(*
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

let rec bigger ~cmp pivot tree =
  match tree with
  | Empty -> Empty
  | Node (a, x, x_val, b) ->
    if cmp x pivot <= 0
      then bigger ~cmp pivot b
      else match a with
        | Empty -> Node (Empty, x, x_val, b)
        | Node (a1, y, y_val, a2) ->
          if cmp y pivot <= 0
            then Node (bigger ~cmp pivot a2, x, x_val, b)
            else Node (bigger ~cmp pivot a1, y, y_val, Node (a2, x, x_val, b))

let rec smaller ~cmp pivot tree =

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