/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

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

  *

  * Copyright (C) 2003-2013

  * 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 The concept of undirected graphs.

 #ifndef LEMON_CONCEPTS_BPGRAPH_H

 #define LEMON_CONCEPTS_BPGRAPH_H

 #include <lemon/concepts/graph_components.h>

 #include <lemon/concepts/maps.h>

 #include <lemon/concept_check.h>

 #include <lemon/core.h>

 namespace lemon {

   namespace concepts {

     /// \ingroup graph_concepts

     ///

     /// \brief Class describing the concept of undirected bipartite graphs.

     ///

     /// This class describes the common interface of all undirected

     /// bipartite graphs.

     ///

     /// Like all concept classes, it only provides an interface

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

     /// undirected bipartite graphs should compile with this class,

     /// but it will not run properly, of course.

     /// An actual graph implementation like \ref ListBpGraph or

     /// \ref SmartBpGraph may have additional functionality.

     ///

     /// The bipartite graphs also fulfill the concept of \ref Graph

     /// "undirected graphs". Bipartite graphs provide a bipartition of

     /// the node set, namely a red and blue set of the nodes. The

     /// nodes can be iterated with the RedNodeIt and BlueNodeIt in the

     /// two node sets. With RedNodeMap and BlueNodeMap values can be

     /// assigned to the nodes in the two sets.

     ///

     /// The edges of the graph cannot connect two nodes of the same

     /// set. The edges inherent orientation is from the red nodes to

     /// the blue nodes.

     ///

     /// \sa Graph

     class BpGraph {

     private:

       /// BpGraphs are \e not copy constructible. Use bpGraphCopy instead.

       BpGraph(const BpGraph&) {}

       /// \brief Assignment of a graph to another one is \e not allowed.

       /// Use bpGraphCopy instead.

       void operator=(const BpGraph&) {}

     public:

       /// Default constructor.

       BpGraph() {}

       /// \brief Undirected graphs should be tagged with \c UndirectedTag.

       ///

       /// Undirected graphs should be tagged with \c UndirectedTag.

       ///

       /// This tag helps the \c enable_if technics to make compile time

       /// specializations for undirected graphs.

       typedef True UndirectedTag;

       /// The node type of the graph

       /// This class identifies a node of the graph. It also serves

       /// as a base class of the node iterators,

       /// thus they convert to this type.

       class Node {

       public:

         /// Default constructor

         /// Default constructor.

         /// \warning It sets the object to an undefined value.

         Node() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         Node(const Node&) { }

         /// %Invalid constructor \& conversion.

         /// Initializes the object to be invalid.

         /// \sa Invalid for more details.

         Node(Invalid) { }

         /// Equality operator

         /// Equality operator.

         ///

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

         /// same object or both are \c INVALID.

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

         /// Inequality operator

         /// Inequality operator.

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

         /// Artificial ordering operator.

         /// Artificial ordering operator.

         ///

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

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

         /// ordering of the items.

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

       };

       /// Class to represent red nodes.

       /// This class represents the red nodes of the graph. It does

       /// not supposed to be used directly, because the nodes can be

       /// represented as Node instances. This class can be used as

       /// template parameter for special map classes.

       class RedNode : public Node {

       public:

         /// Default constructor

         /// Default constructor.

         /// \warning It sets the object to an undefined value.

         RedNode() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         RedNode(const RedNode&) : Node() { }

         /// %Invalid constructor \& conversion.

         /// Initializes the object to be invalid.

         /// \sa Invalid for more details.

         RedNode(Invalid) { }

       };

       /// Class to represent blue nodes.

       /// This class represents the blue nodes of the graph. It does

       /// not supposed to be used directly, because the nodes can be

       /// represented as Node instances. This class can be used as

       /// template parameter for special map classes.

       class BlueNode : public Node {

       public:

         /// Default constructor

         /// Default constructor.

         /// \warning It sets the object to an undefined value.

         BlueNode() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         BlueNode(const BlueNode&) : Node() { }

         /// %Invalid constructor \& conversion.

         /// Initializes the object to be invalid.

         /// \sa Invalid for more details.

         BlueNode(Invalid) { }

       };

       /// Iterator class for the red nodes.

       /// This iterator goes through each red node of the graph.

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

       /// of red nodes in a graph \c g of type \c %BpGraph like this:

       ///\code

       /// int count=0;

       /// for (BpGraph::RedNodeIt n(g); n!=INVALID; ++n) ++count;

       ///\endcode

       class RedNodeIt : public RedNode {

       public:

         /// Default constructor

         /// Default constructor.

