/* -*- C++ -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2003-2006

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, 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.

 *

 */

/// \ingroup graph_concepts

/// \file

/// \brief Undirected bipartite graphs and components of.

#ifndef LEMON_CONCEPT_BPUGRAPH_H

#define LEMON_CONCEPT_BPUGRAPH_H

#include <lemon/concept/graph_component.h>

#include <lemon/concept/graph.h>

#include <lemon/concept/ugraph.h>

#include <lemon/utility.h>

namespace lemon {

  namespace concept {

    /// \addtogroup graph_concepts

    /// @{

    /// \brief Class describing the concept of Bipartite Undirected Graphs.

    ///

    /// This class describes the common interface of all 

    /// Undirected Bipartite Graphs.

    ///

    /// As all concept describing classes it provides only interface

    /// without any sensible implementation. So any algorithm for

    /// bipartite undirected graph should compile with this class, but it 

    /// will not run properly, of course.

    ///

    /// In LEMON bipartite undirected graphs also fulfill the concept of 

    /// the undirected graphs (\ref lemon::concept::UGraph "UGraph Concept"). 

    ///

    /// You can assume that all undirected bipartite graph can be handled

    /// as an undirected graph and consequently as a static graph.

    ///

    /// The bipartite graph stores two types of nodes which are named

    /// ANode and BNode. The graph type contains two types ANode and BNode

    /// which are inherited from Node type. Moreover they have

    /// constructor which converts Node to either ANode or BNode when it is

    /// possible. Therefor everywhere the Node type can be used instead of

    /// ANode and BNode. So the usage of the ANode and BNode is suggested.  

    ///

    /// The iteration on the partition can be done with the ANodeIt and 

    /// BNodeIt classes. The node map can be used to map values to the nodes

    /// and similarly we can use to map values for just the ANodes and

    /// BNodes the ANodeMap and BNodeMap template classes.

    class BpUGraph {

    public:

      /// \todo undocumented

      ///

      typedef True UndirectedTag;

      /// \brief The base type of node iterators, 

      /// or in other words, the trivial node iterator.

      ///

      /// This is the base type of each node iterator,

      /// thus each kind of node iterator converts to this.

      /// More precisely each kind of node iterator should be inherited 

      /// from the trivial node iterator. The Node class represents

      /// both of two types of nodes. 

      class Node {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        Node() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

        Node(const Node&) { }

        /// Invalid constructor \& conversion.

        /// This constructor initializes the iterator to be invalid.

        /// \sa Invalid for more details.

        Node(Invalid) { }

        /// Equality operator

        /// Two iterators are equal if and only if they point to the

        /// same object or both are invalid.

        bool operator==(Node) const { return true; }

        /// Inequality operator

        /// \sa operator==(Node n)

        ///

        bool operator!=(Node) const { return true; }

	/// Artificial ordering operator.

	/// To allow the use of graph descriptors as key type in std::map or

	/// similar associative container we require this.

	///

	/// \note This operator only have to define some strict ordering of

	/// the items; this order has nothing to do with the iteration

	/// ordering of the items.

	///

	/// \bug This is a technical requirement. Do we really need this?

	bool operator<(Node) const { return false; }

      };

      /// \brief The base type of anode iterators, 

      /// or in other words, the trivial anode iterator.

      ///

      /// This is the base type of each anode iterator,

      /// thus each kind of anode iterator converts to this.

      /// More precisely each kind of node iterator should be inherited 

      /// from the trivial anode iterator. The ANode class should be used

      /// only in special cases. Usually the Node type should be used insted

      /// of it. 

      class ANode {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        ANode() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

        ANode(const ANode&) { }

        /// Construct the same node as ANode.

        /// Construct the same node as ANode. It may throws assertion

        /// when the given node is from the BNode set.

        ANode(const Node&) { }

        /// Invalid constructor \& conversion.

        /// This constructor initializes the iterator to be invalid.

