alpar@209: /* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@57:  *
alpar@209:  * This file is a part of LEMON, a generic C++ optimization library.
deba@57:  *
alpar@440:  * Copyright (C) 2003-2009
deba@57:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@57:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@57:  *
deba@57:  * Permission to use, modify and distribute this software is granted
deba@57:  * provided that this copyright notice appears in all copies. For
deba@57:  * precise terms see the accompanying LICENSE file.
deba@57:  *
deba@57:  * This software is provided "AS IS" with no warranty of any kind,
deba@57:  * express or implied, and with no claim as to its suitability for any
deba@57:  * purpose.
deba@57:  *
deba@57:  */
deba@57: 
deba@57: ///\ingroup graph_concepts
deba@57: ///\file
deba@57: ///\brief The concept of Undirected Graphs.
deba@57: 
deba@514: #ifndef LEMON_CONCEPTS_GRAPH_H
deba@514: #define LEMON_CONCEPTS_GRAPH_H
deba@57: 
deba@57: #include <lemon/concepts/graph_components.h>
deba@220: #include <lemon/core.h>
deba@57: 
deba@57: namespace lemon {
deba@57:   namespace concepts {
deba@57: 
deba@57:     /// \ingroup graph_concepts
deba@57:     ///
deba@57:     /// \brief Class describing the concept of Undirected Graphs.
deba@57:     ///
deba@57:     /// This class describes the common interface of all Undirected
deba@57:     /// Graphs.
deba@57:     ///
deba@57:     /// As all concept describing classes it provides only interface
deba@57:     /// without any sensible implementation. So any algorithm for
deba@57:     /// undirected graph should compile with this class, but it will not
deba@57:     /// run properly, of course.
deba@57:     ///
deba@57:     /// The LEMON undirected graphs also fulfill the concept of
deba@57:     /// directed graphs (\ref lemon::concepts::Digraph "Digraph
deba@57:     /// Concept"). Each edges can be seen as two opposite
deba@57:     /// directed arc and consequently the undirected graph can be
deba@57:     /// seen as the direceted graph of these directed arcs. The
deba@57:     /// Graph has the Edge inner class for the edges and
deba@57:     /// the Arc type for the directed arcs. The Arc type is
deba@57:     /// convertible to Edge or inherited from it so from a directed
deba@57:     /// arc we can get the represented edge.
deba@57:     ///
deba@57:     /// In the sense of the LEMON each edge has a default
deba@57:     /// direction (it should be in every computer implementation,
deba@57:     /// because the order of edge's nodes defines an
deba@57:     /// orientation). With the default orientation we can define that
deba@57:     /// the directed arc is forward or backward directed. With the \c
deba@57:     /// direction() and \c direct() function we can get the direction
deba@57:     /// of the directed arc and we can direct an edge.
deba@57:     ///
deba@57:     /// The EdgeIt is an iterator for the edges. We can use
deba@57:     /// the EdgeMap to map values for the edges. The InArcIt and
deba@57:     /// OutArcIt iterates on the same edges but with opposite
deba@78:     /// direction. The IncEdgeIt iterates also on the same edges
deba@57:     /// as the OutArcIt and InArcIt but it is not convertible to Arc just
alpar@209:     /// to Edge.
deba@57:     class Graph {
deba@57:     public:
deba@57:       /// \brief The undirected graph should be tagged by the
deba@57:       /// UndirectedTag.
deba@57:       ///
deba@57:       /// The undirected graph should be tagged by the UndirectedTag. This
alpar@209:       /// tag helps the enable_if technics to make compile time
alpar@209:       /// specializations for undirected graphs.
deba@57:       typedef True UndirectedTag;
deba@57: 
alpar@209:       /// \brief The base type of node iterators,
deba@57:       /// or in other words, the trivial node iterator.
deba@57:       ///
deba@57:       /// This is the base type of each node iterator,
deba@57:       /// thus each kind of node iterator converts to this.
alpar@209:       /// More precisely each kind of node iterator should be inherited
deba@57:       /// from the trivial node iterator.
