LEMON/LEMON-main Changeset - r826:02109e17027f

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Changeset - r826:02109e17027f

« 825:75e602
« 824:974c48

829:7762ca »

r826:02109e17027f

Fri, 12 Feb 2010 21:53:15

[Not Reviewed]

0 comments (0 inline)

alpar (Alpar Juttner)
alpar@cs.elte.hu

Merge

0 12 0

merge default

0 files changed with 90 insertions and 26 deletions:

lemon/bellman_ford.h

lemon/bfs.h

lemon/capacity_scaling.h

lemon/circulation.h

lemon/cost_scaling.h

lemon/dfs.h

lemon/dijkstra.h

lemon/hartmann_orlin.h

lemon/howard.h

lemon/karp.h

lemon/min_cost_arborescence.h

lemon/preflow.h

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lemon/bellman_ford.h

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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.
+		 *
 		 */
 		#ifndef LEMON_BELLMAN_FORD_H
 		#define LEMON_BELLMAN_FORD_H
 		/// \ingroup shortest_path
 		/// \file
 		/// \brief Bellman-Ford algorithm.
 		#include <lemon/list_graph.h>
 		#include <lemon/bits/path_dump.h>
 		#include <lemon/core.h>
 		#include <lemon/error.h>
 		#include <lemon/maps.h>
 		#include <lemon/path.h>
 		#include <limits>
 		namespace lemon {
 		  /// \brief Default OperationTraits for the BellmanFord algorithm class.
 		  ///
 		  /// This operation traits class defines all computational operations
 		  /// and constants that are used in the Bellman-Ford algorithm.
 		  /// The default implementation is based on the \c numeric_limits class.
 		  /// If the numeric type does not have infinity value, then the maximum
 		  /// value is used as extremal infinity value.
 		  template <
 		    typename V,
 		    bool has_inf = std::numeric_limits<V>::has_infinity>
 		  struct BellmanFordDefaultOperationTraits {
 		    /// \e
 		    typedef V Value;
 		    /// \brief Gives back the zero value of the type.
 		    static Value zero() {
 		      return static_cast<Value>(0);
+		    }
 		    /// \brief Gives back the positive infinity value of the type.
 		    static Value infinity() {
 		      return std::numeric_limits<Value>::infinity();
+		    }
 		    /// \brief Gives back the sum of the given two elements.
 		    static Value plus(const Value& left, const Value& right) {
 		      return left + right;
+		    }
 		    /// \brief Gives back \c true only if the first value is less than
 		    /// the second.
 		    static bool less(const Value& left, const Value& right) {
 		      return left < right;
+		    }
 		  };
 		  template <typename V>
 		  struct BellmanFordDefaultOperationTraits<V, false> {
 		    typedef V Value;
 		    static Value zero() {
 		      return static_cast<Value>(0);
+		    }
 		    static Value infinity() {
 		      return std::numeric_limits<Value>::max();
+		    }
 		    static Value plus(const Value& left, const Value& right) {
 		      if (left == infinity() || right == infinity()) return infinity();
 		      return left + right;
+		    }
 		    static bool less(const Value& left, const Value& right) {
 		      return left < right;
+		    }
 		  };
 		  /// \brief Default traits class of BellmanFord class.
 		  ///
 		  /// Default traits class of BellmanFord class.
 		  /// \param GR The type of the digraph.
 		  /// \param LEN The type of the length map.
 		  template<typename GR, typename LEN>
 		  struct BellmanFordDefaultTraits {
 		    /// The type of the digraph the algorithm runs on.
 		    typedef GR Digraph;
 		    /// \brief The type of the map that stores the arc lengths.
 		    ///
 		    /// The type of the map that stores the arc lengths.
 		    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
 		    typedef LEN LengthMap;
 		    /// The type of the arc lengths.
 		    typedef typename LEN::Value Value;
 		    /// \brief Operation traits for Bellman-Ford algorithm.
 		    ///
 		    /// It defines the used operations and the infinity value for the
 		    /// given \c Value type.
 		    /// \see BellmanFordDefaultOperationTraits
 		    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
 		    /// \brief The type of the map that stores the last arcs of the
 		    /// shortest paths.
 		    ///
 		    /// The type of the map that stores the last
 		    /// arcs of the shortest paths.
 		    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename GR::template NodeMap<typename GR::Arc> PredMap;
 		    /// \brief Instantiates a \c PredMap.
 		    ///
 		    /// This function instantiates a \ref PredMap.
 		    /// \param g is the digraph to which we would like to define the
 		    /// \ref PredMap.
 		    static PredMap *createPredMap(const GR& g) {
 		      return new PredMap(g);
+		    }
 		    /// \brief The type of the map that stores the distances of the nodes.
 		    ///
 		    /// The type of the map that stores the distances of the nodes.
 		    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename GR::template NodeMap<typename LEN::Value> DistMap;
 		    /// \brief Instantiates a \c DistMap.
 		    ///
 		    /// This function instantiates a \ref DistMap.
 		    /// \param g is the digraph to which we would like to define the
 		    /// \ref DistMap.
 		    static DistMap *createDistMap(const GR& g) {
 		      return new DistMap(g);
+		    }
 		  };
 		  /// \brief %BellmanFord algorithm class.
 		  ///
 		  /// \ingroup shortest_path
 		  /// This class provides an efficient implementation of the Bellman-Ford
 		  /// algorithm. The maximum time complexity of the algorithm is
 		  /// <tt>O(ne)</tt>.
 		  ///
 		  /// The Bellman-Ford algorithm solves the single-source shortest path
 		  /// problem when the arcs can have negative lengths, but the digraph
 		  /// should not contain directed cycles with negative total length.
 		  /// If all arc costs are non-negative, consider to use the Dijkstra
 		  /// algorithm instead, since it is more efficient.
 		  ///
 		  /// The arc lengths are passed to the algorithm using a
 		  /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any
 		  /// kind of length. The type of the length values is determined by the
 		  /// \ref concepts::ReadMap::Value "Value" type of the length map.
 		  ///
 		  /// There is also a \ref bellmanFord() "function-type interface" for the
 		  /// Bellman-Ford algorithm, which is convenient in the simplier cases and
 		  /// it can be used easier.
 		  ///
 		  /// \tparam GR The type of the digraph the algorithm runs on.
 		  /// The default type is \ref ListDigraph.
 		  /// \tparam LEN A \ref concepts::ReadMap "readable" arc map that specifies
 		  /// the lengths of the arcs. The default map type is
 		  /// \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
 		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm. By default, it is \ref BellmanFordDefaultTraits
 		  /// "BellmanFordDefaultTraits<GR, LEN>".
 		  /// In most cases, this parameter should not be set directly,
 		  /// consider to use the named template parameters instead.
 		#ifdef DOXYGEN
 		  template <typename GR, typename LEN, typename TR>
 		#else
 		  template <typename GR=ListDigraph,
 		            typename LEN=typename GR::template ArcMap<int>,
 		            typename TR=BellmanFordDefaultTraits<GR,LEN> >
 		#endif
 		  class BellmanFord {
 		  public:
 		    ///The type of the underlying digraph.
 		    typedef typename TR::Digraph Digraph;
 		    /// \brief The type of the arc lengths.
 		    typedef typename TR::LengthMap::Value Value;
 		    /// \brief The type of the map that stores the arc lengths.
 		    typedef typename TR::LengthMap LengthMap;
 		    /// \brief The type of the map that stores the last
 		    /// arcs of the shortest paths.
 		    typedef typename TR::PredMap PredMap;
 		    /// \brief The type of the map that stores the distances of the nodes.
 		    typedef typename TR::DistMap DistMap;
 		    /// The type of the paths.
 		    typedef PredMapPath<Digraph, PredMap> Path;
 		    ///\brief The \ref BellmanFordDefaultOperationTraits
 		    /// "operation traits class" of the algorithm.
 		    typedef typename TR::OperationTraits OperationTraits;
 		    ///The \ref BellmanFordDefaultTraits "traits class" of the algorithm.
 		    typedef TR Traits;
 		  private:
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::OutArcIt OutArcIt;
 		    // Pointer to the underlying digraph.
 		    const Digraph *_gr;
 		    // Pointer to the length map
 		    const LengthMap *_length;
 		    // Pointer to the map of predecessors arcs.
 		    PredMap *_pred;
 		    // Indicates if _pred is locally allocated (true) or not.
 		    bool _local_pred;
 		    // Pointer to the map of distances.
 		    DistMap *_dist;
 		    // Indicates if _dist is locally allocated (true) or not.
 		    bool _local_dist;
 		    typedef typename Digraph::template NodeMap<bool> MaskMap;
 		    MaskMap *_mask;
 		    std::vector<Node> _process;
 		    // Creates the maps if necessary.
 		    void create_maps() {
 		      if(!_pred) {
 			_local_pred = true;
 			_pred = Traits::createPredMap(*_gr);
+		      }
 		      if(!_dist) {
 			_local_dist = true;
 			_dist = Traits::createDistMap(*_gr);
+		      }
 		      if(!_mask) {
 		        _mask = new MaskMap(*_gr);
+		      }
+		    }
 		  public :
 		    typedef BellmanFord Create;
 		    /// \name Named Template Parameters
 		    ///@{
 		    template <class T>
 		    struct SetPredMapTraits : public Traits {
 		      typedef T PredMap;
 		      static PredMap *createPredMap(const Digraph&) {
 		        LEMON_ASSERT(false, "PredMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c PredMap type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting
 		    /// \c PredMap type.
 		    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    template <class T>
 		    struct SetPredMap
 		      : public BellmanFord< Digraph, LengthMap, SetPredMapTraits<T> > {
 		      typedef BellmanFord< Digraph, LengthMap, SetPredMapTraits<T> > Create;
 		    };
 		    template <class T>
 		    struct SetDistMapTraits : public Traits {
 		      typedef T DistMap;
 		      static DistMap *createDistMap(const Digraph&) {
