/* -*- C++ -*-

 * src/lemon/graph_wrapper.h - Part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Combinatorial Optimization Research Group, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_GRAPH_WRAPPER_H

#define LEMON_GRAPH_WRAPPER_H

///\ingroup gwrappers

///\file

///\brief Several graph wrappers.

///

///This file contains several useful graph wrapper functions.

///

///\author Marton Makai

#include <lemon/invalid.h>

#include <lemon/maps.h>

#include <lemon/iterable_graph_extender.h>

#include <iostream>

namespace lemon {

  // Graph wrappers

  /*!

    \addtogroup gwrappers

    @{

   */

  /*! 

    Base type for the Graph Wrappers

    \warning Graph wrappers are in even more experimental state than the other

    parts of the lib. Use them at you own risk.

    This is the base type for most of LEMON graph wrappers. 

    This class implements a trivial graph wrapper i.e. it only wraps the 

    functions and types of the graph. The purpose of this class is to 

    make easier implementing graph wrappers. E.g. if a wrapper is 

    considered which differs from the wrapped graph only in some of its 

    functions or types, then it can be derived from GraphWrapper, and only the 

    differences should be implemented.

    \author Marton Makai 

  */

  template<typename _Graph>

  class GraphWrapperBase {

  public:

    typedef _Graph Graph;

    /// \todo Is it needed?

    typedef Graph BaseGraph;

    typedef Graph ParentGraph;

  protected:

    Graph* graph;

    GraphWrapperBase() : graph(0) { }

    void setGraph(Graph& _graph) { graph=&_graph; }

  public:

    GraphWrapperBase(Graph& _graph) : graph(&_graph) { }

    typedef typename Graph::Node Node;

    typedef typename Graph::Edge Edge;

    void first(Node& i) const { graph->first(i); }

    void first(Edge& i) const { graph->first(i); }

    void firstIn(Edge& i, const Node& n) const { graph->firstIn(i, n); }

    void firstOut(Edge& i, const Node& n ) const { graph->firstOut(i, n); }

    void next(Node& i) const { graph->next(i); }

    void next(Edge& i) const { graph->next(i); }

    void nextIn(Edge& i) const { graph->nextIn(i); }

    void nextOut(Edge& i) const { graph->nextOut(i); }

    Node source(const Edge& e) const { return graph->source(e); }

    Node target(const Edge& e) const { return graph->target(e); }

    int nodeNum() const { return graph->nodeNum(); }

    int edgeNum() const { return graph->edgeNum(); }

    Node addNode() const { return Node(graph->addNode()); }

    Edge addEdge(const Node& source, const Node& target) const { 

      return Edge(graph->addEdge(source, target)); }

    void erase(const Node& i) const { graph->erase(i); }

    void erase(const Edge& i) const { graph->erase(i); }

    void clear() const { graph->clear(); }

    bool forward(const Edge& e) const { return graph->forward(e); }

    bool backward(const Edge& e) const { return graph->backward(e); }

    int id(const Node& v) const { return graph->id(v); }

    int id(const Edge& e) const { return graph->id(e); }

    Edge opposite(const Edge& e) const { return Edge(graph->opposite(e)); }

    template <typename _Value>

    class NodeMap : public _Graph::template NodeMap<_Value> {

    public:

      typedef typename _Graph::template NodeMap<_Value> Parent;

      NodeMap(const GraphWrapperBase<_Graph>& gw) : Parent(*gw.graph) { }

      NodeMap(const GraphWrapperBase<_Graph>& gw, const _Value& value)

      : Parent(*gw.graph, value) { }

    };

    template <typename _Value>

    class EdgeMap : public _Graph::template EdgeMap<_Value> {

    public:

      typedef typename _Graph::template EdgeMap<_Value> Parent;

      EdgeMap(const GraphWrapperBase<_Graph>& gw) : Parent(*gw.graph) { }

      EdgeMap(const GraphWrapperBase<_Graph>& gw, const _Value& value)

      : Parent(*gw.graph, value) { }

    };

  };

  template <typename _Graph>

  class GraphWrapper :

    public IterableGraphExtender<GraphWrapperBase<_Graph> > { 

  public:

    typedef _Graph Graph;

    typedef IterableGraphExtender<GraphWrapperBase<_Graph> > Parent;

  protected:

    GraphWrapper() : Parent() { }

  public:

    GraphWrapper(Graph& _graph) { setGraph(_graph); }

  };

  template <typename _Graph>

  class RevGraphWrapperBase : public GraphWrapperBase<_Graph> {

  public:

    typedef _Graph Graph;

    typedef GraphWrapperBase<_Graph> Parent;

  protected:

    RevGraphWrapperBase() : Parent() { }

  public:

    typedef typename Parent::Node Node;

    typedef typename Parent::Edge Edge;

    using Parent::first;

    void firstIn(Edge& i, const Node& n) const { Parent::firstOut(i, n); }

    void firstOut(Edge& i, const Node& n ) const { Parent::firstIn(i, n); }

    using Parent::next;

    void nextIn(Edge& i) const { Parent::nextOut(i); }

    void nextOut(Edge& i) const { Parent::nextIn(i); }

    Node source(const Edge& e) const { return Parent::target(e); }

    Node target(const Edge& e) const { return Parent::source(e); }

  };

  /// A graph wrapper which reverses the orientation of the edges.

