module type OrderedType = Set.OrderedType

module type S  =
  sig
    type elt
    type t
    val empty : t
    val is_empty : t -> bool
    val mem : elt -> t -> bool
    val add : elt -> t -> t
    val singleton : elt -> t
    val remove : elt -> t -> t
    val union : t -> t -> t
    val inter : t -> t -> t
    val disjoint : t -> t -> bool
    val diff : t -> t -> t
    val compare : t -> t -> int
    val equal : t -> t -> bool
    val subset : t -> t -> bool
    val iter : (elt -> unit) -> t -> unit
    val map : (elt -> elt) -> t -> t
    val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a
    val for_all : (elt -> bool) -> t -> bool
    val exists : (elt -> bool) -> t -> bool
    val filter : (elt -> bool) -> t -> t
    val filter_map : (elt -> elt option) -> t -> t
    val partition : (elt -> bool) -> t -> (t * t)
    val cardinal : t -> int
    val elements : t -> elt list
    val min_elt : t -> elt
    val min_elt_opt : t -> elt option
    val max_elt : t -> elt
    val max_elt_opt : t -> elt option
    val choose : t -> elt
    val choose_opt : t -> elt option
    val split : elt -> t -> (t * bool * t)
    val find : elt -> t -> elt
    val find_opt : elt -> t -> elt option
    val find_first : (elt -> bool) -> t -> elt
    val find_first_opt : (elt -> bool) -> t -> elt option
    val find_last : (elt -> bool) -> t -> elt
    val find_last_opt : (elt -> bool) -> t -> elt option
    val of_list : elt list -> t
    val to_seq_from : elt -> t -> elt Stdcompat__seq.t
    val to_seq : t -> elt Stdcompat__seq.t
    val to_rev_seq : t -> elt Stdcompat__seq.t
    val add_seq : elt Stdcompat__seq.t -> t -> t
    val of_seq : elt Stdcompat__seq.t -> t
  end


module Make = Set.Make

(*
module Make (Ord : OrderedType) = struct
  include Set.Make (Ord)

  
    type internal = Empty | Node of internal * elt * internal * int

    external t_of_internal : internal -> t = "%identity"

    external internal_of_t : t -> internal = "%identity"

    let height = function
      | Empty -> 0
      | Node (_, _, _, h) -> h

    let create l v r =
      let hl = height l in
      let hr = height r in
      Node (l, v, r, (if hl >= hr then hl + 1 else hr + 1))

    let bal l v r =
      let hl = match l with Empty -> 0 | Node (_, _, _, h) -> h in
      let hr = match r with Empty -> 0 | Node (_, _, _, h) -> h in
      if hl > hr + 2 then begin
        match l with
          Empty -> invalid_arg "Set.bal"
        | Node (ll, lv, lr, _) ->
            if height ll >= height lr then
              create ll lv (create lr v r)
            else begin
              match lr with
                Empty -> invalid_arg "Set.bal"
              | Node (lrl, lrv, lrr, _) ->
                  create (create ll lv lrl) lrv (create lrr v r)
            end
      end else if hr > hl + 2 then begin
        match r with
          Empty -> invalid_arg "Set.bal"
        | Node (rl, rv, rr, _) ->
            if height rr >= height rl then
              create (create l v rl) rv rr
            else begin
              match rl with
                Empty -> invalid_arg "Set.bal"
              | Node (rll, rlv, rlr, _) ->
                  create (create l v rll) rlv (create rlr rv rr)
            end
      end else
        Node (l, v, r, (if hl >= hr then hl + 1 else hr + 1))


    let rec add_min_element x = function
      | Empty -> internal_of_t (singleton x)
      | Node (l, v, r, _) ->
        bal (add_min_element x l) v r

    let rec add_max_element x = function
      | Empty -> internal_of_t (singleton x)
      | Node (l, v, r, _) ->
        bal l v (add_max_element x r)

    let rec join l v r =
      match (l, r) with
        (Empty, _) -> add_min_element v r
      | (_, Empty) -> add_max_element v l
      | (Node (ll, lv, lr, lh), Node (rl, rv, rr, rh)) ->
          if lh > rh + 2 then bal ll lv (join lr v r) else
          if rh > lh + 2 then bal (join l v rl) rv rr else
          create l v r

    let try_join l v r =
      if (l = Empty || Ord.compare (max_elt (t_of_internal l)) v < 0)
          && (r = Empty || Ord.compare v (min_elt (t_of_internal r)) < 0)
      then join l v r
      else internal_of_t (union (t_of_internal l) (add v (t_of_internal r)))

    let rec remove_min_elt = function
      | Empty -> invalid_arg "Set.remove_min_elt"
      | Node (Empty, _, r, _) -> r
      | Node (l, v, r, _) -> bal (remove_min_elt l) v r

    let try_concat t1 t2 =
      match (t1, t2) with
      | (Empty, t) -> t
      | (t, Empty) -> t
      | (_, _) ->
          try_join t1 (min_elt (t_of_internal t2))
            (remove_min_elt t2)
  