        /// \sa Invalid for more details.

        ANode(Invalid) { }

        /// Equality operator

        /// Two iterators are equal if and only if they point to the

        /// same object or both are invalid.

        bool operator==(ANode) const { return true; }

        /// Inequality operator

        /// \sa operator==(ANode n)

        ///

        bool operator!=(ANode) const { return true; }

	/// Artificial ordering operator.

	/// To allow the use of graph descriptors as key type in std::map or

	/// similar associative container we require this.

	///

	/// \note This operator only have to define some strict ordering of

	/// the items; this order has nothing to do with the iteration

	/// ordering of the items.

	bool operator<(ANode) const { return false; }

      };

      /// \brief The base type of bnode iterators, 

      /// or in other words, the trivial bnode iterator.

      ///

      /// This is the base type of each anode iterator,

      /// thus each kind of anode iterator converts to this.

      /// More precisely each kind of node iterator should be inherited 

      /// from the trivial anode iterator. The BNode class should be used

      /// only in special cases. Usually the Node type should be used insted

      /// of it. 

      class BNode {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        BNode() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

        BNode(const BNode&) { }

        /// Construct the same node as BNode.

        /// Construct the same node as BNode. It may throws assertion

        /// when the given node is from the ANode set.

        BNode(const Node&) { }

        /// Invalid constructor \& conversion.

        /// This constructor initializes the iterator to be invalid.

        /// \sa Invalid for more details.

        BNode(Invalid) { }

        /// Equality operator

        /// Two iterators are equal if and only if they point to the

        /// same object or both are invalid.

        bool operator==(BNode) const { return true; }

        /// Inequality operator

        /// \sa operator==(BNode n)

        ///

        bool operator!=(BNode) const { return true; }

	/// Artificial ordering operator.

	/// To allow the use of graph descriptors as key type in std::map or

	/// similar associative container we require this.

	///

	/// \note This operator only have to define some strict ordering of

	/// the items; this order has nothing to do with the iteration

	/// ordering of the items.

	bool operator<(BNode) const { return false; }

      };

      /// This iterator goes through each node.

      /// This iterator goes through each node.

      /// Its usage is quite simple, for example you can count the number

      /// of nodes in graph \c g of type \c Graph like this:

      ///\code

      /// int count=0;

      /// for (Graph::NodeIt n(g); n!=INVALID; ++n) ++count;

      ///\endcode

      class NodeIt : public Node {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        NodeIt() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

        NodeIt(const NodeIt& n) : Node(n) { }

        /// Invalid constructor \& conversion.

        /// Initialize the iterator to be invalid.

        /// \sa Invalid for more details.

        NodeIt(Invalid) { }

        /// Sets the iterator to the first node.

        /// Sets the iterator to the first node of \c g.

        ///

        NodeIt(const BpUGraph&) { }

        /// Node -> NodeIt conversion.

        /// Sets the iterator to the node of \c the graph pointed by 

	/// the trivial iterator.

        /// This feature necessitates that each time we 

        /// iterate the edge-set, the iteration order is the same.

        NodeIt(const BpUGraph&, const Node&) { }

        /// Next node.

        /// Assign the iterator to the next node.

        ///

        NodeIt& operator++() { return *this; }

      };

      /// This iterator goes through each ANode.

      /// This iterator goes through each ANode.

      /// Its usage is quite simple, for example you can count the number

      /// of nodes in graph \c g of type \c Graph like this:

      ///\code

      /// int count=0;

      /// for (Graph::ANodeIt n(g); n!=INVALID; ++n) ++count;

      ///\endcode

      class ANodeIt : public ANode {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        ANodeIt() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

        ANodeIt(const ANodeIt& n) : Node(n) { }

        /// Invalid constructor \& conversion.

        /// Initialize the iterator to be invalid.

        /// \sa Invalid for more details.