         /// \warning It sets the iterator to an undefined value.

         RedNodeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         RedNodeIt(const RedNodeIt& n) : RedNode(n) { }

         /// %Invalid constructor \& conversion.

         /// Initializes the iterator to be invalid.

         /// \sa Invalid for more details.

         RedNodeIt(Invalid) { }

         /// Sets the iterator to the first red node.

         /// Sets the iterator to the first red node of the given

         /// digraph.

         explicit RedNodeIt(const BpGraph&) { }

         /// Sets the iterator to the given red node.

         /// Sets the iterator to the given red node of the given

         /// digraph.

         RedNodeIt(const BpGraph&, const RedNode&) { }

         /// Next node.

         /// Assign the iterator to the next red node.

         ///

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

       };

       /// Iterator class for the blue nodes.

       /// This iterator goes through each blue node of the graph.

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

       /// of blue nodes in a graph \c g of type \c %BpGraph like this:

       ///\code

       /// int count=0;

       /// for (BpGraph::BlueNodeIt n(g); n!=INVALID; ++n) ++count;

       ///\endcode

       class BlueNodeIt : public BlueNode {

       public:

         /// Default constructor

         /// Default constructor.

         /// \warning It sets the iterator to an undefined value.

         BlueNodeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         BlueNodeIt(const BlueNodeIt& n) : BlueNode(n) { }

         /// %Invalid constructor \& conversion.

         /// Initializes the iterator to be invalid.

         /// \sa Invalid for more details.

         BlueNodeIt(Invalid) { }

         /// Sets the iterator to the first blue node.

         /// Sets the iterator to the first blue node of the given

         /// digraph.

         explicit BlueNodeIt(const BpGraph&) { }

         /// Sets the iterator to the given blue node.

         /// Sets the iterator to the given blue node of the given

         /// digraph.

         BlueNodeIt(const BpGraph&, const BlueNode&) { }

         /// Next node.

         /// Assign the iterator to the next blue node.

         ///

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

       };

       /// Iterator class for the nodes.

       /// This iterator goes through each node of the graph.

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

       /// of nodes in a graph \c g of type \c %BpGraph like this:

       ///\code

       /// int count=0;

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

       ///\endcode

       class NodeIt : public Node {

       public:

         /// Default constructor

         /// Default constructor.

         /// \warning It sets the iterator to an undefined value.

         NodeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

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

         /// %Invalid constructor \& conversion.

         /// Initializes 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 the given digraph.

         ///

         explicit NodeIt(const BpGraph&) { }

         /// Sets the iterator to the given node.

         /// Sets the iterator to the given node of the given digraph.

         ///

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

         /// Next node.

         /// Assign the iterator to the next node.

         ///

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

       };

       /// The edge type of the graph

       /// This class identifies an edge of the graph. It also serves

       /// as a base class of the edge iterators,

       /// thus they will convert to this type.

       class Edge {

       public:

         /// Default constructor

         /// Default constructor.

         /// \warning It sets the object to an undefined value.

         Edge() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         Edge(const Edge&) { }

         /// %Invalid constructor \& conversion.

         /// Initializes the object to be invalid.

         /// \sa Invalid for more details.

         Edge(Invalid) { }

         /// Equality operator

         /// Equality operator.

         ///

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

         /// same object or both are \c INVALID.

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

         /// Inequality operator

         /// Inequality operator.

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

         /// Artificial ordering operator.

         /// Artificial ordering operator.

         ///

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

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

         /// ordering of the edges.

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

       };

       /// Iterator class for the edges.

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

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

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

       ///\code

       /// int count=0;

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

       ///\endcode

       class EdgeIt : public Edge {

       public:

         /// Default constructor

         /// Default constructor.

         /// \warning It sets the iterator to an undefined value.

         EdgeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

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

         /// %Invalid constructor \& conversion.

         /// Initializes the iterator to be invalid.

         /// \sa Invalid for more details.

         EdgeIt(Invalid) { }

         /// Sets the iterator to the first edge.

         /// Sets the iterator to the first edge of the given graph.

         ///

         explicit EdgeIt(const BpGraph&) { }

         /// Sets the iterator to the given edge.

         /// Sets the iterator to the given edge of the given graph.

         ///

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

         /// Next edge

         /// Assign the iterator to the next edge.

         ///

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

       };

       /// Iterator class for the incident 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. the number of incident edges) of a node \c n

       /// in a graph \c g of type \c %BpGraph as follows.

