let plusetfois a b = (a+b, a*b);;

let rec pp2_h n = match n with
  | 0 -> 1
  | _ -> 2 * (pp2_h (n/2))

let pp2 n = if n == 0 then 0 else pp2_h (n-1)

let leeloo l = match l with
  | _::_::_::_::a::_ -> a
  | _ -> failwith "Not enough elements"

let rec coupe l = match l with
  | a::b::q ->
    let qa, qb = coupe q in
    a::qa, b::qb
  | _ -> l, []

let rec colle la lb = match la with
  | [] -> lb
  | a::q -> a::(colle lb q)

let rec compte l x = match l with
  | [] -> 0
  | a::q -> if a == x then 1+(compte q x) else compte q x

let rec sommesi l f = match l with
  | [] -> 0
  | a::q -> if f a then a+(sommesi q f) else (sommesi q f)

let rec majopred_h l f acc acc_n = match l with
  | [] -> 2*acc >= acc_n
  | a::q -> majopred_h q f (if f a then acc+1 else acc) (acc_n+1)
let majopred l f = majopred_h l f 0 0

let rec lexico la lb = match la, lb with
  | [], _ -> true
  | _, [] -> false
  | a::_, b::_ when a < b -> true
  | a::_, b::_ when a > b -> false
  | _::qa, _::qb -> lexico qa qb

let rec aplatir l = match l with
  | [] -> []
  | []::ql -> aplatir ql
  | (a::q)::ql -> a::(aplatir (q::ql))