 		        LEMON_ASSERT(false, "DistMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c DistMap type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting
 		    /// \c DistMap type.
 		    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    template <class T>
 		    struct SetDistMap
 		      : public BellmanFord< Digraph, LengthMap, SetDistMapTraits<T> > {
 		      typedef BellmanFord< Digraph, LengthMap, SetDistMapTraits<T> > Create;
 		    };
 		    template <class T>
 		    struct SetOperationTraitsTraits : public Traits {
 		      typedef T OperationTraits;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c OperationTraits type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting
 		    /// \c OperationTraits type.
 		    /// For more information, see \ref BellmanFordDefaultOperationTraits.
 		    template <class T>
 		    struct SetOperationTraits
 		      : public BellmanFord< Digraph, LengthMap, SetOperationTraitsTraits<T> > {
 		      typedef BellmanFord< Digraph, LengthMap, SetOperationTraitsTraits<T> >
 		      Create;
 		    };
 		    ///@}
 		  protected:
 		    BellmanFord() {}
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// Constructor.
 		    /// \param g The digraph the algorithm runs on.
 		    /// \param length The length map used by the algorithm.
 		    BellmanFord(const Digraph& g, const LengthMap& length) :
 		      _gr(&g), _length(&length),
 		      _pred(0), _local_pred(false),
 		      _dist(0), _local_dist(false), _mask(0) {}
 		    ///Destructor.
 		    ~BellmanFord() {
 		      if(_local_pred) delete _pred;
 		      if(_local_dist) delete _dist;
 		      if(_mask) delete _mask;
+		    }
 		    /// \brief Sets the length map.
 		    ///
 		    /// Sets the length map.
 		    /// \return <tt>(*this)</tt>
 		    BellmanFord &lengthMap(const LengthMap &map) {
 		      _length = &map;
 		      return *this;
+		    }
 		    /// \brief Sets the map that stores the predecessor arcs.
 		    ///
 		    /// Sets the map that stores the predecessor arcs.
 		    /// If you don't use this function before calling \ref run()
 		    /// or \ref init(), an instance will be allocated automatically.
 		    /// The destructor deallocates this automatically allocated map,
 		    /// of course.
 		    /// \return <tt>(*this)</tt>
 		    BellmanFord &predMap(PredMap &map) {
 		      if(_local_pred) {
 			delete _pred;
 			_local_pred=false;
+		      }
 		      _pred = &map;
 		      return *this;
+		    }
 		    /// \brief Sets the map that stores the distances of the nodes.
 		    ///
 		    /// Sets the map that stores the distances of the nodes calculated
 		    /// by the algorithm.
 		    /// If you don't use this function before calling \ref run()
 		    /// or \ref init(), an instance will be allocated automatically.
 		    /// The destructor deallocates this automatically allocated map,
 		    /// of course.
 		    /// \return <tt>(*this)</tt>
 		    BellmanFord &distMap(DistMap &map) {
 		      if(_local_dist) {
 			delete _dist;
 			_local_dist=false;
+		      }
 		      _dist = &map;
 		      return *this;
+		    }
 		    /// \name Execution Control
 		    /// The simplest way to execute the Bellman-Ford algorithm is to use
 		    /// one of the member functions called \ref run().\n
 		    /// If you need better control on the execution, you have to call
 		    /// \ref init() first, then you can add several source nodes
 		    /// with \ref addSource(). Finally the actual path computation can be
 		    /// performed with \ref start(), \ref checkedStart() or
 		    /// \ref limitedStart().
 		    ///@{
 		    /// \brief Initializes the internal data structures.
 		    ///
 		    /// Initializes the internal data structures. The optional parameter
 		    /// is the initial distance of each node.
 		    void init(const Value value = OperationTraits::infinity()) {
 		      create_maps();
 		      for (NodeIt it(*_gr); it != INVALID; ++it) {
 			_pred->set(it, INVALID);
 			_dist->set(it, value);
+		      }
 		      _process.clear();
 		      if (OperationTraits::less(value, OperationTraits::infinity())) {
 			for (NodeIt it(*_gr); it != INVALID; ++it) {
 			  _process.push_back(it);
 			  _mask->set(it, true);
+			}
 		      } else {
 			for (NodeIt it(*_gr); it != INVALID; ++it) {
 			  _mask->set(it, false);
+			}
+		      }
+		    }
 		    /// \brief Adds a new source node.
 		    ///
 		    /// This function adds a new source node. The optional second parameter
 		    /// is the initial distance of the node.
 		    void addSource(Node source, Value dst = OperationTraits::zero()) {
 		      _dist->set(source, dst);
 		      if (!(*_mask)[source]) {
 			_process.push_back(source);
 			_mask->set(source, true);
+		      }
+		    }
 		    /// \brief Executes one round from the Bellman-Ford algorithm.
 		    ///
 		    /// If the algoritm calculated the distances in the previous round
 		    /// exactly for the paths of at most \c k arcs, then this function
 		    /// will calculate the distances exactly for the paths of at most
 		    /// <tt>k+1</tt> arcs. Performing \c k iterations using this function
 		    /// calculates the shortest path distances exactly for the paths
 		    /// consisting of at most \c k arcs.
 		    ///
 		    /// \warning The paths with limited arc number cannot be retrieved
 		    /// easily with \ref path() or \ref predArc() functions. If you also
 		    /// need the shortest paths and not only the distances, you should
 		    /// store the \ref predMap() "predecessor map" after each iteration
 		    /// and build the path manually.
 		    ///
 		    /// \return \c true when the algorithm have not found more shorter
 		    /// paths.
 		    ///
 		    /// \see ActiveIt
 		    bool processNextRound() {
 		      for (int i = 0; i < int(_process.size()); ++i) {
 			_mask->set(_process[i], false);
+		      }
 		      std::vector<Node> nextProcess;
 		      std::vector<Value> values(_process.size());
 		      for (int i = 0; i < int(_process.size()); ++i) {
 			values[i] = (*_dist)[_process[i]];
+		      }
 		      for (int i = 0; i < int(_process.size()); ++i) {
 			for (OutArcIt it(*_gr, _process[i]); it != INVALID; ++it) {
 			  Node target = _gr->target(it);
 			  Value relaxed = OperationTraits::plus(values[i], (*_length)[it]);
 			  if (OperationTraits::less(relaxed, (*_dist)[target])) {
 			    _pred->set(target, it);
 			    _dist->set(target, relaxed);
 			    if (!(*_mask)[target]) {
 			      _mask->set(target, true);
 			      nextProcess.push_back(target);
+			    }
+			  }
+			}
+		      }
 		      _process.swap(nextProcess);
 		      return _process.empty();
+		    }
 		    /// \brief Executes one weak round from the Bellman-Ford algorithm.
 		    ///
 		    /// If the algorithm calculated the distances in the previous round
 		    /// at least for the paths of at most \c k arcs, then this function
 		    /// will calculate the distances at least for the paths of at most
 		    /// <tt>k+1</tt> arcs.
 		    /// This function does not make it possible to calculate the shortest
 		    /// path distances exactly for paths consisting of at most \c k arcs,
 		    /// this is why it is called weak round.
 		    ///
 		    /// \return \c true when the algorithm have not found more shorter
 		    /// paths.
 		    ///
 		    /// \see ActiveIt
 		    bool processNextWeakRound() {
 		      for (int i = 0; i < int(_process.size()); ++i) {
 			_mask->set(_process[i], false);
+		      }
 		      std::vector<Node> nextProcess;
 		      for (int i = 0; i < int(_process.size()); ++i) {
 			for (OutArcIt it(*_gr, _process[i]); it != INVALID; ++it) {
 			  Node target = _gr->target(it);
 			  Value relaxed =
 			    OperationTraits::plus((*_dist)[_process[i]], (*_length)[it]);
 			  if (OperationTraits::less(relaxed, (*_dist)[target])) {
 			    _pred->set(target, it);
 			    _dist->set(target, relaxed);
 			    if (!(*_mask)[target]) {
 			      _mask->set(target, true);
 			      nextProcess.push_back(target);
+			    }
+			  }
+			}
+		      }
 		      _process.swap(nextProcess);
 		      return _process.empty();
+		    }
 		    /// \brief Executes the algorithm.
 		    ///
 		    /// Executes the algorithm.
 		    ///
 		    /// This method runs the Bellman-Ford algorithm from the root node(s)
 		    /// in order to compute the shortest path to each node.
 		    ///
 		    /// The algorithm computes
 		    /// - the shortest path tree (forest),
 		    /// - the distance of each node from the root(s).
 		    ///
 		    /// \pre init() must be called and at least one root node should be
 		    /// added with addSource() before using this function.
 		    void start() {
 		      int num = countNodes(*_gr) - 1;
 		      for (int i = 0; i < num; ++i) {
 			if (processNextWeakRound()) break;
+		      }
+		    }
 		    /// \brief Executes the algorithm and checks the negative cycles.
 		    ///
 		    /// Executes the algorithm and checks the negative cycles.
 		    ///
 		    /// This method runs the Bellman-Ford algorithm from the root node(s)
 		    /// in order to compute the shortest path to each node and also checks
 		    /// if the digraph contains cycles with negative total length.
 		    ///
 		    /// The algorithm computes
 		    /// - the shortest path tree (forest),
 		    /// - the distance of each node from the root(s).
 		    ///
 		    /// \return \c false if there is a negative cycle in the digraph.
 		    ///
 		    /// \pre init() must be called and at least one root node should be
 		    /// added with addSource() before using this function.
 		    bool checkedStart() {
 		      int num = countNodes(*_gr);
 		      for (int i = 0; i < num; ++i) {
 			if (processNextWeakRound()) return true;
+		      }
 		      return _process.empty();
+		    }
 		    /// \brief Executes the algorithm with arc number limit.
 		    ///
 		    /// Executes the algorithm with arc number limit.
 		    ///
 		    /// This method runs the Bellman-Ford algorithm from the root node(s)
 		    /// in order to compute the shortest path distance for each node
