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/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2008

 * 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 demos

///\file

///\brief Demonstrating graph input and output

///

/// This simple demo program gives an example of how to read and write

/// a graph and additional maps (on the nodes or the edges) from/to a

/// stream. 

///

/// \include reader_writer_demo.cc

#include <iostream>

#include <lemon/smart_graph.h>

#include <lemon/lgf_reader.h>

#include <lemon/lgf_writer.h>

#include <lemon/random.h>

using namespace lemon;

int main(int argc, const char *argv[]) {

  const int n = argc > 1 ? std::atoi(argv[1]) : 20;

  const int m = argc > 3 ? std::atoi(argv[3]) : 100;

  SmartDigraph digraph;

  std::stringstream ss;

  try {

    typedef SmartDigraph Digraph;

    typedef Digraph::Node Node;

    typedef Digraph::Arc Arc;

    typedef Digraph::ArcIt ArcIt;

    typedef Digraph::NodeMap<int> PotentialMap;

    typedef Digraph::ArcMap<int> CapacityMap;

    typedef Digraph::ArcMap<std::string> NameMap;

    Digraph digraph;

    PotentialMap potential(digraph);

    CapacityMap capacity(digraph);

    NameMap name(digraph);

    std::vector<Node> nodes;

    for (int i = 0; i < n; ++i) {

      Node node = digraph.addNode();

      potential[node] = rnd[m];

      nodes.push_back(node);

    }

    std::vector<Arc> arcs;

    for (int i = 0; i < e; ++i) {

      int s = rnd[n];

      int t = rnd[n];

      int c = rnd[m];

      Arc arc = digraph.addArc(nodes[s], nodes[t]);

      capacity[arc] = c;

      std::ostringstream os;

      os << "arc \t" << i << std::endl;

      name[arc] = os.str();

      arcs.push_back(arc);

    }

    DigraphWriter<Digraph>(ss, digraph).

      nodeMap("potential", potential).

      arcMap("capacity", capacity).

      arcMap("name", name).

      node("source", nodes[0]).

      node("target", nodes[1]).

      arc("bottleneck", arcs[e / 2]).

      attribute("creator", "lemon library").

      run();

  } catch (DataFormatError& error) {

    std::cerr << error.what() << std::endl;

  }

  try {

    typedef SmartDigraph Digraph;

    typedef Digraph::Node Node;

    typedef Digraph::Arc Arc;

    typedef Digraph::ArcIt ArcIt;

    typedef Digraph::NodeMap<int> LabelMap;

    typedef Digraph::NodeMap<int> PotentialMap;

    typedef Digraph::ArcMap<int> CapacityMap;

    typedef Digraph::ArcMap<std::string> NameMap;

    Digraph digraph;

    LabelMap label(digraph);

    PotentialMap potential(digraph);

    CapacityMap capacity(digraph);

    NameMap name(digraph);

    Node s, t;

    Arc a;

    std::string creator;

    for (int i = 0; i < n; ++i) {

      Node node = digraph.addNode();

      label[node] = i;

    }

    DigraphReader<Digraph>(ss, digraph).

      useNodes(label).

      nodeMap("potential", potential).

      arcMap("capacity", capacity).

      arcMap("name", name).

      node("source", s).

      node("target", t).

      arc("bottleneck", a).

      attribute("creator", creator).

      run();

    DigraphWriter<Digraph>(std::cout, digraph).

      nodeMap("potential", potential).

      arcMap("capacity", capacity).

      arcMap("name", name).

      node("source", s).

      node("target", t).

      arc("bottleneck", a).

      attribute("creator", creator).

      run();

  } catch (DataFormatError& error) {

    std::cerr << error.what() << std::endl;

  }

  return 0;

}

/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2008

 * 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.

 *

 */

#ifndef LEMON_ASSERT_H

#define LEMON_ASSERT_H

/// \ingroup exceptions

/// \file

/// \brief Extended assertion handling

#include <lemon/error.h>

namespace lemon {

  inline void assert_fail_log(const char *file, int line, const char *function,

			      const char *message, const char *assertion)

  {

    std::cerr << file << ":" << line << ": ";

    if (function)

      std::cerr << function << ": ";

    std::cerr << message;

    if (assertion)

      std::cerr << " (assertion '" << assertion << "' failed)";

    std::cerr << std::endl;

  }

  inline void assert_fail_abort(const char *file, int line,

				const char *function, const char* message,

				const char *assertion)

