RhodeCode

CMAKE_MINIMUM_REQUIRED(VERSION 2.6)

SET(PROJECT_NAME "LEMON")

PROJECT(${PROJECT_NAME})

INCLUDE(FindPythonInterp)

INCLUDE(FindWget)

IF(EXISTS ${PROJECT_SOURCE_DIR}/cmake/version.cmake)

  INCLUDE(${PROJECT_SOURCE_DIR}/cmake/version.cmake)

ELSEIF(DEFINED ENV{LEMON_VERSION})

  SET(LEMON_VERSION $ENV{LEMON_VERSION} CACHE STRING "LEMON version string.")

ELSE()

  EXECUTE_PROCESS(

    COMMAND ${PYTHON_EXECUTABLE} ./scripts/chg-len.py

    WORKING_DIRECTORY ${PROJECT_SOURCE_DIR}

    OUTPUT_VARIABLE HG_REVISION_PATH

    ERROR_QUIET

    OUTPUT_STRIP_TRAILING_WHITESPACE

  )

  EXECUTE_PROCESS(

    COMMAND hg id -i

    WORKING_DIRECTORY ${PROJECT_SOURCE_DIR}

    OUTPUT_VARIABLE HG_REVISION

    ERROR_QUIET

    OUTPUT_STRIP_TRAILING_WHITESPACE

  )

  IF(HG_REVISION STREQUAL "")

    SET(HG_REVISION_ID "hg-tip")

  ELSE()

    IF(HG_REVISION_PATH STREQUAL "")

      SET(HG_REVISION_ID ${HG_REVISION})

    ELSE()

      SET(HG_REVISION_ID ${HG_REVISION_PATH}.${HG_REVISION})

    ENDIF()

  ENDIF()

  SET(LEMON_VERSION ${HG_REVISION_ID} CACHE STRING "LEMON version string.")

ENDIF()

SET(PROJECT_VERSION ${LEMON_VERSION})

SET(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)

FIND_PACKAGE(Doxygen)

FIND_PACKAGE(Ghostscript)

FIND_PACKAGE(GLPK 4.33)

FIND_PACKAGE(CPLEX)

FIND_PACKAGE(COIN)

IF(DEFINED ENV{LEMON_CXX_WARNING})

  SET(CXX_WARNING $ENV{LEMON_CXX_WARNING})

ELSE()

  IF(CMAKE_COMPILER_IS_GNUCXX)

    SET(CXX_WARNING "-Wall -W -Wunused -Wformat=2 -Wctor-dtor-privacy -Wnon-virtual-dtor -Wno-char-subscripts -Wwrite-strings -Wno-char-subscripts -Wreturn-type -Wcast-qual -Wcast-align -Wsign-promo -Woverloaded-virtual -fno-strict-aliasing -Wold-style-cast -Wno-unknown-pragmas")

    SET(CMAKE_CXX_FLAGS_DEBUG CACHE STRING "-ggdb")

    SET(CMAKE_C_FLAGS_DEBUG CACHE STRING "-ggdb")

  ELSEIF(MSVC)

    # This part is unnecessary 'casue the same is set by the lemon/core.h.

    # Still keep it as an example.

    SET(CXX_WARNING "/wd4250 /wd4355 /wd4503 /wd4800 /wd4996")

    # Suppressed warnings:

    # C4250: 'class1' : inherits 'class2::member' via dominance

    # C4355: 'this' : used in base member initializer list

    # C4503: 'function' : decorated name length exceeded, name was truncated

    # C4800: 'type' : forcing value to bool 'true' or 'false'

    #        (performance warning)

    # C4996: 'function': was declared deprecated

  ELSE()

  ENDIF()

ENDIF()

SET(LEMON_CXX_WARNING_FLAGS ${CXX_WARNING} CACHE STRING "LEMON warning flags.")

SET(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${LEMON_CXX_WARNING_FLAGS}")

    "Flags used by the C++ compiler during maintainer builds."

    FORCE )

    "Flags used by the C compiler during maintainer builds."

    FORCE )

SET( CMAKE_EXE_LINKER_FLAGS_MAINTAINER

    "-Wl,--warn-unresolved-symbols,--warn-once" CACHE STRING

    "Flags used for linking binaries during maintainer builds."

    FORCE )

SET( CMAKE_SHARED_LINKER_FLAGS_MAINTAINER

    "-Wl,--warn-unresolved-symbols,--warn-once" CACHE STRING

    "Flags used by the shared libraries linker during maintainer builds."