deba@57:       class Node {
deba@57:       public:
deba@57:         /// Default constructor
deba@57: 
deba@57:         /// @warning The default constructor sets the iterator
deba@57:         /// to an undefined value.
deba@57:         Node() { }
deba@57:         /// Copy constructor.
deba@57: 
deba@57:         /// Copy constructor.
deba@57:         ///
deba@57:         Node(const Node&) { }
deba@57: 
deba@57:         /// Invalid constructor \& conversion.
deba@57: 
deba@57:         /// This constructor initializes the iterator to be invalid.
deba@57:         /// \sa Invalid for more details.
deba@57:         Node(Invalid) { }
deba@57:         /// Equality operator
deba@57: 
deba@57:         /// Two iterators are equal if and only if they point to the
deba@57:         /// same object or both are invalid.
deba@57:         bool operator==(Node) const { return true; }
deba@57: 
deba@57:         /// Inequality operator
alpar@209: 
deba@57:         /// \sa operator==(Node n)
deba@57:         ///
deba@57:         bool operator!=(Node) const { return true; }
deba@57: 
alpar@209:         /// Artificial ordering operator.
alpar@209: 
alpar@209:         /// To allow the use of graph descriptors as key type in std::map or
alpar@209:         /// similar associative container we require this.
alpar@209:         ///
alpar@209:         /// \note This operator only have to define some strict ordering of
alpar@209:         /// the items; this order has nothing to do with the iteration
alpar@209:         /// ordering of the items.
alpar@209:         bool operator<(Node) const { return false; }
deba@57: 
deba@57:       };
alpar@209: 
deba@57:       /// This iterator goes through each node.
deba@57: 
deba@57:       /// This iterator goes through each node.
deba@57:       /// Its usage is quite simple, for example you can count the number
deba@57:       /// of nodes in graph \c g of type \c Graph like this:
deba@57:       ///\code
deba@57:       /// int count=0;
deba@57:       /// for (Graph::NodeIt n(g); n!=INVALID; ++n) ++count;
deba@57:       ///\endcode
deba@57:       class NodeIt : public Node {
deba@57:       public:
deba@57:         /// Default constructor
deba@57: 
deba@57:         /// @warning The default constructor sets the iterator
deba@57:         /// to an undefined value.
deba@57:         NodeIt() { }
deba@57:         /// Copy constructor.
alpar@209: 
deba@57:         /// Copy constructor.
deba@57:         ///
deba@57:         NodeIt(const NodeIt& n) : Node(n) { }
deba@57:         /// Invalid constructor \& conversion.
deba@57: 
deba@57:         /// Initialize the iterator to be invalid.
deba@57:         /// \sa Invalid for more details.
deba@57:         NodeIt(Invalid) { }
deba@57:         /// Sets the iterator to the first node.
deba@57: 
deba@57:         /// Sets the iterator to the first node of \c g.
deba@57:         ///
deba@57:         NodeIt(const Graph&) { }
deba@57:         /// Node -> NodeIt conversion.
deba@57: 
alpar@209:         /// Sets the iterator to the node of \c the graph pointed by
alpar@209:         /// the trivial iterator.
alpar@209:         /// This feature necessitates that each time we
deba@57:         /// iterate the arc-set, the iteration order is the same.
deba@57:         NodeIt(const Graph&, const Node&) { }
deba@57:         /// Next node.
deba@57: 
deba@57:         /// Assign the iterator to the next node.
deba@57:         ///
deba@57:         NodeIt& operator++() { return *this; }
deba@57:       };
alpar@209: 
alpar@209: 
deba@57:       /// The base type of the edge iterators.
deba@57: 
deba@57:       /// The base type of the edge iterators.
deba@57:       ///
deba@57:       class Edge {
deba@57:       public:
deba@57:         /// Default constructor
deba@57: 
deba@57:         /// @warning The default constructor sets the iterator
deba@57:         /// to an undefined value.
deba@57:         Edge() { }
deba@57:         /// Copy constructor.
deba@57: 
deba@57:         /// Copy constructor.
deba@57:         ///
deba@57:         Edge(const Edge&) { }
deba@57:         /// Initialize the iterator to be invalid.