        ANodeIt(Invalid) { }

        /// Sets the iterator to the first node.

        /// Sets the iterator to the first node of \c g.

        ///

        ANodeIt(const BpUGraph&) { }

        /// Node -> ANodeIt conversion.

        /// Sets the iterator to the node of \c the graph pointed by 

	/// the trivial iterator.

        /// This feature necessitates that each time we 

        /// iterate the edge-set, the iteration order is the same.

        ANodeIt(const BpUGraph&, const Node&) { }

        /// Next node.

        /// Assign the iterator to the next node.

        ///

        ANodeIt& operator++() { return *this; }

      };

      /// This iterator goes through each BNode.

      /// This iterator goes through each BNode.

      /// Its usage is quite simple, for example you can count the number

      /// of nodes in graph \c g of type \c Graph like this:

      ///\code

      /// int count=0;

      /// for (Graph::BNodeIt n(g); n!=INVALID; ++n) ++count;

      ///\endcode

      class BNodeIt : public BNode {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        BNodeIt() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

        BNodeIt(const BNodeIt& n) : Node(n) { }

        /// Invalid constructor \& conversion.

        /// Initialize the iterator to be invalid.

        /// \sa Invalid for more details.

        BNodeIt(Invalid) { }

        /// Sets the iterator to the first node.

        /// Sets the iterator to the first node of \c g.

        ///

        BNodeIt(const BpUGraph&) { }

        /// Node -> BNodeIt conversion.

        /// Sets the iterator to the node of \c the graph pointed by 

	/// the trivial iterator.

        /// This feature necessitates that each time we 

        /// iterate the edge-set, the iteration order is the same.

        BNodeIt(const BpUGraph&, const Node&) { }

        /// Next node.

        /// Assign the iterator to the next node.

        ///

        BNodeIt& operator++() { return *this; }

      };

      /// The base type of the undirected edge iterators.

      /// The base type of the undirected edge iterators.

      ///

      class UEdge {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        UEdge() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

        UEdge(const UEdge&) { }

        /// Initialize the iterator to be invalid.

        /// Initialize the iterator to be invalid.

        ///

        UEdge(Invalid) { }

        /// Equality operator

        /// Two iterators are equal if and only if they point to the

        /// same object or both are invalid.

        bool operator==(UEdge) const { return true; }

        /// Inequality operator

        /// \sa operator==(UEdge n)

        ///

        bool operator!=(UEdge) const { return true; }

	/// Artificial ordering operator.

	/// To allow the use of graph descriptors as key type in std::map or

	/// similar associative container we require this.

	///

	/// \note This operator only have to define some strict ordering of

	/// the items; this order has nothing to do with the iteration

	/// ordering of the items.

	///

	/// \bug This is a technical requirement. Do we really need this?

	bool operator<(UEdge) const { return false; }

      };

      /// This iterator goes through each undirected edge.

      /// This iterator goes through each undirected edge of a graph.

      /// Its usage is quite simple, for example you can count the number

      /// of undirected edges in a graph \c g of type \c Graph as follows:

      ///\code

      /// int count=0;

      /// for(Graph::UEdgeIt e(g); e!=INVALID; ++e) ++count;

      ///\endcode

      class UEdgeIt : public UEdge {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        UEdgeIt() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

        UEdgeIt(const UEdgeIt& e) : UEdge(e) { }

        /// Initialize the iterator to be invalid.

        /// Initialize the iterator to be invalid.

        ///

        UEdgeIt(Invalid) { }

        /// This constructor sets the iterator to the first undirected edge.

        /// This constructor sets the iterator to the first undirected edge.

        UEdgeIt(const BpUGraph&) { }

        /// UEdge -> UEdgeIt conversion

        /// Sets the iterator to the value of the trivial iterator.

        /// This feature necessitates that each time we

        /// iterate the undirected edge-set, the iteration order is the 

	/// same.