    FORCE )

MARK_AS_ADVANCED(

    CMAKE_CXX_FLAGS_MAINTAINER

    CMAKE_C_FLAGS_MAINTAINER

    CMAKE_EXE_LINKER_FLAGS_MAINTAINER

    CMAKE_SHARED_LINKER_FLAGS_MAINTAINER )

IF(CMAKE_CONFIGURATION_TYPES)

  LIST(APPEND CMAKE_CONFIGURATION_TYPES Maintainer)

  LIST(REMOVE_DUPLICATES CMAKE_CONFIGURATION_TYPES)

  SET(CMAKE_CONFIGURATION_TYPES "${CMAKE_CONFIGURATION_TYPES}" CACHE STRING

      "Add the configurations that we need"

      FORCE)

 endif()

IF(NOT CMAKE_BUILD_TYPE)

  SET(CMAKE_BUILD_TYPE "Release")

ENDIF()

SET( CMAKE_BUILD_TYPE "${CMAKE_BUILD_TYPE}" CACHE STRING

    "Choose the type of build, options are: None(CMAKE_CXX_FLAGS or CMAKE_C_FLAGS used) Debug Release RelWithDebInfo MinSizeRel Maintainer."

    FORCE )

INCLUDE(CheckTypeSize)

CHECK_TYPE_SIZE("long long" LONG_LONG)

SET(LEMON_HAVE_LONG_LONG ${HAVE_LONG_LONG})

ENABLE_TESTING()

IF(${CMAKE_BUILD_TYPE} STREQUAL "Maintainer")

  ADD_CUSTOM_TARGET(check ALL COMMAND ${CMAKE_CTEST_COMMAND})

ELSE()

  ADD_CUSTOM_TARGET(check COMMAND ${CMAKE_CTEST_COMMAND})

ENDIF()

ADD_SUBDIRECTORY(lemon)

IF(${CMAKE_SOURCE_DIR} STREQUAL ${PROJECT_SOURCE_DIR})

  ADD_SUBDIRECTORY(contrib)

  ADD_SUBDIRECTORY(demo)

  ADD_SUBDIRECTORY(tools)

  ADD_SUBDIRECTORY(doc)

  ADD_SUBDIRECTORY(test)

ENDIF()

CONFIGURE_FILE(

  ${PROJECT_SOURCE_DIR}/cmake/LEMONConfig.cmake.in

  ${PROJECT_BINARY_DIR}/cmake/LEMONConfig.cmake

  @ONLY

)

IF(UNIX)

  INSTALL(

    FILES ${PROJECT_BINARY_DIR}/cmake/LEMONConfig.cmake

    DESTINATION share/lemon/cmake

  )

ELSEIF(WIN32)

  INSTALL(

    FILES ${PROJECT_BINARY_DIR}/cmake/LEMONConfig.cmake

    DESTINATION cmake

  )

ENDIF()

IF(${CMAKE_SOURCE_DIR} STREQUAL ${PROJECT_SOURCE_DIR})

  SET(CPACK_PACKAGE_NAME ${PROJECT_NAME})

  SET(CPACK_PACKAGE_VENDOR "EGRES")

  SET(CPACK_PACKAGE_DESCRIPTION_SUMMARY

    "LEMON - Library for Efficient Modeling and Optimization in Networks")

  SET(CPACK_RESOURCE_FILE_LICENSE "${PROJECT_SOURCE_DIR}/LICENSE")

  SET(CPACK_PACKAGE_VERSION ${PROJECT_VERSION})

  SET(CPACK_PACKAGE_INSTALL_DIRECTORY

    "${PROJECT_NAME} ${PROJECT_VERSION}")

  SET(CPACK_PACKAGE_INSTALL_REGISTRY_KEY

    "${PROJECT_NAME} ${PROJECT_VERSION}")

  SET(CPACK_COMPONENTS_ALL headers library html_documentation bin)

  SET(CPACK_COMPONENT_HEADERS_DISPLAY_NAME "C++ headers")

  SET(CPACK_COMPONENT_LIBRARY_DISPLAY_NAME "Dynamic-link library")

  SET(CPACK_COMPONENT_BIN_DISPLAY_NAME "Command line utilities")

  SET(CPACK_COMPONENT_HTML_DOCUMENTATION_DISPLAY_NAME "HTML documentation")

  SET(CPACK_COMPONENT_HEADERS_DESCRIPTION

    "C++ header files")

  SET(CPACK_COMPONENT_LIBRARY_DESCRIPTION

    "DLL and import library")

  SET(CPACK_COMPONENT_BIN_DESCRIPTION

    "Command line utilities")

  SET(CPACK_COMPONENT_HTML_DOCUMENTATION_DESCRIPTION

    "Doxygen generated documentation")

  SET(CPACK_COMPONENT_HEADERS_DEPENDS library)

