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

  *

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

  *

  * Copyright (C) 2003-2009

  * 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_CONCEPT_GRAPH_H

 #define LEMON_CONCEPT_GRAPH_H

 #include <lemon/concepts/graph_components.h>

 #include <lemon/concepts/graph.h>

 #include <lemon/core.h>

 namespace lemon {

   namespace concepts {

     /// \ingroup graph_concepts

     ///

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

     ///

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

     /// Graphs.

     ///

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

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

     /// undirected graph should compile with this class, but it will not

     /// run properly, of course.

     ///

     /// The LEMON undirected graphs also fulfill the concept of

     /// directed graphs (\ref lemon::concepts::Digraph "Digraph

     /// Concept"). Each edges can be seen as two opposite

     /// directed arc and consequently the undirected graph can be

     /// seen as the direceted graph of these directed arcs. The

     /// Graph has the Edge inner class for the edges and

     /// the Arc type for the directed arcs. The Arc type is

     /// convertible to Edge or inherited from it so from a directed

     /// arc we can get the represented edge.

     ///

     /// In the sense of the LEMON each edge has a default

     /// direction (it should be in every computer implementation,

     /// because the order of edge's nodes defines an

     /// orientation). With the default orientation we can define that

     /// the directed arc is forward or backward directed. With the \c

     /// direction() and \c direct() function we can get the direction

     /// of the directed arc and we can direct an edge.

     ///

     /// The EdgeIt is an iterator for the edges. We can use

     /// the EdgeMap to map values for the edges. The InArcIt and

     /// OutArcIt iterates on the same edges but with opposite

     /// direction. The IncEdgeIt iterates also on the same edges

     /// as the OutArcIt and InArcIt but it is not convertible to Arc just

     /// to Edge.

     class Graph {

     public:

       /// \brief The undirected graph should be tagged by the

       /// UndirectedTag.

       ///

       /// The undirected graph should be tagged by the UndirectedTag. This

       /// tag helps the enable_if technics to make compile time

       /// specializations for undirected graphs.

       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.

       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.

         bool operator<(Node) 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 Graph&) { }

         /// 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 arc-set, the iteration order is the same.

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

         /// Next node.

         /// Assign the iterator to the next node.

         ///

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

       };

       /// The base type of the edge iterators.

       /// The base type of the edge iterators.

       ///

       class Edge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         Edge() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

         Edge(const Edge&) { }

         /// 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.

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

       };

       /// This iterator goes through each 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.

         EdgeIt(const Graph&) { }

         /// Edge -> EdgeIt 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.

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

         /// Next edge

         /// Assign the iterator to the next edge.

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

       };

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

       /// arcs of a node.

       ///

       /// This iterator goes trough the incident edges

       /// of a certain node of a graph. You should assume that the

       /// loop arcs will be iterated twice.

       ///

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

       /// degree (i.e. count the number of incident arcs 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 Edge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         IncEdgeIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

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

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         IncEdgeIt(Invalid) { }

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

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

         /// the node.

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

         /// Edge -> IncEdgeIt conversion

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

         /// This feature necessitates that each time we

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

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

         /// Next incident arc

         /// Assign the iterator to the next incident arc

         /// of the corresponding node.

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

       };

       /// The directed arc type.

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

       /// edge or it should be inherited from the undirected

       /// arc.

       class Arc : public Edge {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         Arc() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

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

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         Arc(Invalid) { }

         /// Equality operator

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

         /// same object or both are invalid.

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

         /// Inequality operator

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

         ///

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

       };

       /// This iterator goes through each directed arc.

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

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

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

       ///\code

       /// int count=0;

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

       ///\endcode

       class ArcIt : public Arc {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         ArcIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

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

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         ArcIt(Invalid) { }

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

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

         ///@param g the graph

         ArcIt(const Graph &g) { ignore_unused_variable_warning(g); }

         /// Arc -> ArcIt conversion

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

         /// This feature necessitates that each time we

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

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

         ///Next arc

         /// Assign the iterator to the next arc.

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

       };

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

       /// This iterator goes trough the \e outgoing 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 graph \c g of type \c Graph as follows.

       ///\code

       /// int count=0;

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

       ///\endcode

       class OutArcIt : public Arc {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         OutArcIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

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

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         OutArcIt(Invalid) { }

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

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

         /// the node.