       ///

       ///\code

       /// int count=0;

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

       ///\endcode

       ///

       /// \warning Loop edges will be iterated twice.

       class IncEdgeIt : public Edge {

       public:

         /// Default constructor

         /// Default constructor.

         /// \warning It sets the iterator to an undefined value.

         IncEdgeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

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

         /// %Invalid constructor \& conversion.

         /// Initializes the iterator to be invalid.

         /// \sa Invalid for more details.

         IncEdgeIt(Invalid) { }

         /// Sets the iterator to the first incident edge.

         /// Sets the iterator to the first incident edge of the given node.

         ///

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

         /// Sets the iterator to the given edge.

         /// Sets the iterator to the given edge of the given graph.

         ///

         IncEdgeIt(const BpGraph&, const Edge&) { }

         /// Next incident edge

         /// Assign the iterator to the next incident edge

         /// of the corresponding node.

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

       };

       /// The arc type of the graph

       /// This class identifies a directed arc of the graph. It also serves

       /// as a base class of the arc iterators,

       /// thus they will convert to this type.

       class Arc {

       public:

         /// Default constructor

         /// Default constructor.

         /// \warning It sets the object to an undefined value.

         Arc() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         Arc(const Arc&) { }

         /// %Invalid constructor \& conversion.

         /// Initializes the object to be invalid.

         /// \sa Invalid for more details.

         Arc(Invalid) { }

         /// Equality operator

         /// Equality operator.

         ///

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

         /// same object or both are \c INVALID.

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

         /// Inequality operator

         /// Inequality operator.

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

         /// Artificial ordering operator.

         /// Artificial ordering operator.

         ///

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

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

         /// ordering of the arcs.

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

         /// Converison to \c Edge

         /// Converison to \c Edge.

         ///

         operator Edge() const { return Edge(); }

       };

       /// Iterator class for the arcs.

       /// This iterator goes through each directed arc of the graph.

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

       /// of arcs in a graph \c g of type \c %BpGraph as follows:

       ///\code

       /// int count=0;

       /// for(BpGraph::ArcIt a(g); a!=INVALID; ++a) ++count;

       ///\endcode

       class ArcIt : public Arc {

       public:

         /// Default constructor

         /// Default constructor.

         /// \warning It sets the iterator to an undefined value.

         ArcIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         ArcIt(const ArcIt& e) : Arc(e) { }

         /// %Invalid constructor \& conversion.

         /// Initializes the iterator to be invalid.

         /// \sa Invalid for more details.

         ArcIt(Invalid) { }

         /// Sets the iterator to the first arc.

         /// Sets the iterator to the first arc of the given graph.

         ///

         explicit ArcIt(const BpGraph &g)

         {

           ::lemon::ignore_unused_variable_warning(g);

         }

         /// Sets the iterator to the given arc.

         /// Sets the iterator to the given arc of the given graph.

         ///

         ArcIt(const BpGraph&, const Arc&) { }

         /// Next arc

         /// Assign the iterator to the next arc.

         ///

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

       };

       /// Iterator class for the outgoing arcs of a node.

       /// This iterator goes trough the \e outgoing directed arcs of a

       /// certain node of a graph.

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

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

       /// in a graph \c g of type \c %BpGraph as follows.

       ///\code

       /// int count=0;

       /// for (Digraph::OutArcIt a(g, n); a!=INVALID; ++a) ++count;

       ///\endcode

       class OutArcIt : public Arc {

       public:

         /// Default constructor

         /// Default constructor.

         /// \warning It sets the iterator to an undefined value.

         OutArcIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         OutArcIt(const OutArcIt& e) : Arc(e) { }

         /// %Invalid constructor \& conversion.

         /// Initializes the iterator to be invalid.

         /// \sa Invalid for more details.

         OutArcIt(Invalid) { }

         /// Sets the iterator to the first outgoing arc.

         /// Sets the iterator to the first outgoing arc of the given node.

         ///

         OutArcIt(const BpGraph& n, const Node& g) {

           ::lemon::ignore_unused_variable_warning(n);

           ::lemon::ignore_unused_variable_warning(g);

         }

         /// Sets the iterator to the given arc.

         /// Sets the iterator to the given arc of the given graph.

         ///

         OutArcIt(const BpGraph&, const Arc&) { }

         /// Next outgoing arc

         /// Assign the iterator to the next

         /// outgoing arc of the corresponding node.