 		    /// using only the paths consisting of at most \c num arcs.
 		    ///
 		    /// The algorithm computes
 		    /// - the limited distance of each node from the root(s),
 		    /// - the predecessor arc for each node.
 		    ///
 		    /// \warning The paths with limited arc number cannot be retrieved
 		    /// easily with \ref path() or \ref predArc() functions. If you also
 		    /// need the shortest paths and not only the distances, you should
 		    /// store the \ref predMap() "predecessor map" after each iteration
 		    /// and build the path manually.
 		    ///
 		    /// \pre init() must be called and at least one root node should be
 		    /// added with addSource() before using this function.
 		    void limitedStart(int num) {
 		      for (int i = 0; i < num; ++i) {
 			if (processNextRound()) break;
+		      }
+		    }
 		    /// \brief Runs the algorithm from the given root node.
 		    ///
 		    /// This method runs the Bellman-Ford algorithm from the given root
 		    /// node \c s in order to compute the shortest path to each node.
 		    ///
 		    /// The algorithm computes
 		    /// - the shortest path tree (forest),
 		    /// - the distance of each node from the root(s).
 		    ///
 		    /// \note bf.run(s) is just a shortcut of the following code.
 		    /// \code
 		    ///   bf.init();
 		    ///   bf.addSource(s);
 		    ///   bf.start();
 		    /// \endcode
 		    void run(Node s) {
 		      init();
 		      addSource(s);
 		      start();
+		    }
 		    /// \brief Runs the algorithm from the given root node with arc
 		    /// number limit.
 		    ///
 		    /// This method runs the Bellman-Ford algorithm from the given root
 		    /// node \c s in order to compute the shortest path distance for each
 		    /// node using only the paths consisting of at most \c num arcs.
 		    ///
 		    /// The algorithm computes
 		    /// - the limited distance of each node from the root(s),
 		    /// - the predecessor arc for each node.
 		    ///
 		    /// \warning The paths with limited arc number cannot be retrieved
 		    /// easily with \ref path() or \ref predArc() functions. If you also
 		    /// need the shortest paths and not only the distances, you should
 		    /// store the \ref predMap() "predecessor map" after each iteration
 		    /// and build the path manually.
 		    ///
 		    /// \note bf.run(s, num) is just a shortcut of the following code.
 		    /// \code
 		    ///   bf.init();
 		    ///   bf.addSource(s);
 		    ///   bf.limitedStart(num);
 		    /// \endcode
 		    void run(Node s, int num) {
 		      init();
 		      addSource(s);
 		      limitedStart(num);
+		    }
 		    ///@}
 		    /// \brief LEMON iterator for getting the active nodes.
 		    ///
 		    /// This class provides a common style LEMON iterator that traverses
 		    /// the active nodes of the Bellman-Ford algorithm after the last
 		    /// phase. These nodes should be checked in the next phase to
 		    /// find augmenting arcs outgoing from them.
 		    class ActiveIt {
 		    public:
 		      /// \brief Constructor.
 		      ///
 		      /// Constructor for getting the active nodes of the given BellmanFord
 		      /// instance.
 		      ActiveIt(const BellmanFord& algorithm) : _algorithm(&algorithm)
+		      {
 		        _index = _algorithm->_process.size() - 1;
+		      }
 		      /// \brief Invalid constructor.
 		      ///
 		      /// Invalid constructor.
 		      ActiveIt(Invalid) : _algorithm(0), _index(-1) {}
 		      /// \brief Conversion to \c Node.
 		      ///
 		      /// Conversion to \c Node.
 		      operator Node() const {
 		        return _index >= 0 ? _algorithm->_process[_index] : INVALID;
+		      }
 		      /// \brief Increment operator.
 		      ///
 		      /// Increment operator.
 		      ActiveIt& operator++() {
 		        --_index;
 		        return *this;
+		      }
 		      bool operator==(const ActiveIt& it) const {
 		        return static_cast<Node>(*this) == static_cast<Node>(it);
+		      }
 		      bool operator!=(const ActiveIt& it) const {
 		        return static_cast<Node>(*this) != static_cast<Node>(it);
+		      }
 		      bool operator<(const ActiveIt& it) const {
 		        return static_cast<Node>(*this) < static_cast<Node>(it);
+		      }
 		    private:
 		      const BellmanFord* _algorithm;
 		      int _index;
 		    };
 		    /// \name Query Functions
 		    /// The result of the Bellman-Ford algorithm can be obtained using these
 		    /// functions.\n
 		    /// Either \ref run() or \ref init() should be called before using them.
 		    ///@{
 		    /// \brief The shortest path to the given node.
 		    ///
 		    /// Gives back the shortest path to the given node from the root(s).
 		    ///
 		    /// \warning \c t should be reached from the root(s).
 		    ///
 		    /// \pre Either \ref run() or \ref init() must be called before
 		    /// using this function.
 		    Path path(Node t) const
+		    {
 		      return Path(*_gr, *_pred, t);
+		    }
 		    /// \brief The distance of the given node from the root(s).
 		    ///
 		    /// Returns the distance of the given node from the root(s).
 		    ///
 		    /// \warning If node \c v is not reached from the root(s), then
 		    /// the return value of this function is undefined.
 		    ///
 		    /// \pre Either \ref run() or \ref init() must be called before
 		    /// using this function.
 		    Value dist(Node v) const { return (*_dist)[v]; }
 		    /// \brief Returns the 'previous arc' of the shortest path tree for
 		    /// the given node.
 		    ///
 		    /// This function returns the 'previous arc' of the shortest path
 		    /// tree for node \c v, i.e. it returns the last arc of a
 		    /// shortest path from a root to \c v. It is \c INVALID if \c v
 		    /// is not reached from the root(s) or if \c v is a root.
 		    ///
 		    /// The shortest path tree used here is equal to the shortest path
 		    /// tree used in \ref predNode() and \ref predMap().
 		    ///
 		    /// \pre Either \ref run() or \ref init() must be called before
 		    /// using this function.
 		    Arc predArc(Node v) const { return (*_pred)[v]; }
 		    /// \brief Returns the 'previous node' of the shortest path tree for
 		    /// the given node.
 		    ///
 		    /// This function returns the 'previous node' of the shortest path
 		    /// tree for node \c v, i.e. it returns the last but one node of
 		    /// a shortest path from a root to \c v. It is \c INVALID if \c v
 		    /// is not reached from the root(s) or if \c v is a root.
 		    ///
 		    /// The shortest path tree used here is equal to the shortest path
 		    /// tree used in \ref predArc() and \ref predMap().
 		    ///
 		    /// \pre Either \ref run() or \ref init() must be called before
 		    /// using this function.
 		    Node predNode(Node v) const {
 		      return (*_pred)[v] == INVALID ? INVALID : _gr->source((*_pred)[v]);
+		    }
 		    /// \brief Returns a const reference to the node map that stores the
 		    /// distances of the nodes.
 		    ///
 		    /// Returns a const reference to the node map that stores the distances
 		    /// of the nodes calculated by the algorithm.
 		    ///
 		    /// \pre Either \ref run() or \ref init() must be called before
 		    /// using this function.
 		    const DistMap &distMap() const { return *_dist;}
 		    /// \brief Returns a const reference to the node map that stores the
 		    /// predecessor arcs.
 		    ///
 		    /// Returns a const reference to the node map that stores the predecessor
 		    /// arcs, which form the shortest path tree (forest).
 		    ///
 		    /// \pre Either \ref run() or \ref init() must be called before
 		    /// using this function.
 		    const PredMap &predMap() const { return *_pred; }
 		    /// \brief Checks if a node is reached from the root(s).
 		    ///
 		    /// Returns \c true if \c v is reached from the root(s).
 		    ///
 		    /// \pre Either \ref run() or \ref init() must be called before
 		    /// using this function.
 		    bool reached(Node v) const {
 		      return (*_dist)[v] != OperationTraits::infinity();
+		    }
 		    /// \brief Gives back a negative cycle.
 		    ///
 		    /// This function gives back a directed cycle with negative total
 		    /// length if the algorithm has already found one.
 		    /// Otherwise it gives back an empty path.
 		    lemon::Path<Digraph> negativeCycle() const {
 		      typename Digraph::template NodeMap<int> state(*_gr, -1);
 		      lemon::Path<Digraph> cycle;
 		      for (int i = 0; i < int(_process.size()); ++i) {
 		        if (state[_process[i]] != -1) continue;
 		        for (Node v = _process[i]; (*_pred)[v] != INVALID;
 		             v = _gr->source((*_pred)[v])) {
 		          if (state[v] == i) {
 		            cycle.addFront((*_pred)[v]);
 		            for (Node u = _gr->source((*_pred)[v]); u != v;
 		                 u = _gr->source((*_pred)[u])) {
 		              cycle.addFront((*_pred)[u]);
+		            }
 		            return cycle;
+		          }
 		          else if (state[v] >= 0) {
 		            break;
+		          }
 		          state[v] = i;
+		        }
+		      }
 		      return cycle;
+		    }
 		    ///@}
 		  };
 		  /// \brief Default traits class of bellmanFord() function.
 		  ///
 		  /// Default traits class of bellmanFord() function.
 		  /// \tparam GR The type of the digraph.
 		  /// \tparam LEN The type of the length map.
 		  template <typename GR, typename LEN>
 		  struct BellmanFordWizardDefaultTraits {
 		    /// The type of the digraph the algorithm runs on.
 		    typedef GR Digraph;
 		    /// \brief The type of the map that stores the arc lengths.
 		    ///
 		    /// The type of the map that stores the arc lengths.
 		    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
 		    typedef LEN LengthMap;
 		    /// The type of the arc lengths.
 		    typedef typename LEN::Value Value;
 		    /// \brief Operation traits for Bellman-Ford algorithm.
 		    ///