deba@57: 
deba@57:         /// Initialize the iterator to be invalid.
deba@57:         ///
deba@57:         Edge(Invalid) { }
deba@57:         /// Equality operator
deba@57: 
deba@57:         /// Two iterators are equal if and only if they point to the
deba@57:         /// same object or both are invalid.
deba@57:         bool operator==(Edge) const { return true; }
deba@57:         /// Inequality operator
deba@57: 
deba@57:         /// \sa operator==(Edge n)
deba@57:         ///
deba@57:         bool operator!=(Edge) const { return true; }
deba@57: 
alpar@209:         /// Artificial ordering operator.
alpar@209: 
alpar@209:         /// To allow the use of graph descriptors as key type in std::map or
alpar@209:         /// similar associative container we require this.
alpar@209:         ///
alpar@209:         /// \note This operator only have to define some strict ordering of
alpar@209:         /// the items; this order has nothing to do with the iteration
alpar@209:         /// ordering of the items.
alpar@209:         bool operator<(Edge) const { return false; }
deba@57:       };
deba@57: 
deba@57:       /// This iterator goes through each edge.
deba@57: 
deba@57:       /// This iterator goes through each edge of a graph.
deba@57:       /// Its usage is quite simple, for example you can count the number
deba@57:       /// of edges in a graph \c g of type \c Graph as follows:
deba@57:       ///\code
deba@57:       /// int count=0;
deba@57:       /// for(Graph::EdgeIt e(g); e!=INVALID; ++e) ++count;
deba@57:       ///\endcode
deba@57:       class EdgeIt : public Edge {
deba@57:       public:
deba@57:         /// Default constructor
deba@57: 
deba@57:         /// @warning The default constructor sets the iterator
deba@57:         /// to an undefined value.
deba@57:         EdgeIt() { }
deba@57:         /// Copy constructor.
deba@57: 
deba@57:         /// Copy constructor.
deba@57:         ///
deba@57:         EdgeIt(const EdgeIt& e) : Edge(e) { }
deba@57:         /// Initialize the iterator to be invalid.
deba@57: 
deba@57:         /// Initialize the iterator to be invalid.
deba@57:         ///
deba@57:         EdgeIt(Invalid) { }
deba@57:         /// This constructor sets the iterator to the first edge.
alpar@209: 
deba@57:         /// This constructor sets the iterator to the first edge.
deba@57:         EdgeIt(const Graph&) { }
deba@57:         /// Edge -> EdgeIt conversion
deba@57: 
deba@57:         /// Sets the iterator to the value of the trivial iterator.
deba@57:         /// This feature necessitates that each time we
alpar@209:         /// iterate the edge-set, the iteration order is the
alpar@209:         /// same.
alpar@209:         EdgeIt(const Graph&, const Edge&) { }
deba@57:         /// Next edge
alpar@209: 
deba@57:         /// Assign the iterator to the next edge.
deba@57:         EdgeIt& operator++() { return *this; }
deba@57:       };
deba@57: 
alpar@209:       /// \brief This iterator goes trough the incident undirected
deba@57:       /// arcs of a node.
deba@57:       ///
deba@57:       /// This iterator goes trough the incident edges
alpar@209:       /// of a certain node of a graph. You should assume that the
deba@57:       /// loop arcs will be iterated twice.
alpar@209:       ///
deba@57:       /// Its usage is quite simple, for example you can compute the
deba@57:       /// degree (i.e. count the number of incident arcs of a node \c n
alpar@209:       /// in graph \c g of type \c Graph as follows.
deba@57:       ///
deba@57:       ///\code
deba@57:       /// int count=0;
deba@78:       /// for(Graph::IncEdgeIt e(g, n); e!=INVALID; ++e) ++count;
deba@57:       ///\endcode
deba@78:       class IncEdgeIt : public Edge {
deba@57:       public:
deba@57:         /// Default constructor
deba@57: 
deba@57:         /// @warning The default constructor sets the iterator
deba@57:         /// to an undefined value.
deba@78:         IncEdgeIt() { }
deba@57:         /// Copy constructor.