        UEdgeIt(const BpUGraph&, const UEdge&) { } 

        /// Next undirected edge

        /// Assign the iterator to the next undirected edge.

        UEdgeIt& operator++() { return *this; }

      };

      /// \brief This iterator goes trough the incident undirected 

      /// edges of a node.

      ///

      /// This iterator goes trough the incident undirected edges

      /// of a certain node

      /// of a graph.

      /// Its usage is quite simple, for example you can compute the

      /// degree (i.e. count the number

      /// of incident edges of a node \c n

      /// in graph \c g of type \c Graph as follows.

      ///\code

      /// int count=0;

      /// for(Graph::IncEdgeIt e(g, n); e!=INVALID; ++e) ++count;

      ///\endcode

      class IncEdgeIt : public UEdge {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        IncEdgeIt() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

        IncEdgeIt(const IncEdgeIt& e) : UEdge(e) { }

        /// Initialize the iterator to be invalid.

        /// Initialize the iterator to be invalid.

        ///

        IncEdgeIt(Invalid) { }

        /// This constructor sets the iterator to first incident edge.

        /// This constructor set the iterator to the first incident edge of

        /// the node.

        IncEdgeIt(const BpUGraph&, const Node&) { }

        /// UEdge -> IncEdgeIt conversion

        /// Sets the iterator to the value of the trivial iterator \c e.

        /// This feature necessitates that each time we 

        /// iterate the edge-set, the iteration order is the same.

        IncEdgeIt(const BpUGraph&, const UEdge&) { }

        /// Next incident edge

        /// Assign the iterator to the next incident edge

	/// of the corresponding node.

        IncEdgeIt& operator++() { return *this; }

      };

      /// The directed edge type.

      /// The directed edge type. It can be converted to the

      /// undirected edge.

      class Edge : public UEdge {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        Edge() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

        Edge(const Edge& e) : UEdge(e) { }

        /// Initialize the iterator to be invalid.

        /// Initialize the iterator to be invalid.

        ///

        Edge(Invalid) { }

        /// Equality operator

        /// Two iterators are equal if and only if they point to the

        /// same object or both are invalid.

        bool operator==(Edge) const { return true; }

        /// Inequality operator

        /// \sa operator==(Edge n)

        ///

        bool operator!=(Edge) const { return true; }

	/// Artificial ordering operator.

	/// To allow the use of graph descriptors as key type in std::map or

	/// similar associative container we require this.

	///

	/// \note This operator only have to define some strict ordering of

	/// the items; this order has nothing to do with the iteration

	/// ordering of the items.

	///

	/// \bug This is a technical requirement. Do we really need this?

	bool operator<(Edge) const { return false; }

      }; 

      /// This iterator goes through each directed edge.

      /// This iterator goes through each edge of a graph.

      /// Its usage is quite simple, for example you can count the number

      /// of edges in a graph \c g of type \c Graph as follows:

      ///\code

      /// int count=0;

      /// for(Graph::EdgeIt e(g); e!=INVALID; ++e) ++count;

      ///\endcode

      class EdgeIt : public Edge {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        EdgeIt() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

        EdgeIt(const EdgeIt& e) : Edge(e) { }

        /// Initialize the iterator to be invalid.

        /// Initialize the iterator to be invalid.

        ///

        EdgeIt(Invalid) { }

        /// This constructor sets the iterator to the first edge.

        /// This constructor sets the iterator to the first edge of \c g.

        ///@param g the graph

        EdgeIt(const BpUGraph &g) { ignore_unused_variable_warning(g); }

        /// Edge -> EdgeIt conversion

        /// Sets the iterator to the value of the trivial iterator \c e.

        /// This feature necessitates that each time we 

        /// iterate the edge-set, the iteration order is the same.

        EdgeIt(const BpUGraph&, const Edge&) { } 

        ///Next edge

        /// Assign the iterator to the next edge.