  ///\warning Graph wrappers are in even more experimental state than the other

  ///parts of the lib. Use them at you own risk.

  ///

  /// Let \f$G=(V, A)\f$ be a directed graph and 

  /// suppose that a graph instange \c g of type 

  /// \c ListGraph implements \f$G\f$.

  /// \code

  /// ListGraph g;

  /// \endcode

  /// For each directed edge 

  /// \f$e\in A\f$, let \f$\bar e\f$ denote the edge obtained by 

  /// reversing its orientation. 

  /// Then RevGraphWrapper implements the graph structure with node-set 

  /// \f$V\f$ and edge-set 

  /// \f$\{\bar e : e\in A \}\f$, i.e. the graph obtained from \f$G\f$ be 

  /// reversing the orientation of its edges. The following code shows how 

  /// such an instance can be constructed.

  /// \code

  /// RevGraphWrapper<ListGraph> gw(g);

  /// \endcode

  ///\author Marton Makai

  template<typename _Graph>

  class RevGraphWrapper : 

    public IterableGraphExtender<RevGraphWrapperBase<_Graph> > {

  public:

    typedef _Graph Graph;

    typedef IterableGraphExtender<

      RevGraphWrapperBase<_Graph> > Parent;

  protected:

    RevGraphWrapper() { }

  public:

    RevGraphWrapper(_Graph& _graph) { setGraph(_graph); }

  };

  template <typename _Graph, typename NodeFilterMap, typename EdgeFilterMap>

  class SubGraphWrapperBase : public GraphWrapperBase<_Graph> {

  public:

    typedef _Graph Graph;

    typedef GraphWrapperBase<_Graph> Parent;

  protected:

    NodeFilterMap* node_filter_map;

    EdgeFilterMap* edge_filter_map;

    SubGraphWrapperBase() : Parent(), 

			    node_filter_map(0), edge_filter_map(0) { }

    void setNodeFilterMap(NodeFilterMap& _node_filter_map) {

      node_filter_map=&_node_filter_map;

    }

    void setEdgeFilterMap(EdgeFilterMap& _edge_filter_map) {

      edge_filter_map=&_edge_filter_map;

    }

  public:

//     SubGraphWrapperBase(Graph& _graph, 

// 			NodeFilterMap& _node_filter_map, 

// 			EdgeFilterMap& _edge_filter_map) : 

//       Parent(&_graph), 

//       node_filter_map(&node_filter_map), 

//       edge_filter_map(&edge_filter_map) { }

    typedef typename Parent::Node Node;

    typedef typename Parent::Edge Edge;

    void first(Node& i) const { 

      Parent::first(i); 

      while (i!=INVALID && !(*node_filter_map)[i]) Parent::next(i); 

    }

    void first(Edge& i) const { 

      Parent::first(i); 

      while (i!=INVALID && !(*edge_filter_map)[i]) Parent::next(i); 

    }

    void firstIn(Edge& i, const Node& n) const { 

      Parent::firstIn(i, n); 

      while (i!=INVALID && !(*edge_filter_map)[i]) Parent::nextIn(i); 

    }

    void firstOut(Edge& i, const Node& n) const { 

      Parent::firstOut(i, n); 

      while (i!=INVALID && !(*edge_filter_map)[i]) Parent::nextOut(i); 

    }

    void next(Node& i) const { 

      Parent::next(i); 

      while (i!=INVALID && !(*node_filter_map)[i]) Parent::next(i); 

    }

    void next(Edge& i) const { 

      Parent::next(i); 

      while (i!=INVALID && !(*edge_filter_map)[i]) Parent::next(i); 

    }

    void nextIn(Edge& i) const { 

      Parent::nextIn(i); 

      while (i!=INVALID && !(*edge_filter_map)[i]) Parent::nextIn(i); 

    }

    void nextOut(Edge& i) const { 

      Parent::nextOut(i); 

      while (i!=INVALID && !(*edge_filter_map)[i]) Parent::nextOut(i); 

    }

    /// This function hides \c n in the graph, i.e. the iteration 

    /// jumps over it. This is done by simply setting the value of \c n  

    /// to be false in the corresponding node-map.