         ///@param n the node

         ///@param g the graph

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

           ignore_unused_variable_warning(n);

           ignore_unused_variable_warning(g);

         }

         /// Arc -> OutArcIt conversion

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

         /// This feature necessitates that each time we

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

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

         ///Next outgoing arc

         /// Assign the iterator to the next

         /// outgoing arc of the corresponding node.

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

       };

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

       /// This iterator goes trough the \e incoming 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 graph \c g of type \c Graph as follows.

       ///\code

       /// int count=0;

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

       ///\endcode

       class InArcIt : public Arc {

       public:

         /// Default constructor

         /// @warning The default constructor sets the iterator

         /// to an undefined value.

         InArcIt() { }

         /// Copy constructor.

         /// Copy constructor.

         ///

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

         /// Initialize the iterator to be invalid.

         /// Initialize the iterator to be invalid.

         ///

         InArcIt(Invalid) { }

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

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

         /// the node.

         ///@param n the node

         ///@param g the graph

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

           ignore_unused_variable_warning(n);

           ignore_unused_variable_warning(g);

         }

         /// Arc -> InArcIt conversion

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

         /// This feature necessitates that each time we

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

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

         /// Next incoming arc

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

         ///

         InArcIt& 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

       template<class T>

       class NodeMap : public ReadWriteMap< Node, T >

       {

       public:

         ///\e

         NodeMap(const Graph&) { }

         ///\e

         NodeMap(const Graph&, T) { }

       private:

         ///Copy constructor

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

         ///Assignment operator

         template <typename CMap>

         NodeMap& operator=(const CMap&) {

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

           return *this;

         }

       };

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

       ///

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

       /// \sa Reference

       template<class T>

       class ArcMap : public ReadWriteMap<Arc,T>

       {

       public:

         ///\e

         ArcMap(const Graph&) { }

         ///\e

         ArcMap(const Graph&, T) { }

       private:

         ///Copy constructor

         ArcMap(const ArcMap& em) : ReadWriteMap<Arc,T>(em) { }

         ///Assignment operator

         template <typename CMap>

         ArcMap& operator=(const CMap&) {

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

           return *this;

         }

       };

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

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

       /// \sa Reference

       template<class T>

       class EdgeMap : public ReadWriteMap<Edge,T>

       {

       public:

         ///\e

         EdgeMap(const Graph&) { }

         ///\e

         EdgeMap(const Graph&, T) { }

       private:

         ///Copy constructor

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

         ///Assignment operator

         template <typename CMap>

         EdgeMap& operator=(const CMap&) {

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

           return *this;

         }

       };

       /// \brief Direct the given edge.

       ///

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

       /// will be the given node.

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

         return INVALID;

       }

       /// \brief Direct the given edge.

       ///

       /// Direct the given edge. The returned arc

       /// represents the given edge and the direction comes

       /// from the bool parameter. The source of the edge and

       /// the directed arc is the same when the given bool is true.

       Arc direct(const Edge&, bool) const {

         return INVALID;

       }

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

       ///

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

       /// the corresponding edge's default orientation.

       bool direction(Arc) const { return true; }

       /// \brief Returns the opposite directed arc.

       ///

       /// Returns the opposite directed arc.

       Arc oppositeArc(Arc) const { return INVALID; }

       /// \brief Opposite node on an arc

       ///

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

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

       /// \brief First node of the edge.

       ///

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

       ///

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

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

       /// to query the two nodes of the arc. The direction of the arc

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

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

       /// of the directed versions of the arcs.

       /// \sa direction

       Node u(Edge) const { return INVALID; }

       /// \brief Second node of the edge.

       Node v(Edge) const { return INVALID; }

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

       Node source(Arc) const { return INVALID; }

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

       Node target(Arc) const { return INVALID; }

       /// \brief Returns the id of the node.

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

       /// \brief Returns the id of the edge.

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

       /// \brief Returns the id of the arc.

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

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

       int maxNodeId() const { return -1; }

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

       int maxEdgeId() const { return -1; }

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

       int maxArcId() const { return -1; }

       void first(Node&) const {}

       void next(Node&) 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(Edge) const { return -1; }

       // Dummy parameter.

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

       /// \brief Base node of the iterator

       ///

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

       Node baseNode(OutArcIt 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(OutArcIt 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(InArcIt 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(InArcIt 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() {

           checkConcept<IterableGraphComponent<>, _Graph>();

           checkConcept<IDableGraphComponent<>, _Graph>();

           checkConcept<MappableGraphComponent<>, _Graph>();

         }

       };

     };

   }

 }

 #endif