        EdgeIt& operator++() { return *this; }

      };

      /// This iterator goes trough the outgoing directed edges of a node.

      /// This iterator goes trough the \e outgoing edges of a certain node

      /// of a graph.

      /// Its usage is quite simple, for example you can count the number

      /// of outgoing edges of a node \c n

      /// in graph \c g of type \c Graph as follows.

      ///\code

      /// int count=0;

      /// for (Graph::OutEdgeIt e(g, n); e!=INVALID; ++e) ++count;

      ///\endcode

      class OutEdgeIt : public Edge {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        OutEdgeIt() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

        OutEdgeIt(const OutEdgeIt& e) : Edge(e) { }

        /// Initialize the iterator to be invalid.

        /// Initialize the iterator to be invalid.

        ///

        OutEdgeIt(Invalid) { }

        /// This constructor sets the iterator to the first outgoing edge.

        /// This constructor sets the iterator to the first outgoing edge of

        /// the node.

        ///@param n the node

        ///@param g the graph

        OutEdgeIt(const BpUGraph& n, const Node& g) {

	  ignore_unused_variable_warning(n);

	  ignore_unused_variable_warning(g);

	}

        /// Edge -> OutEdgeIt conversion

        /// Sets the iterator to the value of the trivial iterator.

	/// This feature necessitates that each time we 

        /// iterate the edge-set, the iteration order is the same.

        OutEdgeIt(const BpUGraph&, const Edge&) { }

        ///Next outgoing edge

        /// Assign the iterator to the next 

        /// outgoing edge of the corresponding node.

        OutEdgeIt& operator++() { return *this; }

      };

      /// This iterator goes trough the incoming directed edges of a node.

      /// This iterator goes trough the \e incoming edges of a certain node

      /// of a graph.

      /// Its usage is quite simple, for example you can count the number

      /// of outgoing edges of a node \c n

      /// in graph \c g of type \c Graph as follows.

      ///\code

      /// int count=0;

      /// for(Graph::InEdgeIt e(g, n); e!=INVALID; ++e) ++count;

      ///\endcode

      class InEdgeIt : public Edge {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        InEdgeIt() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

        InEdgeIt(const InEdgeIt& e) : Edge(e) { }

        /// Initialize the iterator to be invalid.

        /// Initialize the iterator to be invalid.

        ///

        InEdgeIt(Invalid) { }

        /// This constructor sets the iterator to first incoming edge.

        /// This constructor set the iterator to the first incoming edge of

        /// the node.

        ///@param n the node

        ///@param g the graph

        InEdgeIt(const BpUGraph& g, const Node& n) { 

	  ignore_unused_variable_warning(n);

	  ignore_unused_variable_warning(g);

	}

        /// Edge -> InEdgeIt conversion

        /// Sets the iterator to the value of the trivial iterator \c e.

        /// This feature necessitates that each time we 

        /// iterate the edge-set, the iteration order is the same.

        InEdgeIt(const BpUGraph&, const Edge&) { }

        /// Next incoming edge

        /// Assign the iterator to the next inedge of the corresponding node.

        ///

        InEdgeIt& operator++() { return *this; }

      };

      /// \brief Read write map of the nodes to type \c T.

      /// 

      /// ReadWrite map of the nodes to type \c T.

      /// \sa Reference

      /// \warning Making maps that can handle bool type (NodeMap<bool>)

      /// needs some extra attention!

      /// \todo Wrong documentation

      template<class T> 

      class NodeMap : public ReadWriteMap< Node, T >

      {

      public:

        ///\e

        NodeMap(const BpUGraph&) { }

        ///\e

        NodeMap(const BpUGraph&, T) { }

        ///Copy constructor

        NodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }

        ///Assignment operator

        NodeMap& operator=(const NodeMap&) { return *this; }

        // \todo fix this concept

      };

      /// \brief Read write map of the ANodes to type \c T.

