(* Exercice 1 *)
(* Insertion sort *)
let rec insert l x = match l with
  | [] -> [x]
  | y::t -> if x <= y then x::l else y::(insert t x)
;;

let insertion_sort l =
  List.fold_left
    (fun acc x -> insert acc x)
    []
    l
;;

(* Selection sort *)
let rec min_l l = match l with
  | [] -> invalid_arg "Empty list"
  | [x] -> x, []
  | x::q ->
    let y, qy = min_l q in
    if x < y then x, q else y, (x::qy)
;;

let rec selection_sort l = match l with
  | [] | _::[] -> l
  | _ ->
    let m, q = min_l l in
    m::(selection_sort q)
;;

(* Exercice 3 *)
let rec split l n =
  if n = 0 then [], l
  else match l with
    | [] -> failwith "Splitting empty list"
    | a::q ->
      let qa, lb = split q (n-1) in
      a::qa, lb
;;

let rec fuse la lb = match la, lb with
  | [], _ -> lb
  | _, [] -> la
  | a::qa, b::qb ->
    if a > b then
      b::(fuse la qb)
    else
      a::(fuse qa lb)
;;

let rec fusion_sort l =
  let n = List.length l in
  if n <= 1 then l else
  let la, lb = split l (n/2) in
  let sa = fusion_sort la in
  let sb = fusion_sort lb in
  fuse sa sb
;;