    void hide(const Node& n) const { node_filter_map->set(n, false); }

    /// This function hides \c e in the graph, i.e. the iteration 

    /// jumps over it. This is done by simply setting the value of \c e  

    /// to be false in the corresponding edge-map.

    void hide(const Edge& e) const { edge_filter_map->set(e, false); }

    /// The value of \c n is set to be true in the node-map which stores 

    /// hide information. If \c n was hidden previuosly, then it is shown 

    /// again

     void unHide(const Node& n) const { node_filter_map->set(n, true); }

    /// The value of \c e is set to be true in the edge-map which stores 

    /// hide information. If \c e was hidden previuosly, then it is shown 

    /// again

    void unHide(const Edge& e) const { edge_filter_map->set(e, true); }

    /// Returns true if \c n is hidden.

    bool hidden(const Node& n) const { return !(*node_filter_map)[n]; }

    /// Returns true if \c n is hidden.

    bool hidden(const Edge& e) const { return !(*edge_filter_map)[e]; }

    /// \warning This is a linear time operation and works only if s

    /// \c Graph::NodeIt is defined.

    /// \todo assign tags.

    int nodeNum() const { 

      int i=0;

      Node n;

      for (first(n); n!=INVALID; next(n)) ++i;

      return i; 

    }

    /// \warning This is a linear time operation and works only if 

    /// \c Graph::EdgeIt is defined.

    /// \todo assign tags.

    int edgeNum() const { 

      int i=0;

      Edge e;

      for (first(e); e!=INVALID; next(e)) ++i;

      return i; 

    }

  };

  /*! \brief A graph wrapper for hiding nodes and edges from a graph.

  \warning Graph wrappers are in even more experimental state than the other

  parts of the lib. Use them at you own risk.

  This wrapper shows a graph with filtered node-set and 

  edge-set. 

  Given a bool-valued map on the node-set and one on 

  the edge-set of the graph, the iterators show only the objects 

  having true value. We have to note that this does not mean that an 

  induced subgraph is obtained, the node-iterator cares only the filter 

  on the node-set, and the edge-iterators care only the filter on the 

  edge-set.

  \code

  typedef SmartGraph Graph;

  Graph g;

  typedef Graph::Node Node;

  typedef Graph::Edge Edge;

  Node u=g.addNode(); //node of id 0

  Node v=g.addNode(); //node of id 1

  Node e=g.addEdge(u, v); //edge of id 0

  Node f=g.addEdge(v, u); //edge of id 1

  Graph::NodeMap<bool> nm(g, true);

  nm.set(u, false);

  Graph::EdgeMap<bool> em(g, true);

  em.set(e, false);

  typedef SubGraphWrapper<Graph, Graph::NodeMap<bool>, Graph::EdgeMap<bool> > SubGW;

  SubGW gw(g, nm, em);

  for (SubGW::NodeIt n(gw); n!=INVALID; ++n) std::cout << g.id(n) << std::endl;

  std::cout << ":-)" << std::endl;

  for (SubGW::EdgeIt e(gw); e!=INVALID; ++e) std::cout << g.id(e) << std::endl;

  \endcode

  The output of the above code is the following.

  \code

  1

  :-)

  1

  \endcode

  Note that \c n is of type \c SubGW::NodeIt, but it can be converted to

  \c Graph::Node that is why \c g.id(n) can be applied.

  For other examples see also the documentation of NodeSubGraphWrapper and 

  EdgeSubGraphWrapper.

  \author Marton Makai

  */

  template<typename _Graph, typename NodeFilterMap, 

	   typename EdgeFilterMap>

  class SubGraphWrapper : 

    public IterableGraphExtender<

    SubGraphWrapperBase<_Graph, NodeFilterMap, EdgeFilterMap> > {

  public:

    typedef _Graph Graph;

    typedef IterableGraphExtender<

      SubGraphWrapperBase<_Graph, NodeFilterMap, EdgeFilterMap> > Parent;

  protected:

    SubGraphWrapper() { }

  public:

    SubGraphWrapper(_Graph& _graph, NodeFilterMap& _node_filter_map, 

		    EdgeFilterMap& _edge_filter_map) { 

      setGraph(_graph);

      setNodeFilterMap(_node_filter_map);

      setEdgeFilterMap(_edge_filter_map);

    }

  };

  /*! \brief A wrapper for hiding nodes from a graph.

  \warning Graph wrappers are in even more experimental state than the other

  parts of the lib. Use them at you own risk.

  A wrapper for hiding nodes from a graph.

  This wrapper specializes SubGraphWrapper in the way that only the node-set 

  can be filtered. Note that this does not mean of considering induced 

  subgraph, the edge-iterators consider the original edge-set.