 		    /// It defines the used operations and the infinity value for the
 		    /// given \c Value type.
 		    /// \see BellmanFordDefaultOperationTraits
 		    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
 		    /// \brief The type of the map that stores the last
 		    /// arcs of the shortest paths.
 		    ///
 		    /// The type of the map that stores the last arcs of the shortest paths.
 		    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename GR::template NodeMap<typename GR::Arc> PredMap;
 		    /// \brief Instantiates a \c PredMap.
 		    ///
 		    /// This function instantiates a \ref PredMap.
 		    /// \param g is the digraph to which we would like to define the
 		    /// \ref PredMap.
 		    static PredMap *createPredMap(const GR &g) {
 		      return new PredMap(g);
+		    }
 		    /// \brief The type of the map that stores the distances of the nodes.
 		    ///
 		    /// The type of the map that stores the distances of the nodes.
 		    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename GR::template NodeMap<Value> DistMap;
 		    /// \brief Instantiates a \c DistMap.
 		    ///
 		    /// This function instantiates a \ref DistMap.
 		    /// \param g is the digraph to which we would like to define the
 		    /// \ref DistMap.
 		    static DistMap *createDistMap(const GR &g) {
 		      return new DistMap(g);
+		    }
 		    ///The type of the shortest paths.
 		    ///The type of the shortest paths.
 		    ///It must meet the \ref concepts::Path "Path" concept.
 		    typedef lemon::Path<Digraph> Path;
 		  };
 		  /// \brief Default traits class used by BellmanFordWizard.
 		  ///
 		  /// Default traits class used by BellmanFordWizard.
 		  /// \tparam GR The type of the digraph.
 		  /// \tparam LEN The type of the length map.
 		  template <typename GR, typename LEN>
 		  class BellmanFordWizardBase
 		    : public BellmanFordWizardDefaultTraits<GR, LEN> {
 		    typedef BellmanFordWizardDefaultTraits<GR, LEN> Base;
 		  protected:
 		    // Type of the nodes in the digraph.
 		    typedef typename Base::Digraph::Node Node;
 		    // Pointer to the underlying digraph.
 		    void *_graph;
 		    // Pointer to the length map
 		    void *_length;
 		    // Pointer to the map of predecessors arcs.
 		    void *_pred;
 		    // Pointer to the map of distances.
 		    void *_dist;
 		    //Pointer to the shortest path to the target node.
 		    void *_path;
 		    //Pointer to the distance of the target node.
 		    void *_di;
 		    public:
 		    /// Constructor.
 		    /// This constructor does not require parameters, it initiates
 		    /// all of the attributes to default values \c 0.
 		    BellmanFordWizardBase() :
 		      _graph(0), _length(0), _pred(0), _dist(0), _path(0), _di(0) {}
 		    /// Constructor.
 		    /// This constructor requires two parameters,
 		    /// others are initiated to \c 0.
 		    /// \param gr The digraph the algorithm runs on.
 		    /// \param len The length map.
 		    BellmanFordWizardBase(const GR& gr,
 					  const LEN& len) :
 		      _graph(reinterpret_cast<void*>(const_cast<GR*>(&gr))),
 		      _length(reinterpret_cast<void*>(const_cast<LEN*>(&len))),
 		      _pred(0), _dist(0), _path(0), _di(0) {}
 		  };
 		  /// \brief Auxiliary class for the function-type interface of the
 		  /// \ref BellmanFord "Bellman-Ford" algorithm.
 		  ///
 		  /// This auxiliary class is created to implement the
 		  /// \ref bellmanFord() "function-type interface" of the
 		  /// \ref BellmanFord "Bellman-Ford" algorithm.
 		  /// It does not have own \ref run() method, it uses the
 		  /// functions and features of the plain \ref BellmanFord.
 		  ///
 		  /// This class should only be used through the \ref bellmanFord()
 		  /// function, which makes it easier to use the algorithm.
 		  ///
 		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm.
 		  template<class TR>
 		  class BellmanFordWizard : public TR {
 		    typedef TR Base;
 		    typedef typename TR::Digraph Digraph;
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::OutArcIt ArcIt;
 		    typedef typename TR::LengthMap LengthMap;
 		    typedef typename LengthMap::Value Value;
 		    typedef typename TR::PredMap PredMap;
 		    typedef typename TR::DistMap DistMap;
 		    typedef typename TR::Path Path;
 		  public:
 		    /// Constructor.
 		    BellmanFordWizard() : TR() {}
 		    /// \brief Constructor that requires parameters.
 		    ///
 		    /// Constructor that requires parameters.
 		    /// These parameters will be the default values for the traits class.
 		    /// \param gr The digraph the algorithm runs on.
 		    /// \param len The length map.
 		    BellmanFordWizard(const Digraph& gr, const LengthMap& len)
 		      : TR(gr, len) {}
 		    /// \brief Copy constructor
 		    BellmanFordWizard(const TR &b) : TR(b) {}
 		    ~BellmanFordWizard() {}
 		    /// \brief Runs the Bellman-Ford algorithm from the given source node.
 		    ///
 		    /// This method runs the Bellman-Ford algorithm from the given source
 		    /// node in order to compute the shortest path to each node.
 		    void run(Node s) {
 		      BellmanFord<Digraph,LengthMap,TR>
 			bf(*reinterpret_cast<const Digraph*>(Base::_graph),
 		           *reinterpret_cast<const LengthMap*>(Base::_length));
 		      if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
 		      if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
 		      bf.run(s);
+		    }
 		    /// \brief Runs the Bellman-Ford algorithm to find the shortest path
 		    /// between \c s and \c t.
 		    ///
 		    /// This method runs the Bellman-Ford algorithm from node \c s
 		    /// in order to compute the shortest path to node \c t.
 		    /// Actually, it computes the shortest path to each node, but using
 		    /// this function you can retrieve the distance and the shortest path
 		    /// for a single target node easier.
 		    ///
 		    /// \return \c true if \c t is reachable form \c s.
 		    bool run(Node s, Node t) {
 		      BellmanFord<Digraph,LengthMap,TR>
 		        bf(*reinterpret_cast<const Digraph*>(Base::_graph),
 		           *reinterpret_cast<const LengthMap*>(Base::_length));
 		      if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
 		      if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
 		      bf.run(s);
 		      if (Base::_path) *reinterpret_cast<Path*>(Base::_path) = bf.path(t);
 		      if (Base::_di) *reinterpret_cast<Value*>(Base::_di) = bf.dist(t);
 		      return bf.reached(t);
+		    }
 		    template<class T>
 		    struct SetPredMapBase : public Base {
 		      typedef T PredMap;
 		      static PredMap *createPredMap(const Digraph &) { return 0; };
 		      SetPredMapBase(const TR &b) : TR(b) {}
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// the predecessor map.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting
 		    /// the map that stores the predecessor arcs of the nodes.
 		    template<class T>
 		    BellmanFordWizard<SetPredMapBase<T> > predMap(const T &t) {
 		      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return BellmanFordWizard<SetPredMapBase<T> >(*this);
+		    }
 		    template<class T>
 		    struct SetDistMapBase : public Base {
 		      typedef T DistMap;
 		      static DistMap *createDistMap(const Digraph &) { return 0; };
 		      SetDistMapBase(const TR &b) : TR(b) {}
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// the distance map.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting
 		    /// the map that stores the distances of the nodes calculated
 		    /// by the algorithm.
 		    template<class T>
 		    BellmanFordWizard<SetDistMapBase<T> > distMap(const T &t) {
 		      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return BellmanFordWizard<SetDistMapBase<T> >(*this);
+		    }
 		    template<class T>
 		    struct SetPathBase : public Base {
 		      typedef T Path;
 		      SetPathBase(const TR &b) : TR(b) {}
 		    };
 		    /// \brief \ref named-func-param "Named parameter" for getting
 		    /// the shortest path to the target node.
 		    ///
 		    /// \ref named-func-param "Named parameter" for getting
 		    /// the shortest path to the target node.
 		    template<class T>
 		    BellmanFordWizard<SetPathBase<T> > path(const T &t)
+		    {
 		      Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return BellmanFordWizard<SetPathBase<T> >(*this);
+		    }
 		    /// \brief \ref named-func-param "Named parameter" for getting
 		    /// the distance of the target node.
 		    ///
 		    /// \ref named-func-param "Named parameter" for getting
 		    /// the distance of the target node.
 		    BellmanFordWizard dist(const Value &d)
+		    {
 		      Base::_di=reinterpret_cast<void*>(const_cast<Value*>(&d));
 		      return *this;
+		    }
 		  };
 		  /// \brief Function type interface for the \ref BellmanFord "Bellman-Ford"
 		  /// algorithm.
 		  ///
 		  /// \ingroup shortest_path
 		  /// Function type interface for the \ref BellmanFord "Bellman-Ford"
 		  /// algorithm.
 		  ///
 		  /// This function also has several \ref named-templ-func-param
 		  /// "named parameters", they are declared as the members of class
 		  /// \ref BellmanFordWizard.
 		  /// The following examples show how to use these parameters.
 		  /// \code
 		  ///   // Compute shortest path from node s to each node
 		  ///   bellmanFord(g,length).predMap(preds).distMap(dists).run(s);
 		  ///
 		  ///   // Compute shortest path from s to t
 		  ///   bool reached = bellmanFord(g,length).path(p).dist(d).run(s,t);
 		  /// \endcode
 		  /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()"
 		  /// to the end of the parameter list.
 		  /// \sa BellmanFordWizard
 		  /// \sa BellmanFord
 		  template<typename GR, typename LEN>
 		  BellmanFordWizard<BellmanFordWizardBase<GR,LEN> >
 		  bellmanFord(const GR& digraph,
 			      const LEN& length)
+		  {
 		    return BellmanFordWizard<BellmanFordWizardBase<GR,LEN> >(digraph, length);
+		  }
 		} //END OF NAMESPACE LEMON
 		#endif

