(* Exercice 0 *)
let zip ta tb = Array.map2 (fun a b -> a,b) ta tb;;

(* Exercice 1 *)
let tirette t =
  let n = Array.length t in
  Array.init (n/2) (fun i -> t.(i) + t.(n-i-1))
;;

(* Exercice 2 *)
let quarante_deux t =
  let n = Array.length t in
  let count = ref 0 in
  let i = ref 0 in
  while !i < n && !count <= 42 do
    if t.(!i) mod 42 = 0 then
      count := !count + 1;
    i := !i + 42
  done;
  !count = 42
;;

(* Exercice 3 *)
let croissant t =
  let n = Array.length t in
  let i = ref 0 in
  while !i+1 < n && t.(!i) <= t.(!i+1) do
    i := !i+1
  done;
  !i >= (n-1)
;;

(* Exercice 4 *)
let bitonique t =
  let n = Array.length t in
  let grows = ref true in
  let i = ref 0 in
  let res = ref true in
  while !res && !i+1 < n do
    if !grows then
      (if t.(!i) > t.(!i+1) then
        grows := false)
    else
      if t.(!i) < t.(!i+1) then
        res := false;
    i := !i + 1
  done;
  !res
;;

(* Exercice 5 *)
let psrn ta tb = Array.fold_left
  (fun acc (a,b) -> acc +. (a *. b))
  0.
  (Array.map2
    (fun a b -> a,b)
    ta
    tb
  )
;;



(* Exercice 6 *)
let rotation m =
  let nx = Array.length m in
  if nx = 0 then [||] else
  let ny = Array.length m.(0) in
  Array.init_matrix
    ny
    nx
    (fun x y -> m.(y).(ny-x-1))
;;

(* Exercice 7 *)
let plsci t =
  let n = Array.length t in
  let current_start = ref 0 in
  let start = ref 0 in
  let max_length = ref (min 1 n) in
  for i = 0 to n-1 do
    if i+1 = n || t.(i) != t.(i+1) then (
      let length = i - !current_start + 1 in
      if !max_length < length then (
        max_length := length;
        start := !current_start
      );
      current_start := i+1
    )
  done;
  !start, !max_length
;;

(* Exercice 8 *)
let sorteren t =
  let zero, one, two = Array.fold_left
    (fun (zero, one, two) a -> match a with
      | 0 -> zero+1,one,two
      | 1 -> zero,one+1,two
      | 2 -> zero,one,two+1
      | _ -> invalid_arg ""
    )
    (0,0,0)
    t
  in
  for i = 0 to zero+one+two-1 do
    t.(i) <- if i < zero then 0
      else if i < zero+one then 1
      else 2
  done
;;

(* Exercice 9 *)
let dominant s =
  let counts = Array.make 126 0 in
  String.iter (fun c ->
    let c = Char.code c in
    counts.(c) <- counts.(c) + 1;
  ) s;
  let _, max_c =
    Array.fold_left
      (fun (c, max_c) a ->
        c+1,
        if a > counts.(max_c) then c else max_c
      )
      (0,0)
      counts
  in
  Char.chr max_c
;;