deba@57: 
deba@57:         /// Copy constructor.
deba@57:         ///
deba@78:         IncEdgeIt(const IncEdgeIt& e) : Edge(e) { }
deba@57:         /// Initialize the iterator to be invalid.
deba@57: 
deba@57:         /// Initialize the iterator to be invalid.
deba@57:         ///
deba@78:         IncEdgeIt(Invalid) { }
deba@57:         /// This constructor sets the iterator to first incident arc.
alpar@209: 
deba@57:         /// This constructor set the iterator to the first incident arc of
deba@57:         /// the node.
deba@78:         IncEdgeIt(const Graph&, const Node&) { }
deba@78:         /// Edge -> IncEdgeIt conversion
deba@57: 
deba@57:         /// Sets the iterator to the value of the trivial iterator \c e.
alpar@209:         /// This feature necessitates that each time we
deba@57:         /// iterate the arc-set, the iteration order is the same.
deba@78:         IncEdgeIt(const Graph&, const Edge&) { }
deba@57:         /// Next incident arc
deba@57: 
deba@57:         /// Assign the iterator to the next incident arc
alpar@209:         /// of the corresponding node.
deba@78:         IncEdgeIt& operator++() { return *this; }
deba@57:       };
deba@57: 
deba@57:       /// The directed arc type.
deba@57: 
deba@57:       /// The directed arc type. It can be converted to the
deba@57:       /// edge or it should be inherited from the undirected
deba@57:       /// arc.
deba@57:       class Arc : public Edge {
deba@57:       public:
deba@57:         /// Default constructor
deba@57: 
deba@57:         /// @warning The default constructor sets the iterator
deba@57:         /// to an undefined value.
deba@57:         Arc() { }
deba@57:         /// Copy constructor.
deba@57: 
deba@57:         /// Copy constructor.
deba@57:         ///
deba@57:         Arc(const Arc& e) : Edge(e) { }
deba@57:         /// Initialize the iterator to be invalid.
deba@57: 
deba@57:         /// Initialize the iterator to be invalid.
deba@57:         ///
deba@57:         Arc(Invalid) { }
deba@57:         /// Equality operator
deba@57: 
deba@57:         /// Two iterators are equal if and only if they point to the
deba@57:         /// same object or both are invalid.
deba@57:         bool operator==(Arc) const { return true; }
deba@57:         /// Inequality operator
deba@57: 
deba@57:         /// \sa operator==(Arc n)
deba@57:         ///
deba@57:         bool operator!=(Arc) const { return true; }
deba@57: 
alpar@209:         /// Artificial ordering operator.
alpar@209: 
alpar@209:         /// To allow the use of graph descriptors as key type in std::map or
alpar@209:         /// similar associative container we require this.
alpar@209:         ///
alpar@209:         /// \note This operator only have to define some strict ordering of
alpar@209:         /// the items; this order has nothing to do with the iteration
alpar@209:         /// ordering of the items.
alpar@209:         bool operator<(Arc) const { return false; }
alpar@209: 
alpar@209:       };
deba@57:       /// This iterator goes through each directed arc.
deba@57: 
deba@57:       /// This iterator goes through each arc of a graph.
deba@57:       /// Its usage is quite simple, for example you can count the number
deba@57:       /// of arcs in a graph \c g of type \c Graph as follows:
deba@57:       ///\code
deba@57:       /// int count=0;
deba@57:       /// for(Graph::ArcIt e(g); e!=INVALID; ++e) ++count;
deba@57:       ///\endcode
deba@57:       class ArcIt : public Arc {
deba@57:       public:
deba@57:         /// Default constructor
deba@57: 
deba@57:         /// @warning The default constructor sets the iterator
deba@57:         /// to an undefined value.
deba@57:         ArcIt() { }
deba@57:         /// Copy constructor.
deba@57: 
deba@57:         /// Copy constructor.
deba@57:         ///
deba@57:         ArcIt(const ArcIt& e) : Arc(e) { }
deba@57:         /// Initialize the iterator to be invalid.
deba@57: 
deba@57:         /// Initialize the iterator to be invalid.