lemon/bfs.h

Show inline comments

 		/* -*- 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_BFS_H
 		#define LEMON_BFS_H
 		///\ingroup search
 		///\file
 		///\brief BFS algorithm.
 		#include <lemon/list_graph.h>
 		#include <lemon/bits/path_dump.h>
 		#include <lemon/core.h>
 		#include <lemon/error.h>
 		#include <lemon/maps.h>
 		#include <lemon/path.h>
 		namespace lemon {
 		  ///Default traits class of Bfs class.
 		  ///Default traits class of Bfs class.
 		  ///\tparam GR Digraph type.
 		  template<class GR>
 		  struct BfsDefaultTraits
+		  {
 		    ///The type of the digraph the algorithm runs on.
 		    typedef GR Digraph;
 		    ///\brief The type of the map that stores the predecessor
 		    ///arcs of the shortest paths.
 		    ///
 		    ///The type of the map that stores the predecessor
 		    ///arcs of the shortest paths.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
 		    ///Instantiates a \c PredMap.
 		    ///This function instantiates a \ref PredMap.
 		    ///\param g is the digraph, to which we would like to define the
 		    ///\ref PredMap.
 		    static PredMap *createPredMap(const Digraph &g)
+		    {
 		      return new PredMap(g);
+		    }
 		    ///The type of the map that indicates which nodes are processed.
 		    ///The type of the map that indicates which nodes are processed.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    ///By default, it is a NullMap.
 		    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
 		    ///Instantiates a \c ProcessedMap.
 		    ///This function instantiates a \ref ProcessedMap.
 		    ///\param g is the digraph, to which
 		    ///we would like to define the \ref ProcessedMap
 		#ifdef DOXYGEN
 		    static ProcessedMap *createProcessedMap(const Digraph &g)
 		#else
 		    static ProcessedMap *createProcessedMap(const Digraph &)
 		#endif
+		    {
 		      return new ProcessedMap();
+		    }
 		    ///The type of the map that indicates which nodes are reached.
 		    ///The type of the map that indicates which nodes are reached.
 		    ///It must conform to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
 		    typedef typename Digraph::template NodeMap<bool> ReachedMap;
 		    ///Instantiates a \c ReachedMap.
 		    ///This function instantiates a \ref ReachedMap.
 		    ///\param g is the digraph, to which
 		    ///we would like to define the \ref ReachedMap.
 		    static ReachedMap *createReachedMap(const Digraph &g)
+		    {
 		      return new ReachedMap(g);
+		    }
 		    ///The type of the map that stores the distances of the nodes.
 		    ///The type of the map that stores the distances of the nodes.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename Digraph::template NodeMap<int> DistMap;
 		    ///Instantiates a \c DistMap.
 		    ///This function instantiates a \ref DistMap.
 		    ///\param g is the digraph, to which we would like to define the
 		    ///\ref DistMap.
 		    static DistMap *createDistMap(const Digraph &g)
+		    {
 		      return new DistMap(g);
+		    }
 		  };
 		  ///%BFS algorithm class.
 		  ///\ingroup search
 		  ///This class provides an efficient implementation of the %BFS algorithm.
 		  ///
 		  ///There is also a \ref bfs() "function-type interface" for the BFS
 		  ///algorithm, which is convenient in the simplier cases and it can be
 		  ///used easier.
 		  ///
 		  ///\tparam GR The type of the digraph the algorithm runs on.
 		  ///The default type is \ref ListDigraph.
 		  ///\tparam TR The traits class that defines various types used by the
 		  ///algorithm. By default, it is \ref BfsDefaultTraits
 		  ///"BfsDefaultTraits<GR>".
 		  ///In most cases, this parameter should not be set directly,
 		  ///consider to use the named template parameters instead.
 		#ifdef DOXYGEN
 		  template <typename GR,
 		            typename TR>
 		#else
 		  template <typename GR=ListDigraph,
 		            typename TR=BfsDefaultTraits<GR> >
 		#endif
 		  class Bfs {
 		  public:
 		    ///The type of the digraph the algorithm runs on.
 		    typedef typename TR::Digraph Digraph;
 		    ///\brief The type of the map that stores the predecessor arcs of the
 		    ///shortest paths.
 		    typedef typename TR::PredMap PredMap;
 		    ///The type of the map that stores the distances of the nodes.
 		    typedef typename TR::DistMap DistMap;
 		    ///The type of the map that indicates which nodes are reached.
 		    typedef typename TR::ReachedMap ReachedMap;
 		    ///The type of the map that indicates which nodes are processed.
 		    typedef typename TR::ProcessedMap ProcessedMap;
 		    ///The type of the paths.
 		    typedef PredMapPath<Digraph, PredMap> Path;
 		    ///The \ref BfsDefaultTraits "traits class" of the algorithm.
 		    typedef TR Traits;
 		  private:
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::OutArcIt OutArcIt;
 		    //Pointer to the underlying digraph.
 		    const Digraph *G;
 		    //Pointer to the map of predecessor arcs.
 		    PredMap *_pred;
 		    //Indicates if _pred is locally allocated (true) or not.
 		    bool local_pred;
 		    //Pointer to the map of distances.
 		    DistMap *_dist;
 		    //Indicates if _dist is locally allocated (true) or not.
 		    bool local_dist;
 		    //Pointer to the map of reached status of the nodes.
 		    ReachedMap *_reached;
 		    //Indicates if _reached is locally allocated (true) or not.
 		    bool local_reached;
 		    //Pointer to the map of processed status of the nodes.
 		    ProcessedMap *_processed;
 		    //Indicates if _processed is locally allocated (true) or not.
 		    bool local_processed;
 		    std::vector<typename Digraph::Node> _queue;
 		    int _queue_head,_queue_tail,_queue_next_dist;
 		    int _curr_dist;
 		    //Creates the maps if necessary.
 		    void create_maps()
+		    {
 		      if(!_pred) {
 		        local_pred = true;
 		        _pred = Traits::createPredMap(*G);
+		      }
 		      if(!_dist) {
 		        local_dist = true;
 		        _dist = Traits::createDistMap(*G);
+		      }
 		      if(!_reached) {
 		        local_reached = true;
 		        _reached = Traits::createReachedMap(*G);
+		      }
 		      if(!_processed) {
 		        local_processed = true;
 		        _processed = Traits::createProcessedMap(*G);
+		      }
+		    }
 		  protected:
 		    Bfs() {}
 		  public:
 		    typedef Bfs Create;
 		    ///\name Named Template Parameters
 		    ///@{
 		    template <class T>
 		    struct SetPredMapTraits : public Traits {
 		      typedef T PredMap;
 		      static PredMap *createPredMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "PredMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c PredMap type.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c PredMap type.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    template <class T>
 		    struct SetPredMap : public Bfs< Digraph, SetPredMapTraits<T> > {
 		      typedef Bfs< Digraph, SetPredMapTraits<T> > Create;
 		    };
 		    template <class T>
 		    struct SetDistMapTraits : public Traits {
 		      typedef T DistMap;
 		      static DistMap *createDistMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "DistMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c DistMap type.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c DistMap type.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    template <class T>
 		    struct SetDistMap : public Bfs< Digraph, SetDistMapTraits<T> > {
 		      typedef Bfs< Digraph, SetDistMapTraits<T> > Create;
 		    };
 		    template <class T>
 		    struct SetReachedMapTraits : public Traits {
 		      typedef T ReachedMap;
 		      static ReachedMap *createReachedMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "ReachedMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c ReachedMap type.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c ReachedMap type.
 		    ///It must conform to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
 		    template <class T>
 		    struct SetReachedMap : public Bfs< Digraph, SetReachedMapTraits<T> > {
 		      typedef Bfs< Digraph, SetReachedMapTraits<T> > Create;
 		    };
 		    template <class T>
 		    struct SetProcessedMapTraits : public Traits {
 		      typedef T ProcessedMap;
 		      static ProcessedMap *createProcessedMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "ProcessedMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c ProcessedMap type.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c ProcessedMap type.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    template <class T>
 		    struct SetProcessedMap : public Bfs< Digraph, SetProcessedMapTraits<T> > {
 		      typedef Bfs< Digraph, SetProcessedMapTraits<T> > Create;
 		    };
 		    struct SetStandardProcessedMapTraits : public Traits {
 		      typedef typename Digraph::template NodeMap<bool> ProcessedMap;
