(**************************************************************************)
(*                                                                        *)
    : a generic graph library for OCaml                         
   Copyright ( C ) 2004 - 2010                                               
     ,     and   
(*                                                                        *)
(*  This software is free software; you can redistribute it and/or        *)
   modify it under the terms of the GNU Library General Public           
   License version 2.1 , with the special exception on linking            
(*  described in file LICENSE.                                            *)
(*                                                                        *)
(*  This software is distributed in the hope that it will be useful,      *)
(*  but WITHOUT ANY WARRANTY; without even the implied warranty of        *)
(*  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                  *)
(*                                                                        *)
(**************************************************************************)

  $ I d : kruskal.mli , v 1.5 2005 - 06 - 30 10:48:55 filliatr Exp $

*  's minimum - spanning - tree algorithm .

* Minimal graph signature for  . 
     Sub - signature of { ! Sig . G } .
    Sub-signature of {!Sig.G}. *)
module type G = sig
  type t
  module V : Sig.COMPARABLE
  module E : sig
    type t
    type label
    val label : t -> label
    val dst : t -> V.t
    val src : t -> V.t
  end
  val fold_vertex : (V.t -> 'a -> 'a) -> t -> 'a -> 'a
  val iter_edges_e : (E.t -> unit) -> t ->  unit
end

* Functor providing an implementation of  's minimum - spanning - tree 
     algorithm . 
     Parameter [ W ] ensures that label on edges are comparable .
    algorithm.
    Parameter [W] ensures that label on edges are comparable. *)
module Make(G: G)(W: Sig.ORDERED_TYPE with type t = G.E.label) : sig
  val spanningtree : G.t -> G.E.t list
end

* { 2 Generic version where union - find implementation is provided }

(** Signature of union-find. *)
module type UNIONFIND = sig
  type elt
  type t
  val init : elt list -> t
  val find : elt -> t -> elt
  val union : elt -> elt -> t -> unit
end

* Functor providing an implementation of  's minimum - spanning - tree 
     algorithm using a user - defined union - find algorithm . 
     Parameter [ W ] ensures that label on edges are comparable .
    algorithm using a user-defined union-find algorithm.
    Parameter [W] ensures that label on edges are comparable. *)
module Generic
    (G: G)
    (W: Sig.ORDERED_TYPE with type t = G.E.label)
    (UF: UNIONFIND with type elt = G.V.t) :
sig
  val spanningtree : G.t -> G.E.t list
end

************************************************************************
                                                                        
                                                                        
  This software is free software; you can redistribute it and/or        
  described in file LICENSE.                                            
                                                                        
  This software is distributed in the hope that it will be useful,      
  but WITHOUT ANY WARRANTY; without even the implied warranty of        
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                  
                                                                        
************************************************************************
* Signature of union-find. 
    : a generic graph library for OCaml                         
   Copyright ( C ) 2004 - 2010                                               
     ,     and   
   modify it under the terms of the GNU Library General Public           
   License version 2.1 , with the special exception on linking            

  $ I d : kruskal.mli , v 1.5 2005 - 06 - 30 10:48:55 filliatr Exp $

*  's minimum - spanning - tree algorithm .

* Minimal graph signature for  . 
     Sub - signature of { ! Sig . G } .
    Sub-signature of {!Sig.G}. *)
module type G = sig
  type t
  module V : Sig.COMPARABLE
  module E : sig
    type t
    type label
    val label : t -> label
    val dst : t -> V.t
    val src : t -> V.t
  end
  val fold_vertex : (V.t -> 'a -> 'a) -> t -> 'a -> 'a
  val iter_edges_e : (E.t -> unit) -> t ->  unit
end

* Functor providing an implementation of  's minimum - spanning - tree 
     algorithm . 
     Parameter [ W ] ensures that label on edges are comparable .
    algorithm.
    Parameter [W] ensures that label on edges are comparable. *)
module Make(G: G)(W: Sig.ORDERED_TYPE with type t = G.E.label) : sig
  val spanningtree : G.t -> G.E.t list
end

* { 2 Generic version where union - find implementation is provided }

module type UNIONFIND = sig
  type elt
  type t
  val init : elt list -> t
  val find : elt -> t -> elt
  val union : elt -> elt -> t -> unit
end

* Functor providing an implementation of  's minimum - spanning - tree 
     algorithm using a user - defined union - find algorithm . 
     Parameter [ W ] ensures that label on edges are comparable .
    algorithm using a user-defined union-find algorithm.
    Parameter [W] ensures that label on edges are comparable. *)
module Generic
    (G: G)
    (W: Sig.ORDERED_TYPE with type t = G.E.label)
    (UF: UNIONFIND with type elt = G.V.t) :
sig
  val spanningtree : G.t -> G.E.t list
end