deba@57:         ///
deba@57:         ArcIt(Invalid) { }
deba@57:         /// This constructor sets the iterator to the first arc.
alpar@209: 
deba@57:         /// This constructor sets the iterator to the first arc of \c g.
deba@57:         ///@param g the graph
deba@57:         ArcIt(const Graph &g) { ignore_unused_variable_warning(g); }
deba@57:         /// Arc -> ArcIt conversion
deba@57: 
deba@57:         /// Sets the iterator to the value of the trivial iterator \c e.
alpar@209:         /// This feature necessitates that each time we
deba@57:         /// iterate the arc-set, the iteration order is the same.
alpar@209:         ArcIt(const Graph&, const Arc&) { }
deba@57:         ///Next arc
alpar@209: 
deba@57:         /// Assign the iterator to the next arc.
deba@57:         ArcIt& operator++() { return *this; }
deba@57:       };
alpar@209: 
deba@57:       /// This iterator goes trough the outgoing directed arcs of a node.
deba@57: 
deba@57:       /// This iterator goes trough the \e outgoing arcs of a certain node
deba@57:       /// of a graph.
deba@57:       /// Its usage is quite simple, for example you can count the number
deba@57:       /// of outgoing arcs of a node \c n
deba@57:       /// in graph \c g of type \c Graph as follows.
deba@57:       ///\code
deba@57:       /// int count=0;
deba@57:       /// for (Graph::OutArcIt e(g, n); e!=INVALID; ++e) ++count;
deba@57:       ///\endcode
alpar@209: 
deba@57:       class OutArcIt : public Arc {
deba@57:       public:
deba@57:         /// Default constructor
deba@57: 
deba@57:         /// @warning The default constructor sets the iterator
deba@57:         /// to an undefined value.
deba@57:         OutArcIt() { }
deba@57:         /// Copy constructor.
deba@57: 
deba@57:         /// Copy constructor.
deba@57:         ///
deba@57:         OutArcIt(const OutArcIt& e) : Arc(e) { }
deba@57:         /// Initialize the iterator to be invalid.
deba@57: 
deba@57:         /// Initialize the iterator to be invalid.
deba@57:         ///
deba@57:         OutArcIt(Invalid) { }
deba@57:         /// This constructor sets the iterator to the first outgoing arc.
alpar@209: 
deba@57:         /// This constructor sets the iterator to the first outgoing arc of
deba@57:         /// the node.
deba@57:         ///@param n the node
deba@57:         ///@param g the graph
deba@57:         OutArcIt(const Graph& n, const Node& g) {
alpar@209:           ignore_unused_variable_warning(n);
alpar@209:           ignore_unused_variable_warning(g);
alpar@209:         }
deba@57:         /// Arc -> OutArcIt conversion
deba@57: 
deba@57:         /// Sets the iterator to the value of the trivial iterator.
alpar@209:         /// This feature necessitates that each time we
deba@57:         /// iterate the arc-set, the iteration order is the same.
deba@57:         OutArcIt(const Graph&, const Arc&) { }
deba@57:         ///Next outgoing arc
alpar@209: 
alpar@209:         /// Assign the iterator to the next
deba@57:         /// outgoing arc of the corresponding node.
deba@57:         OutArcIt& operator++() { return *this; }
deba@57:       };
deba@57: 
deba@57:       /// This iterator goes trough the incoming directed arcs of a node.
deba@57: 
deba@57:       /// This iterator goes trough the \e incoming arcs of a certain node
deba@57:       /// of a graph.
deba@57:       /// Its usage is quite simple, for example you can count the number
deba@57:       /// of outgoing arcs of a node \c n
deba@57:       /// in graph \c g of type \c Graph as follows.
deba@57:       ///\code
deba@57:       /// int count=0;
deba@57:       /// for(Graph::InArcIt e(g, n); e!=INVALID; ++e) ++count;
deba@57:       ///\endcode
deba@57: 
deba@57:       class InArcIt : public Arc {
deba@57:       public:
deba@57:         /// Default constructor
deba@57: 
deba@57:         /// @warning The default constructor sets the iterator
deba@57:         /// to an undefined value.
