(* Exercice 1 *)

let rec somme_liste l = match l with
| [] -> 0
| a::q -> a + somme_liste q;;

let rec taille_liste l = match l with
| [] -> 0
| _::q -> 1 + taille_liste q;;

let rec pow valeur exposant = match exposant with
| 0 -> 1
| i -> valeur * (pow valeur (i - 1));;

(* On peut remplacer i - 1 par exposant - 1 car les deux noms coexistent. *)
let rec part_ent_log2 nombre =
  if nombre = 0 then failwith "Boum !";
  (* Il est toujours utile de connaître les exceptions tôt. *)
  if nombre = 1 then 0
  else 1 + (part_ent_log2 (nombre / 2));;

let rec est_dans_liste element l = match l with
  | [] -> false
  | a::q -> a = element || est_dans_liste element q;;

(* Exercice 2 *)

let biggest l = match l with
  | [] -> failwith "Empty list"
  | x::q -> List.fold_left
    (fun acc a -> max acc a)
    x
    q
;;

(* Exercice 3 *)

let prod l = List.fold_left (fun acc x -> acc *. x) 1. l;;

(* Exercice 4 *)

let rec is_ordered l = match l with
  | a::(b::q) -> a <= b && is_ordered (b::q)
  | _ -> true
;;

(* Exercice 5 *)

let rec is_rev_ordered l = match l with
  | a::b::q -> a >= b && is_rev_ordered (b::q)
  | _ -> true
;;

let rec has_ordering l = match l with
  | a::b::q -> if a < b then
      is_ordered (b::q)
    else if a > b then
      is_rev_ordered (b::q)
    else has_ordering (b::q)
  | _ -> true;;