(*
Copyright (c) 2013, Simon Cruanes
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(** {1 Splay trees} *)

(** See http://en.wikipedia.org/wiki/Splay_tree and
    Okasaki's "purely functional data structures" p46 *)

type ('a, 'b) t = (('a, 'b) tree * ('a -> 'a -> int))
  (** A splay tree with the given comparison function *)
and ('a, 'b) tree =
  | Empty
  | Node of (('a,'b) tree * 'a * 'b * ('a,'b) tree)
  (** A splay tree containing values of type 'a *)

let empty ~cmp =
  (Empty, cmp)

let is_empty (tree, _) =
  match tree with
  | Empty -> true
  | Node _ -> false

(** Partition the tree into (elements <= pivot, elements > pivot) *)
let rec partition ~cmp pivot tree =
  match tree with
  | Empty -> Empty, Empty
  | Node (a, x, x_val, b) ->
    if cmp x pivot <= 0
      then begin
        match b with
        | Empty -> (tree, Empty)
        | Node (b1, y, y_val, b2) ->
          if cmp y pivot <= 0
            then
              let small, big = partition ~cmp pivot b2 in
              Node (Node (a, x, x_val, b1), y, y_val, small), big
            else
              let small, big = partition ~cmp pivot b1 in
              Node (a, x, x_val, small), Node (big, y, y_val, b2)
      end else begin
        match a with
        | Empty -> (Empty, tree)
        | Node (a1, y, y_val, a2) ->
          if cmp y pivot <= 0
            then
              let small, big = partition ~cmp pivot a2 in
              Node (a1, y, y_val, small), Node (big, x, x_val, b)
            else
              let small, big = partition ~cmp pivot a1 in
              small, Node (big, y, y_val, Node (a2, x, x_val, b))
      end

(** Insert the pair (key -> value) in the tree *)
let insert (tree, cmp) k v =
  let small, big = partition ~cmp k tree in
  let tree' = Node (small, k, v, big) in
  tree', cmp

let remove (tree, cmp) k = failwith "not implemented"

let replace (tree, cmp) k = failwith "not implemented"

(** Returns the top value, or raise Not_found is empty *)
let top (tree, _) =
  match tree with
  | Empty -> raise Not_found
  | Node (_, k, v, _) -> k, v

(** Access minimum value *)
let min (tree, _) =
  let rec min tree =
    match tree with
    | Empty -> raise Not_found
    | Node (Empty, k, v, _) -> k, v
    | Node (l, _, _, _) -> min l
  in min tree

(** Get minimum value and remove it from the tree *)
let delete_min (tree, cmp) =
  let rec delete_min tree = match tree with
  | Empty -> raise Not_found
  | Node (Empty, x, x_val, b) -> x, x_val, b
  | Node (Node (Empty, x, x_val, b), y, y_val, c) ->
    x, x_val, Node (b, y, y_val, c)  (* rebalance *)
  | Node (Node (a, x, x_val, b), y, y_val, c) ->
    let m, m_val, a' = delete_min a in
    m, m_val, Node (a', x, x_val, Node (b, y, y_val, c))
  in
  let m, m_val, tree' = delete_min tree in
  m, m_val, (tree', cmp)

(** Find the value for the given key (or raise Not_found).
    It also returns the splayed tree *)
let find (tree, cmp) k =
  failwith "not implemented" 

let find_fold (tree, cmp) k f acc =
  acc (* TODO *)

(** Iterate on elements *)
let iter (tree, _) f =
  let rec iter tree =
    match tree with
    | Empty -> ()
    | Node (a, x, x_val, b) ->
      iter a;
      f x x_val;
      iter b
  in iter tree

(** Number of elements (linear) *)
let size t =
  let r = ref 0 in
  iter t (fun _ _ -> incr r);
  !r

let get_cmp (_, cmp) = cmp