  {

    assert_fail_log(file, line, function, message, assertion);

    std::abort();

  }

  namespace _assert_bits {

    inline const char* cstringify(const std::string& str) {

      return str.c_str();

    }

    inline const char* cstringify(const char* str) {

      return str;

    }    

  }

}

#endif // LEMON_ASSERT_H

#undef LEMON_ASSERT

#undef LEMON_FIXME

#undef LEMON_DEBUG

#if (defined(LEMON_ASSERT_LOG) ? 1 : 0) +		\

  (defined(LEMON_ASSERT_ABORT) ? 1 : 0) +		\

  (defined(LEMON_ASSERT_CUSTOM) ? 1 : 0) > 1

#error "LEMON assertion system is not set properly"

#endif

#if ((defined(LEMON_ASSERT_LOG) ? 1 : 0) +		\

     (defined(LEMON_ASSERT_ABORT) ? 1 : 0) +		\

     (defined(LEMON_ASSERT_CUSTOM) ? 1 : 0) == 1 ||	\

     defined(LEMON_ENABLE_ASSERTS)) &&			\

  (defined(LEMON_DISABLE_ASSERTS) ||			\

   defined(NDEBUG))

#error "LEMON assertion system is not set properly"

#endif

#if defined LEMON_ASSERT_LOG

#  undef LEMON_ASSERT_HANDLER

#  define LEMON_ASSERT_HANDLER ::lemon::assert_fail_log

#elif defined LEMON_ASSERT_ABORT

#  undef LEMON_ASSERT_HANDLER

#  define LEMON_ASSERT_HANDLER ::lemon::assert_fail_abort

#elif defined LEMON_ASSERT_CUSTOM

#  undef LEMON_ASSERT_HANDLER

#  ifndef LEMON_CUSTOM_ASSERT_HANDLER

#    error "LEMON_CUSTOM_ASSERT_HANDLER is not set"

#  endif

#  define LEMON_ASSERT_HANDLER LEMON_CUSTOM_ASSERT_HANDLER

#elif defined LEMON_DISABLE_ASSERTS

#  undef LEMON_ASSERT_HANDLER

#elif defined NDEBUG

#  undef LEMON_ASSERT_HANDLER

#else

#  define LEMON_ASSERT_HANDLER ::lemon::assert_fail_abort

#endif

#ifndef LEMON_FUNCTION_NAME

#endif

#ifdef DOXYGEN

/// \ingroup exceptions

///

/// \brief Macro for assertion with customizable message

///

/// Macro for assertion with customizable message.  \param exp An

/// expression that must be convertible to \c bool.  If it is \c

/// false, then an assertion is raised. The concrete behaviour depends

/// on the settings of the assertion system.  \param msg A <tt>const

/// char*</tt> parameter, which can be used to provide information

/// about the circumstances of the failed assertion.

///

/// The assertions are enabled in the default behaviour.

/// You can disable them with the following code:

/// \code

/// #define LEMON_DISABLE_ASSERTS

/// \endcode

/// or with compilation parameters:

/// \code

/// g++ -DLEMON_DISABLE_ASSERTS

/// make CXXFLAGS='-DLEMON_DISABLE_ASSERTS'

/// \endcode

/// The checking is also disabled when the standard macro \c NDEBUG is defined.

/// 

/// The LEMON assertion system has a wide range of customization

/// properties. As a default behaviour the failed assertion prints a

/// short log message to the standard error and aborts the execution.

///

/// The following modes can be used in the assertion system: 

///

/// - \c LEMON_ASSERT_LOG The failed assertion prints a short log

///   message to the standard error and continues the execution.

/// - \c LEMON_ASSERT_ABORT This mode is similar to the \c

///   LEMON_ASSERT_LOG, but it aborts the program. It is the default

///   behaviour.

/// - \c LEMON_ASSERT_CUSTOM The user can define own assertion handler

///   function.

///   \code

///     void custom_assert_handler(const char* file, int line, const char* function,

///                                const char* message, const char* assertion);

///   \endcode

///   The name of the function should be defined as the \c

///   LEMON_CUSTOM_ASSERT_HANDLER macro name. 

///   \code

///     #define LEMON_CUSTOM_ASSERT_HANDLER custom_assert_handler

///   \endcode

///   Whenever an assertion is occured, the custom assertion

///   handler is called with appropiate parameters.

///

/// The assertion mode can also be changed within one compilation unit.

/// If the macros are redefined with other settings and the

/// \ref lemon/assert.h "assert.h" file is reincluded, then the

/// behaviour is changed appropiately to the new settings.