  SET(CPACK_COMPONENT_HEADERS_GROUP "Development")

  SET(CPACK_COMPONENT_LIBRARY_GROUP "Development")

  SET(CPACK_COMPONENT_HTML_DOCUMENTATION_GROUP "Documentation")

  SET(CPACK_COMPONENT_GROUP_DEVELOPMENT_DESCRIPTION

    "Components needed to develop software using LEMON")

  SET(CPACK_COMPONENT_GROUP_DOCUMENTATION_DESCRIPTION

    "Documentation of LEMON")

  SET(CPACK_ALL_INSTALL_TYPES Full Developer)

  SET(CPACK_COMPONENT_HEADERS_INSTALL_TYPES Developer Full)

  SET(CPACK_COMPONENT_LIBRARY_INSTALL_TYPES Developer Full)

  SET(CPACK_COMPONENT_HTML_DOCUMENTATION_INSTALL_TYPES Full)

  SET(CPACK_GENERATOR "NSIS")

  SET(CPACK_NSIS_MUI_ICON "${PROJECT_SOURCE_DIR}/cmake/nsis/lemon.ico")

  SET(CPACK_NSIS_MUI_UNIICON "${PROJECT_SOURCE_DIR}/cmake/nsis/uninstall.ico")

  #SET(CPACK_PACKAGE_ICON "${PROJECT_SOURCE_DIR}/cmake/nsis\\\\installer.bmp")

  SET(CPACK_NSIS_INSTALLED_ICON_NAME "bin\\\\lemon.ico")

  SET(CPACK_NSIS_DISPLAY_NAME "${CPACK_PACKAGE_INSTALL_DIRECTORY} ${PROJECT_NAME}")

  SET(CPACK_NSIS_HELP_LINK "http:\\\\\\\\lemon.cs.elte.hu")

  SET(CPACK_NSIS_URL_INFO_ABOUT "http:\\\\\\\\lemon.cs.elte.hu")

  SET(CPACK_NSIS_CONTACT "lemon-user@lemon.cs.elte.hu")

  SET(CPACK_NSIS_CREATE_ICONS_EXTRA "

    };

    ///\brief \ref named-func-param "Named parameter" for setting

    ///the processed map.

    ///

    ///\ref named-templ-param "Named parameter" function for setting

    ///the map that indicates which nodes are processed.

    template<class T>

    BfsWizard<SetProcessedMapBase<T> > processedMap(const T &t)

    {

      Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));

      return BfsWizard<SetProcessedMapBase<T> >(*this);

    }

    template<class T>

    struct SetPathBase : public Base {

      typedef T Path;

      SetPathBase(const TR &b) : TR(b) {}

    };

    ///\brief \ref named-func-param "Named parameter"

    ///for getting the shortest path to the target node.

    ///

    ///\ref named-func-param "Named parameter"

    ///for getting the shortest path to the target node.

    template<class T>

    BfsWizard<SetPathBase<T> > path(const T &t)

    {

      Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));

      return BfsWizard<SetPathBase<T> >(*this);

    }

    ///\brief \ref named-func-param "Named parameter"

    ///for getting the distance of the target node.

    ///

    ///\ref named-func-param "Named parameter"

    ///for getting the distance of the target node.

    BfsWizard dist(const int &d)

    {

      Base::_di=const_cast<int*>(&d);

      return *this;

    }

  };

  ///Function-type interface for BFS algorithm.

  /// \ingroup search

  ///Function-type interface for BFS algorithm.

  ///

  ///This function also has several \ref named-func-param "named parameters",

  ///they are declared as the members of class \ref BfsWizard.

  ///The following examples show how to use these parameters.

  ///\code

  ///  // Compute shortest path from node s to each node

  ///  bfs(g).predMap(preds).distMap(dists).run(s);

  ///

  ///  // Compute shortest path from s to t

  ///  bool reached = bfs(g).path(p).dist(d).run(s,t);

  ///\endcode

  ///\warning Don't forget to put the \ref BfsWizard::run(Node) "run()"

  ///to the end of the parameter list.

  ///\sa BfsWizard

  ///\sa Bfs

  template<class GR>

  BfsWizard<BfsWizardBase<GR> >

  bfs(const GR &digraph)

  {

    return BfsWizard<BfsWizardBase<GR> >(digraph);

  }

#ifdef DOXYGEN

  /// \brief Visitor class for BFS.

  ///

  /// This class defines the interface of the BfsVisit events, and

  /// it could be the base of a real visitor class.

  template <typename GR>

  struct BfsVisitor {

    typedef GR Digraph;

    typedef typename Digraph::Arc Arc;

    typedef typename Digraph::Node Node;

    /// \brief Called for the source node(s) of the BFS.