deba@57:         InArcIt() { }
deba@57:         /// Copy constructor.
deba@57: 
deba@57:         /// Copy constructor.
deba@57:         ///
deba@57:         InArcIt(const InArcIt& e) : Arc(e) { }
deba@57:         /// Initialize the iterator to be invalid.
deba@57: 
deba@57:         /// Initialize the iterator to be invalid.
deba@57:         ///
deba@57:         InArcIt(Invalid) { }
deba@57:         /// This constructor sets the iterator to first incoming arc.
alpar@209: 
deba@57:         /// This constructor set the iterator to the first incoming arc of
deba@57:         /// the node.
deba@57:         ///@param n the node
deba@57:         ///@param g the graph
alpar@209:         InArcIt(const Graph& g, const Node& n) {
alpar@209:           ignore_unused_variable_warning(n);
alpar@209:           ignore_unused_variable_warning(g);
alpar@209:         }
deba@57:         /// Arc -> InArcIt conversion
deba@57: 
deba@57:         /// Sets the iterator to the value of the trivial iterator \c e.
alpar@209:         /// This feature necessitates that each time we
deba@57:         /// iterate the arc-set, the iteration order is the same.
deba@57:         InArcIt(const Graph&, const Arc&) { }
deba@57:         /// Next incoming arc
deba@57: 
deba@57:         /// Assign the iterator to the next inarc of the corresponding node.
deba@57:         ///
deba@57:         InArcIt& operator++() { return *this; }
deba@57:       };
deba@57: 
deba@57:       /// \brief Read write map of the nodes to type \c T.
alpar@209:       ///
deba@57:       /// ReadWrite map of the nodes to type \c T.
deba@57:       /// \sa Reference
alpar@209:       template<class T>
deba@57:       class NodeMap : public ReadWriteMap< Node, T >
deba@57:       {
deba@57:       public:
deba@57: 
deba@57:         ///\e
deba@57:         NodeMap(const Graph&) { }
deba@57:         ///\e
deba@57:         NodeMap(const Graph&, T) { }
deba@57: 
kpeter@263:       private:
deba@57:         ///Copy constructor
deba@57:         NodeMap(const NodeMap& nm) : ReadWriteMap< Node, T >(nm) { }
deba@57:         ///Assignment operator
deba@57:         template <typename CMap>
alpar@209:         NodeMap& operator=(const CMap&) {
deba@57:           checkConcept<ReadMap<Node, T>, CMap>();
alpar@209:           return *this;
deba@57:         }
deba@57:       };
deba@57: 
deba@57:       /// \brief Read write map of the directed arcs to type \c T.
deba@57:       ///
deba@57:       /// Reference map of the directed arcs to type \c T.
deba@57:       /// \sa Reference
alpar@209:       template<class T>
deba@57:       class ArcMap : public ReadWriteMap<Arc,T>
deba@57:       {
deba@57:       public:
deba@57: 
deba@57:         ///\e
deba@57:         ArcMap(const Graph&) { }
deba@57:         ///\e
deba@57:         ArcMap(const Graph&, T) { }
kpeter@263:       private:
deba@57:         ///Copy constructor
deba@57:         ArcMap(const ArcMap& em) : ReadWriteMap<Arc,T>(em) { }
deba@57:         ///Assignment operator
deba@57:         template <typename CMap>
alpar@209:         ArcMap& operator=(const CMap&) {
deba@57:           checkConcept<ReadMap<Arc, T>, CMap>();
alpar@209:           return *this;
deba@57:         }
deba@57:       };
deba@57: 
deba@57:       /// Read write map of the edges to type \c T.
deba@57: 
deba@57:       /// Reference map of the arcs to type \c T.