  \author Marton Makai

  */

  template<typename Graph, typename NodeFilterMap>

  class NodeSubGraphWrapper : 

    public SubGraphWrapper<Graph, NodeFilterMap, 

			   ConstMap<typename Graph::Edge,bool> > {

  public:

    typedef SubGraphWrapper<Graph, NodeFilterMap, 

			    ConstMap<typename Graph::Edge,bool> > Parent;

  protected:

    ConstMap<typename Graph::Edge, bool> const_true_map;

  public:

    NodeSubGraphWrapper(Graph& _graph, NodeFilterMap& _node_filter_map) : 

      Parent(), const_true_map(true) { 

      Parent::setGraph(_graph);

      Parent::setNodeFilterMap(_node_filter_map);

      Parent::setEdgeFilterMap(const_true_map);

    }

  };

  /*! \brief A wrapper for hiding edges from a graph.

  \warning Graph wrappers are in even more experimental state than the other

  parts of the lib. Use them at you own risk.

  A wrapper for hiding edges from a graph.

  This wrapper specializes SubGraphWrapper in the way that only the edge-set 

  can be filtered. The usefulness of this wrapper is demonstrated in the 

  problem of searching a maximum number of edge-disjoint shortest paths 

  between 

  two nodes \c s and \c t. Shortest here means being shortest w.r.t. 

  non-negative edge-lengths. Note that 

  the comprehension of the presented solution 

  need's some knowledge from elementary combinatorial optimization. 

  If a single shortest path is to be 

  searched between two nodes \c s and \c t, then this can be done easily by 

  applying the Dijkstra algorithm class. What happens, if a maximum number of 

  edge-disjoint shortest paths is to be computed. It can be proved that an 

  edge can be in a shortest path if and only if it is tight with respect to 

  the potential function computed by Dijkstra. Moreover, any path containing 

  only such edges is a shortest one. Thus we have to compute a maximum number 

  of edge-disjoint paths between \c s and \c t in the graph which has edge-set 

  all the tight edges. The computation will be demonstrated on the following 

  graph, which is read from a dimacs file.

  \dot

  digraph lemon_dot_example {

  node [ shape=ellipse, fontname=Helvetica, fontsize=10 ];

  n0 [ label="0 (s)" ];

  n1 [ label="1" ];

  n2 [ label="2" ];

  n3 [ label="3" ];

  n4 [ label="4" ];

  n5 [ label="5" ];

  n6 [ label="6 (t)" ];

  edge [ shape=ellipse, fontname=Helvetica, fontsize=10 ];

  n5 ->  n6 [ label="9, length:4" ];

  n4 ->  n6 [ label="8, length:2" ];

  n3 ->  n5 [ label="7, length:1" ];

  n2 ->  n5 [ label="6, length:3" ];

  n2 ->  n6 [ label="5, length:5" ];

  n2 ->  n4 [ label="4, length:2" ];

  n1 ->  n4 [ label="3, length:3" ];

  n0 ->  n3 [ label="2, length:1" ];

  n0 ->  n2 [ label="1, length:2" ];

  n0 ->  n1 [ label="0, length:3" ];

  }

  \enddot

  \code

  Graph g;

  Node s, t;

  LengthMap length(g);

  readDimacs(std::cin, g, length, s, t);

  cout << "edges with lengths (of form id, source--length->target): " << endl;

  for(EdgeIt e(g); e!=INVALID; ++e) 

    cout << g.id(e) << ", " << g.id(g.source(e)) << "--" 

         << length[e] << "->" << g.id(g.target(e)) << endl;

  cout << "s: " << g.id(s) << " t: " << g.id(t) << endl;

  \endcode

  Next, the potential function is computed with Dijkstra.

  \code

  typedef Dijkstra<Graph, LengthMap> Dijkstra;

  Dijkstra dijkstra(g, length);

  dijkstra.run(s);

  \endcode

  Next, we consrtruct a map which filters the edge-set to the tight edges.

  \code

  typedef TightEdgeFilterMap<Graph, const Dijkstra::DistMap, LengthMap> 

    TightEdgeFilter;

  TightEdgeFilter tight_edge_filter(g, dijkstra.distMap(), length);

  typedef EdgeSubGraphWrapper<Graph, TightEdgeFilter> SubGW;

  SubGW gw(g, tight_edge_filter);

  \endcode

  Then, the maximum nimber of edge-disjoint \c s-\c t paths are computed 

  with a max flow algorithm Preflow.

