/* -*- C++ -*-

 /**

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

    @defgroup gwrappers Wrapper Classes for Graphs

  *

    \brief This group contains several wrapper classes for graphs

  * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

    @ingroup graphs

  * (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

     The main parts of LEMON are the different graph structures, 

     generic graph algorithms, graph concepts which couple these, and 

     graph wrappers. While the previous ones are more or less clear, the 

     latter notion needs further explanation.

     Graph wrappers are graph classes which serve for considering graph 

     structures in different ways. A short example makes the notion much 

     clearer. 

     Suppose that we have an instance \c g of a directed graph

     type say \c ListGraph and an algorithm 

     \code template<typename Graph> int algorithm(const Graph&); \endcode 

     is needed to run on the reversely oriented graph. 

     It may be expensive (in time or in memory usage) to copy 

     \c g with the reverse orientation. 

     Thus, a wrapper class

     \code template<typename Graph> class RevGraphWrapper; \endcode is used. 

     The code looks as follows

     \code

     ListGraph g;

     RevGraphWrapper<ListGraph> rgw(g);

     int result=algorithm(rgw);

     \endcode

     After running the algorithm, the original graph \c g 

     remains untouched. Thus the graph wrapper used above is to consider the 

     original graph with reverse orientation. 

     This techniques gives rise to an elegant code, and 

     based on stable graph wrappers, complex algorithms can be 

     implemented easily. 

     In flow, circulation and bipartite matching problems, the residual 

     graph is of particular importance. Combining a wrapper implementing 

     this, shortest path algorithms and minimum mean cycle algorithms, 

     a range of weighted and cardinality optimization algorithms can be 

     obtained. For lack of space, for other examples, 

     the interested user is referred to the detailed documentation of graph 

     wrappers. 

     The behavior of graph wrappers can be very different. Some of them keep 

     capabilities of the original graph while in other cases this would be 

     meaningless. This means that the concepts that they are a model of depend 

     on the graph wrapper, and the wrapped graph(s). 

     If an edge of \c rgw is deleted, this is carried out by 

     deleting the corresponding edge of \c g. But for a residual 

     graph, this operation has no sense. 

     Let we stand one more example here to simplify your work. 

     wrapper class

     \code template<typename Graph> class RevGraphWrapper; \endcode 

     has constructor 

     <tt> RevGraphWrapper(Graph& _g)</tt>. 

     This means that in a situation, 

     when a <tt> const ListGraph& </tt> reference to a graph is given, 

     then it have to be instantiated with <tt>Graph=const ListGraph</tt>.

     \code

     int algorithm1(const ListGraph& g) {

     RevGraphWrapper<const ListGraph> rgw(g);

     return algorithm2(rgw);

     }

     \endcode

     \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); }

    The main parts of LEMON are the different graph structures, 

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

    generic graph algorithms, graph concepts which couple these, and 

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

    graph wrappers. While the previous ones are more or less clear, the 

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

    latter notion needs further explanation.

    Graph wrappers are graph classes which serve for considering graph 

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

    structures in different ways. A short example makes the notion much 

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

    clearer. 

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

    Suppose that we have an instance \c g of a directed graph

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

    type say \c ListGraph and an algorithm 

    \code template<typename Graph> int algorithm(const Graph&); \endcode 

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

    is needed to run on the reversely oriented graph. 

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

    It may be expensive (in time or in memory usage) to copy 

    \c g with the reverse orientation. 

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

    Thus, a wrapper class

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

    \code template<typename Graph> class RevGraphWrapper; \endcode is used. 

    The code looks as follows

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

    \code

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

    ListGraph g;

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

    RevGraphWrapper<ListGraph> rgw(g);

    int result=algorithm(rgw);

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

    \endcode

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

    After running the algorithm, the original graph \c g 

    remains untouched. Thus the graph wrapper used above is to consider the 

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

    original graph with reverse orientation. 

    This techniques gives rise to an elegant code, and 

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

    based on stable graph wrappers, complex algorithms can be 

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

    implemented easily. 

    In flow, circulation and bipartite matching problems, the residual 

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

    graph is of particular importance. Combining a wrapper implementing 

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

    this, shortest path algorithms and minimum mean cycle algorithms, 

    a range of weighted and cardinality optimization algorithms can be 

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

    obtained. For lack of space, for other examples, 

    the interested user is referred to the detailed documentation of graph 

     template <typename _Value>

    wrappers. 

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

    The behavior of graph wrappers can be very different. Some of them keep 

     public:

    capabilities of the original graph while in other cases this would be 

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

    meaningless. This means that the concepts that they are a model of depend 

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

    on the graph wrapper, and the wrapped graph(s). 

