RhodeCode

\endcode

\subsection cs-funcs Constants, Macros

The names of constants and macros should look like the following.

\code

ALL_UPPER_CASE_WITH_UNDERSCORES

\endcode

\subsection cs-loc-var Class and instance member variables, auto variables

\code

all_lower_case_with_underscores

\endcode

\subsection pri-loc-var Private member variables

Private member variables should start with underscore

\code

_start_with_underscores

\endcode

\brief Algorithms for finding maximum flows.

This group describes the algorithms for finding maximum flows and

feasible circulations.

The maximum flow problem is to find a flow between a single source and

a single target that is maximum. Formally, there is a \f$G=(V,A)\f$

directed graph, an \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity

function and given \f$s, t \in V\f$ source and target node. The

maximum flow is the \f$f_a\f$ solution of the next optimization problem:

\f[ 0 \le f_a \le c_a \f]

\f[ \max \sum_{v\in\delta^{+}(s)}f_{uv} - \sum_{v\in\delta^{-}(s)}f_{vu}\f]

LEMON contains several algorithms for solving maximum flow problems:

- \ref lemon::EdmondsKarp "Edmonds-Karp"

- \ref lemon::Preflow "Goldberg's Preflow algorithm"

- \ref lemon::DinitzSleatorTarjan "Dinitz's blocking flow algorithm with dynamic trees"

- \ref lemon::GoldbergTarjan "Preflow algorithm with dynamic trees"

In most cases the \ref lemon::Preflow "Preflow" algorithm provides the

fastest method to compute the maximum flow. All impelementations

provides functions to query the minimum cut, which is the dual linear

programming problem of the maximum flow.

@ingroup algs

\brief Algorithms for finding minimum cut in graphs.

This group describes the algorithms for finding minimum cut in graphs.

The minimum cut problem is to find a non-empty and non-complete

\f$X\f$ subset of the vertices with minimum overall capacity on

outgoing arcs. Formally, there is \f$G=(V,A)\f$ directed graph, an

\f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum

cut is the \f$X\f$ solution of the next optimization problem:

LEMON contains several algorithms related to minimum cut problems:

- \ref lemon::HaoOrlin "Hao-Orlin algorithm" to calculate minimum cut

  in directed graphs

- \ref lemon::NagamochiIbaraki "Nagamochi-Ibaraki algorithm" to

  calculate minimum cut in undirected graphs

- \ref lemon::GomoryHuTree "Gomory-Hu tree computation" to calculate all

  pairs minimum cut in undirected graphs

If you want to find minimum cut just between two distinict nodes,

please see the \ref max_flow "Maximum Flow page".

This group describes the algorithms for discovering the graph properties

like connectivity, bipartiteness, euler property, simplicity etc.

\image html edge_biconnected_components.png

\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth

*/

/**

@defgroup planar Planarity embedding and drawing

@ingroup algs

\brief Algorithms for planarity checking, embedding and drawing

\image html planar.png

\image latex planar.eps "Plane graph" width=\textwidth

*/

/**

@defgroup matching Matching algorithms

@ingroup algs

\brief Algorithms for finding matchings in graphs and bipartite graphs.

This group contains algorithm objects and functions to calculate

matchings in graphs and bipartite graphs. The general matching problem is

\brief Graph Input-Output methods

This group describes the tools for importing and exporting graphs

and graph related data. Now it supports the LEMON format, the

\c DIMACS format and the encapsulated postscript (EPS) format.

*/

/**

@defgroup lemon_io Lemon Input-Output

@ingroup io_group

\brief Reading and writing \ref lgf-format "Lemon Graph Format".

*/

/**

@defgroup eps_io Postscript exporting

@ingroup io_group

\brief General \c EPS drawer and graph exporter

This group describes general \c EPS drawing methods and special

graph exporting tools.

