/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2007

 * 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/bits/utility.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 IncArcIt 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::IncArcIt e(g, n); e!=INVALID; ++e) ++count;

      ///\endcode

      class IncArcIt : public Edge {

      public:

        /// Default constructor

        /// @warning The default constructor sets the iterator

        /// to an undefined value.

        IncArcIt() { }

        /// Copy constructor.

        /// Copy constructor.

        ///

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

        /// Initialize the iterator to be invalid.

        /// Initialize the iterator to be invalid.

        ///

        IncArcIt(Invalid) { }

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

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

        /// the node.

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

        /// Edge -> IncArcIt 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.

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

        /// Next incident arc

        /// Assign the iterator to the next incident arc

	/// of the corresponding node.

        IncArcIt& 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) { }

        ///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) { }

        ///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) { }

        ///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(IncArcIt) const {

	return INVALID;

      }

      /// \brief Running node of the iterator

      ///

      /// Returns the running node of the iterator

      Node runningNode(IncArcIt) const {

	return INVALID;

      }

      template <typename Graph>

      struct Constraints {

	void constraints() {

	  checkConcept<IterableGraphComponent<>, Graph>();

	  checkConcept<IDableGraphComponent<>, Graph>();

	  checkConcept<MappableGraphComponent<>, Graph>();

	}

      };

    };

  }

}

#endif