    ///

    /// This function is called for the source node(s) of the BFS.

    void start(const Node& node) {}

    /// \brief Called when a node is reached first time.

    ///

    /// This function is called when a node is reached first time.

    void reach(const Node& node) {}

    /// \brief Called when a node is processed.

    ///

    /// This function is called when a node is processed.

    void process(const Node& node) {}

    /// \brief Called when an arc reaches a new node.

    ///

    /// This function is called when the BFS finds an arc whose target node

    /// is not reached yet.

    void discover(const Arc& arc) {}

    /// \brief Called when an arc is examined but its target node is

    /// already discovered.

    ///

    /// This function is called when an arc is examined but its target node is

    /// already discovered.

    void examine(const Arc& arc) {}

  };

#else

  template <typename GR>

  struct BfsVisitor {

    typedef GR Digraph;

    typedef typename Digraph::Arc Arc;

    typedef typename Digraph::Node Node;

    void start(const Node&) {}

    void reach(const Node&) {}

    void process(const Node&) {}

    void discover(const Arc&) {}

    void examine(const Arc&) {}

    template <typename _Visitor>

    struct Constraints {

      void constraints() {

        Arc arc;

        Node node;

        visitor.start(node);

        visitor.reach(node);

        visitor.process(node);

        visitor.discover(arc);

        visitor.examine(arc);

      }

      _Visitor& visitor;

    };

  };

#endif

  /// \brief Default traits class of BfsVisit class.

  ///

  /// Default traits class of BfsVisit class.

  /// \tparam GR The type of the digraph the algorithm runs on.

  template<class GR>

  struct BfsVisitDefaultTraits {

    /// \brief The type of the digraph the algorithm runs on.

    typedef GR Digraph;

    /// \brief The type of the map that indicates which nodes are reached.

    ///

    /// The type of the map that indicates which nodes are reached.

    /// It must conform to

    ///the \ref concepts::ReadWriteMap "ReadWriteMap" concept.

    typedef typename Digraph::template NodeMap<bool> ReachedMap;

    /// \brief Instantiates a ReachedMap.

    ///

    /// This function instantiates a ReachedMap.

    /// \param digraph is the digraph, to which

    /// we would like to define the ReachedMap.

    static ReachedMap *createReachedMap(const Digraph &digraph) {

      return new ReachedMap(digraph);

    }

  };

  /// \ingroup search

  ///

  /// \brief BFS algorithm class with visitor interface.

  ///

  /// This class provides an efficient implementation of the BFS algorithm

  /// with visitor interface.

  ///

  /// The BfsVisit class provides an alternative interface to the Bfs

  /// class. It works with callback mechanism, the BfsVisit object calls

  /// the member functions of the \c Visitor class on every BFS event.

  ///

  /// This interface of the BFS algorithm should be used in special cases

  /// when extra actions have to be performed in connection with certain

  /// events of the BFS algorithm. Otherwise consider to use Bfs or bfs()

  /// instead.

  ///

  /// \tparam GR The type of the digraph the algorithm runs on.

  /// The default type is \ref ListDigraph.

  /// The value of GR is not used directly by \ref BfsVisit,

  /// it is only passed to \ref BfsVisitDefaultTraits.

  /// \tparam VS The Visitor type that is used by the algorithm.

  /// \ref BfsVisitor "BfsVisitor<GR>" is an empty visitor, which

  /// does not observe the BFS events. If you want to observe the BFS

  /// events, you should implement your own visitor class.

  /// \tparam TR The traits class that defines various types used by the

  /// algorithm. By default, it is \ref BfsVisitDefaultTraits

  /// "BfsVisitDefaultTraits<GR>".

  /// In most cases, this parameter should not be set directly,

  /// consider to use the named template parameters instead.

#ifdef DOXYGEN

  template <typename GR, typename VS, typename TR>

#else

  template <typename GR = ListDigraph,

            typename VS = BfsVisitor<GR>,

            typename TR = BfsVisitDefaultTraits<GR> >

#endif

  class BfsVisit {

  public:

    ///The traits class.

    typedef TR Traits;

    ///The type of the digraph the algorithm runs on.

    typedef typename Traits::Digraph Digraph;

    ///The visitor type used by the algorithm.

    typedef VS Visitor;

    ///The type of the map that indicates which nodes are reached.

    typedef typename Traits::ReachedMap ReachedMap;

  private:

    typedef typename Digraph::Node Node;

    typedef typename Digraph::NodeIt NodeIt;

    typedef typename Digraph::Arc Arc;

    typedef typename Digraph::OutArcIt OutArcIt;

    //Pointer to the underlying digraph.

    const Digraph *_digraph;

    //Pointer to the visitor object.