*/

                      << ": The following mandatory arguments are missing.\n";

          ok=false;

          showHelp(i);

        }

    for(Groups::iterator i=_groups.begin();i!=_groups.end();++i)

      if(i->second.mandatory||i->second.only_one)

        {

          int set=0;

          for(GroupData::Opts::iterator o=i->second.opts.begin();

              o!=i->second.opts.end();++o)

            if(_opts.find(*o)->second.set) ++set;

          if(i->second.mandatory&&!set) {

            ok=false;

            for(GroupData::Opts::iterator o=i->second.opts.begin();

                o!=i->second.opts.end();++o)

              showHelp(_opts.find(*o));

          }

          if(i->second.only_one&&set>1) {

            ok=false;

            for(GroupData::Opts::iterator o=i->second.opts.begin();

                o!=i->second.opts.end();++o)

              showHelp(_opts.find(*o));

          }

        }

    if(!ok) {

      std::cerr << "\nType '" << _command_name <<

        " --help' to obtain a short summary on the usage.\n\n";

      exit(1);

    }

  }

/// 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

///   \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

    {

      return new ReachedMap(G);

    }

    ///The type of the map that stores the dists of the nodes.

    ///The type of the map that stores the dists of the nodes.

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    ///

    typedef typename Digraph::template NodeMap<int> DistMap;

    ///Instantiates a DistMap.

    ///This function instantiates a \ref DistMap.

    static DistMap *createDistMap(const GR &G)

    {

      return new DistMap(G);

    }

  };

  ///%BFS algorithm class.

  ///\ingroup search

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

  ///

  ///\tparam GR The digraph type the algorithm runs on. The default value is

    {

      return new ReachedMap(G);

    }

    ///The type of the map that stores the dists of the nodes.

    ///The type of the map that stores the dists of the nodes.

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    ///

    typedef NullMap<typename Digraph::Node,int> DistMap;

    ///Instantiates a DistMap.

    ///This function instantiates a \ref DistMap.

#ifdef DOXYGEN

    static DistMap *createDistMap(const GR &g)

#else

    static DistMap *createDistMap(const GR &)

#endif

    {

      return new DistMap();

    }

  };

  /// Default traits used by \ref BfsWizard

  /// \ingroup search

  ///

  /// \brief %BFS Visit algorithm class.

  ///

  /// 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

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

  ///

  /// \ref ListDigraph. The value of _Digraph is not used directly by Bfs, it

  /// is only passed to \ref BfsDefaultTraits.

  /// \tparam _Visitor The Visitor object for the algorithm. The

  /// \ref BfsVisitor "BfsVisitor<_Digraph>" 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 _Traits Traits class to set various data types used by the

  /// algorithm. The default traits class is

  /// \ref BfsVisitDefaultTraits "BfsVisitDefaultTraits<_Digraph>".

  /// See \ref BfsVisitDefaultTraits for the documentation of

  /// a Bfs visit traits class.

#ifdef DOXYGEN

    /// @{

    /// Readable map concept

    /// Readable map concept.

    ///

    template<typename K, typename T>

    class ReadMap

    {

    public:

      /// The key type of the map.

      typedef K Key;

      typedef T Value;

      /// Returns the value associated with the given key.

      Value operator[](const Key &) const {

        return *static_cast<Value *>(0);

      }

      template<typename _ReadMap>

      struct Constraints {

        void constraints() {

          Value val = m[key];

          val = m[key];

    /// Writable map concept

    /// Writable map concept.

    ///

    template<typename K, typename T>

    class WriteMap

    {

    public:

      /// The key type of the map.

      typedef K Key;

      typedef T Value;

      /// Sets the value associated with the given key.

      void set(const Key &, const Value &) {}

      /// Default constructor.

      WriteMap() {}

      template <typename _WriteMap>

      struct Constraints {

        void constraints() {

          m.set(key, val);

    /// Read/writable map concept

    /// Read/writable map concept.

    ///

    template<typename K, typename T>

    class ReadWriteMap : public ReadMap<K,T>,

                         public WriteMap<K,T>

    {

    public:

      /// The key type of the map.

      typedef K Key;

      typedef T Value;

      /// Returns the value associated with the given key.

      Value operator[](const Key &) const {

        return *static_cast<Value *>(0);

      }

      /// Sets the value associated with the given key.

      void set(const Key &, const Value &) {}

      template<typename _ReadWriteMap>

      struct Constraints {

    /// Dereferable map concept

    /// Dereferable map concept.

    ///

    template<typename K, typename T, typename R, typename CR>

    class ReferenceMap : public ReadWriteMap<K,T>

    {

    public:

      /// Tag for reference maps.

      typedef True ReferenceMapTag;

      /// The key type of the map.

      typedef K Key;

      typedef T Value;

      /// The reference type of the map.

      typedef R Reference;

      /// The const reference type of the map.

      typedef CR ConstReference;

    public:

      /// Returns a reference to the value associated with the given key.