  (*
    
      type enumeration = End | More of elt * internal * enumeration

      let rec snoc_enum s e =
        match s with
          Empty -> e
        | Node (l, v, r, _h) -> snoc_enum r (More(v, l, e))

      let rec rev_seq_of_enum_ c () = match c with
        | End -> Stdcompat__seq.Nil
        | More (x, t, rest) ->
            Stdcompat__seq.Cons (x, rev_seq_of_enum_ (snoc_enum t rest))

      let to_rev_seq (s : t) =
        let s : internal = Obj.magic s in
        rev_seq_of_enum_ (snoc_enum s End)
    
    (*
      let to_rev_seq s =
        Stdcompat__list.to_seq (List.rev (elements s))
    *)
  *)

  (*
    let of_list l = List.fold_left (fun s item -> add item s) empty l
  *)

  (*
    
      let rec iter f = function
        | Empty -> ()
        | Node (l, v, r, _) as t ->
            iter f l;
            f v;
            iter f r

      let iter (f : elt -> unit) (s : t) : unit =
        iter f (internal_of_t s)

      let rec fold f s a =
        match s with
        | Empty -> a
        | Node (l, v, r, _) as t ->
            let a = fold f l a in
            let a = f v a in
            fold f r a

      let fold (f : elt -> 'a -> 'a) (s : t) (a : 'a) : 'a =
        fold f (internal_of_t s) a
    
    (*
      let iter f s =
        List.iter f (elements s)

      let fold f s a =
        List.fold_left (fun a item -> f item a) a (elements s)
    *)
  *)

  (*
    
      let rec filter_map f = function
        | Empty -> Empty
        | Node (l, v, r, _) as t ->
           (* enforce left-to-right evaluation order *)
           let l' = filter_map f l in
           let v' = f v in
           let r' = filter_map f r in
           begin match v' with
             | Some v' ->
                if l == l' && v == v' && r == r' then t
                else try_join l' v' r'
             | None ->
                try_concat l' r'
           end

      let filter_map (f : elt -> elt option) (s : t) : t =
        t_of_internal (filter_map f (internal_of_t s))
    
    (*
      type map_changed =
        | Changed of t
        | Unchanged of elt list

      let filter_map f s =
        match
          fold (fun item accu ->
            match accu, f item with
            | Changed set, None -> Changed set
            | Changed set, Some item' -> Changed (add item' set)
            | Unchanged list, None -> Changed (of_list list)
            | Unchanged list, Some item' ->
               if item == item' then Unchanged (item :: list)
               else Changed (add item' (of_list list)))
          s (Unchanged [])
        with
        | Changed s -> s
        | Unchanged _ -> s
    *)
  *)

(*

    type split_bis =
      | Found
      | NotFound of internal * (unit -> internal)

    let rec split_bis x = function
      | Empty ->
          NotFound (Empty, (fun () -> Empty))
      | Node (l, v, r, _) ->
          let c = Ord.compare x v in
          if c = 0 then Found
          else if c < 0 then
            match split_bis x l with
            | Found -> Found
            | NotFound (ll, rl) -> NotFound (ll, (fun () -> join (rl ()) v r))
          else
            match split_bis x r with
            | Found -> Found
            | NotFound (lr, rr) -> NotFound (join l v lr, rr)

    let rec disjoint s1 s2 =
      match (s1, s2) with
        (Empty, _) | (_, Empty) -> true
      | (Node (l1, v1, r1, _), t2) ->
          if s1 == s2 then false
          else match split_bis v1 t2 with
              NotFound(l2, r2) -> disjoint l1 l2 && disjoint r1 (r2 ())
            | Found -> false

    let disjoint (s1 : t) (s2 : t) : bool =
      disjoint (internal_of_t s1) (internal_of_t s2)

(*
  let disjoint s s' =
    is_empty (inter s s')
*)
*)

(*
  let add_seq i m =
    Stdcompat__seq.fold_left (fun s x -> add x s) m i

  let of_seq i = add_seq i empty


  let rec cons_enum s e =
    match s with
      Empty -> e
    | Node (l, v, r, _h) -> cons_enum l (More(v, r, e))

  let rec seq_of_enum_ c () = match c with
    | End -> Stdcompat__seq.Nil
    | More (x, t, rest) ->
        Stdcompat__seq.Cons (x, seq_of_enum_ (cons_enum t rest))

  let to_seq (s : t) =
    let s : internal = Obj.magic s in
    seq_of_enum_ (cons_enum s End)

  let to_seq_from low s =
    let s : internal = Obj.magic s in
    let rec aux low s c = match s with
      | Empty -> c
      | Node (l, v, r, _h) ->
          begin match Ord.compare v low with
            | 0 -> More (v, r, c)
            | n when n<0 -> aux low r c
            | _ -> aux low l (More (v, r, c))
          end
    in
    seq_of_enum_ (aux low s End)

(*
  let to_seq s =
    Stdcompat__list.to_seq (elements s)

  let elements_from low s =
    let rec cut l =
      match l with
      | [] -> []
      | hd :: tl ->
        if Ord.compare low hd < 0 then
          cut tl
        else
          l in
     cut (elements s)

  let to_seq_from low s =
    Stdcompat__list.to_seq (elements_from low s)
*)
*)

