83 lines
1.8 KiB
OCaml
83 lines
1.8 KiB
OCaml
(* Exercice 1 *)
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let rec somme_liste l = match l with
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| [] -> 0
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| a::q -> a + somme_liste q;;
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assert (somme_liste [1; 3; 2] = 6);;
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let rec taille_liste l = match l with
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| [] -> 0
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| _::q -> 1 + taille_liste q;;
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assert (taille_liste [1; 3; 2] = 3);;
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let rec pow valeur exposant = match exposant with
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| 0 -> 1
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| i -> valeur * (pow valeur (i - 1));;
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assert (pow 4 3 = 64);;
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(* On peut remplacer i - 1 par exposant - 1 car les deux noms coexistent. *)
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let rec part_ent_log2 nombre =
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if nombre = 0 then failwith "Boum !";
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(* Il est toujours utile de connaître les exceptions tôt. *)
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if nombre = 1 then 0
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else 1 + (part_ent_log2 (nombre / 2));;
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assert (part_ent_log2 10 = 3);;
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let rec est_dans_liste element l = match l with
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| [] -> false
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| a::q -> a = element || est_dans_liste element q;;
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assert (est_dans_liste 2 [1; 3; 2]);;
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assert (not (est_dans_liste 4 [1; 3; 2]));;
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(* Exercice 2 *)
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let biggest l = match l with
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| [] -> failwith "Empty list"
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| x::q -> List.fold_left
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(fun acc a -> max acc a)
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x
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q
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;;
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assert (biggest [0; 7; 4] == 7);;
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(* Exercice 3 *)
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let prod l = List.fold_left (fun acc x -> acc *. x) 1. l;;
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assert (abs_float (prod [1.5; 2.; 3.] -. 9.) <= 1e-14 );;
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(* Exercice 4 *)
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let rec is_ordered l = match l with
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| a::(b::q) -> a <= b && is_ordered (b::q)
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| _ -> true
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;;
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assert (is_ordered [1; 5; 6]);;
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assert (not (is_ordered [5.6; 7.8; 3.]));;
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(* Exercice 5 *)
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let rec is_rev_ordered l = match l with
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| a::b::q -> a >= b && is_rev_ordered (b::q)
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| _ -> true
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;;
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let rec has_ordering l = match l with
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| a::b::q -> if a < b then
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is_ordered (b::q)
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else if a > b then
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is_rev_ordered (b::q)
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else has_ordering (b::q)
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| _ -> true;;
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assert (has_ordering [1; 1; 2; 2; 3]);;
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assert (has_ordering [3; 2; 1; 1]);;
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assert (not (has_ordering [1; 1; 2; 1]));;
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