    Visitor *_visitor;

    //Pointer to the map of reached status of the nodes.

    ReachedMap *_reached;

    //Indicates if _reached is locally allocated (true) or not.

    bool local_reached;

    std::vector<typename Digraph::Node> _list;

    int _list_front, _list_back;

    //Creates the maps if necessary.

    void create_maps() {

      if(!_reached) {

        local_reached = true;

        _reached = Traits::createReachedMap(*_digraph);

      }

    }

  protected:

    BfsVisit() {}

  public:

    typedef BfsVisit Create;

    /// \name Named Template Parameters

    ///@{

    template <class T>

    struct SetReachedMapTraits : public Traits {

      typedef T ReachedMap;

      static ReachedMap *createReachedMap(const Digraph &digraph) {

        LEMON_ASSERT(false, "ReachedMap is not initialized");

        return 0; // ignore warnings

      }

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

 *

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

 *

 * Copyright (C) 2003-2010

 * 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 concepts of graph components.

#ifndef LEMON_CONCEPTS_GRAPH_COMPONENTS_H

#define LEMON_CONCEPTS_GRAPH_COMPONENTS_H

#include <lemon/core.h>

#include <lemon/concepts/maps.h>

#include <lemon/bits/alteration_notifier.h>

namespace lemon {

  namespace concepts {

    /// \brief Concept class for \c Node, \c Arc and \c Edge types.

    ///

    /// This class describes the concept of \c Node, \c Arc and \c Edge

    /// subtypes of digraph and graph types.

    ///

    /// \note This class is a template class so that we can use it to

    /// create graph skeleton classes. The reason for this is that \c Node

    /// and \c Arc (or \c Edge) types should \e not derive from the same

    /// base class. For \c Node you should instantiate it with character

    /// \c 'n', for \c Arc with \c 'a' and for \c Edge with \c 'e'.

#ifndef DOXYGEN

    template <char sel = '0'>

#endif

    class GraphItem {

    public:

      /// \brief Default constructor.

      ///

      /// Default constructor.

      /// \warning The default constructor is not required to set

      /// the item to some well-defined value. So you should consider it

      /// as uninitialized.

      GraphItem() {}

      /// \brief Copy constructor.

      ///

      /// Copy constructor.

      GraphItem(const GraphItem &) {}

      /// \brief Constructor for conversion from \c INVALID.

      ///

      /// Constructor for conversion from \c INVALID.

      /// It initializes the item to be invalid.

      /// \sa Invalid for more details.

      GraphItem(Invalid) {}

      /// \brief Assignment operator.

      ///

      /// Assignment operator for the item.

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

      /// \brief Assignment operator for INVALID.

      ///

      /// This operator makes the item invalid.

      GraphItem& operator=(Invalid) { return *this; }

      /// \brief Equality operator.

      ///

      /// Equality operator.

      bool operator==(const GraphItem&) const { return false; }

      /// \brief Inequality operator.

      ///

      /// Inequality operator.

      bool operator!=(const GraphItem&) const { return false; }

      /// \brief Ordering operator.

      ///

      /// This operator defines an ordering of the items.

      /// It makes possible to use graph item types as key types in

      /// associative containers (e.g. \c std::map).

      ///

      /// \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<(const GraphItem&) const { return false; }

      template<typename _GraphItem>

      struct Constraints {

        void constraints() {

          _GraphItem i1;

          i1=INVALID;

          _GraphItem i2 = i1;

          _GraphItem i3 = INVALID;

          i1 = i2 = i3;

          bool b;

          b = (ia == ib) && (ia != ib);

          b = (ia == INVALID) && (ib != INVALID);

          b = (ia < ib);

        }

        const _GraphItem &ia;

        const _GraphItem &ib;

      };

    };

    /// \brief Base skeleton class for directed graphs.

    ///

    /// This class describes the base interface of directed graph types.

    /// All digraph %concepts have to conform to this class.

    /// It just provides types for nodes and arcs and functions

    /// to get the source and the target nodes of arcs.

    class BaseDigraphComponent {

    public:

      typedef BaseDigraphComponent Digraph;

      /// \brief Node class of the digraph.

      ///

      /// This class represents the nodes of the digraph.

      typedef GraphItem<'n'> Node;

      /// \brief Arc class of the digraph.

      ///

      /// This class represents the arcs of the digraph.

      typedef GraphItem<'a'> Arc;

      /// \brief Return the source node of an arc.

      ///

      /// This function returns the source node of an arc.

      Node source(const Arc&) const { return INVALID; }

      /// \brief Return the target node of an arc.

      ///

      /// This function returns the target node of an arc.

