RhodeCode

CMAKE_MINIMUM_REQUIRED(VERSION 2.6)

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

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

ELSE(EXISTS ${CMAKE_SOURCE_DIR}/cmake/version.cmake)

  SET(PROJECT_NAME "LEMON")

  SET(PROJECT_VERSION "hg-tip" CACHE STRING "LEMON version string.")

ENDIF(EXISTS ${CMAKE_SOURCE_DIR}/cmake/version.cmake)

PROJECT(${PROJECT_NAME})

SET(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)

INCLUDE(FindDoxygen)

INCLUDE(FindGhostscript)

FIND_PACKAGE(GLPK 4.33)

FIND_PACKAGE(CPLEX)

FIND_PACKAGE(COIN)

IF(MSVC)

# Suppressed warnings:

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

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

# C4800: 'type' : forcing value to bool 'true' or 'false' (performance warning)

# C4996: 'function': was declared deprecated

ENDIF(MSVC)

INCLUDE(CheckTypeSize)

CHECK_TYPE_SIZE("long long" LEMON_LONG_LONG)

ENABLE_TESTING()

ADD_SUBDIRECTORY(lemon)

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

  ADD_SUBDIRECTORY(demo)

  ADD_SUBDIRECTORY(tools)

  ADD_SUBDIRECTORY(doc)

  ADD_SUBDIRECTORY(test)

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

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

  IF(WIN32)

    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")

EXTRA_DIST += \

	lemon/lemon.pc.in \

pkgconfig_DATA += lemon/lemon.pc

lib_LTLIBRARIES += lemon/libemon.la

lemon_libemon_la_SOURCES = \

	lemon/arg_parser.cc \

	lemon/base.cc \

	lemon/color.cc \

	lemon/lp_base.cc \

	lemon/lp_skeleton.cc \

	lemon/random.cc \

	lemon/bits/windows.cc

nodist_lemon_HEADERS = lemon/config.h	

lemon_libemon_la_CXXFLAGS = \

	$(AM_CXXFLAGS) \

	$(GLPK_CFLAGS) \

	$(CPLEX_CFLAGS) \

	$(SOPLEX_CXXFLAGS) \

	$(CLP_CXXFLAGS) \

	$(CBC_CXXFLAGS)

lemon_libemon_la_LDFLAGS = \

	$(GLPK_LIBS) \

	$(CPLEX_LIBS) \

	$(SOPLEX_LIBS) \

	$(CLP_LIBS) \

	$(CBC_LIBS)

if HAVE_GLPK

lemon_libemon_la_SOURCES += lemon/glpk.cc

endif

if HAVE_CPLEX

lemon_libemon_la_SOURCES += lemon/cplex.cc

endif

if HAVE_SOPLEX

lemon_libemon_la_SOURCES += lemon/soplex.cc

endif

if HAVE_CLP

lemon_libemon_la_SOURCES += lemon/clp.cc

endif

if HAVE_CBC

lemon_libemon_la_SOURCES += lemon/cbc.cc

endif

lemon_HEADERS += \

	lemon/adaptors.h \

	lemon/arg_parser.h \

	lemon/assert.h \

	lemon/bfs.h \

	lemon/bin_heap.h \

	lemon/cbc.h \

	lemon/circulation.h \

	lemon/clp.h \

	lemon/color.h \

	lemon/concept_check.h \

	lemon/connectivity.h \

	lemon/counter.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 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 have 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;

          _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 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);

      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;

          int nid = digraph.id(node);

          nid = digraph.id(node);

          node = digraph.nodeFromId(nid);

          typename _Digraph::Arc arc;

          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; }

  protected:

    struct NodeT {

      int first_out, first_in;

      NodeT() : first_out(-1), first_in(-1) {}

    };

    typedef typename ItemSetTraits<GR, Node>::

    template Map<NodeT>::Type NodesImplBase;

    NodesImplBase* _nodes;

    struct ArcT {

      Node source, target;

      int next_out, next_in;

      int prev_out, prev_in;

      ArcT() : prev_out(-1), prev_in(-1) {}

    };

    std::vector<ArcT> arcs;

    int first_arc;

    int first_free_arc;

    const GR* _graph;

    void initalize(const GR& graph, NodesImplBase& nodes) {

      _graph = &graph;

      _nodes = &nodes;

    }

  public:

    class Arc {

      friend class ListArcSetBase<GR>;

    protected:

      Arc(int _id) : id(_id) {}

      int id;

    public:

      Arc() {}

      Arc(Invalid) : id(-1) {}

      bool operator==(const Arc& arc) const { return id == arc.id; }

      bool operator!=(const Arc& arc) const { return id != arc.id; }

      bool operator<(const Arc& arc) const { return id < arc.id; }

    };

    ListArcSetBase() : first_arc(-1), first_free_arc(-1) {}

    Arc addArc(const Node& u, const Node& v) {

      int n;

      if (first_free_arc == -1) {

        n = arcs.size();

        arcs.push_back(ArcT());

      } else {

        n = first_free_arc;

        first_free_arc = arcs[first_free_arc].next_in;

      }

      arcs[n].next_in = (*_nodes)[v].first_in;

      if ((*_nodes)[v].first_in != -1) {

        arcs[(*_nodes)[v].first_in].prev_in = n;

      }

      (*_nodes)[v].first_in = n;

      arcs[n].next_out = (*_nodes)[u].first_out;

      if ((*_nodes)[u].first_out != -1) {

        arcs[(*_nodes)[u].first_out].prev_out = n;

      }

      (*_nodes)[u].first_out = n;

      arcs[n].source = u;

      arcs[n].target = v;

      return Arc(n);

    }

    void erase(const Arc& arc) {

      int n = arc.id;

      if (arcs[n].prev_in != -1) {

        arcs[arcs[n].prev_in].next_in = arcs[n].next_in;

      } else {

        (*_nodes)[arcs[n].target].first_in = arcs[n].next_in;

      }

      if (arcs[n].next_in != -1) {

        arcs[arcs[n].next_in].prev_in = arcs[n].prev_in;

      }

      if (arcs[n].prev_out != -1) {

        arcs[arcs[n].prev_out].next_out = arcs[n].next_out;

      } else {

        (*_nodes)[arcs[n].source].first_out = arcs[n].next_out;

      }

      if (arcs[n].next_out != -1) {

        arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;

      }

    }

    void clear() {

      Node node;

    };

    std::vector<ArcT> arcs;

    int first_arc;

    int first_free_arc;

    const GR* _graph;

    void initalize(const GR& graph, NodesImplBase& nodes) {

      _graph = &graph;

      _nodes = &nodes;

    }

  public:

    class Edge {

      friend class ListEdgeSetBase;

    protected:

      int id;

      explicit Edge(int _id) { id = _id;}

    public:

      Edge() {}

      Edge (Invalid) { id = -1; }

      bool operator==(const Edge& arc) const {return id == arc.id;}

      bool operator!=(const Edge& arc) const {return id != arc.id;}

      bool operator<(const Edge& arc) const {return id < arc.id;}

    };

    class Arc {

      friend class ListEdgeSetBase;

    protected:

      Arc(int _id) : id(_id) {}

      int id;

    public:

      operator Edge() const { return edgeFromId(id / 2); }

      Arc() {}

      Arc(Invalid) : id(-1) {}

      bool operator==(const Arc& arc) const { return id == arc.id; }

      bool operator!=(const Arc& arc) const { return id != arc.id; }

      bool operator<(const Arc& arc) const { return id < arc.id; }

    };

    ListEdgeSetBase() : first_arc(-1), first_free_arc(-1) {}

    Edge addEdge(const Node& u, const Node& v) {

      int n;

      if (first_free_arc == -1) {

        n = arcs.size();

        arcs.push_back(ArcT());

        arcs.push_back(ArcT());

      } else {

        n = first_free_arc;

        first_free_arc = arcs[n].next_out;

      }

      arcs[n].target = u;

      arcs[n | 1].target = v;

      arcs[n].next_out = (*_nodes)[v].first_out;

      if ((*_nodes)[v].first_out != -1) {

        arcs[(*_nodes)[v].first_out].prev_out = n;

      }

      (*_nodes)[v].first_out = n;

      arcs[n].prev_out = -1;

      if ((*_nodes)[u].first_out != -1) {

        arcs[(*_nodes)[u].first_out].prev_out = (n | 1);

      }

      arcs[n | 1].next_out = (*_nodes)[u].first_out;

      (*_nodes)[u].first_out = (n | 1);

      arcs[n | 1].prev_out = -1;

      return Edge(n / 2);

    }

    void erase(const Edge& arc) {

      int n = arc.id * 2;

      if (arcs[n].next_out != -1) {

        arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;

      }

      if (arcs[n].prev_out != -1) {

        arcs[arcs[n].prev_out].next_out = arcs[n].next_out;