 		      static ProcessedMap *createProcessedMap(const Digraph &g)
+		      {
 		        return new ProcessedMap(g);
 		        return 0; // ignore warnings
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
 		    ///If you don't set it explicitly, it will be automatically allocated.
 		    struct SetStandardProcessedMap :
 		      public Bfs< Digraph, SetStandardProcessedMapTraits > {
 		      typedef Bfs< Digraph, SetStandardProcessedMapTraits > Create;
 		    };
 		    ///@}
 		  public:
 		    ///Constructor.
 		    ///Constructor.
 		    ///\param g The digraph the algorithm runs on.
 		    Bfs(const Digraph &g) :
 		      G(&g),
 		      _pred(NULL), local_pred(false),
 		      _dist(NULL), local_dist(false),
 		      _reached(NULL), local_reached(false),
 		      _processed(NULL), local_processed(false)
 		    { }
 		    ///Destructor.
 		    ~Bfs()
+		    {
 		      if(local_pred) delete _pred;
 		      if(local_dist) delete _dist;
 		      if(local_reached) delete _reached;
 		      if(local_processed) delete _processed;
+		    }
 		    ///Sets the map that stores the predecessor arcs.
 		    ///Sets the map that stores the predecessor arcs.
 		    ///If you don't use this function before calling \ref run(Node) "run()"
 		    ///or \ref init(), an instance will be allocated automatically.
 		    ///The destructor deallocates this automatically allocated map,
 		    ///of course.
 		    ///\return <tt> (*this) </tt>
 		    Bfs &predMap(PredMap &m)
+		    {
 		      if(local_pred) {
 		        delete _pred;
 		        local_pred=false;
+		      }
 		      _pred = &m;
 		      return *this;
+		    }
 		    ///Sets the map that indicates which nodes are reached.
 		    ///Sets the map that indicates which nodes are reached.
 		    ///If you don't use this function before calling \ref run(Node) "run()"
 		    ///or \ref init(), an instance will be allocated automatically.
 		    ///The destructor deallocates this automatically allocated map,
 		    ///of course.
 		    ///\return <tt> (*this) </tt>
 		    Bfs &reachedMap(ReachedMap &m)
+		    {
 		      if(local_reached) {
 		        delete _reached;
 		        local_reached=false;
+		      }
 		      _reached = &m;
 		      return *this;
+		    }
 		    ///Sets the map that indicates which nodes are processed.
 		    ///Sets the map that indicates which nodes are processed.
 		    ///If you don't use this function before calling \ref run(Node) "run()"
 		    ///or \ref init(), an instance will be allocated automatically.
 		    ///The destructor deallocates this automatically allocated map,
 		    ///of course.
 		    ///\return <tt> (*this) </tt>
 		    Bfs &processedMap(ProcessedMap &m)
+		    {
 		      if(local_processed) {
 		        delete _processed;
 		        local_processed=false;
+		      }
 		      _processed = &m;
 		      return *this;
+		    }
 		    ///Sets the map that stores the distances of the nodes.
 		    ///Sets the map that stores the distances of the nodes calculated by
 		    ///the algorithm.
 		    ///If you don't use this function before calling \ref run(Node) "run()"
 		    ///or \ref init(), an instance will be allocated automatically.
 		    ///The destructor deallocates this automatically allocated map,
 		    ///of course.
 		    ///\return <tt> (*this) </tt>
 		    Bfs &distMap(DistMap &m)
+		    {
 		      if(local_dist) {
 		        delete _dist;
 		        local_dist=false;
+		      }
 		      _dist = &m;
 		      return *this;
+		    }
 		  public:
 		    ///\name Execution Control
 		    ///The simplest way to execute the BFS algorithm is to use one of the
 		    ///member functions called \ref run(Node) "run()".\n
 		    ///If you need better control on the execution, you have to call
 		    ///\ref init() first, then you can add several source nodes with
 		    ///\ref addSource(). Finally the actual path computation can be
 		    ///performed with one of the \ref start() functions.
 		    ///@{
 		    ///\brief Initializes the internal data structures.
 		    ///
 		    ///Initializes the internal data structures.
 		    void init()
+		    {
 		      create_maps();
 		      _queue.resize(countNodes(*G));
 		      _queue_head=_queue_tail=0;
 		      _curr_dist=1;
 		      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
 		        _pred->set(u,INVALID);
 		        _reached->set(u,false);
 		        _processed->set(u,false);
+		      }
+		    }
 		    ///Adds a new source node.
 		    ///Adds a new source node to the set of nodes to be processed.
 		    ///
 		    void addSource(Node s)
+		    {
 		      if(!(*_reached)[s])
+		        {
 		          _reached->set(s,true);
 		          _pred->set(s,INVALID);
 		          _dist->set(s,0);
 		          _queue[_queue_head++]=s;
 		          _queue_next_dist=_queue_head;
+		        }
+		    }
 		    ///Processes the next node.
 		    ///Processes the next node.
 		    ///
 		    ///\return The processed node.
 		    ///
 		    ///\pre The queue must not be empty.
 		    Node processNextNode()
+		    {
 		      if(_queue_tail==_queue_next_dist) {
 		        _curr_dist++;
 		        _queue_next_dist=_queue_head;
+		      }
 		      Node n=_queue[_queue_tail++];
 		      _processed->set(n,true);
 		      Node m;
 		      for(OutArcIt e(*G,n);e!=INVALID;++e)
 		        if(!(*_reached)[m=G->target(e)]) {
 		          _queue[_queue_head++]=m;
 		          _reached->set(m,true);
 		          _pred->set(m,e);
 		          _dist->set(m,_curr_dist);
+		        }
 		      return n;
+		    }
 		    ///Processes the next node.
 		    ///Processes the next node and checks if the given target node
 		    ///is reached. If the target node is reachable from the processed
 		    ///node, then the \c reach parameter will be set to \c true.
 		    ///
 		    ///\param target The target node.
 		    ///\retval reach Indicates if the target node is reached.
 		    ///It should be initially \c false.
 		    ///
 		    ///\return The processed node.
 		    ///
 		    ///\pre The queue must not be empty.
 		    Node processNextNode(Node target, bool& reach)
+		    {
 		      if(_queue_tail==_queue_next_dist) {
 		        _curr_dist++;
 		        _queue_next_dist=_queue_head;
+		      }
 		      Node n=_queue[_queue_tail++];
 		      _processed->set(n,true);
 		      Node m;
 		      for(OutArcIt e(*G,n);e!=INVALID;++e)
 		        if(!(*_reached)[m=G->target(e)]) {
 		          _queue[_queue_head++]=m;
 		          _reached->set(m,true);
 		          _pred->set(m,e);
 		          _dist->set(m,_curr_dist);
 		          reach = reach || (target == m);
+		        }
 		      return n;
+		    }
 		    ///Processes the next node.
 		    ///Processes the next node and checks if at least one of reached
 		    ///nodes has \c true value in the \c nm node map. If one node
 		    ///with \c true value is reachable from the processed node, then the
 		    ///\c rnode parameter will be set to the first of such nodes.
 		    ///
 		    ///\param nm A \c bool (or convertible) node map that indicates the
 		    ///possible targets.
 		    ///\retval rnode The reached target node.
 		    ///It should be initially \c INVALID.
 		    ///
 		    ///\return The processed node.
 		    ///
 		    ///\pre The queue must not be empty.
 		    template<class NM>
 		    Node processNextNode(const NM& nm, Node& rnode)
+		    {
 		      if(_queue_tail==_queue_next_dist) {
 		        _curr_dist++;
 		        _queue_next_dist=_queue_head;
+		      }
 		      Node n=_queue[_queue_tail++];
 		      _processed->set(n,true);
 		      Node m;
 		      for(OutArcIt e(*G,n);e!=INVALID;++e)
 		        if(!(*_reached)[m=G->target(e)]) {
 		          _queue[_queue_head++]=m;
 		          _reached->set(m,true);
 		          _pred->set(m,e);
 		          _dist->set(m,_curr_dist);
 		          if (nm[m] && rnode == INVALID) rnode = m;
+		        }
 		      return n;
+		    }
 		    ///The next node to be processed.
 		    ///Returns the next node to be processed or \c INVALID if the queue
 		    ///is empty.
 		    Node nextNode() const
+		    {
 		      return _queue_tail<_queue_head?_queue[_queue_tail]:INVALID;
+		    }
 		    ///Returns \c false if there are nodes to be processed.
 		    ///Returns \c false if there are nodes to be processed
 		    ///in the queue.
 		    bool emptyQueue() const { return _queue_tail==_queue_head; }
 		    ///Returns the number of the nodes to be processed.
 		    ///Returns the number of the nodes to be processed
 		    ///in the queue.
 		    int queueSize() const { return _queue_head-_queue_tail; }
 		    ///Executes the algorithm.
 		    ///Executes the algorithm.
 		    ///
 		    ///This method runs the %BFS algorithm from the root node(s)
 		    ///in order to compute the shortest path to each node.
 		    ///
 		    ///The algorithm computes
 		    ///- the shortest path tree (forest),
 		    ///- the distance of each node from the root(s).
 		    ///
 		    ///\pre init() must be called and at least one root node should be
 		    ///added with addSource() before using this function.
 		    ///
 		    ///\note <tt>b.start()</tt> is just a shortcut of the following code.
 		    ///\code
 		    ///  while ( !b.emptyQueue() ) {
 		    ///    b.processNextNode();
 		    ///  }
 		    ///\endcode
 		    void start()
+		    {
 		      while ( !emptyQueue() ) processNextNode();
+		    }
 		    ///Executes the algorithm until the given target node is reached.
 		    ///Executes the algorithm until the given target node is reached.
 		    ///
 		    ///This method runs the %BFS algorithm from the root node(s)
 		    ///in order to compute the shortest path to \c t.
 		    ///
 		    ///The algorithm computes
 		    ///- the shortest path to \c t,
 		    ///- the distance of \c t from the root(s).
 		    ///
 		    ///\pre init() must be called and at least one root node should be
 		    ///added with addSource() before using this function.
 		    ///
 		    ///\note <tt>b.start(t)</tt> is just a shortcut of the following code.
 		    ///\code
 		    ///  bool reach = false;
 		    ///  while ( !b.emptyQueue() && !reach ) {
 		    ///    b.processNextNode(t, reach);
 		    ///  }
 		    ///\endcode
 		    void start(Node t)
+		    {
 		      bool reach = false;
 		      while ( !emptyQueue() && !reach ) processNextNode(t, reach);
+		    }
 		    ///Executes the algorithm until a condition is met.
 		    ///Executes the algorithm until a condition is met.
 		    ///
 		    ///This method runs the %BFS algorithm from the root node(s) in
 		    ///order to compute the shortest path to a node \c v with
 		    /// <tt>nm[v]</tt> true, if such a node can be found.
 		    ///
 		    ///\param nm A \c bool (or convertible) node map. The algorithm
 		    ///will stop when it reaches a node \c v with <tt>nm[v]</tt> true.
 		    ///
 		    ///\return The reached node \c v with <tt>nm[v]</tt> true or
 		    ///\c INVALID if no such node was found.
 		    ///
 		    ///\pre init() must be called and at least one root node should be
 		    ///added with addSource() before using this function.
 		    ///
 		    ///\note <tt>b.start(nm)</tt> is just a shortcut of the following code.
 		    ///\code
 		    ///  Node rnode = INVALID;
 		    ///  while ( !b.emptyQueue() && rnode == INVALID ) {
 		    ///    b.processNextNode(nm, rnode);
 		    ///  }
 		    ///  return rnode;
 		    ///\endcode
 		    template<class NodeBoolMap>
 		    Node start(const NodeBoolMap &nm)
+		    {
 		      Node rnode = INVALID;
 		      while ( !emptyQueue() && rnode == INVALID ) {
 		        processNextNode(nm, rnode);
+		      }
 		      return rnode;
+		    }
 		    ///Runs the algorithm from the given source node.
 		    ///This method runs the %BFS algorithm from node \c s
 		    ///in order to compute the shortest path to each node.
 		    ///
 		    ///The algorithm computes
 		    ///- the shortest path tree,
 		    ///- the distance of each node from the root.
 		    ///
 		    ///\note <tt>b.run(s)</tt> is just a shortcut of the following code.
 		    ///\code
 		    ///  b.init();
 		    ///  b.addSource(s);
 		    ///  b.start();
 		    ///\endcode
 		    void run(Node s) {
 		      init();
 		      addSource(s);
 		      start();
+		    }
 		    ///Finds the shortest path between \c s and \c t.
 		    ///This method runs the %BFS algorithm from node \c s
 		    ///in order to compute the shortest 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>b.run(s,t)</tt> is just a
 		    ///shortcut of the following code.
 		    ///\code
 		    ///  b.init();
 		    ///  b.addSource(s);
 		    ///  b.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 %BFS algorithm in order to visit all nodes
 		    ///in the digraph.
 		    ///
 		    ///\note <tt>b.run(s)</tt> is just a shortcut of the following code.
 		    ///\code
 		    ///  b.init();
 		    ///  for (NodeIt n(gr); n != INVALID; ++n) {
 		    ///    if (!b.reached(n)) {
 		    ///      b.addSource(n);
 		    ///      b.start();
 		    ///    }
 		    ///  }
 		    ///\endcode
 		    void run() {
 		      init();
 		      for (NodeIt n(*G); n != INVALID; ++n) {
 		        if (!reached(n)) {
 		          addSource(n);
 		          start();
+		        }
+		      }
+		    }
 		    ///@}
 		    ///\name Query Functions
 		    ///The results of the BFS algorithm can be obtained using these
 		    ///functions.\n
 		    ///Either \ref run(Node) "run()" or \ref start() should be called
 		    ///before using them.
 		    ///@{
 		    ///The shortest path to the given node.
 		    ///Returns the shortest path to the given node from the root(s).
 		    ///
 		    ///\warning \c t should be reached from the root(s).
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    Path path(Node t) const { return Path(*G, *_pred, t); }
 		    ///The distance of the given node from the root(s).
 		    ///Returns the distance of the given node from the root(s).
 		    ///
 		    ///\warning If node \c v is not reached from the root(s), then
 		    ///the return value of this function is undefined.
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    int dist(Node v) const { return (*_dist)[v]; }
 		    ///\brief Returns the 'previous arc' of the shortest path tree for
 		    ///the given node.
 		    ///
 		    ///This function returns the 'previous arc' of the shortest path
 		    ///tree for the node \c v, i.e. it returns the last arc of a
 		    ///shortest path from a root to \c v. It is \c INVALID if \c v
 		    ///is not reached from the root(s) or if \c v is a root.
 		    ///
 		    ///The shortest path tree used here is equal to the shortest path
 		    ///tree used in \ref predNode() and \ref predMap().
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    Arc predArc(Node v) const { return (*_pred)[v];}
 		    ///\brief Returns the 'previous node' of the shortest path tree for
 		    ///the given node.
 		    ///
 		    ///This function returns the 'previous node' of the shortest path
 		    ///tree for the node \c v, i.e. it returns the last but one node
 		    ///of a shortest path from a root to \c v. It is \c INVALID
 		    ///if \c v is not reached from the root(s) or if \c v is a root.
 		    ///
 		    ///The shortest path tree used here is equal to the shortest path
 		    ///tree used in \ref predArc() and \ref predMap().
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
 		                                  G->source((*_pred)[v]); }
 		    ///\brief Returns a const reference to the node map that stores the
 		    /// distances of the nodes.
 		    ///
 		    ///Returns a const reference to the node map that stores the distances
 		    ///of the nodes calculated by the algorithm.
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    const DistMap &distMap() const { return *_dist;}
 		    ///\brief Returns a const reference to the node map that stores the
 		    ///predecessor arcs.
 		    ///
 		    ///Returns a const reference to the node map that stores the predecessor
 		    ///arcs, which form the shortest path tree (forest).
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    const PredMap &predMap() const { return *_pred;}
 		    ///Checks if the given node is reached from the root(s).
 		    ///Returns \c true if \c v is reached from the root(s).
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    bool reached(Node v) const { return (*_reached)[v]; }
 		    ///@}
 		  };
 		  ///Default traits class of bfs() function.
 		  ///Default traits class of bfs() function.
 		  ///\tparam GR Digraph type.
 		  template<class GR>
 		  struct BfsWizardDefaultTraits
+		  {
 		    ///The type of the digraph the algorithm runs on.
 		    typedef GR Digraph;
 		    ///\brief The type of the map that stores the predecessor
 		    ///arcs of the shortest paths.
 		    ///
 		    ///The type of the map that stores the predecessor
 		    ///arcs of the shortest paths.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
 		    ///Instantiates a PredMap.
 		    ///This function instantiates a PredMap.
 		    ///\param g is the digraph, to which we would like to define the
 		    ///PredMap.
 		    static PredMap *createPredMap(const Digraph &g)
+		    {
 		      return new PredMap(g);
+		    }
 		    ///The type of the map that indicates which nodes are processed.
 		    ///The type of the map that indicates which nodes are processed.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    ///By default, it is a NullMap.
 		    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
 		    ///Instantiates a ProcessedMap.
 		    ///This function instantiates a ProcessedMap.
 		    ///\param g is the digraph, to which
 		    ///we would like to define the ProcessedMap.