(*
  exception Find of elt


  let rec find_internal x = function
      Empty -> raise Not_found
    | Node (l, v, r, _h) ->
        let c = Ord.compare x v in
        if c = 0 then v
        else find_internal x (if c < 0 then l else r)

  let find x (s : t) =
    let s : internal = Obj.magic s in
    find_internal x s

(*
  let find x s =
    try
      iter (fun y ->
        if Ord.compare x y = 0 then
          raise (Find y)) s;
      raise Not_found
    with Find y -> y
*)
*)

(*
  let min_elt_opt s =
    Stdcompat__tools.option_find min_elt s

  let max_elt_opt s =
    Stdcompat__tools.option_find max_elt s

  let choose_opt s =
    Stdcompat__tools.option_find choose s


  let rec find_first_aux v0 f = function
      Empty ->
        v0
    | Node (l, v, r, _h) ->
        if f v then
          find_first_aux v f l
        else
          find_first_aux v0 f r

  let rec find_first_internal f = function
      Empty ->
        raise Not_found
    | Node (l, v, r, _h) ->
        if f v then
          find_first_aux v f l
        else
          find_first_internal f r

  let find_first f (s : t) =
    let s : internal = Obj.magic s in
    find_first_internal f s

  let rec find_first_opt_aux v0 f = function
      Empty ->
        Some v0
    | Node (l, v, r, _h) ->
        if f v then
          find_first_opt_aux v f l
        else
          find_first_opt_aux v0 f r

  let rec find_first_opt_internal f = function
      Empty ->
        None
    | Node (l, v, r, _h) ->
        if f v then
          find_first_opt_aux v f l
        else
          find_first_opt_internal f r

  let find_first_opt f (s : t) =
    let s : internal = Obj.magic s in
    find_first_opt_internal f s

  let rec find_last_aux v0 f = function
      Empty ->
        v0
    | Node (l, v, r, _h) ->
        if f v then
          find_last_aux v f r
        else
          find_last_aux v0 f l

  let rec find_last_internal f = function
      Empty ->
        raise Not_found
    | Node (l, v, r, _h) ->
        if f v then
          find_last_aux v f r
        else
          find_last_internal f l

  let find_last f (s : t) =
    let s : internal = Obj.magic s in
    find_last_internal f s

  let rec find_last_opt_aux v0 f = function
      Empty ->
        Some v0
    | Node (l, v, r, _h) ->
        if f v then
          find_last_opt_aux v f r
        else
          find_last_opt_aux v0 f l

  let rec find_last_opt_internal f = function
      Empty ->
        None
    | Node (l, v, r, _h) ->
        if f v then
          find_last_opt_aux v f r
        else
          find_last_opt_internal f l

  let find_last_opt f (s : t) =
    let s : internal = Obj.magic s in
    find_last_opt_internal f s

  let rec find_opt_internal x = function
      Empty -> None
    | Node (l, v, r, _h) ->
        let c = Ord.compare x v in
        if c = 0 then Some v
        else find_opt_internal x (if c < 0 then l else r)

  let find_opt f (s : t) =
    let s : internal = Obj.magic s in
    find_opt_internal f s

(*
  let find_opt x s =
    Stdcompat__tools.option_find (find x) s

  exception Find of elt

  let find_first_opt p s =
    try
      iter (fun x ->
        if p x then
          raise (Find x)) s;
      None
    with Find x -> Some x

  let find_first p s =
    try
      iter (fun x ->
        if p x then
          raise (Find x)) s;
      raise Not_found
    with Find x -> x

  exception Local_not_found

  let find_last_opt p s =
    let last = ref None in
    try
      iter (fun x ->
        if p x then
          last := Some x
        else
          match !last with
          | None -> raise Local_not_found
          | Some x -> raise (Find x)) s;
      !last
    with
    | Local_not_found -> None
    | Find x -> !last

  let find_last p s =
    match find_last_opt p s with
    | None -> raise Not_found
    | Some x -> x
*)
*)

(*

  let rec map f = function
    | Empty -> Empty
    | Node (l, v, r, _) as t ->
       (* enforce left-to-right evaluation order *)
       let l' = map f l in
       let v' = f v in
       let r' = map f r in
       if l == l' && v == v' && r == r' then t
       else try_join l' v' r'

  let map f s =
    (Obj.magic (map f (Obj.magic s : internal)) : t)

(*
  let map f s =
    match
      fold (fun item accu ->
        let item' = f item in
        match accu with
        | Changed set -> Changed (add item' set)
        | Unchanged list ->
           if item == item' then Unchanged (item :: list)
           else Changed (add item' (of_list list)))
      s (Unchanged [])
    with
    | Changed s -> s
    | Unchanged _ -> s
*)
*)

(*
   let split x s =
     let add item (passed, (l, present, r)) =
       if passed then
         (passed, (l, present, add item r))
       else
         let o = Ord.compare item x in
         if o < 0 then (passed, (add item l, present, add item r))
         else if o > 0 then (true, (l, false, add item r))
         else (true, (l, true, r)) in
     snd (fold add s (false, (empty, false, empty)))
*)
end
*)