      Node target(const Arc&) const { return INVALID; }

      /// \brief Return the opposite node on the given arc.

      ///

      /// This function returns the opposite node on the given arc.

      Node oppositeNode(const Node&, const Arc&) const {

        return INVALID;

      }

      template <typename _Digraph>

      struct Constraints {

        typedef typename _Digraph::Node Node;

        typedef typename _Digraph::Arc Arc;

        void constraints() {

          checkConcept<GraphItem<'n'>, Node>();

          checkConcept<GraphItem<'a'>, Arc>();

          {

            Node n;

            Arc e(INVALID);

            n = digraph.source(e);

            n = digraph.target(e);

            n = digraph.oppositeNode(n, e);

          }

        }

        const _Digraph& digraph;

      };

    };

    /// \brief Base skeleton class for undirected graphs.

    ///

    /// This class describes the base interface of undirected graph types.

    /// All graph %concepts have to conform to this class.

    /// It extends the interface of \ref BaseDigraphComponent with an

    /// \c Edge type and functions to get the end nodes of edges,

    /// to convert from arcs to edges and to get both direction of edges.

    class BaseGraphComponent : public BaseDigraphComponent {

    public:

      typedef BaseGraphComponent Graph;

      typedef BaseDigraphComponent::Node Node;

      typedef BaseDigraphComponent::Arc Arc;

      /// \brief Undirected edge class of the graph.

      ///

      /// This class represents the undirected edges of the graph.

      /// Undirected graphs can be used as directed graphs, each edge is

      /// represented by two opposite directed arcs.

      class Edge : public GraphItem<'e'> {

        typedef GraphItem<'e'> Parent;

      public:

        /// \brief Default constructor.

        ///

        /// Default constructor.

        /// \warning The default constructor is not required to set

        /// the item to some well-defined value. So you should consider it

        /// as uninitialized.

        Edge() {}

        /// \brief Copy constructor.

        ///

        /// Copy constructor.

        Edge(const Edge &) : Parent() {}

        /// \brief Constructor for conversion from \c INVALID.

        ///

        /// Constructor for conversion from \c INVALID.

        /// It initializes the item to be invalid.

        /// \sa Invalid for more details.

        Edge(Invalid) {}

        /// \brief Constructor for conversion from an arc.

        ///

        /// Constructor for conversion from an arc.

        /// Besides the core graph item functionality each arc should

        /// be convertible to the represented edge.

        Edge(const Arc&) {}

     };

      /// \brief Return one end node of an edge.

      ///

      /// This function returns one end node of an edge.

      Node u(const Edge&) const { return INVALID; }

      /// \brief Return the other end node of an edge.

      ///

      /// This function returns the other end node of an edge.

      Node v(const Edge&) const { return INVALID; }

      /// \brief Return a directed arc related to an edge.

      ///

      /// This function returns a directed arc from its direction and the

      /// represented edge.

      Arc direct(const Edge&, bool) const { return INVALID; }

      /// \brief Return a directed arc related to an edge.

      ///

      /// This function returns a directed arc from its source node and the

      /// represented edge.

      Arc direct(const Edge&, const Node&) const { return INVALID; }

      /// \brief Return the direction of the arc.

      ///

      /// Returns the direction of the arc. Each arc represents an

      /// edge with a direction. It gives back the

      /// direction.

      bool direction(const Arc&) const { return true; }

      /// \brief Return the opposite arc.

      ///

      /// This function returns the opposite arc, i.e. the arc representing

      /// the same edge and has opposite direction.

      Arc oppositeArc(const Arc&) const { return INVALID; }

      template <typename _Graph>

      struct Constraints {

        typedef typename _Graph::Node Node;

        typedef typename _Graph::Arc Arc;

        typedef typename _Graph::Edge Edge;

        void constraints() {

          checkConcept<BaseDigraphComponent, _Graph>();

          checkConcept<GraphItem<'e'>, Edge>();

          {

            Node n;

            Edge ue(INVALID);

            Arc e;

            n = graph.u(ue);

            n = graph.v(ue);

            e = graph.direct(ue, true);

            e = graph.direct(ue, false);

            e = graph.direct(ue, n);

            e = graph.oppositeArc(e);

            ue = e;

            bool d = graph.direction(e);

            ignore_unused_variable_warning(d);

          }

        }

        const _Graph& graph;

      };

    };

    /// \brief Skeleton class for \e idable directed graphs.

    ///

    /// This class describes the interface of \e idable directed graphs.

    /// It extends \ref BaseDigraphComponent with the core ID functions.

    /// The ids of the items must be unique and immutable.