      /// 

      /// ReadWrite map of the ANodes to type \c T.

      /// \sa Reference

      /// \warning Making maps that can handle bool type (NodeMap<bool>)

      /// needs some extra attention!

      /// \todo Wrong documentation

      template<class T> 

      class ANodeMap : public ReadWriteMap< Node, T >

      {

      public:

        ///\e

        ANodeMap(const BpUGraph&) { }

        ///\e

        ANodeMap(const BpUGraph&, T) { }

        ///Copy constructor

        ANodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }

        ///Assignment operator

        ANodeMap& operator=(const NodeMap&) { return *this; }

        // \todo fix this concept

      };

      /// \brief Read write map of the BNodes to type \c T.

      /// 

      /// ReadWrite map of the BNodes to type \c T.

      /// \sa Reference

      /// \warning Making maps that can handle bool type (NodeMap<bool>)

      /// needs some extra attention!

      /// \todo Wrong documentation

      template<class T> 

      class BNodeMap : public ReadWriteMap< Node, T >

      {

      public:

        ///\e

        BNodeMap(const BpUGraph&) { }

        ///\e

        BNodeMap(const BpUGraph&, T) { }

        ///Copy constructor

        BNodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }

        ///Assignment operator

        BNodeMap& operator=(const NodeMap&) { return *this; }

        // \todo fix this concept

      };

      /// \brief Read write map of the directed edges to type \c T.

      ///

      /// Reference map of the directed edges to type \c T.

      /// \sa Reference

      /// \warning Making maps that can handle bool type (EdgeMap<bool>)

      /// needs some extra attention!

      /// \todo Wrong documentation

      template<class T> 

      class EdgeMap : public ReadWriteMap<Edge,T>

      {

      public:

        ///\e

        EdgeMap(const BpUGraph&) { }

        ///\e

        EdgeMap(const BpUGraph&, T) { }

        ///Copy constructor

        EdgeMap(const EdgeMap& em) : ReadWriteMap<Edge,T>(em) { }

        ///Assignment operator

        EdgeMap& operator=(const EdgeMap&) { return *this; }

        // \todo fix this concept    

      };

      /// Read write map of the undirected edges to type \c T.

      /// Reference map of the edges to type \c T.

      /// \sa Reference

      /// \warning Making maps that can handle bool type (UEdgeMap<bool>)

      /// needs some extra attention!

      /// \todo Wrong documentation

      template<class T> 

      class UEdgeMap : public ReadWriteMap<UEdge,T>

      {

      public:

        ///\e

        UEdgeMap(const BpUGraph&) { }

        ///\e

        UEdgeMap(const BpUGraph&, T) { }

        ///Copy constructor

        UEdgeMap(const UEdgeMap& em) : ReadWriteMap<UEdge,T>(em) {}

        ///Assignment operator

        UEdgeMap &operator=(const UEdgeMap&) { return *this; }

        // \todo fix this concept    

      };

      /// \brief Direct the given undirected edge.

      ///

      /// Direct the given undirected edge. The returned edge source

      /// will be the given edge.

      Edge direct(const UEdge&, const Node&) const {

	return INVALID;

      }

      /// \brief Direct the given undirected edge.

      ///

      /// Direct the given undirected edge. The returned edge source

      /// will be the source of the undirected edge if the given bool

      /// is true.

      Edge direct(const UEdge&, bool) const {

	return INVALID;

      }

      /// \brief Returns true when the given node is an ANode.

      ///

      /// Returns true when the given node is an ANode.

      bool aNode(Node) const { return true;}

      /// \brief Returns true when the given node is an BNode.

      ///

      /// Returns true when the given node is an BNode.

      bool bNode(Node) const { return true;}

      /// \brief Returns the edge's end node which is in the ANode set.

      ///

      /// Returns the edge's end node which is in the ANode set.

      Node aNode(UEdge) const { return INVALID;}

      /// \brief Returns the edge's end node which is in the BNode set.