      Reference operator[](const Key &) {

        return *static_cast<Value *>(0);

      }

    {

      return new ReachedMap(G);

    }

    ///The type of the map that stores the dists of the nodes.

    ///The type of the map that stores the dists of the nodes.

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    ///

    typedef typename Digraph::template NodeMap<int> DistMap;

    ///Instantiates a DistMap.

    ///This function instantiates a \ref DistMap.

    static DistMap *createDistMap(const GR &G)

    {

      return new DistMap(G);

    }

  };

  ///%DFS algorithm class.

  ///\ingroup search

  ///This class provides an efficient implementation of the %DFS algorithm.

  ///

  ///\tparam GR The digraph type the algorithm runs on. The default value is

    {

      return new ReachedMap(G);

    }

    ///The type of the map that stores the dists of the nodes.

    ///The type of the map that stores the dists of the nodes.

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    ///

    typedef NullMap<typename Digraph::Node,int> DistMap;

    ///Instantiates a DistMap.

    ///This function instantiates a \ref DistMap.

#ifdef DOXYGEN

    static DistMap *createDistMap(const GR &g)

#else

    static DistMap *createDistMap(const GR &)

#endif

    {

      return new DistMap();

    }

  };

  /// Default traits used by \ref DfsWizard

  };

  /// %DFS Visit algorithm class.

  /// \ingroup search

  /// This class provides an efficient implementation of the %DFS algorithm

  /// with visitor interface.

  ///

  /// The %DfsVisit class provides an alternative interface to the Dfs

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

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

  ///

  /// \ref ListDigraph. The value of _Digraph is not used directly by Dfs, it

  /// is only passed to \ref DfsDefaultTraits.

  /// \tparam _Visitor The Visitor object for the algorithm. The

  /// \ref DfsVisitor "DfsVisitor<_Digraph>" is an empty Visitor which

  /// does not observe the Dfs events. If you want to observe the dfs

  /// events you should implement your own Visitor class.

  /// \tparam _Traits Traits class to set various data types used by the

  /// algorithm. The default traits class is

  /// \ref DfsVisitDefaultTraits "DfsVisitDefaultTraits<_Digraph>".

  /// See \ref DfsVisitDefaultTraits for the documentation of

  /// a Dfs visit traits class.

  ///

    {

      return new ProcessedMap();

    }

    ///The type of the map that stores the dists of the nodes.

    ///The type of the map that stores the dists of the nodes.

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    ///

    typedef typename Digraph::template NodeMap<typename LM::Value> DistMap;

    ///Instantiates a DistMap.

    ///This function instantiates a \ref DistMap.

    static DistMap *createDistMap(const GR &G)

    {

      return new DistMap(G);

    }

  };

  ///%Dijkstra algorithm class.

  /// \ingroup shortest_path

  ///This class provides an efficient implementation of %Dijkstra algorithm.

  ///The arc lengths are passed to the algorithm using a

  ///\ref concepts::ReadMap "ReadMap",

        return new ProcessedMap(G);

      }

    };

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

    ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.

    ///

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

    ///for setting the ProcessedMap type to be Digraph::NodeMap<bool>.

    ///If you don't set it explicitely, it will be automatically allocated.

    template <class T>

    struct DefProcessedMapToBeDefaultMap

      : public Dijkstra< Digraph, LengthMap, DefDigraphProcessedMapTraits> {

    };

    template <class H, class CR>

    struct DefHeapTraits : public Traits {

      typedef CR HeapCrossRef;

      typedef H Heap;

      static HeapCrossRef *createHeapCrossRef(const Digraph &) {

        throw UninitializedParameter();

      }

      static Heap *createHeap(HeapCrossRef &)

      {

        throw UninitializedParameter();

    {

      return new ProcessedMap();

    }

    ///The type of the map that stores the dists of the nodes.

    ///The type of the map that stores the dists of the nodes.

    ///It must meet the \ref concepts::WriteMap "WriteMap" concept.

    ///

    typedef NullMap<typename Digraph::Node,typename LM::Value> DistMap;

    ///Instantiates a DistMap.