    /// This concept is part of the Digraph concept.

    template <typename BAS = BaseDigraphComponent>

    class IDableDigraphComponent : public BAS {

    public:

      typedef BAS Base;

      typedef typename Base::Node Node;

      typedef typename Base::Arc Arc;

      /// \brief Return a unique integer id for the given node.

      ///

      /// This function returns a unique integer id for the given node.

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

      /// \brief Return the node by its unique id.

      ///

      /// This function returns the node by its unique id.

      /// If the digraph does not contain a node with the given id,

      /// then the result of the function is undefined.

      Node nodeFromId(int) const { return INVALID; }

      /// \brief Return a unique integer id for the given arc.

      ///

      /// This function returns a unique integer id for the given arc.

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

      /// \brief Return the arc by its unique id.

      ///

      /// This function returns the arc by its unique id.

      /// If the digraph does not contain an arc with the given id,

      /// then the result of the function is undefined.

      Arc arcFromId(int) const { return INVALID; }

      /// \brief Return an integer greater or equal to the maximum

      /// node id.

      ///

      /// This function returns an integer greater or equal to the

      /// maximum node id.

      int maxNodeId() const { return -1; }

      /// \brief Return an integer greater or equal to the maximum

      /// arc id.

      ///

      /// This function returns an integer greater or equal to the

      /// maximum arc id.

      int maxArcId() const { return -1; }

      template <typename _Digraph>

      struct Constraints {

        void constraints() {

          checkConcept<Base, _Digraph >();

          typename _Digraph::Node node;

          node=INVALID;

          int nid = digraph.id(node);

          nid = digraph.id(node);

          node = digraph.nodeFromId(nid);

          typename _Digraph::Arc arc;

          arc=INVALID;

          int eid = digraph.id(arc);

          eid = digraph.id(arc);

          arc = digraph.arcFromId(eid);

          nid = digraph.maxNodeId();

          ignore_unused_variable_warning(nid);

          eid = digraph.maxArcId();

          ignore_unused_variable_warning(eid);

        }

        const _Digraph& digraph;

      };

    };

    /// \brief Skeleton class for \e idable undirected graphs.

    ///

    /// This class describes the interface of \e idable undirected

    /// graphs. It extends \ref IDableDigraphComponent with the core ID

    /// functions of undirected graphs.

    /// The ids of the items must be unique and immutable.

    /// This concept is part of the Graph concept.

    template <typename BAS = BaseGraphComponent>

    class IDableGraphComponent : public IDableDigraphComponent<BAS> {

    public:

      typedef BAS Base;

      typedef typename Base::Edge Edge;

      using IDableDigraphComponent<Base>::id;

      /// \brief Return a unique integer id for the given edge.

      ///

      /// This function returns a unique integer id for the given edge.

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

      /// \brief Return the edge by its unique id.

      ///

      /// This function returns the edge by its unique id.

      /// If the graph does not contain an edge with the given id,

      /// then the result of the function is undefined.

      Edge edgeFromId(int) const { return INVALID; }

      /// \brief Return an integer greater or equal to the maximum

      /// edge id.

      ///

      /// This function returns an integer greater or equal to the

      /// maximum edge id.

      int maxEdgeId() const { return -1; }

      template <typename _Graph>

      struct Constraints {

        void constraints() {

          checkConcept<IDableDigraphComponent<Base>, _Graph >();

          typename _Graph::Edge edge;

          int ueid = graph.id(edge);

          ueid = graph.id(edge);

          edge = graph.edgeFromId(ueid);

          ueid = graph.maxEdgeId();

          ignore_unused_variable_warning(ueid);

        }

        const _Graph& graph;

      };

    };

    /// \brief Concept class for \c NodeIt, \c ArcIt and \c EdgeIt types.

    ///

    /// This class describes the concept of \c NodeIt, \c ArcIt and

    /// \c EdgeIt subtypes of digraph and graph types.

    template <typename GR, typename Item>

    class GraphItemIt : public Item {

    public:

      /// \brief Default constructor.

      ///

      /// Default constructor.

      /// \warning The default constructor is not required to set

      /// the iterator to some well-defined value. So you should consider it

      /// as uninitialized.

      GraphItemIt() {}

      /// \brief Copy constructor.

      ///

      /// Copy constructor.

      GraphItemIt(const GraphItemIt& it) : Item(it) {}

      /// \brief Constructor that sets the iterator to the first item.

      ///

      /// Constructor that sets the iterator to the first item.

      explicit GraphItemIt(const GR&) {}

      /// \brief Constructor for conversion from \c INVALID.

      ///

      /// Constructor for conversion from \c INVALID.

      /// It initializes the iterator to be invalid.

      /// \sa Invalid for more details.