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

       };

       /// Iterator class for the incoming arcs of a node.

       /// This iterator goes trough the \e incoming directed arcs of a

       /// certain node of a graph.

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

       /// of incoming arcs of a node \c n

       /// in a graph \c g of type \c %BpGraph as follows.

       ///\code

       /// int count=0;

       /// for (Digraph::InArcIt a(g, n); a!=INVALID; ++a) ++count;

       ///\endcode

       class InArcIt : public Arc {

       public:

         /// Default constructor

         /// Default constructor.

         /// \warning It sets the iterator to an undefined value.

         InArcIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         InArcIt(const InArcIt& e) : Arc(e) { }

         /// %Invalid constructor \& conversion.

         /// Initializes the iterator to be invalid.

         /// \sa Invalid for more details.

         InArcIt(Invalid) { }

         /// Sets the iterator to the first incoming arc.

         /// Sets the iterator to the first incoming arc of the given node.

         ///

         InArcIt(const BpGraph& g, const Node& n) {

           ::lemon::ignore_unused_variable_warning(n);

           ::lemon::ignore_unused_variable_warning(g);

         }

         /// Sets the iterator to the given arc.

         /// Sets the iterator to the given arc of the given graph.

         ///

         InArcIt(const BpGraph&, const Arc&) { }

         /// Next incoming arc

         /// Assign the iterator to the next

         /// incoming arc of the corresponding node.

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

       };

       /// \brief Standard graph map type for the nodes.

       ///

       /// Standard graph map type for the nodes.

       /// It conforms to the ReferenceMap concept.

       template<class T>

       class NodeMap : public ReferenceMap<Node, T, T&, const T&>

       {

       public:

         /// Constructor

         explicit NodeMap(const BpGraph&) { }

         /// Constructor with given initial value

         NodeMap(const BpGraph&, T) { }

       private:

         ///Copy constructor

         NodeMap(const NodeMap& nm) :

           ReferenceMap<Node, T, T&, const T&>(nm) { }

         ///Assignment operator

         template <typename CMap>

         NodeMap& operator=(const CMap&) {

           checkConcept<ReadMap<Node, T>, CMap>();

           return *this;

         }

       };

       /// \brief Standard graph map type for the red nodes.

       ///

       /// Standard graph map type for the red nodes.

       /// It conforms to the ReferenceMap concept.

       template<class T>

       class RedNodeMap : public ReferenceMap<Node, T, T&, const T&>

       {

       public:

         /// Constructor

         explicit RedNodeMap(const BpGraph&) { }

         /// Constructor with given initial value

         RedNodeMap(const BpGraph&, T) { }

       private:

         ///Copy constructor

         RedNodeMap(const RedNodeMap& nm) :

           ReferenceMap<Node, T, T&, const T&>(nm) { }

         ///Assignment operator

         template <typename CMap>

         RedNodeMap& operator=(const CMap&) {

           checkConcept<ReadMap<Node, T>, CMap>();

           return *this;

         }

       };

       /// \brief Standard graph map type for the blue nodes.

       ///

       /// Standard graph map type for the blue nodes.

       /// It conforms to the ReferenceMap concept.

       template<class T>

       class BlueNodeMap : public ReferenceMap<Node, T, T&, const T&>

       {

       public:

         /// Constructor

         explicit BlueNodeMap(const BpGraph&) { }

         /// Constructor with given initial value

         BlueNodeMap(const BpGraph&, T) { }

       private:

         ///Copy constructor

         BlueNodeMap(const BlueNodeMap& nm) :

           ReferenceMap<Node, T, T&, const T&>(nm) { }

         ///Assignment operator

         template <typename CMap>

         BlueNodeMap& operator=(const CMap&) {

           checkConcept<ReadMap<Node, T>, CMap>();

           return *this;

         }

       };

       /// \brief Standard graph map type for the arcs.

       ///

       /// Standard graph map type for the arcs.

       /// It conforms to the ReferenceMap concept.

       template<class T>

       class ArcMap : public ReferenceMap<Arc, T, T&, const T&>

       {

       public:

         /// Constructor

         explicit ArcMap(const BpGraph&) { }

         /// Constructor with given initial value

         ArcMap(const BpGraph&, T) { }

       private:

         ///Copy constructor

         ArcMap(const ArcMap& em) :

           ReferenceMap<Arc, T, T&, const T&>(em) { }

         ///Assignment operator

         template <typename CMap>

         ArcMap& operator=(const CMap&) {

           checkConcept<ReadMap<Arc, T>, CMap>();

           return *this;

         }

       };

       /// \brief Standard graph map type for the edges.