      } else {

        (*_nodes)[arcs[n | 1].target].first_out = arcs[n].next_out;

      }

      if (arcs[n | 1].next_out != -1) {

        arcs[arcs[n | 1].next_out].prev_out = arcs[n | 1].prev_out;

      }

    typedef typename GR::Node Node;

    typedef typename GR::NodeIt NodeIt;

  protected:

    struct NodeT {

      int first_out, first_in;

      NodeT() : first_out(-1), first_in(-1) {}

    };

    typedef typename ItemSetTraits<GR, Node>::

    template Map<NodeT>::Type NodesImplBase;

    NodesImplBase* _nodes;

    struct ArcT {

      Node source, target;

      int next_out, next_in;

      ArcT() {}

    };

    std::vector<ArcT> arcs;

    const GR* _graph;

    void initalize(const GR& graph, NodesImplBase& nodes) {

      _graph = &graph;

      _nodes = &nodes;

    }

  public:

    class Arc {

      friend class SmartArcSetBase<GR>;

    protected:

      Arc(int _id) : id(_id) {}

      int id;

    public:

      Arc() {}

      Arc(Invalid) : id(-1) {}

      bool operator==(const Arc& arc) const { return id == arc.id; }

      bool operator!=(const Arc& arc) const { return id != arc.id; }

      bool operator<(const Arc& arc) const { return id < arc.id; }

    };

    SmartArcSetBase() {}

    Arc addArc(const Node& u, const Node& v) {

      int n = arcs.size();

      arcs.push_back(ArcT());

      arcs[n].next_in = (*_nodes)[v].first_in;

      (*_nodes)[v].first_in = n;

      arcs[n].next_out = (*_nodes)[u].first_out;

      (*_nodes)[u].first_out = n;

      arcs[n].source = u;

      arcs[n].target = v;

      return Arc(n);

    }

    void clear() {

      Node node;

      for (first(node); node != INVALID; next(node)) {

        (*_nodes)[node].first_in = -1;

        (*_nodes)[node].first_out = -1;

      }

      arcs.clear();

    }

    void first(Node& node) const {

      _graph->first(node);

    }

    void next(Node& node) const {

      _graph->next(node);

    }

    void first(Arc& arc) const {

      arc.id = arcs.size() - 1;

    }

    void next(Arc& arc) const {

      --arc.id;

    }

    void firstOut(Arc& arc, const Node& node) const {

      arc.id = (*_nodes)[node].first_out;

    }

    void nextOut(Arc& arc) const {

      arc.id = arcs[arc.id].next_out;

    }

    void firstIn(Arc& arc, const Node& node) const {

      arc.id = (*_nodes)[node].first_in;

    }

      Node target;

      int next_out;

      ArcT() {}

    };

    std::vector<ArcT> arcs;

    const GR* _graph;

    void initalize(const GR& graph, NodesImplBase& nodes) {

      _graph = &graph;

      _nodes = &nodes;

    }

  public:

    class Edge {

      friend class SmartEdgeSetBase;

    protected:

      int id;

      explicit Edge(int _id) { id = _id;}

    public:

      Edge() {}

      Edge (Invalid) { id = -1; }

      bool operator==(const Edge& arc) const {return id == arc.id;}

      bool operator!=(const Edge& arc) const {return id != arc.id;}

      bool operator<(const Edge& arc) const {return id < arc.id;}

    };

    class Arc {

      friend class SmartEdgeSetBase;

    protected:

      Arc(int _id) : id(_id) {}

      int id;

    public:

      operator Edge() const { return edgeFromId(id / 2); }

      Arc() {}

      Arc(Invalid) : id(-1) {}

      bool operator==(const Arc& arc) const { return id == arc.id; }

      bool operator!=(const Arc& arc) const { return id != arc.id; }

      bool operator<(const Arc& arc) const { return id < arc.id; }

    };

    SmartEdgeSetBase() {}

    Edge addEdge(const Node& u, const Node& v) {

      int n = arcs.size();

      arcs.push_back(ArcT());

      arcs.push_back(ArcT());

      arcs[n].target = u;

      arcs[n | 1].target = v;

      arcs[n].next_out = (*_nodes)[v].first_out;

      (*_nodes)[v].first_out = n;

      arcs[n | 1].next_out = (*_nodes)[u].first_out;

      (*_nodes)[u].first_out = (n | 1);

      return Edge(n / 2);

    }

    void clear() {

      Node node;

      for (first(node); node != INVALID; next(node)) {

        (*_nodes)[node].first_out = -1;