      GraphItemIt(Invalid) {}

      /// \brief Assignment operator.

      ///

      /// Assignment operator for the iterator.

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

      /// \brief Increment the iterator.

      ///

      /// This operator increments the iterator, i.e. assigns it to the

      /// next item.

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

      /// \brief Equality operator

      ///

      /// Equality operator.

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

      /// same object or both are invalid.

      bool operator==(const GraphItemIt&) const { return true;}

      /// \brief Inequality operator

      ///

      /// Inequality operator.

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

      /// same object or both are invalid.

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

      template<typename _GraphItemIt>

      struct Constraints {

        void constraints() {

          checkConcept<GraphItem<>, _GraphItemIt>();

          _GraphItemIt it1(g);

          _GraphItemIt it2;

          _GraphItemIt it3 = it1;

          _GraphItemIt it4 = INVALID;

          it2 = ++it1;

          ++it2 = it1;

          ++(++it1);

          Item bi = it1;

          bi = it2;

        }

        const GR& g;

      };

    };

    /// \brief Concept class for \c InArcIt, \c OutArcIt and

    /// \c IncEdgeIt types.

    ///

    /// This class describes the concept of \c InArcIt, \c OutArcIt

    /// and \c IncEdgeIt subtypes of digraph and graph types.

    ///

    /// \note Since these iterator classes do not inherit from the same

    /// base class, there is an additional template parameter (selector)

    /// \c sel. For \c InArcIt you should instantiate it with character

    /// \c 'i', for \c OutArcIt with \c 'o' and for \c IncEdgeIt with \c 'e'.

    template <typename GR,

              typename Item = typename GR::Arc,

              typename Base = typename GR::Node,

              char sel = '0'>

    class GraphIncIt : public Item {

    public:

      /// \brief Default constructor.

      ///

      /// Default constructor.

      /// \warning The default constructor is not required to set

      /// the iterator to some well-defined value. So you should consider it

      /// as uninitialized.

      GraphIncIt() {}

      /// \brief Copy constructor.

      ///

      /// Copy constructor.

      GraphIncIt(const GraphIncIt& it) : Item(it) {}

      /// \brief Constructor that sets the iterator to the first

      /// incoming or outgoing arc.

      ///

      /// Constructor that sets the iterator to the first arc

      /// incoming to or outgoing from the given node.

      explicit GraphIncIt(const GR&, const Base&) {}

      /// \brief Constructor for conversion from \c INVALID.

      ///

      /// Constructor for conversion from \c INVALID.

      /// It initializes the iterator to be invalid.

      /// \sa Invalid for more details.

      GraphIncIt(Invalid) {}

      /// \brief Assignment operator.

      ///

      /// Assignment operator for the iterator.

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

      /// \brief Increment the iterator.

      ///

      /// This operator increments the iterator, i.e. assigns it to the

      /// next arc incoming to or outgoing from the given node.

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

      /// \brief Equality operator

      ///

      /// Equality operator.

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

      /// same object or both are invalid.

      bool operator==(const GraphIncIt&) const { return true;}

      /// \brief Inequality operator

      ///

      /// Inequality operator.

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

      /// same object or both are invalid.

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

      template <typename _GraphIncIt>

      struct Constraints {

        void constraints() {

          checkConcept<GraphItem<sel>, _GraphIncIt>();

          _GraphIncIt it1(graph, node);

          _GraphIncIt it2;

          _GraphIncIt it3 = it1;

          _GraphIncIt it4 = INVALID;

          it2 = ++it1;

          ++it2 = it1;

          ++(++it1);

          Item e = it1;

          e = it2;

        }

        const Base& node;

        const GR& graph;

      };

    };

    /// \brief Skeleton class for iterable directed graphs.

    ///

    /// This class describes the interface of iterable directed

    /// graphs. It extends \ref BaseDigraphComponent with the core

    /// iterable interface.

    /// This concept is part of the Digraph concept.

    template <typename BAS = BaseDigraphComponent>

    class IterableDigraphComponent : public BAS {

    public:

      typedef BAS Base;

      typedef typename Base::Node Node;

      typedef typename Base::Arc Arc;

      typedef IterableDigraphComponent Digraph;

      /// \name Base Iteration

      ///

      /// This interface provides functions for iteration on digraph items.

      ///

      /// @{

      /// \brief Return the first node.

      ///

      /// This function gives back the first node in the iteration order.

      void first(Node&) const {}

      /// \brief Return the next node.

      ///

      /// This function gives back the next node in the iteration order.

      void next(Node&) const {}

      /// \brief Return the first arc.

      ///

      /// This function gives back the first arc in the iteration order.

      void first(Arc&) const {}

      /// \brief Return the next arc.