    ///This function instantiates a \ref DistMap.

#ifdef DOXYGEN

    static DistMap *createDistMap(const GR &g)

#else

    static DistMap *createDistMap(const GR &)

#endif

    {

      return new DistMap();

    }

  };

  /// Default traits used by \ref DijkstraWizard

  bool _absoluteNodeSizes;

  bool _absoluteArcWidths;

  bool _negY;

  bool _preScale;

  ///Constructor

  ///Constructor

  ///\param _g  Reference to the graph to be printed.

  ///\param _os 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.

  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),

      os << "%%BoundingBox: "

         << int(floor(bb.left()   * _scale - _xBorder)) << ' '

         << int(floor(bb.bottom() * _scale - _yBorder)) << ' '

         << int(ceil(bb.right()  * _scale + _xBorder)) << ' '

         << int(ceil(bb.top()    * _scale + _yBorder)) << '\n';

    }

    os << "%%EndComments\n";

    //x1 y1 x2 y2 x3 y3 cr cg cb w

    os << "/lb { setlinewidth setrgbcolor newpath moveto\n"

       << "      4 2 roll 1 index 1 index curveto stroke } bind def\n";

    //x y r

    //x y r

    os << "/sq { newpath 2 index 1 index add 2 index 2 index add moveto\n"

       << "      2 index 1 index sub 2 index 2 index add lineto\n"

       << "      2 index 1 index sub 2 index 2 index sub lineto\n"

       << "      2 index 1 index add 2 index 2 index sub lineto\n"

       << "      closepath pop pop pop} bind def\n";

    //x y r

    os << "/di { newpath 2 index 1 index add 2 index moveto\n"

       << "      2 index             2 index 2 index add lineto\n"

       << "      2 index 1 index sub 2 index             lineto\n"

       << "      2 index             2 index 2 index sub lineto\n"

       << "      closepath pop pop pop} bind def\n";

       << "   } bind def\n";

    os << "/nsq { 0 0 0 setrgbcolor 5 index 5 index 5 index sq fill\n"

       << "     setrgbcolor " << 1+_nodeBorderQuotient << " div sq fill\n"

       << "   } bind def\n";

    os << "/ndi { 0 0 0 setrgbcolor 5 index 5 index 5 index di fill\n"

       << "     setrgbcolor " << 1+_nodeBorderQuotient << " div di fill\n"

       << "   } bind def\n";

    os << "/nfemale { 0 0 0 setrgbcolor 3 index "

       << _nodeBorderQuotient/(1+_nodeBorderQuotient)

       << " 1.5 mul mul setlinewidth\n"

       << "  newpath 5 index 5 index moveto "

       << "5 index 5 index 5 index 3.01 mul sub\n"

       << "  5 index 5 index 5 index c fill\n"

       << "  setrgbcolor " << 1+_nodeBorderQuotient << " div c fill\n"

       << "  } bind def\n";

    os << "/nmale {\n"

       << "  0 0 0 setrgbcolor 3 index "

       << _nodeBorderQuotient/(1+_nodeBorderQuotient)

       <<" 1.5 mul mul setlinewidth\n"

       << "  newpath 5 index 5 index moveto\n"

       << "  5 index 4 index 1 mul 1.5 mul add\n"

       << "  5 index 5 index 3 sqrt 1.5 mul mul add\n"

       << "  1 index 1 index lineto\n"

       << "  1 index 1 index 7 index sub moveto\n"

       << "  1 index 1 index lineto\n"

       << "  stroke\n"

       << "  5 index 5 index 5 index c fill\n"

       << "  setrgbcolor " << 1+_nodeBorderQuotient << " div c fill\n"

       << "  } bind def\n";

    os << "/arrl " << _arrowLength << " def\n";

    os << "/arrw " << _arrowWidth << " def\n";

    // l dx_norm dy_norm

    os << "/lrl { 2 index mul exch 2 index mul exch rlineto pop} bind def\n";

    //len w dx_norm dy_norm x1 y1 cr cg cb

       << "       /w exch def /len exch def\n"

      //         << "       0.1 setlinewidth x1 y1 moveto dx len mul dy len mul rlineto stroke"

       << "       newpath x1 dy w 2 div mul add y1 dx w 2 div mul sub moveto\n"

