(* Exercice 1: 4pts *)
(* 1-3 *)
(* à tester soi-même *)
(* 4 *)
(* retourne la liste l dans laquelle les doublons ont été supprimés en commençant par la gauche *)
(* 5 *)
let mystere_rt l =
  let rec aux l ll =
    match l with
      [] -> ll
    | e :: tl -> aux tl (if List.mem e ll then ll else e :: ll)
  in aux (List.rev l) []

(* Exercice 2: 11pts *)
(* 6 *)
let rec remove_fst x l =
  match l with
    [] -> []
  | e :: tl -> if e = x then remove_fst x tl else l

(* 7 *)
let rec remove_fst x l =
  match l with
    [] -> []
  | e :: tl -> if e = x then remove_fst x tl else l

(* 8 *)
let suivant l =
  let rec aux l u =
    match l with
      [] -> u
    | x :: tl -> aux (remove_fst x l) (x :: count_fst x l :: u)
  in List.rev (aux l [])

(* 9 *)
let suite n =
  let rec aux n u =
    if n = 0 then u
    else aux (pred n) (suivant u)
  in aux n [1]

(* 10 *)
let suite_gen n first next =
  let rec aux n u =
    if n = 0 then u
    else aux (pred n) (next u)
  in aux n first

(* 11 *)
let notre_suite n = suite_gen n [1] suivant

(* Exercice 3: 5pts *)
(* 12 *)
let make_tree root subtrees = T(root, subtrees)

(* 13 *)
let tree_subtrees tree = let T(_, subtrees) = tree in subtrees

let tree_root tree = let T(root, _) = tree in root

(* 14 *)
let rec depth_first tree : int list =
  tree_root tree :: List.flatten
                      (List.map depth_first (tree_subtrees tree))