  \code

  ConstMap<Edge, int> const_1_map(1);

  Graph::EdgeMap<int> flow(g, 0);

  Preflow<SubGW, int, ConstMap<Edge, int>, Graph::EdgeMap<int> > 

    preflow(gw, s, t, const_1_map, flow);

  preflow.run();

  \endcode

  Last, the output is:

  \code  

  cout << "maximum number of edge-disjoint shortest path: " 

       << preflow.flowValue() << endl;

  cout << "edges of the maximum number of edge-disjoint shortest s-t paths: " 

       << endl;

  for(EdgeIt e(g); e!=INVALID; ++e) 

    if (flow[e])

      cout << " " << g.id(g.source(e)) << "--" 

	   << length[e] << "->" << g.id(g.target(e)) << endl;

  \endcode

  The program has the following (expected :-)) output:

  \code

  edges with lengths (of form id, source--length->target):

   9, 5--4->6

   8, 4--2->6

   7, 3--1->5

   6, 2--3->5

   5, 2--5->6

   4, 2--2->4

   3, 1--3->4

   2, 0--1->3

   1, 0--2->2

   0, 0--3->1

  s: 0 t: 6

  maximum number of edge-disjoint shortest path: 2

  edges of the maximum number of edge-disjoint shortest s-t paths:

   9, 5--4->6

   8, 4--2->6

   7, 3--1->5

   4, 2--2->4

   2, 0--1->3

   1, 0--2->2

  \endcode

  \author Marton Makai

  */

  template<typename Graph, typename EdgeFilterMap>

  class EdgeSubGraphWrapper : 

    public SubGraphWrapper<Graph, ConstMap<typename Graph::Node,bool>, 

			   EdgeFilterMap> {

  public:

    typedef SubGraphWrapper<Graph, ConstMap<typename Graph::Node,bool>, 

			    EdgeFilterMap> Parent;

  protected:

    ConstMap<typename Graph::Node, bool> const_true_map;

  public:

    EdgeSubGraphWrapper(Graph& _graph, EdgeFilterMap& _edge_filter_map) : 

      Parent(), const_true_map(true) { 

      Parent::setGraph(_graph);

      Parent::setNodeFilterMap(const_true_map);

      Parent::setEdgeFilterMap(_edge_filter_map);

    }

  };

  template<typename Graph>

  class UndirGraphWrapper : public GraphWrapper<Graph> {

  public:

    typedef GraphWrapper<Graph> Parent; 

  protected:

    UndirGraphWrapper() : GraphWrapper<Graph>() { }

  public:

    typedef typename GraphWrapper<Graph>::Node Node;

    typedef typename GraphWrapper<Graph>::NodeIt NodeIt;

    typedef typename GraphWrapper<Graph>::Edge Edge;

    typedef typename GraphWrapper<Graph>::EdgeIt EdgeIt;

    UndirGraphWrapper(Graph& _graph) : GraphWrapper<Graph>(_graph) { }  

    class OutEdgeIt {

      friend class UndirGraphWrapper<Graph>;

      bool out_or_in; //true iff out

      typename Graph::OutEdgeIt out;

      typename Graph::InEdgeIt in;

    public:

      OutEdgeIt() { }

      OutEdgeIt(const Invalid& i) : Edge(i) { }

      OutEdgeIt(const UndirGraphWrapper<Graph>& _G, const Node& _n) {

	out_or_in=true; _G.graph->first(out, _n);

	if (!(_G.graph->valid(out))) { out_or_in=false; _G.graph->first(in, _n);	}

      } 

      operator Edge() const { 

	if (out_or_in) return Edge(out); else return Edge(in); 

      }

    };

    typedef OutEdgeIt InEdgeIt; 

    using GraphWrapper<Graph>::first;

    OutEdgeIt& first(OutEdgeIt& i, const Node& p) const { 

      i=OutEdgeIt(*this, p); return i;

    }

    using GraphWrapper<Graph>::next;

    OutEdgeIt& next(OutEdgeIt& e) const {

      if (e.out_or_in) {

	typename Graph::Node n=this->graph->source(e.out);

	this->graph->next(e.out);

	if (!this->graph->valid(e.out)) { 

	  e.out_or_in=false; this->graph->first(e.in, n); }

      } else {

	this->graph->next(e.in);

      }

      return e;

    }

    Node aNode(const OutEdgeIt& e) const { 

      if (e.out_or_in) return this->graph->source(e); else 

	return this->graph->target(e); }

    Node bNode(const OutEdgeIt& e) const { 

      if (e.out_or_in) return this->graph->target(e); else 

	return this->graph->source(e); }

    //    KEEP_MAPS(Parent, UndirGraphWrapper);

  };

//   /// \brief An undirected graph template.

//   ///

//   ///\warning Graph wrappers are in even more experimental state than the other

//   ///parts of the lib. Use them at your own risk.

//   ///

//   /// An undirected graph template.

//   /// This class works as an undirected graph and a directed graph of 

//   /// class \c Graph is used for the physical storage.

