(*
 * Graph: generic graph library
 * Copyright (C) 2004
 * Sylvain Conchon, Jean-Christophe Filliatre and Julien Signoles
 * 
 * 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, as published by the Free Software Foundation.
 * 
 * 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.
 * 
 * See the GNU Library General Public License version 2 for more details
 * (enclosed in the file LGPL).
 *)

(* $Id: kruskal.ml,v 1.5 2005/06/30 10:48:55 filliatr Exp $ *)

open Util

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

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

module Generic
  (G: G)
  (W : Sig.ORDERED_TYPE with type t=G.E.label)
  (UF: UNIONFIND with type elt=G.V.t) =
struct
    
  let spanningtree g =   
    let vertices = G.fold_vertex (fun v a -> v :: a) g [] in
    let uf = UF.init vertices in
    let edges = 
      let l = ref [] in
      G.iter_edges_e (fun e -> l:=e::!l) g;
      List.sort (fun e e'-> W.compare (G.E.label e) (G.E.label e')) !l
    in
    let s = ref [] in
    let cover e =
      let u,v = G.E.src e , G.E.dst e in
      if G.V.compare (UF.find u uf) (UF.find v uf) <> 0 then
	(UF.union u v uf; s:=e::!s)
    in
    List.iter cover edges;!s

end

module Make
  (G: G)
  (W : Sig.ORDERED_TYPE with type t=G.E.label)
  = 
  Generic(G)(W)(Unionfind.Make(G.V))