       << "       len w sub arrl sub dx dy lrl\n"

       << "       arrw dy dx neg lrl\n"

       << "       dx arrl w add mul dy w 2 div arrw add mul sub\n"

       << "       dy arrl w add mul dx w 2 div arrw add mul add rlineto\n"

       << "       dx arrl w add mul neg dy w 2 div arrw add mul sub\n"

       << "       dy arrl w add mul neg dx w 2 div arrw add mul add rlineto\n"

       << "       arrw dy dx neg lrl\n"

       << "       len w sub arrl sub neg dx dy lrl\n"

       << "       closepath fill } bind def\n";

          double sw=0;

          for(typename std::vector<Arc>::iterator e=i;e!=j;++e)

            sw+=_arcWidths[*e]*_arcWidthScale+_parArcDist;

          sw-=_parArcDist;

          sw/=-2.0;

          dim2::Point<double>

            dvec(mycoords[g.target(*i)]-mycoords[g.source(*i)]);

          double l=std::sqrt(dvec.normSquare());

          //\todo better 'epsilon' would be nice here.

          dim2::Point<double> d(dvec/std::max(l,EPSILON));

           dim2::Point<double> m;

//            m=dim2::Point<double>(mycoords[g.source(*i)])+

//             dvec*(double(_nodeSizes[g.source(*i)])/

//                (_nodeSizes[g.source(*i)]+_nodeSizes[g.target(*i)]));

           m=dim2::Point<double>(mycoords[g.source(*i)])+

            d*(l+_nodeSizes[g.source(*i)]-_nodeSizes[g.target(*i)])/2.0;

          for(typename std::vector<Arc>::iterator e=i;e!=j;++e) {

            sw+=_arcWidths[*e]*_arcWidthScale/2.0;

            dim2::Point<double> mm=m+rot90(d)*sw/.75;

            if(_drawArrows) {

              rn = _arrowLength+_arcWidths[*e]*_arcWidthScale;

              rn*=rn;

              t2=(t1+t2)/2;t1=0;

              for(int ii=0;ii<INTERPOL_PREC;++ii)

                if((bez((t1+t2)/2)-apoint).normSquare()>rn) t1=(t1+t2)/2;

                else t2=(t1+t2)/2;

              dim2::Point<double> linend=bez((t1+t2)/2);

              bez=bez.before((t1+t2)/2);

//               rn=_nodeSizes[g.source(*e)]*_nodeScale;

//               node_shape=_nodeShapes[g.source(*e)];

//               t1=0;t2=1;

//               for(int i=0;i<INTERPOL_PREC;++i)

//                 else t2=(t1+t2)/2;

//               bez=bez.after((t1+t2)/2);

              os << _arcWidths[*e]*_arcWidthScale << " setlinewidth "

                 << _arcColors[*e].red() << ' '

                 << _arcColors[*e].green() << ' '

                 << _arcColors[*e].blue() << " setrgbcolor newpath\n"

                 << bez.p1.x << ' ' <<  bez.p1.y << " moveto\n"

                 << bez.p2.x << ' ' << bez.p2.y << ' '

                 << bez.p3.x << ' ' << bez.p3.y << ' '

                 << bez.p4.x << ' ' << bez.p4.y << " curveto stroke\n";

              dim2::Point<double> dd(rot90(linend-apoint));

              dd*=(.5*_arcWidths[*e]*_arcWidthScale+_arrowWidth)/

  ///

  /// The \c useNodes() and \c useArcs() functions are used to tell the reader

  /// that the nodes or arcs should not be constructed (added to the

  /// graph) during the reading, but instead the label map of the items

  /// are given as a parameter of these functions. An

  /// application of these functions is multipass reading, which is

  /// important if two \c \@arcs sections must be read from the

  /// file. In this case the first phase would read the node set and one

  /// of the arc sets, while the second phase would read the second arc

  /// set into an \e ArcSet class (\c SmartArcSet or \c ListArcSet).

  /// The previously read label node map should be passed to the \c

  /// useNodes() functions. Another application of multipass reading when

  /// a single pass, because the arcs are not constructed when the node

  /// maps are read.

  template <typename _Digraph>

  class DigraphReader {

  public:

    typedef _Digraph Digraph;

    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

  private:

  public:

    ///Constructor.

