#use "list_tools.ml" ;;
(* exercice 1 *)

let rec is_prefix l ll = match (l,ll) with
    (_,[]) -> false
  |(l,e::l2) when prefix(l,e) = true -> true
  |(_,e::l2) -> is_prefix l l2 ;;

let rec decodable list = match list with
    [] -> true
  | (e::l)  when is_prefix e l = true -> false
  | (_::l) -> decodable l  ;;

(*exercice 2 *)

let rec refill (nb,obj) list = match list with
    [] -> (nb,obj)::list
  | (x,y)::l when obj = y -> (x+nb,y)::l
  | (x,y):: l -> (x,y)::refill (nb,obj) l

let destock (nb,obj) stock =
  if nb <= 0
  then
    invalid_arg " nb must be positif "
  else
    let rec stk (nb,obj) stock = match stock with
        [] -> stock
      |(x,y):: l when obj = y && nb <= x -> (x-nb,y)::l
      |(x,y):: l when obj = y && nb > x  -> l
      |(x,y):: l -> (x,y):: stk (nb,obj) l
    in
    let rec stk2 (nb,obj) stock =
      match stock with
          [] -> nb
        |(x,y):: l when obj = y && nb <= x -> 0
        |(x,y):: l when obj = y && nb > x  -> nb-x
        |(x,y):: l -> stk2 (nb,obj) l
    in stk(nb,obj) stock, stk2 (nb,obj) stock;;

(* exercice 3 *)
let river n rank =
  if n <= 0
  then
    invalid_arg " n must be positif"
  else
    if rank <= 0
    then
      invalid_arg " k must be positif"
    else
      let rec riv n rank = match rank with
          0 -> []
        | _ -> n::riv(n +sum_digits n) (rank - 1)
      in riv n rank ;;

let meeting n rank =
  let a = common (river 1 rank,river n rank)
  and b = common (river 3 rank,river n rank)
  and c = common (river 9 rank,river n rank) in
    if a <> 0
    then
      (1,a)
    else
     if  b <> 0
    then
      (3,b)
    else
       if c <> 0
       then
         (9,c)
       else

         (0,0) ;;