#  define LEMON_ASSERT(exp, msg)					\

  (static_cast<void> (!!(exp) ? 0 : (					\

    LEMON_ASSERT_HANDLER(__FILE__, __LINE__,				\

			 LEMON_FUNCTION_NAME,				\

			 ::lemon::_assert_bits::cstringify(msg), #exp), 0)))

/// \ingroup exceptions

///

/// \brief Macro for mark not yet implemented features.

///

/// Macro for mark not yet implemented features and outstanding bugs.

/// It is close to be the shortcut of the following code:

/// \code

///   LEMON_ASSERT(false, msg);

/// \endcode

///

/// \see LEMON_ASSERT 

#  define LEMON_FIXME(msg)						\

  (LEMON_ASSERT_HANDLER(__FILE__, __LINE__, LEMON_FUNCTION_NAME,	\

			::lemon::_assert_bits::cstringify(msg),		\

			static_cast<const char*>(0)))

/// \ingroup exceptions

///

/// \brief Macro for internal assertions

///

/// Macro for internal assertions, it is used in the library to check

/// the consistency of results of algorithms, several pre- and

/// postconditions and invariants. The checking is disabled by

/// default, but it can be turned on with the macro \c

/// LEMON_ENABLE_DEBUG.

/// \code

/// #define LEMON_ENABLE_DEBUG

/// \endcode

/// or with compilation parameters:

/// \code

/// g++ -DLEMON_ENABLE_DEBUG

/// make CXXFLAGS='-DLEMON_ENABLE_DEBUG'

/// \endcode

///

/// This macro works like the \c LEMON_ASSERT macro, therefore the

/// current behaviour depends on the settings of \c LEMON_ASSERT

/// macro.

///

/// \see LEMON_ASSERT 

#  define LEMON_DEBUG(exp, msg)						\

  (static_cast<void> (!!(exp) ? 0 : (					\

    LEMON_ASSERT_HANDLER(__FILE__, __LINE__,                            \

			 LEMON_FUNCTION_NAME,				\

			 ::lemon::_assert_bits::cstringify(msg), #exp), 0)))

#else

#  ifndef LEMON_ASSERT_HANDLER

#    define LEMON_ASSERT(exp, msg)  (static_cast<void>(0))

#    define LEMON_FIXME(msg) (static_cast<void>(0))

#    define LEMON_DEBUG(exp, msg) (static_cast<void>(0))

#  else

#    define LEMON_ASSERT(exp, msg)					\

       (static_cast<void> (!!(exp) ? 0 : (				\

        LEMON_ASSERT_HANDLER(__FILE__, __LINE__,                        \

			     LEMON_FUNCTION_NAME,			\

			     ::lemon::_assert_bits::cstringify(msg),	\

			     #exp), 0)))

#    define LEMON_FIXME(msg)						\

       (LEMON_ASSERT_HANDLER(__FILE__, __LINE__, LEMON_FUNCTION_NAME,	\

			     ::lemon::_assert_bits::cstringify(msg),	\

			     static_cast<const char*>(0)))

#    if LEMON_ENABLE_DEBUG

#      define LEMON_DEBUG(exp, msg)

         (static_cast<void> (!!(exp) ? 0 : (         \

           LEMON_ASSERT_HANDLER(__FILE__, __LINE__,  \

                                LEMON_FUNCTION_NAME, \

				::lemon::_assert_bits::cstringify(msg),	\

				#exp), 0)))

#    else

#      define LEMON_DEBUG(exp, msg) (static_cast<void>(0))

#    endif

#  endif

#endif

#ifdef DOXYGEN

#else

#endif

/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2008

 * 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.

 *

 */

#ifndef LEMON_GRAPH_TO_EPS_H

#define LEMON_GRAPH_TO_EPS_H

#include<iostream>

#include<fstream>

#include<sstream>

#include<algorithm>

#include<vector>

#ifndef WIN32

#include<sys/time.h>

#include<ctime>

#else

#include<windows.h>

#endif

#include<lemon/math.h>

#include<lemon/bits/invalid.h>

#include<lemon/dim2.h>

#include<lemon/maps.h>

#include<lemon/color.h>

#include<lemon/bits/bezier.h>

///\ingroup eps_io

///\file

///\brief A well configurable tool for visualizing graphs

namespace lemon {

  namespace _graph_to_eps_bits {

    template<class MT>

    class _NegY {

    public:

      typedef typename MT::Key Key;

      typedef typename MT::Value Value;

      const MT ↦

      int yscale;