    ///\param run indicates whether or not the timer starts immediately.

    ///

    Timer(bool run=true) :_running(run) {_reset();}

    ///\name Control the state of the timer

    ///Basically a Timer can be either running or stopped,

    ///but it provides a bit finer control on the execution.

    ///The \ref Timer also counts the number of \ref start()

    ///executions, and is stops only after the same amount (or more)

    ///of recursive functions.

    ///

    ///@{

    ///Reset and stop the time counters

    ///This function resets and stops the time counters

    ///\sa restart()

    void reset()

    {

      _running=0;

  check(dijkstra_test.dist(t)==13,"Dijkstra found a wrong path.");

  Path<Digraph> p = dijkstra_test.path(t);

  check(p.length()==4,"getPath() found a wrong path.");

  check(checkPath(G, p),"path() found a wrong path.");

  check(pathSource(G, p) == s,"path() found a wrong path.");

  check(pathTarget(G, p) == t,"path() found a wrong path.");

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

    Node u=G.source(e);

    Node v=G.target(e);

  }

  for(NodeIt v(G); v!=INVALID; ++v){

    check(dijkstra_test.reached(v),"Each node should be reached.");

    if ( dijkstra_test.predArc(v)!=INVALID ) {

      Arc e=dijkstra_test.predArc(v);

      Node u=G.source(e);

      check(u==dijkstra_test.predNode(v),"Wrong tree.");

      check(dijkstra_test.dist(v) - dijkstra_test.dist(u) == length[e],

    }

  }

  {

    NullMap<Node,Arc> myPredMap;

    dijkstra(G,length).predMap(myPredMap).run(s);

  }

}

int main() {

  checkDijkstra<ListDigraph>();

  checkDijkstra<SmartDigraph>();

        check(++con == INVALID, "There is more connecting arc.");

      }

    }

    ArcLookUp<Digraph> al1(fg);

    DynArcLookUp<Digraph> al2(fg);

    AllArcLookUp<Digraph> al3(fg);

    for (NodeIt src(fg); src != INVALID; ++src) {

      for (NodeIt trg(fg); trg != INVALID; ++trg) {

        Arc con1 = al1(src, trg);

        Arc con2 = al2(src, trg);

        Arc con3 = al3(src, trg);

        Arc con4 = findArc(fg, src, trg);

        check(con1 != INVALID, "There is no connecting arc.");

        check(fg.source(con1) == src, "Wrong source.");

        check(fg.target(con1) == trg, "Wrong target.");

      }

    }

  }

}

template <typename Graph>

void checkFindEdges() {

  TEMPLATE_GRAPH_TYPEDEFS(Graph);

  Graph graph;

  for (int i = 0; i < 10; ++i) {

    graph.addNode();

  }

  typename DescriptorMap<Graph, Node>::InverseMap invNodes(nodes);

  for (int i = 0; i < 100; ++i) {

    int src = rnd[invNodes.size()];

    int trg = rnd[invNodes.size()];

    graph.addEdge(invNodes[src], invNodes[trg]);

  }

  typename Graph::template EdgeMap<int> found(graph, 0);

  DescriptorMap<Graph, Edge> edges(graph);

  for (NodeIt src(graph); src != INVALID; ++src) {

    for (NodeIt trg(graph); trg != INVALID; ++trg) {

      for (ConEdgeIt<Graph> con(graph, src, trg); con != INVALID; ++con) {

        check( (graph.u(con) == src && graph.v(con) == trg) ||

        ++found[con];

        check(found[con] <= 2, "The edge found more than twice.");

      }

    }

  }

  for (EdgeIt it(graph); it != INVALID; ++it) {

    check( (graph.u(it) != graph.v(it) && found[it] == 2) ||

           (graph.u(it) == graph.v(it) && found[it] == 1),

           "The edge is not found correctly.");

  }

}

    ConstMap<A,C> map5 = map4;

    map4 = constMap<A>(C(2));

    map4.setAll(C(3));

    checkConcept<ReadWriteMap<A,int>, ConstMap<A,int> >();

    check(constMap<A>(10)[A()] == 10, "Something is wrong with ConstMap");

    checkConcept<ReadWriteMap<A,int>, ConstMap<A,Const<int,10> > >();