deba@57:       /// \sa Reference
alpar@209:       template<class T>
deba@57:       class EdgeMap : public ReadWriteMap<Edge,T>
deba@57:       {
deba@57:       public:
deba@57: 
deba@57:         ///\e
deba@57:         EdgeMap(const Graph&) { }
deba@57:         ///\e
deba@57:         EdgeMap(const Graph&, T) { }
kpeter@263:       private:
deba@57:         ///Copy constructor
deba@57:         EdgeMap(const EdgeMap& em) : ReadWriteMap<Edge,T>(em) {}
deba@57:         ///Assignment operator
deba@57:         template <typename CMap>
alpar@209:         EdgeMap& operator=(const CMap&) {
deba@57:           checkConcept<ReadMap<Edge, T>, CMap>();
alpar@209:           return *this;
deba@57:         }
deba@57:       };
deba@57: 
deba@57:       /// \brief Direct the given edge.
deba@57:       ///
deba@57:       /// Direct the given edge. The returned arc source
deba@57:       /// will be the given node.
deba@57:       Arc direct(const Edge&, const Node&) const {
alpar@209:         return INVALID;
deba@57:       }
deba@57: 
deba@57:       /// \brief Direct the given edge.
deba@57:       ///
deba@57:       /// Direct the given edge. The returned arc
deba@57:       /// represents the given edge and the direction comes
deba@57:       /// from the bool parameter. The source of the edge and
deba@57:       /// the directed arc is the same when the given bool is true.
deba@57:       Arc direct(const Edge&, bool) const {
alpar@209:         return INVALID;
deba@57:       }
deba@57: 
deba@57:       /// \brief Returns true if the arc has default orientation.
deba@57:       ///
deba@57:       /// Returns whether the given directed arc is same orientation as
deba@57:       /// the corresponding edge's default orientation.
deba@57:       bool direction(Arc) const { return true; }
deba@57: 
deba@57:       /// \brief Returns the opposite directed arc.
deba@57:       ///
deba@57:       /// Returns the opposite directed arc.
deba@57:       Arc oppositeArc(Arc) const { return INVALID; }
deba@57: 
deba@57:       /// \brief Opposite node on an arc
deba@57:       ///
deba@57:       /// \return the opposite of the given Node on the given Edge
deba@57:       Node oppositeNode(Node, Edge) const { return INVALID; }
deba@57: 
deba@57:       /// \brief First node of the edge.
deba@57:       ///
deba@57:       /// \return the first node of the given Edge.
deba@57:       ///
deba@57:       /// Naturally edges don't have direction and thus
deba@57:       /// don't have source and target node. But we use these two methods
deba@57:       /// to query the two nodes of the arc. The direction of the arc
deba@57:       /// which arises this way is called the inherent direction of the
deba@57:       /// edge, and is used to define the "default" direction
deba@57:       /// of the directed versions of the arcs.
deba@57:       /// \sa direction
deba@57:       Node u(Edge) const { return INVALID; }
deba@57: 
deba@57:       /// \brief Second node of the edge.
deba@57:       Node v(Edge) const { return INVALID; }
deba@57: 
deba@57:       /// \brief Source node of the directed arc.
deba@57:       Node source(Arc) const { return INVALID; }
deba@57: 
deba@57:       /// \brief Target node of the directed arc.
deba@57:       Node target(Arc) const { return INVALID; }
deba@57: 
deba@61:       /// \brief Returns the id of the node.
alpar@209:       int id(Node) const { return -1; }
deba@61: 
deba@61:       /// \brief Returns the id of the edge.
alpar@209:       int id(Edge) const { return -1; }
deba@61: 
deba@61:       /// \brief Returns the id of the arc.
alpar@209:       int id(Arc) const { return -1; }
deba@61: 
deba@61:       /// \brief Returns the node with the given id.
deba@61:       ///
deba@61:       /// \pre The argument should be a valid node id in the graph.
alpar@209:       Node nodeFromId(int) const { return INVALID; }
deba@61: 
deba@61:       /// \brief Returns the edge with the given id.
deba@61:       ///
deba@61:       /// \pre The argument should be a valid edge id in the graph.
alpar@209:       Edge edgeFromId(int) const { return INVALID; }
deba@61: 
deba@61:       /// \brief Returns the arc with the given id.
deba@61:       ///
deba@61:       /// \pre The argument should be a valid arc id in the graph.