      _NegY(const MT &m,bool b) : map(m), yscale(1-b*2) {}

      Value operator[](Key n) { return Value(map[n].x,map[n].y*yscale);}

    };

  }

///Default traits class of \ref GraphToEps

///Default traits class of \ref GraphToEps

///

///\c G is the type of the underlying graph.

template<class G>

struct DefaultGraphToEpsTraits

{

  typedef G Graph;

  typedef typename Graph::Node Node;

  typedef typename Graph::NodeIt NodeIt;

  typedef typename Graph::Arc Arc;

  typedef typename Graph::ArcIt ArcIt;

  typedef typename Graph::InArcIt InArcIt;

  typedef typename Graph::OutArcIt OutArcIt;

  const Graph &g;

  std::ostream& os;

  typedef ConstMap<typename Graph::Node,dim2::Point<double> > CoordsMapType;

  CoordsMapType _coords;

  ConstMap<typename Graph::Node,double > _nodeSizes;

  ConstMap<typename Graph::Node,int > _nodeShapes;

  ConstMap<typename Graph::Node,Color > _nodeColors;

  ConstMap<typename Graph::Arc,Color > _arcColors;

  ConstMap<typename Graph::Arc,double > _arcWidths;

  double _arcWidthScale;

  double _nodeScale;

  double _xBorder, _yBorder;

  double _scale;

  double _nodeBorderQuotient;

  bool _drawArrows;

  double _arrowLength, _arrowWidth;

  bool _showNodes, _showArcs;

  bool _enableParallel;

  double _parArcDist;

  bool _showNodeText;

  ConstMap<typename Graph::Node,bool > _nodeTexts;  

  double _nodeTextSize;

  bool _showNodePsText;

  ConstMap<typename Graph::Node,bool > _nodePsTexts;  

  char *_nodePsTextsPreamble;

  bool _undirected;

  bool _pleaseRemoveOsStream;

  bool _scaleToA4;

  std::string _title;

  std::string _copyright;

  enum NodeTextColorType 

    { DIST_COL=0, DIST_BW=1, CUST_COL=2, SAME_COL=3 } _nodeTextColorType;

  ConstMap<typename Graph::Node,Color > _nodeTextColors;

  bool _autoNodeScale;

  bool _autoArcWidthScale;

  bool _absoluteNodeSizes;

  bool _absoluteArcWidths;

  bool _negY;

  bool _preScale;

  ///Constructor

  ///Constructor

  ///\param _g is a reference to the graph to be printed

  ///\param _os is a reference to the output stream.

  ///\param _os is a reference to the output stream.

  ///\param _pros If it is \c true, then the \c ostream referenced by \c _os

  ///will be explicitly deallocated by the destructor.

  ///By default it is <tt>std::cout</tt>

  DefaultGraphToEpsTraits(const G &_g,std::ostream& _os=std::cout,

			  bool _pros=false) :

    g(_g), os(_os),

    _coords(dim2::Point<double>(1,1)), _nodeSizes(1), _nodeShapes(0),

    _nodeColors(WHITE), _arcColors(BLACK),

    _arcWidths(1.0), _arcWidthScale(0.003),

    _nodeScale(.01), _xBorder(10), _yBorder(10), _scale(1.0),

    _nodeBorderQuotient(.1),

    _drawArrows(false), _arrowLength(1), _arrowWidth(0.3),

    _showNodes(true), _showArcs(true),

    _enableParallel(false), _parArcDist(1),

    _showNodeText(false), _nodeTexts(false), _nodeTextSize(1),

    _showNodePsText(false), _nodePsTexts(false), _nodePsTextsPreamble(0),

    _undirected(lemon::UndirectedTagIndicator<G>::value),

    _pleaseRemoveOsStream(_pros), _scaleToA4(false),

    _nodeTextColorType(SAME_COL), _nodeTextColors(BLACK),

    _autoNodeScale(false),

    _autoArcWidthScale(false),

    _absoluteNodeSizes(false),

    _absoluteArcWidths(false),

    _negY(false),

    _preScale(true)

  {}

};

///Auxiliary class to implement the named parameters of \ref graphToEps()

