(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(** An imperative implementation of partitions via Union-Find *)

(** Paths are compressed imperatively at each lookup of a
    canonical representative. Each union also modifies in-place
    the partition structure.

    Nota: for the moment we use Pervasive's comparison for
    choosing the smallest object as representative. This could
    be made more generic.
*)

module type PartitionSig = sig

  (** The type of elements in the partition *)
  type elt

  (** A set structure over elements *)
  type set

  (** The type of partitions *)
  type t

  (** Initialise an empty partition *)
  val create : unit -> t

  (** Add (in place) an element in the partition, or do nothing
      if the element is already in the partition. *)
  val add : elt -> t -> unit

  (** Find the canonical representative of an element.
      Raise [not_found] if the element isn't known yet. *)
  val find : elt -> t -> elt

  (** Merge (in place) the equivalence classes of two elements.
      This will add the elements in the partition if necessary. *)
  val union : elt -> elt -> t -> unit

  (** Merge (in place) the equivalence classes of many elements. *)
  val union_set : set -> t -> unit

  (** Listing the different components of the partition *)
  val partition : t -> set list

end

module Make :
  functor (S:Set.S) ->
    functor (M:Map.S with type key = S.elt) ->
      PartitionSig with type elt = S.elt and type set = S.t