//   /// \ingroup graphs

  template<typename Graph>

  class UndirGraph : public UndirGraphWrapper<Graph> {

    typedef UndirGraphWrapper<Graph> Parent;

  protected:

    Graph gr;

  public:

    UndirGraph() : UndirGraphWrapper<Graph>() { 

      Parent::setGraph(gr); 

    }

    //    KEEP_MAPS(Parent, UndirGraph);

  };

  template <typename _Graph, 

	    typename ForwardFilterMap, typename BackwardFilterMap>

  class SubBidirGraphWrapperBase : public GraphWrapperBase<_Graph> {

  public:

    typedef _Graph Graph;

    typedef GraphWrapperBase<_Graph> Parent;

  protected:

    ForwardFilterMap* forward_filter;

    BackwardFilterMap* backward_filter;

    SubBidirGraphWrapperBase() : Parent(), 

				 forward_filter(0), backward_filter(0) { }

    void setForwardFilterMap(ForwardFilterMap& _forward_filter) {

      forward_filter=&_forward_filter;

    }

    void setBackwardFilterMap(BackwardFilterMap& _backward_filter) {

      backward_filter=&_backward_filter;

    }

  public:

//     SubGraphWrapperBase(Graph& _graph, 

// 			NodeFilterMap& _node_filter_map, 

// 			EdgeFilterMap& _edge_filter_map) : 

//       Parent(&_graph), 

//       node_filter_map(&node_filter_map), 

//       edge_filter_map(&edge_filter_map) { }

    typedef typename Parent::Node Node;

    typedef typename _Graph::Edge GraphEdge;

    template <typename T> class EdgeMap;

    /// SubBidirGraphWrapperBase<..., ..., ...>::Edge is inherited from 

    /// _Graph::Edge. It contains an extra bool flag which is true 

    /// if and only if the 

    /// edge is the backward version of the original edge.

    class Edge : public _Graph::Edge {

      friend class SubBidirGraphWrapperBase<

	Graph, ForwardFilterMap, BackwardFilterMap>;

      template<typename T> friend class EdgeMap;

    protected:

      bool backward; //true, iff backward

    public:

      Edge() { }

      /// \todo =false is needed, or causes problems?

      /// If \c _backward is false, then we get an edge corresponding to the 

      /// original one, otherwise its oppositely directed pair is obtained.

      Edge(const typename _Graph::Edge& e, bool _backward/*=false*/) : 

	_Graph::Edge(e), backward(_backward) { }

      Edge(Invalid i) : _Graph::Edge(i), backward(true) { }

      bool operator==(const Edge& v) const { 

	return (this->backward==v.backward && 

		static_cast<typename _Graph::Edge>(*this)==

		static_cast<typename _Graph::Edge>(v));

      } 

      bool operator!=(const Edge& v) const { 

	return (this->backward!=v.backward || 

		static_cast<typename _Graph::Edge>(*this)!=

		static_cast<typename _Graph::Edge>(v));

      }

    };

    void first(Node& i) const { 

      Parent::first(i); 

    }

    void first(Edge& i) const { 

      Parent::first(i); 

      i.backward=false;

      while (*static_cast<GraphEdge*>(&i)!=INVALID && 

	     !(*forward_filter)[i]) Parent::next(i);

      if (*static_cast<GraphEdge*>(&i)==INVALID) {

	Parent::first(i); 

	i.backward=true;

	while (*static_cast<GraphEdge*>(&i)!=INVALID && 

	       !(*backward_filter)[i]) Parent::next(i);

      }

    }

    void firstIn(Edge& i, const Node& n) const { 

      Parent::firstIn(i, n); 

      i.backward=false;

      while (*static_cast<GraphEdge*>(&i)!=INVALID && 

	     !(*forward_filter)[i]) Parent::nextOut(i);

      if (*static_cast<GraphEdge*>(&i)==INVALID) {

	Parent::firstOut(i, n); 

	i.backward=true;

	while (*static_cast<GraphEdge*>(&i)!=INVALID && 

	       !(*backward_filter)[i]) Parent::nextOut(i);

      }

    }

    void firstOut(Edge& i, const Node& n) const { 

      Parent::firstOut(i, n); 

      i.backward=false;

      while (*static_cast<GraphEdge*>(&i)!=INVALID && 

	     !(*forward_filter)[i]) Parent::nextOut(i);

      if (*static_cast<GraphEdge*>(&i)==INVALID) {

	Parent::firstIn(i, n); 

	i.backward=true;

	while (*static_cast<GraphEdge*>(&i)!=INVALID && 

	       !(*backward_filter)[i]) Parent::nextIn(i);

      }

    }

    void next(Node& i) const { 

      Parent::next(i); 

