c"; "d"; "e"]
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#+end_src
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**** Solution
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#+begin_src ocaml
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let flatten nodes =
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let rec f = function
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| One x -> [x]
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| Many xs -> List.concat_map f xs
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in nodes |> List.concat_map f
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(* Or without List.concat_map *)
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let flatten2 nodes =
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let rec f acc = function
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| [] -> acc
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| One n::ns -> f (n::acc) ns
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| Many ns::rest -> f (f acc ns) rest
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in f [] nodes |> List.rev
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#+end_src
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