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

    If an edge of \c rgw is deleted, this is carried out by 

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

    deleting the corresponding edge of \c g. But for a residual 

     };

    graph, this operation has no sense. 

    Let we stand one more example here to simplify your work. 

     template <typename _Value>

    wrapper class

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

    \code template<typename Graph> class RevGraphWrapper; \endcode 

     public:

    has constructor 

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

    <tt> RevGraphWrapper(Graph& _g)</tt>. 

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

    This means that in a situation, 

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

    when a <tt> const ListGraph& </tt> reference to a graph is given, 

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

    then it have to be instantiated with <tt>Graph=const ListGraph</tt>.

     };

    \code

    int algorithm1(const ListGraph& g) {

   };

    RevGraphWrapper<const ListGraph> rgw(g);

    return algorithm2(rgw);

   template <typename _Graph>

    }

   class GraphWrapper :

    \endcode

     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() { 

       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, */

 		     const CapacityMap& _capacity, const FlowMap& _flow) :

       /*graph(&_graph),*/ capacity(&_capacity), flow(&_flow) { }

     ResForwardFilter() : /*graph(0),*/ capacity(0), flow(0) { }

     void setCapacity(const CapacityMap& _capacity) { capacity=&_capacity; }

     void setFlow(const FlowMap& _flow) { flow=&_flow; }

     bool operator[](const typename Graph::Edge& e) const {

       return (Number((*flow)[e]) < Number((*capacity)[e]));

     }

   };

   template<typename Graph, typename Number,

 	   typename CapacityMap, typename FlowMap>

   class ResBackwardFilter {

     const CapacityMap* capacity;

     const FlowMap* flow;

   public:

     ResBackwardFilter(/*const Graph& _graph,*/ 

 		      const CapacityMap& _capacity, const FlowMap& _flow) :

       /*graph(&_graph),*/ capacity(&_capacity), flow(&_flow) { }

     ResBackwardFilter() : /*graph(0),*/ capacity(0), flow(0) { }

     void setCapacity(const CapacityMap& _capacity) { capacity=&_capacity; }

     void setFlow(const FlowMap& _flow) { flow=&_flow; }

     bool operator[](const typename Graph::Edge& e) const {

       return (Number(0) < Number((*flow)[e]));

     }

   };

   /// A wrapper for composing the residual graph for directed flow and circulation problems.

   ///\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 the residual graph for directed flow and circulation problems.

   template<typename Graph, typename Number, 

 	   typename CapacityMap, typename FlowMap>

   class ResGraphWrapper : 

     public SubBidirGraphWrapper< 

     Graph, 

     ResForwardFilter<Graph, Number, CapacityMap, FlowMap>,  

     ResBackwardFilter<Graph, Number, CapacityMap, FlowMap> > {

   public:

     typedef SubBidirGraphWrapper< 

       Graph, 

       ResForwardFilter<Graph, Number, CapacityMap, FlowMap>,  

       ResBackwardFilter<Graph, Number, CapacityMap, FlowMap> > Parent;

   protected:

     const CapacityMap* capacity;

     FlowMap* flow;

     ResForwardFilter<Graph, Number, CapacityMap, FlowMap> forward_filter;

     ResBackwardFilter<Graph, Number, CapacityMap, FlowMap> backward_filter;

     ResGraphWrapper() : Parent(), 

  			capacity(0), flow(0) { }

     void setCapacityMap(const CapacityMap& _capacity) {

       capacity=&_capacity;

       forward_filter.setCapacity(_capacity);

       backward_filter.setCapacity(_capacity);

     }

     void setFlowMap(FlowMap& _flow) {

       flow=&_flow;

       forward_filter.setFlow(_flow);

       backward_filter.setFlow(_flow);

     }

   public:

     ResGraphWrapper(Graph& _graph, const CapacityMap& _capacity, 

 		       FlowMap& _flow) : 

       Parent(), capacity(&_capacity), flow(&_flow), 

       forward_filter(/*_graph,*/ _capacity, _flow), 

       backward_filter(/*_graph,*/ _capacity, _flow) {

       Parent::setGraph(_graph);

       Parent::setForwardFilterMap(forward_filter);

       Parent::setBackwardFilterMap(backward_filter);

     }

     typedef typename Parent::Edge Edge;

     void augment(const Edge& e, Number a) const {

       if (Parent::forward(e))  

 	flow->set(e, (*flow)[e]+a);

       else  

 	flow->set(e, (*flow)[e]-a);

     }

     /// \brief Residual capacity map.

     ///

     /// In generic residual graphs the residual capacity can be obtained 

     /// as a map. 

     class ResCap {

     protected: