RhodeCode

The authors of the 1.x series are

 * Balazs Dezso <deba@inf.elte.hu>

 * Alpar Juttner <alpar@cs.elte.hu>

 * Peter Kovacs <kpeter@inf.elte.hu>

 * Akos Ladanyi <ladanyi@tmit.bme.hu>

For more details on the actual contribution, please visit the history

of the main LEMON source repository: http://lemon.cs.elte.hu/hg/lemon

Moreover, this version is heavily based on the 0.x series of

LEMON. Here is the list of people who contributed to those versions.

 * Mihaly Barasz <klao@cs.elte.hu>

 * Johanna Becker <beckerjc@cs.elte.hu>

 * Attila Bernath <athos@cs.elte.hu>

 * Balazs Dezso <deba@inf.elte.hu>

 * Peter Hegyi <hegyi@tmit.bme.hu>

 * Alpar Juttner <alpar@cs.elte.hu>

 * Peter Kovacs <kpeter@inf.elte.hu>

 * Akos Ladanyi <ladanyi@tmit.bme.hu>

 * Marton Makai <marci@cs.elte.hu>

 * Jacint Szabo <jacint@cs.elte.hu>

Again, please visit the history of the old LEMON repository for more

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

 *

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

 *

 * Copyright (C) 2003-2009

 * 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.

 *

 */

namespace lemon {

/*!

\page lgf-format LEMON Graph Format (LGF)

The \e LGF is a <em>column oriented</em>

file format for storing graphs and associated data like

node and edge maps.

Each line with \c '#' first non-whitespace

character is considered as a comment line.

Otherwise the file consists of sections starting with

a header line. The header lines starts with an \c '@' character followed by the

type of section. The standard section types are \c \@nodes, \c

\@arcs and \c \@edges

and \@attributes. Each header line may also have an optional

\e name, which can be use to distinguish the sections of the same

type.

The standard sections are column oriented, each line consists of

<em>token</em>s separated by whitespaces. A token can be \e plain or

\e quoted. A plain token is just a sequence of non-whitespace characters,

while a quoted token is a

character sequence surrounded by double quotes, and it can also

contain whitespaces and escape sequences.

The \c \@nodes section describes a set of nodes and associated

maps. The first is a header line, its columns are the names of the

maps appearing in the following lines.

One of the maps must be called \c

"label", which plays special role in the file.

The following

non-empty lines until the next section describes nodes of the

graph. Each line contains the values of the node maps

associated to the current node.

\code

 @nodes

 label  coordinates  size    title

 1      (10,20)      10      "First node"

 2      (80,80)      8       "Second node"

 3      (40,10)      10      "Third node"

\endcode

values. The source and target tokens must be node labels.

\code

 @arcs

         capacity

 1   2   16

 1   3   12

 2   3   18

\endcode

The \c \@edges is just a synonym of \c \@arcs. The \@arcs section can

also store the edge set of an undirected graph. In such case there is

a conventional method for store arc maps in the file, if two columns

can be regarded as the values of an arc map.

The \c \@attributes section contains key-value pairs, each line

consists of two tokens, an attribute name, and then an attribute

value. The value of the attribute could be also a label value of a

node or an edge, or even an edge label prefixed with \c '+' or \c '-',

which regards to the forward or backward directed arc of the

corresponding edge.

\code

 @attributes

 source 1

 target 3

 caption "LEMON test digraph"

\endcode

The \e LGF can contain extra sections, but there is no restriction on

the format of such sections.

*/

}

//  LocalWords:  whitespace whitespaces

EXTRA_DIST += \

	lemon/lemon.pc.in \

	lemon/CMakeLists.txt \

	lemon/config.h.cmake

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/bucket_heap.h \

	lemon/cbc.h \

	lemon/circulation.h \

	lemon/clp.h \

	lemon/color.h \

	lemon/concept_check.h \

	lemon/connectivity.h \

	lemon/counter.h \

	lemon/core.h \

	lemon/cplex.h \

	lemon/dfs.h \

	lemon/dijkstra.h \

	lemon/dim2.h \

	lemon/dimacs.h \

	lemon/edge_set.h \

	lemon/elevator.h \

	lemon/error.h \

	lemon/euler.h \

	lemon/fib_heap.h \

	lemon/full_graph.h \

	lemon/glpk.h \

	lemon/gomory_hu.h \

	lemon/graph_to_eps.h \

	lemon/grid_graph.h \

	lemon/hypercube_graph.h \

	lemon/kruskal.h \

	lemon/hao_orlin.h \

	lemon/lgf_reader.h \

	lemon/lgf_writer.h \

	lemon/list_graph.h \

	lemon/lp.h \

	lemon/lp_base.h \

	lemon/lp_skeleton.h \

	lemon/list_graph.h \

	lemon/maps.h \

	lemon/matching.h \

	lemon/math.h \

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

 *

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

 *

 * Copyright (C) 2003-2009

 * 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_BITS_PATH_DUMP_H

#define LEMON_BITS_PATH_DUMP_H

#include <lemon/core.h>

#include <lemon/concept_check.h>

namespace lemon {

  template <typename _Digraph, typename _PredMap>

  class PredMapPath {

  public:

    typedef True RevPathTag;

    typedef _Digraph Digraph;

    typedef typename Digraph::Arc Arc;

    typedef _PredMap PredMap;

    PredMapPath(const Digraph& _digraph, const PredMap& _predMap,

                typename Digraph::Node _target)

      : digraph(_digraph), predMap(_predMap), target(_target) {}

    int length() const {

      int len = 0;

      typename Digraph::Node node = target;

      typename Digraph::Arc arc;

      while ((arc = predMap[node]) != INVALID) {

        node = digraph.source(arc);

        ++len;

      }

      return len;

    }

    bool empty() const {

    }

    class RevArcIt {

    public:

      RevArcIt() {}

      RevArcIt(Invalid) : path(0), current(INVALID) {}

      RevArcIt(const PredMapPath& _path)

        : path(&_path), current(_path.target) {

        if (path->predMap[current] == INVALID) current = INVALID;

      }

      operator const typename Digraph::Arc() const {

        return path->predMap[current];

      }

      RevArcIt& operator++() {

        current = path->digraph.source(path->predMap[current]);

        if (path->predMap[current] == INVALID) current = INVALID;

        return *this;

      }

      bool operator==(const RevArcIt& e) const {

        return current == e.current;

      }

      bool operator!=(const RevArcIt& e) const {

        return current != e.current;

      }

      bool operator<(const RevArcIt& e) const {

        return current < e.current;

      }

    private:

      const PredMapPath* path;

      typename Digraph::Node current;

    };

  private:

    const Digraph& digraph;

    const PredMap& predMap;

    typename Digraph::Node target;

  };

  template <typename _Digraph, typename _PredMatrixMap>

  class PredMatrixMapPath {

  public:

    typedef True RevPathTag;

    typedef _Digraph Digraph;

    typedef typename Digraph::Arc Arc;

    typedef _PredMatrixMap PredMatrixMap;

    PredMatrixMapPath(const Digraph& _digraph,

                      const PredMatrixMap& _predMatrixMap,

                      typename Digraph::Node _source,

                      typename Digraph::Node _target)

      : digraph(_digraph), predMatrixMap(_predMatrixMap),

        source(_source), target(_target) {}

    int length() const {

      int len = 0;

      typename Digraph::Node node = target;

      typename Digraph::Arc arc;

      while ((arc = predMatrixMap(source, node)) != INVALID) {

        node = digraph.source(arc);

        ++len;

      }

      return len;

    }

    bool empty() const {

    }

    class RevArcIt {

    public:

      RevArcIt() {}

      RevArcIt(Invalid) : path(0), current(INVALID) {}

      RevArcIt(const PredMatrixMapPath& _path)

        : path(&_path), current(_path.target) {

        if (path->predMatrixMap(path->source, current) == INVALID)

          current = INVALID;

      }

      operator const typename Digraph::Arc() const {

        return path->predMatrixMap(path->source, current);

      }

      RevArcIt& operator++() {

        current =

          path->digraph.source(path->predMatrixMap(path->source, current));

        if (path->predMatrixMap(path->source, current) == INVALID)

          current = INVALID;

        return *this;

      }

      bool operator==(const RevArcIt& e) const {

        return current == e.current;

      }

      bool operator!=(const RevArcIt& e) const {

        return current != e.current;

      }

      bool operator<(const RevArcIt& e) const {

        return current < e.current;

      }

    private:

      const PredMatrixMapPath* path;

      typename Digraph::Node current;

    };

  private:

    const Digraph& digraph;

    const PredMatrixMap& predMatrixMap;

    typename Digraph::Node source;

    typename Digraph::Node target;

  };

}

#endif

  }

  /// \brief Function to count the number of the inc-edges to node \c n.

  ///

  /// This function counts the number of the inc-edges to node \c n

  /// in the undirected graph \c g.

  template <typename Graph>

  inline int countIncEdges(const Graph& g,  const typename Graph::Node& n) {

    return countNodeDegree<Graph, typename Graph::IncEdgeIt>(g, n);

  }

  namespace _core_bits {

    template <typename Digraph, typename Item, typename RefMap>

    class MapCopyBase {

    public:

      virtual void copy(const Digraph& from, const RefMap& refMap) = 0;

      virtual ~MapCopyBase() {}

    };

    template <typename Digraph, typename Item, typename RefMap,

              typename FromMap, typename ToMap>

    class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {

    public:

      MapCopy(const FromMap& map, ToMap& tmap)

        : _map(map), _tmap(tmap) {}

      virtual void copy(const Digraph& digraph, const RefMap& refMap) {

        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;

        for (ItemIt it(digraph); it != INVALID; ++it) {

          _tmap.set(refMap[it], _map[it]);

        }

      }

    private:

      const FromMap& _map;

      ToMap& _tmap;

    };

    template <typename Digraph, typename Item, typename RefMap, typename It>

    class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {

    public:

      ItemCopy(const Item& item, It& it) : _item(item), _it(it) {}

      virtual void copy(const Digraph&, const RefMap& refMap) {

        _it = refMap[_item];

      }

    private:

      Item _item;

      It& _it;

    };

    template <typename Digraph, typename Item, typename RefMap, typename Ref>

    class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {

    public:

      RefCopy(Ref& map) : _map(map) {}

      virtual void copy(const Digraph& digraph, const RefMap& refMap) {

        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;

        for (ItemIt it(digraph); it != INVALID; ++it) {

          _map.set(it, refMap[it]);

        }

      }

    private:

      Ref& _map;

    };

    template <typename Digraph, typename Item, typename RefMap,

              typename CrossRef>

    class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {

    public:

      CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}

      virtual void copy(const Digraph& digraph, const RefMap& refMap) {

        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;

        for (ItemIt it(digraph); it != INVALID; ++it) {

          _cmap.set(refMap[it], it);

        }

      }

    private:

      CrossRef& _cmap;

    };

    template <typename Digraph, typename Enable = void>

    struct DigraphCopySelector {

      template <typename From, typename NodeRefMap, typename ArcRefMap>

      static void copy(const From& from, Digraph &to,

                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {

        for (typename From::NodeIt it(from); it != INVALID; ++it) {

          nodeRefMap[it] = to.addNode();

        }

        for (typename From::ArcIt it(from); it != INVALID; ++it) {

          arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],

                                    nodeRefMap[from.target(it)]);

        }

      }

    };

    template <typename Digraph>

    struct DigraphCopySelector<

      Digraph,

      typename enable_if<typename Digraph::BuildTag, void>::type>

    {

      template <typename From, typename NodeRefMap, typename ArcRefMap>

      static void copy(const From& from, Digraph &to,

                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {

        to.build(from, nodeRefMap, arcRefMap);

      }

    };

    template <typename Graph, typename Enable = void>

    struct GraphCopySelector {

      template <typename From, typename NodeRefMap, typename EdgeRefMap>

      static void copy(const From& from, Graph &to,

                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {

        for (typename From::NodeIt it(from); it != INVALID; ++it) {

          nodeRefMap[it] = to.addNode();

        }

        for (typename From::EdgeIt it(from); it != INVALID; ++it) {

          edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],

                                      nodeRefMap[from.v(it)]);

        }

      }

    };

    template <typename Graph>

    struct GraphCopySelector<

      Graph,

      typename enable_if<typename Graph::BuildTag, void>::type>

    {

      template <typename From, typename NodeRefMap, typename EdgeRefMap>

      static void copy(const From& from, Graph &to,

                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {

        to.build(from, nodeRefMap, edgeRefMap);

      }

    };

  }

  /// \brief Class to copy a digraph.

  ///

  /// Class to copy a digraph to another digraph (duplicate a digraph). The

  /// simplest way of using it is through the \c digraphCopy() function.

  ///

  /// This class not only make a copy of a digraph, but it can create

  /// references and cross references between the nodes and arcs of

  /// the two digraphs, and it can copy maps to use with the newly created

  /// digraph.

  ///

  /// To make a copy from a digraph, first an instance of DigraphCopy

  /// should be created, then the data belongs to the digraph should

  /// assigned to copy. In the end, the \c run() member should be

  /// called.