      }

      arcs.clear();

    }

    void first(Node& node) const {

      _graph->first(node);

    }

    void next(Node& node) const {

      _graph->next(node);

    }

    void first(Arc& arc) const {

      arc.id = arcs.size() - 1;

    }

    void next(Arc& arc) const {

      --arc.id;

    }

    void first(Edge& arc) const {

      arc.id = arcs.size() / 2 - 1;

    }

    void next(Edge& arc) const {

      --arc.id;

    }

  "   11     0    0    0    0  -10    0\n"

  "   12   -20  -27    0  -30  -30  -20\n"

  "\n"                

  "@arcs\n"

  "       cost  cap low1 low2 low3\n"

  " 1  2    70   11    0    8    8\n"

  " 1  3   150    3    0    1    0\n"

  " 1  4    80   15    0    2    2\n"

  " 2  8    80   12    0    0    0\n"

  " 3  5   140    5    0    3    1\n"

  " 4  6    60   10    0    1    0\n"

  " 4  7    80    2    0    0    0\n"

  " 4  8   110    3    0    0    0\n"

  " 5  7    60   14    0    0    0\n"

  " 5 11   120   12    0    0    0\n"

  " 6  3     0    3    0    0    0\n"

  " 6  9   140    4    0    0    0\n"

  " 6 10    90    8    0    0    0\n"

  " 7  1    30    5    0    0   -5\n"

  " 8 12    60   16    0    4    3\n"

  " 9 12    50    6    0    0    0\n"

  "10 12    70   13    0    5    2\n"

  "10  2   100    7    0    0    0\n"

  "10  7    60   10    0    0   -3\n"

  "11 10    20   14    0    6  -20\n"

  "12 11    30   10    0    0  -10\n"

  "\n"

  "@attributes\n"

  "source 1\n"

  "target 12\n";

enum SupplyType {

  EQ,

  GEQ,

  LEQ

};

// Check the interface of an MCF algorithm

template <typename GR, typename Value, typename Cost>

class McfClassConcept

{

public:

  template <typename MCF>

  struct Constraints {

    void constraints() {

      checkConcept<concepts::Digraph, GR>();

      const MCF& const_mcf = mcf;

      b = mcf.reset()

             .run();

      c = const_mcf.totalCost();

      x = const_mcf.template totalCost<double>();

      const_mcf.flowMap(fm);

      const_mcf.potentialMap(pm);

    }

    typedef typename GR::Node Node;

    typedef typename GR::Arc Arc;

    typedef concepts::ReadMap<Node, Value> NM;

    typedef concepts::ReadMap<Arc, Value> VAM;

    typedef concepts::ReadMap<Arc, Cost> CAM;

    typedef concepts::WriteMap<Arc, Value> FlowMap;

    typedef concepts::WriteMap<Node, Cost> PotMap;

    FlowMap fm;

    PotMap pm;

    bool b;

    double x;

    typename MCF::Value v;

    typename MCF::Cost c;

  };

};

// Check the feasibility of the given flow (primal soluiton)

template < typename GR, typename LM, typename UM,

           typename SM, typename FM >

bool checkFlow( const GR& gr, const LM& lower, const UM& upper,

                const SM& supply, const FM& flow,

                SupplyType type = EQ )

{

  TEMPLATE_DIGRAPH_TYPEDEFS(GR);

  for (ArcIt e(gr); e != INVALID; ++e) {

    if (flow[e] < lower[e] || flow[e] > upper[e]) return false;

  }

  for (NodeIt n(gr); n != INVALID; ++n) {

    typename SM::Value sum = 0;

    for (OutArcIt e(gr, n); e != INVALID; ++e)

      sum += flow[e];

    for (InArcIt e(gr, n); e != INVALID; ++e)

      sum -= flow[e];

    bool b = (type ==  EQ && sum == supply[n]) ||

             (type == GEQ && sum >= supply[n]) ||

             (type == LEQ && sum <= supply[n]);

    if (!b) return false;

  }

  return true;

}

// Check the feasibility of the given potentials (dual soluiton)

// using the "Complementary Slackness" optimality condition

template < typename GR, typename LM, typename UM,

           typename CM, typename SM, typename FM, typename PM >

bool checkPotential( const GR& gr, const LM& lower, const UM& upper,

                     const CM& cost, const SM& supply, const FM& flow, 

                     const PM& pi, SupplyType type )

{

  TEMPLATE_DIGRAPH_TYPEDEFS(GR);