    ConstMap<A,Const<int,10> > map6;

    ConstMap<A,Const<int,10> > map7 = map6;

    map6 = constMap<A,int,10>();

    map7 = constMap<A,Const<int,10> >();

  }

  // IdentityMap

  {

    checkConcept<ReadMap<A,A>, IdentityMap<A> >();

    IdentityMap<A> map1;

    IdentityMap<A> map2 = map1;

    map1 = identityMap<A>();

    checkConcept<ReadMap<double,double>, IdentityMap<double> >();

          "Something is wrong with IdentityMap");

  }

  // RangeMap

  {

    checkConcept<ReferenceMap<int,B,B&,const B&>, RangeMap<B> >();

    RangeMap<B> map1;

    RangeMap<B> map2(10);

    RangeMap<B> map3(10,B());

    RangeMap<B> map4 = map1;

    RangeMap<B> map5 = rangeMap<B>();

    RangeMap<B> map6 = rangeMap<B>(10);

    SparseMap<A,B> map2 = B();

    SparseMap<A,B> map3 = sparseMap<A,B>();

    SparseMap<A,B> map4 = sparseMap<A>(B());

    checkConcept< ReferenceMap<double, int, int&, const int&>,

                  SparseMap<double, int> >();

    std::map<double, int> m;

    SparseMap<double, int> map5(m);

    SparseMap<double, int> map6(m,10);

    SparseMap<double, int> map7 = sparseMap(m);

    SparseMap<double, int> map8 = sparseMap(m,10);

          "Something is wrong with SparseMap");

    map5[1.0] = map6[3.14] = 100;

          "Something is wrong with SparseMap");

  }

  // ComposeMap

  {

    typedef ComposeMap<DoubleMap, ReadMap<B,A> > CompMap;

    checkConcept<ReadMap<B,double>, CompMap>();

    CompMap map1(DoubleMap(),ReadMap<B,A>());

    CompMap map2 = composeMap(DoubleMap(), ReadMap<B,A>());

    SparseMap<double, bool> m1(false); m1[3.14] = true;

    RangeMap<double> m2(2); m2[0] = 3.0; m2[1] = 3.14;

  }

  // CombineMap

  {

    typedef CombineMap<DoubleMap, DoubleMap, std::plus<double> > CombMap;

    checkConcept<ReadMap<A,double>, CombMap>();

    CombMap map1(DoubleMap(), DoubleMap());

    CombMap map2 = combineMap(DoubleMap(), DoubleMap(), std::plus<double>());

    check(combineMap(constMap<B,int,2>(), identityMap<B>(), &binc)[B()] == 3,

          "Something is wrong with CombineMap");

  }

  // FunctorToMap, MapToFunctor

  {

    checkConcept<ReadMap<A,B>, FunctorToMap<F,A,B> >();

    checkConcept<ReadMap<A,B>, FunctorToMap<F> >();

    FunctorToMap<F> map1;

    FunctorToMap<F> map2(F());

    B b = functorToMap(F())[A()];

    checkConcept<ReadMap<A,B>, MapToFunctor<ReadMap<A,B> > >();

    MapToFunctor<ReadMap<A,B> > map(ReadMap<A,B>());

          "Something is wrong with FunctorToMap or MapToFunctor");

    check(functorToMap(mapToFunctor(constMap<A,int>(2)))[A()] == 2,

          "Something is wrong with FunctorToMap or MapToFunctor");

  }

  // ConvertMap

  {

    ConvertMap<RangeMap<bool>, int> map1(rangeMap(1, true));

    ConvertMap<RangeMap<bool>, int> map2 = convertMap<int>(rangeMap(2, false));

  }

  // ForkMap

  {

    checkConcept<DoubleWriteMap, ForkMap<DoubleWriteMap, DoubleWriteMap> >();

    typedef RangeMap<double> RM;

    typedef SparseMap<int, double> SM;

    RM m1(10, -1);

    SM m2(-1);

    checkConcept<ReadWriteMap<int, double>, ForkMap<RM, SM> >();

    checkConcept<ReadWriteMap<int, double>, ForkMap<SM, RM> >();

    ForkMap<RM, SM> map1(m1,m2);

    ForkMap<SM, RM> map2 = forkMap(m2,m1);

    map2.set(5, 10);