  ///

  /// The next code copies a digraph with several data:

  ///\code

  ///  DigraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);

  ///  // Create references for the nodes

  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);

  ///  cg.nodeRef(nr);

  ///  // Create cross references (inverse) for the arcs

  ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);

  ///  cg.arcCrossRef(acr);

  ///  // Copy an arc map

  ///  OrigGraph::ArcMap<double> oamap(orig_graph);

  ///  NewGraph::ArcMap<double> namap(new_graph);

  ///  cg.arcMap(oamap, namap);

  ///  // Copy a node

  ///  OrigGraph::Node on;

  ///  NewGraph::Node nn;

  ///  cg.node(on, nn);

  ///  // Execute copying

  ///  cg.run();

  ///\endcode

  template <typename From, typename To>

  class DigraphCopy {

  private:

    typedef typename From::Node Node;

    typedef typename From::NodeIt NodeIt;

    typedef typename From::Arc Arc;

    typedef typename From::ArcIt ArcIt;

    typedef typename To::Node TNode;

    typedef typename To::Arc TArc;

    typedef typename From::template NodeMap<TNode> NodeRefMap;

    typedef typename From::template ArcMap<TArc> ArcRefMap;

  public:

    /// \brief Constructor of DigraphCopy.

    ///

    /// Constructor of DigraphCopy for copying the content of the

    /// \c from digraph into the \c to digraph.

    DigraphCopy(const From& from, To& to)

      : _from(from), _to(to) {}

    /// \brief Destructor of DigraphCopy

    ///

    /// Destructor of DigraphCopy.

    ~DigraphCopy() {

      for (int i = 0; i < int(_node_maps.size()); ++i) {

        delete _node_maps[i];

      }

      for (int i = 0; i < int(_arc_maps.size()); ++i) {

        delete _arc_maps[i];

      }

    }

    ///Processes the next arc.

    ///Processes the next arc.

    ///

    ///\return The processed arc.

    ///

    ///\pre The stack must not be empty.

    Arc processNextArc()

    {

      Node m;

      Arc e=_stack[_stack_head];

      if(!(*_reached)[m=G->target(e)]) {

        _pred->set(m,e);

        _reached->set(m,true);

        ++_stack_head;

        _stack[_stack_head] = OutArcIt(*G, m);

        _dist->set(m,_stack_head);

      }

      else {

        m=G->source(e);

        ++_stack[_stack_head];

      }

      while(_stack_head>=0 && _stack[_stack_head]==INVALID) {

        _processed->set(m,true);

        --_stack_head;

        if(_stack_head>=0) {

          m=G->source(_stack[_stack_head]);

          ++_stack[_stack_head];

        }

      }

      return e;

    }

    ///Next arc to be processed.

    ///Next arc to be processed.

    ///

    ///\return The next arc to be processed or \c INVALID if the stack

    ///is empty.

    OutArcIt nextArc() const

    {

      return _stack_head>=0?_stack[_stack_head]:INVALID;

    }

    ///Returns \c false if there are nodes to be processed.

    ///Returns \c false if there are nodes to be processed

    ///in the queue (stack).

    bool emptyQueue() const { return _stack_head<0; }

    ///Returns the number of the nodes to be processed.

    ///Returns the number of the nodes to be processed

    ///in the queue (stack).

    int queueSize() const { return _stack_head+1; }

    ///Executes the algorithm.

    ///Executes the algorithm.

    ///

    ///This method runs the %DFS algorithm from the root node

    ///in order to compute the DFS path to each node.

    ///

    /// The algorithm computes

    ///- the %DFS tree,

    ///- the distance of each node from the root in the %DFS tree.

    ///

    ///\pre init() must be called and a root node should be

    ///added with addSource() before using this function.

    ///

    ///\note <tt>d.start()</tt> is just a shortcut of the following code.

    ///\code

    ///  while ( !d.emptyQueue() ) {

    ///    d.processNextArc();

    ///  }

    ///\endcode

    void start()

    {

      while ( !emptyQueue() ) processNextArc();

    }

    ///Executes the algorithm until the given target node is reached.

    ///Executes the algorithm until the given target node is reached.

    ///

    ///This method runs the %DFS algorithm from the root node

    ///in order to compute the DFS path to \c t.

    ///

    ///The algorithm computes

    ///- the %DFS path to \c t,

    ///- the distance of \c t from the root in the %DFS tree.

    ///

    ///\pre init() must be called and a root node should be

    ///added with addSource() before using this function.

    void start(Node t)

    {

        processNextArc();

    }

    ///Executes the algorithm until a condition is met.

    ///Executes the algorithm until a condition is met.

    ///

    ///This method runs the %DFS algorithm from the root node

    ///until an arc \c a with <tt>am[a]</tt> true is found.

    ///

    ///\param am A \c bool (or convertible) arc map. The algorithm

    ///will stop when it reaches an arc \c a with <tt>am[a]</tt> true.