///Auxiliary class to implement the named parameters of \ref graphToEps()

template<class T> class GraphToEps : public T 

{

  // Can't believe it is required by the C++ standard

  using T::g;

  using T::os;

  using T::_coords;

  using T::_nodeSizes;

  using T::_nodeShapes;

  using T::_nodeColors;

  using T::_arcColors;

  using T::_arcWidths;

  using T::_arcWidthScale;

  using T::_nodeScale;

  using T::_xBorder;

  using T::_yBorder;

  using T::_scale;

  using T::_nodeBorderQuotient;

  using T::_drawArrows;

  using T::_arrowLength;

  using T::_arrowWidth;

  using T::_showNodes;

  using T::_showArcs;

  using T::_enableParallel;

  using T::_parArcDist;

  using T::_showNodeText;

  using T::_nodeTexts;  

  using T::_nodeTextSize;

  using T::_showNodePsText;

  using T::_nodePsTexts;  

  using T::_nodePsTextsPreamble;

  using T::_undirected;

  using T::_pleaseRemoveOsStream;

  using T::_scaleToA4;

  using T::_title;

  using T::_copyright;

  using T::NodeTextColorType;

  using T::CUST_COL;

    typedef True BuildTag;

    template <typename CPath>

    void build(const CPath& path) {

      for (typename CPath::ArcIt it(path); it != INVALID; ++it) {

        addBack(it);

      }

    }

    template <typename CPath>

    void buildRev(const CPath& path) {

      for (typename CPath::RevArcIt it(path); it != INVALID; ++it) {

        addFront(it);

      }

    }

  };

  /// \brief A structure for representing directed paths in a digraph.

  ///

  /// A structure for representing directed path in a digraph.

  /// \param Digraph The digraph type in which the path is.

  ///

  /// In a sense, the path can be treated as a list of arcs. The

  /// lemon path type stores just this list. As a consequence it

  /// cannot enumerate the nodes in the path and the source node of

  /// a zero length path is undefined.

  ///

  /// This implementation is completly static, i.e. it can be copy constucted

  /// or copy assigned from another path, but otherwise it cannot be

  /// modified.

  ///

  /// Being the the most memory efficient path type in LEMON,

  /// it is intented to be

  /// used when you want to store a large number of paths.

  template <typename _Digraph>

  class StaticPath {

  public:

    typedef _Digraph Digraph;

    typedef typename Digraph::Arc Arc;

    /// \brief Default constructor

    ///

    /// Default constructor

    StaticPath() : len(0), arcs(0) {}

    /// \brief Template copy constructor

    ///

    /// This path can be initialized from any other path type.

    template <typename CPath>

    StaticPath(const CPath& cpath) : arcs(0) {

      copyPath(*this, cpath);

    }

    /// \brief Destructor of the path

    ///

    /// Destructor of the path

    ~StaticPath() {

      if (arcs) delete[] arcs;

    }

    /// \brief Template copy assignment

    ///

    /// This path can be made equal to any other path type. It simply

    /// makes a copy of the given path.

    template <typename CPath>

    StaticPath& operator=(const CPath& cpath) {

      copyPath(*this, cpath);

      return *this;

    }

    /// \brief Iterator class to iterate on the arcs of the paths

    ///

    /// This class is used to iterate on the arcs of the paths

    ///

    /// Of course it converts to Digraph::Arc

    class ArcIt {

      friend class StaticPath;

    public:

      /// Default constructor

      ArcIt() {}

      /// Invalid constructor

      ArcIt(Invalid) : path(0), idx(-1) {}

      /// Initializate the constructor to the first arc of path

      ArcIt(const StaticPath &_path) 

        : path(&_path), idx(_path.empty() ? -1 : 0) {}

    private:

      /// Constructor with starting point

      ArcIt(const StaticPath &_path, int _idx) 

        : idx(_idx), path(&_path) {}

    public:

      ///Conversion to Digraph::Arc

      operator const Arc&() const {

        return path->nth(idx);

      }

      /// Next arc

      ArcIt& operator++() { 

        ++idx;

        if (idx >= path->length()) idx = -1; 

        return *this; 

      }

      /// Comparison operator

      bool operator==(const ArcIt& e) const { return idx==e.idx; }

      /// Comparison operator

      bool operator!=(const ArcIt& e) const { return idx!=e.idx; }

      /// Comparison operator

      bool operator<(const ArcIt& e) const { return idx<e.idx; }

    private:

      const StaticPath *path;

      int idx;

    };

    /// \brief The nth arc.

    ///

    /// \pre n is in the [0..length() - 1] range

    const Arc& nth(int n) const {

      return arcs[n];

    }

    /// \brief The arc iterator pointing to the nth arc.