    }

    void next(Edge& i) const { 

      if (!(i.backward)) {

	Parent::next(i);

	while (*static_cast<GraphEdge*>(&i)!=INVALID && 

	       !(*forward_filter)[i]) Parent::next(i);

	if (*static_cast<GraphEdge*>(&i)==INVALID) {

	  Parent::first(i); 

	  i.backward=true;

	  while (*static_cast<GraphEdge*>(&i)!=INVALID && 

		 !(*backward_filter)[i]) Parent::next(i);

	}

      } else {

	Parent::next(i);

	while (*static_cast<GraphEdge*>(&i)!=INVALID && 

	       !(*backward_filter)[i]) Parent::next(i);

      }

    }

    void nextIn(Edge& i) const { 

      if (!(i.backward)) {

	Node n=Parent::target(i);

	Parent::nextIn(i);

	while (*static_cast<GraphEdge*>(&i)!=INVALID && 

	       !(*forward_filter)[i]) Parent::nextIn(i);

	if (*static_cast<GraphEdge*>(&i)==INVALID) {

	  Parent::firstOut(i, n); 

	  i.backward=true;

	  while (*static_cast<GraphEdge*>(&i)!=INVALID && 

		 !(*backward_filter)[i]) Parent::nextOut(i);

	}

      } else {

	Parent::nextOut(i);

	while (*static_cast<GraphEdge*>(&i)!=INVALID && 

	       !(*backward_filter)[i]) Parent::nextOut(i);

      }

    }

    void nextOut(Edge& i) const { 

      if (!(i.backward)) {

	Node n=Parent::source(i);

	Parent::nextOut(i);

	while (*static_cast<GraphEdge*>(&i)!=INVALID && 

	       !(*forward_filter)[i]) Parent::nextOut(i);

	if (*static_cast<GraphEdge*>(&i)==INVALID) {

	  Parent::firstIn(i, n); 

	  i.backward=true;

	  while (*static_cast<GraphEdge*>(&i)!=INVALID && 

		 !(*backward_filter)[i]) Parent::nextIn(i);

	}

      } else {

	Parent::nextIn(i);

	while (*static_cast<GraphEdge*>(&i)!=INVALID && 

	       !(*backward_filter)[i]) Parent::nextIn(i);

      }

    }

    Node source(Edge e) const { 

      return ((!e.backward) ? this->graph->source(e) : this->graph->target(e)); }

    Node target(Edge e) const { 

      return ((!e.backward) ? this->graph->target(e) : this->graph->source(e)); }

    /// Gives back the opposite edge.

    Edge opposite(const Edge& e) const { 

      Edge f=e;

      f.backward=!f.backward;

      return f;

    }

    /// \warning This is a linear time operation and works only if 

    /// \c Graph::EdgeIt is defined.

    /// \todo hmm

    int edgeNum() const { 

      int i=0;

      Edge e;

      for (first(e); e!=INVALID; next(e)) ++i;

      return i; 

    }

    bool forward(const Edge& e) const { return !e.backward; }

    bool backward(const Edge& e) const { return e.backward; }

    template <typename T>

    /// \c SubBidirGraphWrapperBase<..., ..., ...>::EdgeMap contains two 

    /// _Graph::EdgeMap one for the forward edges and 

    /// one for the backward edges.

    class EdgeMap {

      template <typename TT> friend class EdgeMap;

      typename _Graph::template EdgeMap<T> forward_map, backward_map; 

    public:

      typedef T Value;

      typedef Edge Key;

      EdgeMap(const SubBidirGraphWrapperBase<_Graph, 

	      ForwardFilterMap, BackwardFilterMap>& g) : 

	forward_map(*(g.graph)), backward_map(*(g.graph)) { }

      EdgeMap(const SubBidirGraphWrapperBase<_Graph, 

	      ForwardFilterMap, BackwardFilterMap>& g, T a) : 

	forward_map(*(g.graph), a), backward_map(*(g.graph), a) { }

      void set(Edge e, T a) { 

	if (!e.backward) 

	  forward_map.set(e, a); 

	else 

	  backward_map.set(e, a); 

      }

//       typename _Graph::template EdgeMap<T>::ConstReference 

//       operator[](Edge e) const { 

// 	if (!e.backward) 

// 	  return forward_map[e]; 

// 	else 

// 	  return backward_map[e]; 

//       }

//      typename _Graph::template EdgeMap<T>::Reference 

      T operator[](Edge e) const { 

	if (!e.backward) 

	  return forward_map[e]; 

	else 

	  return backward_map[e]; 

      }

      void update() { 

	forward_map.update(); 

	backward_map.update();

      }

    };

  };

  ///\brief A wrapper for composing a subgraph of a 

  /// bidirected graph made from a directed one. 