       ///

       /// Standard graph map type for the edges.

       /// It conforms to the ReferenceMap concept.

       template<class T>

       class EdgeMap : public ReferenceMap<Edge, T, T&, const T&>

       {

       public:

         /// Constructor

         explicit EdgeMap(const BpGraph&) { }

         /// Constructor with given initial value

         EdgeMap(const BpGraph&, T) { }

       private:

         ///Copy constructor

         EdgeMap(const EdgeMap& em) :

           ReferenceMap<Edge, T, T&, const T&>(em) {}

         ///Assignment operator

         template <typename CMap>

         EdgeMap& operator=(const CMap&) {

           checkConcept<ReadMap<Edge, T>, CMap>();

           return *this;

         }

       };

       /// \brief Gives back %true for red nodes.

       ///

       /// Gives back %true for red nodes.

       bool red(const Node&) const { return true; }

       /// \brief Gives back %true for blue nodes.

       ///

       /// Gives back %true for blue nodes.

       bool blue(const Node&) const { return true; }

       /// \brief Converts the node to red node object.

       ///

       /// This function converts unsafely the node to red node

       /// object. It should be called only if the node is from the red

       /// partition or INVALID.

       RedNode asRedNodeUnsafe(const Node&) const { return RedNode(); }

       /// \brief Converts the node to blue node object.

       ///

       /// This function converts unsafely the node to blue node

       /// object. It should be called only if the node is from the red

       /// partition or INVALID.

       BlueNode asBlueNodeUnsafe(const Node&) const { return BlueNode(); }

       /// \brief Converts the node to red node object.

       ///

       /// This function converts safely the node to red node

       /// object. If the node is not from the red partition, then it

       /// returns INVALID.

       RedNode asRedNode(const Node&) const { return RedNode(); }

       /// \brief Converts the node to blue node object.

       ///

       /// This function converts unsafely the node to blue node

       /// object. If the node is not from the blue partition, then it

       /// returns INVALID.

       BlueNode asBlueNode(const Node&) const { return BlueNode(); }

       /// \brief Gives back the red end node of the edge.

       ///

       /// Gives back the red end node of the edge.

       RedNode redNode(const Edge&) const { return RedNode(); }

       /// \brief Gives back the blue end node of the edge.

       ///

       /// Gives back the blue end node of the edge.

       BlueNode blueNode(const Edge&) const { return BlueNode(); }

       /// \brief The first node of the edge.

       ///

       /// It is a synonim for the \c redNode().

       Node u(Edge) const { return INVALID; }

       /// \brief The second node of the edge.

       ///

       /// It is a synonim for the \c blueNode().

       Node v(Edge) const { return INVALID; }

       /// \brief The source node of the arc.

       ///

       /// Returns the source node of the given arc.

       Node source(Arc) const { return INVALID; }

       /// \brief The target node of the arc.

       ///

       /// Returns the target node of the given arc.

       Node target(Arc) const { return INVALID; }

       /// \brief The ID of the node.

       ///

       /// Returns the ID of the given node.

       int id(Node) const { return -1; }

       /// \brief The red ID of the node.

       ///

       /// Returns the red ID of the given node.

       int id(RedNode) const { return -1; }

       /// \brief The blue ID of the node.

       ///

       /// Returns the blue ID of the given node.

       int id(BlueNode) const { return -1; }

       /// \brief The ID of the edge.

       ///

       /// Returns the ID of the given edge.

       int id(Edge) const { return -1; }

       /// \brief The ID of the arc.

       ///

       /// Returns the ID of the given arc.

       int id(Arc) const { return -1; }

       /// \brief The node with the given ID.

       ///

       /// Returns the node with the given ID.

       /// \pre The argument should be a valid node ID in the graph.

       Node nodeFromId(int) const { return INVALID; }

       /// \brief The edge with the given ID.

       ///

       /// Returns the edge with the given ID.

       /// \pre The argument should be a valid edge ID in the graph.

       Edge edgeFromId(int) const { return INVALID; }

       /// \brief The arc with the given ID.

       ///

       /// Returns the arc with the given ID.

       /// \pre The argument should be a valid arc ID in the graph.

       Arc arcFromId(int) const { return INVALID; }

       /// \brief An upper bound on the node IDs.

       ///

       /// Returns an upper bound on the node IDs.

       int maxNodeId() const { return -1; }

       /// \brief An upper bound on the red IDs.