      ///

      /// Returns the edge's end node which is in the BNode set.

      Node bNode(UEdge) const { return INVALID;}

      /// \brief Returns true if the edge has default orientation.

      ///

      /// Returns whether the given directed edge is same orientation as

      /// the corresponding undirected edge.

      bool direction(Edge) const { return true; }

      /// \brief Returns the opposite directed edge.

      ///

      /// Returns the opposite directed edge.

      Edge oppositeEdge(Edge) const { return INVALID; }

      /// \brief Opposite node on an edge

      ///

      /// \return the opposite of the given Node on the given Edge

      Node oppositeNode(Node, UEdge) const { return INVALID; }

      /// \brief First node of the undirected edge.

      ///

      /// \return the first node of the given UEdge.

      ///

      /// Naturally uectected edges don't have direction and thus

      /// don't have source and target node. But we use these two methods

      /// to query the two endnodes of the edge. The direction of the edge

      /// which arises this way is called the inherent direction of the

      /// undirected edge, and is used to define the "default" direction

      /// of the directed versions of the edges.

      /// \sa direction

      Node source(UEdge) const { return INVALID; }

      /// \brief Second node of the undirected edge.

      Node target(UEdge) const { return INVALID; }

      /// \brief Source node of the directed edge.

      Node source(Edge) const { return INVALID; }

      /// \brief Target node of the directed edge.

      Node target(Edge) const { return INVALID; }

      /// \brief Base node of the iterator

      ///

      /// Returns the base node (the source in this case) of the iterator

      Node baseNode(OutEdgeIt e) const {

	return source(e);

      }

      /// \brief Running node of the iterator

      ///

      /// Returns the running node (the target in this case) of the

      /// iterator

      Node runningNode(OutEdgeIt e) const {

	return target(e);

      }

      /// \brief Base node of the iterator

      ///

      /// Returns the base node (the target in this case) of the iterator

      Node baseNode(InEdgeIt e) const {

	return target(e);

      }

      /// \brief Running node of the iterator

      ///

      /// Returns the running node (the source in this case) of the

      /// iterator

      Node runningNode(InEdgeIt e) const {

	return source(e);

      }

      /// \brief Base node of the iterator

      ///

      /// Returns the base node of the iterator

      Node baseNode(IncEdgeIt) const {

	return INVALID;

      }

      /// \brief Running node of the iterator

      ///

      /// Returns the running node of the iterator

      Node runningNode(IncEdgeIt) const {

	return INVALID;

      }

      template <typename Graph>

      struct Constraints {

	void constraints() {

	}

      };

    };

    /// \brief An empty non-static undirected graph class.

    ///    

    /// This class provides everything that \ref BpUGraph does.

    /// Additionally it enables building graphs from scratch.

    class ExtendableBpUGraph : public BpUGraph {

    public:

      /// \brief Add a new ANode to the graph.

      ///

      /// Add a new ANode to the graph.

      /// \return the new node.

      Node addANode();

      /// \brief Add a new ANode to the graph.

      ///

      /// Add a new ANode to the graph.

      /// \return the new node.

      Node addBNode();

      /// \brief Add a new undirected edge to the graph.

      ///

      /// Add a new undirected edge to the graph. One of the nodes

      /// should be ANode and the other should be BNode.

      /// \pre The nodes are not in the same nodeset.

      /// \return the new edge.

      UEdge addEdge(const Node& from, const Node& to);

      /// \brief Resets the graph.

      ///

      /// This function deletes all undirected edges and nodes of the graph.

      /// It also frees the memory allocated to store them.

      void clear() { }

      template <typename Graph>

      struct Constraints {

	void constraints() {}

      };

    };

    /// \brief An empty erasable undirected graph class.

    ///

    /// This class is an extension of \ref ExtendableBpUGraph. It makes it

    /// possible to erase undirected edges or nodes.