alpar@209:       Arc arcFromId(int) const { return INVALID; }
deba@61: 
deba@61:       /// \brief Returns an upper bound on the node IDs.
alpar@209:       int maxNodeId() const { return -1; }
deba@61: 
deba@61:       /// \brief Returns an upper bound on the edge IDs.
alpar@209:       int maxEdgeId() const { return -1; }
deba@61: 
deba@61:       /// \brief Returns an upper bound on the arc IDs.
alpar@209:       int maxArcId() const { return -1; }
deba@61: 
deba@57:       void first(Node&) const {}
deba@57:       void next(Node&) const {}
deba@57: 
deba@57:       void first(Edge&) const {}
deba@57:       void next(Edge&) const {}
deba@57: 
deba@57:       void first(Arc&) const {}
deba@57:       void next(Arc&) const {}
deba@57: 
deba@57:       void firstOut(Arc&, Node) const {}
deba@57:       void nextOut(Arc&) const {}
deba@57: 
deba@57:       void firstIn(Arc&, Node) const {}
deba@57:       void nextIn(Arc&) const {}
deba@57: 
deba@57:       void firstInc(Edge &, bool &, const Node &) const {}
deba@57:       void nextInc(Edge &, bool &) const {}
deba@57: 
deba@61:       // The second parameter is dummy.
deba@61:       Node fromId(int, Node) const { return INVALID; }
deba@61:       // The second parameter is dummy.
deba@61:       Edge fromId(int, Edge) const { return INVALID; }
deba@61:       // The second parameter is dummy.
deba@61:       Arc fromId(int, Arc) const { return INVALID; }
deba@61: 
deba@61:       // Dummy parameter.
alpar@209:       int maxId(Node) const { return -1; }
deba@61:       // Dummy parameter.
alpar@209:       int maxId(Edge) const { return -1; }
deba@61:       // Dummy parameter.
alpar@209:       int maxId(Arc) const { return -1; }
deba@61: 
deba@57:       /// \brief Base node of the iterator
deba@57:       ///
deba@57:       /// Returns the base node (the source in this case) of the iterator
deba@57:       Node baseNode(OutArcIt e) const {
alpar@209:         return source(e);
deba@57:       }
deba@57:       /// \brief Running node of the iterator
deba@57:       ///
deba@57:       /// Returns the running node (the target in this case) of the
deba@57:       /// iterator
deba@57:       Node runningNode(OutArcIt e) const {
alpar@209:         return target(e);
deba@57:       }
deba@57: 
deba@57:       /// \brief Base node of the iterator
deba@57:       ///
deba@57:       /// Returns the base node (the target in this case) of the iterator
deba@57:       Node baseNode(InArcIt e) const {
alpar@209:         return target(e);
deba@57:       }
deba@57:       /// \brief Running node of the iterator
deba@57:       ///
deba@57:       /// Returns the running node (the source in this case) of the
deba@57:       /// iterator
deba@57:       Node runningNode(InArcIt e) const {
alpar@209:         return source(e);
deba@57:       }
deba@57: 
deba@57:       /// \brief Base node of the iterator
deba@57:       ///
deba@57:       /// Returns the base node of the iterator
deba@78:       Node baseNode(IncEdgeIt) const {
alpar@209:         return INVALID;
deba@57:       }
alpar@209: 
deba@57:       /// \brief Running node of the iterator
deba@57:       ///
deba@57:       /// Returns the running node of the iterator
deba@78:       Node runningNode(IncEdgeIt) const {
alpar@209:         return INVALID;
deba@57:       }
deba@57: 
deba@125:       template <typename _Graph>
deba@57:       struct Constraints {
alpar@209:         void constraints() {
alpar@209:           checkConcept<IterableGraphComponent<>, _Graph>();
alpar@209:           checkConcept<IDableGraphComponent<>, _Graph>();
alpar@209:           checkConcept<MappableGraphComponent<>, _Graph>();
alpar@209:         }
deba@57:       };
deba@57: 
deba@57:     };
deba@57: 
deba@57:   }
deba@57: 
deba@57: }
deba@57: 
deba@57: #endif