    ///

    ///\return The reached arc \c a with <tt>am[a]</tt> true or

    ///\c INVALID if no such arc was found.

    ///

    ///\pre init() must be called and a root node should be

    ///added with addSource() before using this function.

    ///

    ///\warning Contrary to \ref Bfs and \ref Dijkstra, \c am is an arc map,

    ///not a node map.

    template<class ArcBoolMap>

    Arc start(const ArcBoolMap &am)

    {

      while ( !emptyQueue() && !am[_stack[_stack_head]] )

        processNextArc();

      return emptyQueue() ? INVALID : _stack[_stack_head];

    }

    ///Runs the algorithm from the given source node.

    ///This method runs the %DFS algorithm from node \c s

    ///in order to compute the DFS path to each node.

    ///

    ///The algorithm computes

    ///- the %DFS tree,

    ///- the distance of each node from the root in the %DFS tree.

    ///

    ///\note <tt>d.run(s)</tt> is just a shortcut of the following code.

    ///\code

    ///  d.init();

    ///  d.addSource(s);

    ///  d.start();

    ///\endcode

    void run(Node s) {

      init();

      addSource(s);

      start();

    }

    ///Finds the %DFS path between \c s and \c t.

    ///This method runs the %DFS algorithm from node \c s

    ///in order to compute the DFS path to node \c t

    ///(it stops searching when \c t is processed)

    ///

    ///\return \c true if \c t is reachable form \c s.

    ///

    ///\note Apart from the return value, <tt>d.run(s,t)</tt> is

    ///just a shortcut of the following code.

    ///\code

    ///  d.init();

    ///  d.addSource(s);

    ///  d.start(t);

    ///\endcode

    bool run(Node s,Node t) {

      init();

      addSource(s);

      start(t);

      return reached(t);

    }

    ///Runs the algorithm to visit all nodes in the digraph.

    ///This method runs the %DFS algorithm in order to compute the

    ///%DFS path to each node.

    ///

    ///The algorithm computes

    ///- the %DFS tree (forest),

    ///- the distance of each node from the root(s) in the %DFS tree.

    ///

    ///\note <tt>d.run()</tt> is just a shortcut of the following code.

    ///\code

    ///  d.init();

    ///  for (NodeIt n(digraph); n != INVALID; ++n) {

    ///    if (!d.reached(n)) {

    ///      d.addSource(n);

    ///      d.start();

    ///    }

    ///  }

    ///\endcode

    void run() {

      init();

      for (NodeIt it(*G); it != INVALID; ++it) {

        if (!reached(it)) {

          addSource(it);

    }

    /// \brief Processes the next arc.

    ///

    /// Processes the next arc.

    ///

    /// \return The processed arc.

    ///

    /// \pre The stack must not be empty.

    Arc processNextArc() {

      Arc e = _stack[_stack_head];

      Node m = _digraph->target(e);

      if(!(*_reached)[m]) {

        _visitor->discover(e);

        _visitor->reach(m);

        _reached->set(m, true);

        _digraph->firstOut(_stack[++_stack_head], m);

      } else {

        _visitor->examine(e);

        m = _digraph->source(e);

        _digraph->nextOut(_stack[_stack_head]);

      }

      while (_stack_head>=0 && _stack[_stack_head] == INVALID) {

        _visitor->leave(m);

        --_stack_head;

        if (_stack_head >= 0) {

          _visitor->backtrack(_stack[_stack_head]);

          m = _digraph->source(_stack[_stack_head]);

          _digraph->nextOut(_stack[_stack_head]);

        } else {

          _visitor->stop(m);

        }

      }

      return e;

    }

    /// \brief Next arc to be processed.

    ///

    /// Next arc to be processed.

    ///

    /// \return The next arc to be processed or INVALID if the stack is

    /// empty.

    Arc nextArc() const {

      return _stack_head >= 0 ? _stack[_stack_head] : INVALID;

    }

    /// \brief Returns \c false if there are nodes

    /// to be processed.

    ///

    /// Returns \c false if there are nodes

    /// to be processed in the queue (stack).

    bool emptyQueue() const { return _stack_head < 0; }

    /// \brief Returns the number of the nodes to be processed.

    ///

    /// Returns the number of the nodes to be processed in the queue (stack).

    int queueSize() const { return _stack_head + 1; }

    /// \brief Executes the algorithm.

    ///

    /// Executes the algorithm.

    ///

    /// This method runs the %DFS algorithm from the root node

    /// in order to compute the %DFS path to each node.