  ///

  /// A wrapper for composing a subgraph of a 

  /// bidirected graph made from a directed one. 

  ///

  ///\warning Graph wrappers are in even more experimental state than the other

  ///parts of the lib. Use them at you own risk.

  ///

  /// Let \f$G=(V, A)\f$ be a directed graph and for each directed edge 

  /// \f$e\in A\f$, let \f$\bar e\f$ denote the edge obtained by

  /// reversing its orientation. We are given moreover two bool valued 

  /// maps on the edge-set, 

  /// \f$forward\_filter\f$, and \f$backward\_filter\f$. 

  /// SubBidirGraphWrapper implements the graph structure with node-set 

  /// \f$V\f$ and edge-set 

  /// \f$\{e : e\in A \mbox{ and } forward\_filter(e) \mbox{ is true}\}+\{\bar e : e\in A \mbox{ and } backward\_filter(e) \mbox{ is true}\}\f$. 

  /// The purpose of writing + instead of union is because parallel 

  /// edges can arise. (Similarly, antiparallel edges also can arise).

  /// In other words, a subgraph of the bidirected graph obtained, which 

  /// is given by orienting the edges of the original graph in both directions.

  /// As the oppositely directed edges are logically different, 

  /// the maps are able to attach different values for them. 

  ///

  /// An example for such a construction is \c RevGraphWrapper where the 

  /// forward_filter is everywhere false and the backward_filter is 

  /// everywhere true. We note that for sake of efficiency, 

  /// \c RevGraphWrapper is implemented in a different way. 

  /// But BidirGraphWrapper is obtained from 

  /// SubBidirGraphWrapper by considering everywhere true 

  /// valued maps both for forward_filter and backward_filter. 

  /// Finally, one of the most important applications of SubBidirGraphWrapper 

  /// is ResGraphWrapper, which stands for the residual graph in directed 

  /// flow and circulation problems. 

  /// As wrappers usually, the SubBidirGraphWrapper implements the 

  /// above mentioned graph structure without its physical storage, 

  /// that is the whole stuff is stored in constant memory. 

  template<typename _Graph, 

	   typename ForwardFilterMap, typename BackwardFilterMap>

  class SubBidirGraphWrapper : 

    public IterableGraphExtender<

    SubBidirGraphWrapperBase<_Graph, ForwardFilterMap, BackwardFilterMap> > {

  public:

    typedef _Graph Graph;

    typedef IterableGraphExtender<

      SubBidirGraphWrapperBase<

      _Graph, ForwardFilterMap, BackwardFilterMap> > Parent;

  protected:

    SubBidirGraphWrapper() { }

  public:

    SubBidirGraphWrapper(_Graph& _graph, ForwardFilterMap& _forward_filter, 

			 BackwardFilterMap& _backward_filter) { 

      setGraph(_graph);

      setForwardFilterMap(_forward_filter);

      setBackwardFilterMap(_backward_filter);

    }

  };

  ///\brief A wrapper for composing bidirected graph from a directed one. 

  ///

  ///\warning Graph wrappers are in even more experimental state than the other

  ///parts of the lib. Use them at you own risk.

  ///

  /// A wrapper for composing bidirected graph from a directed one. 

  /// A bidirected graph is composed over the directed one without physical 

  /// storage. As the oppositely directed edges are logically different ones 

  /// the maps are able to attach different values for them.

  template<typename Graph>

  class BidirGraphWrapper : 

    public SubBidirGraphWrapper<

    Graph, 

    ConstMap<typename Graph::Edge, bool>, 

    ConstMap<typename Graph::Edge, bool> > {

  public:

    typedef  SubBidirGraphWrapper<

      Graph, 

      ConstMap<typename Graph::Edge, bool>, 

      ConstMap<typename Graph::Edge, bool> > Parent; 

  protected:

    ConstMap<typename Graph::Edge, bool> cm;

    BidirGraphWrapper() : Parent(), cm(true) { 

      Parent::setForwardFilterMap(cm);

      Parent::setBackwardFilterMap(cm);

    }

  public:

    BidirGraphWrapper(Graph& _graph) : Parent(), cm(true) { 

      Parent::setGraph(_graph);

      Parent::setForwardFilterMap(cm);

      Parent::setBackwardFilterMap(cm);

    }

    int edgeNum() const { 

      return 2*this->graph->edgeNum();

    }

    //    KEEP_MAPS(Parent, BidirGraphWrapper);

  };

  template<typename Graph, typename Number,

	   typename CapacityMap, typename FlowMap>

  class ResForwardFilter {

    //    const Graph* graph;

    const CapacityMap* capacity;

    const FlowMap* flow;

  public:

    ResForwardFilter(/*const Graph& _graph, */