       ///

       /// Returns an upper bound on the red IDs.

       int maxRedId() const { return -1; }

       /// \brief An upper bound on the blue IDs.

       ///

       /// Returns an upper bound on the blue IDs.

       int maxBlueId() const { return -1; }

       /// \brief An upper bound on the edge IDs.

       ///

       /// Returns an upper bound on the edge IDs.

       int maxEdgeId() const { return -1; }

       /// \brief An upper bound on the arc IDs.

       ///

       /// Returns an upper bound on the arc IDs.

       int maxArcId() const { return -1; }

       /// \brief The direction of the arc.

       ///

       /// Returns \c true if the given arc goes from a red node to a blue node.

       bool direction(Arc) const { return true; }

       /// \brief Direct the edge.

       ///

       /// Direct the given edge. The returned arc

       /// represents the given edge and its direction comes

       /// from the bool parameter. If it is \c true, then the source of the node

       /// will be a red node.

       Arc direct(Edge, bool) const {

         return INVALID;

       }

       /// \brief Direct the edge.

       ///

       /// Direct the given edge. The returned arc represents the given

       /// edge and its source node is the given node.

       Arc direct(Edge, Node) const {

         return INVALID;

       }

       /// \brief The oppositely directed arc.

       ///

       /// Returns the oppositely directed arc representing the same edge.

       Arc oppositeArc(Arc) const { return INVALID; }

       /// \brief The opposite node on the edge.

       ///

       /// Returns the opposite node on the given edge.

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

       void first(Node&) const {}

       void next(Node&) const {}

       void firstRed(RedNode&) const {}

       void nextRed(RedNode&) const {}

       void firstBlue(BlueNode&) const {}

       void nextBlue(BlueNode&) const {}

       void first(Edge&) const {}

       void next(Edge&) const {}

       void first(Arc&) const {}

       void next(Arc&) const {}

       void firstOut(Arc&, Node) const {}

       void nextOut(Arc&) const {}

       void firstIn(Arc&, Node) const {}

       void nextIn(Arc&) const {}

       void firstInc(Edge &, bool &, const Node &) const {}

       void nextInc(Edge &, bool &) const {}

       // The second parameter is dummy.

       Node fromId(int, Node) const { return INVALID; }

       // The second parameter is dummy.

       Edge fromId(int, Edge) const { return INVALID; }

       // The second parameter is dummy.

       Arc fromId(int, Arc) const { return INVALID; }

       // Dummy parameter.

       int maxId(Node) const { return -1; }

       // Dummy parameter.

       int maxId(RedNode) const { return -1; }

       // Dummy parameter.

       int maxId(BlueNode) const { return -1; }

       // Dummy parameter.

       int maxId(Edge) const { return -1; }

       // Dummy parameter.

       int maxId(Arc) const { return -1; }

       /// \brief The base node of the iterator.

       ///

       /// Returns the base node of the given incident edge iterator.

       Node baseNode(IncEdgeIt) const { return INVALID; }

       /// \brief The running node of the iterator.

       ///

       /// Returns the running node of the given incident edge iterator.

       Node runningNode(IncEdgeIt) const { return INVALID; }

       /// \brief The base node of the iterator.

       ///

       /// Returns the base node of the given outgoing arc iterator

       /// (i.e. the source node of the corresponding arc).

       Node baseNode(OutArcIt) const { return INVALID; }

       /// \brief The running node of the iterator.

       ///

       /// Returns the running node of the given outgoing arc iterator

       /// (i.e. the target node of the corresponding arc).

       Node runningNode(OutArcIt) const { return INVALID; }

       /// \brief The base node of the iterator.

       ///

       /// Returns the base node of the given incoming arc iterator

       /// (i.e. the target node of the corresponding arc).

       Node baseNode(InArcIt) const { return INVALID; }

       /// \brief The running node of the iterator.

       ///

       /// Returns the running node of the given incoming arc iterator

       /// (i.e. the source node of the corresponding arc).

       Node runningNode(InArcIt) const { return INVALID; }

       template <typename _BpGraph>

       struct Constraints {

         void constraints() {

           checkConcept<BaseBpGraphComponent, _BpGraph>();

           checkConcept<IterableBpGraphComponent<>, _BpGraph>();

           checkConcept<IDableBpGraphComponent<>, _BpGraph>();

           checkConcept<MappableBpGraphComponent<>, _BpGraph>();

         }

       };

     };

   }

 }

 #endif