    ArcIt nthIt(int n) const {

      return ArcIt(*this, n);

    }

    /// \brief The length of the path.

    int length() const { return len; }

    /// \brief Return true when the path is empty.

    int empty() const { return len == 0; }

    /// \break Erase all arcs in the digraph.

    void clear() {

      len = 0;

      if (arcs) delete[] arcs;

      arcs = 0;

    }

    /// \brief The first arc of the path.

    const Arc& front() const {

      return arcs[0];

    }

    /// \brief The last arc of the path.

    const Arc& back() const {

      return arcs[len - 1];

    }

    typedef True BuildTag;

    template <typename CPath>

    void build(const CPath& path) {

      len = path.length();

      arcs = new Arc[len];

      int index = 0;

      for (typename CPath::ArcIt it(path); it != INVALID; ++it) {

        arcs[index] = it;

        ++index;

      }

    }

    template <typename CPath>

    void buildRev(const CPath& path) {

      len = path.length();

      arcs = new Arc[len];

      int index = len;

      for (typename CPath::RevArcIt it(path); it != INVALID; ++it) {

        --index;

        arcs[index] = it;

      }

    }

  private:

    int len;

    Arc* arcs;

  };

  ///////////////////////////////////////////////////////////////////////

  // Additional utilities

  ///////////////////////////////////////////////////////////////////////

  namespace _path_bits {

    template <typename Path, typename Enable = void>

      static const bool value = false;

    };

    > {

      static const bool value = true;

    };

    template <typename Target, typename Source,

    struct PathCopySelector {

      static void copy(Target& target, const Source& source) {

        target.clear();

        for (typename Source::ArcIt it(source); it != INVALID; ++it) {

          target.addBack(it);

        }

      }

    };

      static void copy(Target& target, const Source& source) {

        target.clear();

        for (typename Source::RevArcIt it(source); it != INVALID; ++it) {

          target.addFront(it);

        }

      }

    };

      static void copy(Target& target, const Source& source) {

        target.clear();

        target.build(source);

      }

    };

    template <typename Target, typename Source>

      static void copy(Target& target, const Source& source) {

        target.clear();

        target.buildRev(source);

      }

    };

  }

  /// \brief Make a copy of a path.

  ///

  ///  This function makes a copy of a path.

  template <typename Target, typename Source>

  void copyPath(Target& target, const Source& source) {

    checkConcept<concepts::PathDumper<typename Source::Digraph>, Source>();

    _path_bits::PathCopySelector<Target, Source>::copy(target, source);

  }

  /// \brief Check the consistency of a path.

  ///

  /// This function checks that the target of each arc is the same

  /// as the source of the next one. 

  /// 

  template <typename Digraph, typename Path>

  bool checkPath(const Digraph& digraph, const Path& path) {

    typename Path::ArcIt it(path);

    if (it == INVALID) return true;

    typename Digraph::Node node = digraph.target(it);

    ++it;

    while (it != INVALID) {

      if (digraph.source(it) != node) return false;

      node = digraph.target(it);

      ++it;

    }

    return true;

  }

  /// \brief The source of a path

  ///

  /// This function returns the source of the given path.

  template <typename Digraph, typename Path>

  typename Digraph::Node pathSource(const Digraph& digraph, const Path& path) {

    return digraph.source(path.front());

  }

  /// \brief The target of a path

  ///

  /// This function returns the target of the given path.

  template <typename Digraph, typename Path>

  typename Digraph::Node pathTarget(const Digraph& digraph, const Path& path) {

    return digraph.target(path.back());

  }

  /// \brief Class which helps to iterate through the nodes of a path

  ///

  /// In a sense, the path can be treated as a list of arcs. The

  /// lemon path type stores only this list. As a consequence, it

  /// cannot enumerate the nodes in the path and the zero length paths

  /// cannot have a source node.

  ///

  /// This class implements the node iterator of a path structure. To

  /// provide this feature, the underlying digraph should be passed to

  /// the constructor of the iterator.

  template <typename Path>

  class PathNodeIt {

  private:

    const typename Path::Digraph *_digraph;

    typename Path::ArcIt _it;

    typename Path::Digraph::Node _nd;

  public:

    typedef typename Path::Digraph Digraph;

    typedef typename Digraph::Node Node;

    /// Default constructor

    PathNodeIt() {}

    /// Invalid constructor

    PathNodeIt(Invalid) 

      : _digraph(0), _it(INVALID), _nd(INVALID) {}

    /// Constructor