 		#ifdef DOXYGEN
 		    static ProcessedMap *createProcessedMap(const Digraph &g)
 		#else
 		    static ProcessedMap *createProcessedMap(const Digraph &)
 		#endif
+		    {
 		      return new ProcessedMap();
+		    }
 		    ///The type of the map that indicates which nodes are reached.
 		    ///The type of the map that indicates which nodes are reached.
 		    ///It must conform to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
 		    typedef typename Digraph::template NodeMap<bool> ReachedMap;
 		    ///Instantiates a ReachedMap.
 		    ///This function instantiates a ReachedMap.
 		    ///\param g is the digraph, to which
 		    ///we would like to define the ReachedMap.
 		    static ReachedMap *createReachedMap(const Digraph &g)
+		    {
 		      return new ReachedMap(g);
+		    }
 		    ///The type of the map that stores the distances of the nodes.
 		    ///The type of the map that stores the distances of the nodes.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename Digraph::template NodeMap<int> DistMap;
 		    ///Instantiates a DistMap.
 		    ///This function instantiates a DistMap.
 		    ///\param g is the digraph, to which we would like to define
 		    ///the DistMap
 		    static DistMap *createDistMap(const Digraph &g)
+		    {
 		      return new DistMap(g);
+		    }
 		    ///The type of the shortest paths.
 		    ///The type of the shortest paths.
 		    ///It must conform to the \ref concepts::Path "Path" concept.
 		    typedef lemon::Path<Digraph> Path;
 		  };
 		  /// Default traits class used by BfsWizard
 		  /// Default traits class used by BfsWizard.
 		  /// \tparam GR The type of the digraph.
 		  template<class GR>
 		  class BfsWizardBase : public BfsWizardDefaultTraits<GR>
+		  {
 		    typedef BfsWizardDefaultTraits<GR> Base;
 		  protected:
 		    //The type of the nodes in the digraph.
 		    typedef typename Base::Digraph::Node Node;
 		    //Pointer to the digraph the algorithm runs on.
 		    void *_g;
 		    //Pointer to the map of reached nodes.
 		    void *_reached;
 		    //Pointer to the map of processed nodes.
 		    void *_processed;
 		    //Pointer to the map of predecessors arcs.
 		    void *_pred;
 		    //Pointer to the map of distances.
 		    void *_dist;
 		    //Pointer to the shortest path to the target node.
 		    void *_path;
 		    //Pointer to the distance of the target node.
 		    int *_di;
 		    public:
 		    /// Constructor.
 		    /// This constructor does not require parameters, it initiates
 		    /// all of the attributes to \c 0.
 		    BfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),
 		                      _dist(0), _path(0), _di(0) {}
 		    /// Constructor.
 		    /// This constructor requires one parameter,
 		    /// others are initiated to \c 0.
 		    /// \param g The digraph the algorithm runs on.
 		    BfsWizardBase(const GR &g) :
 		      _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
 		      _reached(0), _processed(0), _pred(0), _dist(0),  _path(0), _di(0) {}
 		  };
 		  /// Auxiliary class for the function-type interface of BFS algorithm.
 		  /// This auxiliary class is created to implement the
 		  /// \ref bfs() "function-type interface" of \ref Bfs algorithm.
 		  /// It does not have own \ref run(Node) "run()" method, it uses the
 		  /// functions and features of the plain \ref Bfs.
 		  ///
 		  /// This class should only be used through the \ref bfs() function,
 		  /// which makes it easier to use the algorithm.
 		  ///
 		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm.
 		  template<class TR>
 		  class BfsWizard : public TR
+		  {
 		    typedef TR Base;
 		    typedef typename TR::Digraph Digraph;
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::OutArcIt OutArcIt;
 		    typedef typename TR::PredMap PredMap;
 		    typedef typename TR::DistMap DistMap;
 		    typedef typename TR::ReachedMap ReachedMap;
 		    typedef typename TR::ProcessedMap ProcessedMap;
 		    typedef typename TR::Path Path;
 		  public:
 		    /// Constructor.
 		    BfsWizard() : TR() {}
 		    /// Constructor that requires parameters.
 		    /// Constructor that requires parameters.
 		    /// These parameters will be the default values for the traits class.
 		    /// \param g The digraph the algorithm runs on.
 		    BfsWizard(const Digraph &g) :
 		      TR(g) {}
 		    ///Copy constructor
 		    BfsWizard(const TR &b) : TR(b) {}
 		    ~BfsWizard() {}
 		    ///Runs BFS algorithm from the given source node.
 		    ///This method runs BFS algorithm from node \c s
 		    ///in order to compute the shortest path to each node.
 		    void run(Node s)
+		    {
 		      Bfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
 		      if (Base::_pred)
 		        alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
 		      if (Base::_dist)
 		        alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
 		      if (Base::_reached)
 		        alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
 		      if (Base::_processed)
 		        alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
 		      if (s!=INVALID)
 		        alg.run(s);
 		      else
 		        alg.run();
+		    }
 		    ///Finds the shortest path between \c s and \c t.
 		    ///This method runs BFS algorithm from node \c s
 		    ///in order to compute the shortest path to node \c t
 		    ///(it stops searching when \c t is processed).
 		    ///
 		    ///\return \c true if \c t is reachable form \c s.
 		    bool run(Node s, Node t)
+		    {
 		      Bfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
 		      if (Base::_pred)
 		        alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
 		      if (Base::_dist)
 		        alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
 		      if (Base::_reached)
 		        alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
 		      if (Base::_processed)
 		        alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
 		      alg.run(s,t);
 		      if (Base::_path)
 		        *reinterpret_cast<Path*>(Base::_path) = alg.path(t);
 		      if (Base::_di)
 		        *Base::_di = alg.dist(t);
 		      return alg.reached(t);
+		    }
 		    ///Runs BFS algorithm to visit all nodes in the digraph.
 		    ///This method runs BFS algorithm in order to visit all nodes
 		    ///in the digraph.
 		    void run()
+		    {
 		      run(INVALID);
+		    }
 		    template<class T>
 		    struct SetPredMapBase : public Base {
 		      typedef T PredMap;
 		      static PredMap *createPredMap(const Digraph &) { return 0; };
 		      SetPredMapBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///the predecessor map.
 		    ///
 		    ///\ref named-templ-param "Named parameter" function for setting
 		    ///the map that stores the predecessor arcs of the nodes.
 		    template<class T>
 		    BfsWizard<SetPredMapBase<T> > predMap(const T &t)
+		    {
 		      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return BfsWizard<SetPredMapBase<T> >(*this);
+		    }
 		    template<class T>
 		    struct SetReachedMapBase : public Base {
 		      typedef T ReachedMap;
 		      static ReachedMap *createReachedMap(const Digraph &) { return 0; };
 		      SetReachedMapBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///the reached map.
 		    ///
 		    ///\ref named-templ-param "Named parameter" function for setting
 		    ///the map that indicates which nodes are reached.
 		    template<class T>
 		    BfsWizard<SetReachedMapBase<T> > reachedMap(const T &t)
+		    {
 		      Base::_reached=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return BfsWizard<SetReachedMapBase<T> >(*this);
+		    }
 		    template<class T>
 		    struct SetDistMapBase : public Base {
 		      typedef T DistMap;
 		      static DistMap *createDistMap(const Digraph &) { return 0; };
 		      SetDistMapBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///the distance map.
 		    ///
 		    ///\ref named-templ-param "Named parameter" function for setting
 		    ///the map that stores the distances of the nodes calculated
 		    ///by the algorithm.
 		    template<class T>
 		    BfsWizard<SetDistMapBase<T> > distMap(const T &t)
+		    {
 		      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return BfsWizard<SetDistMapBase<T> >(*this);
+		    }
 		    template<class T>
 		    struct SetProcessedMapBase : public Base {
 		      typedef T ProcessedMap;
 		      static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
 		      SetProcessedMapBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-func-param "Named parameter" for setting
 		    ///the processed map.
 		    ///
 		    ///\ref named-templ-param "Named parameter" function for setting
 		    ///the map that indicates which nodes are processed.
 		    template<class T>
 		    BfsWizard<SetProcessedMapBase<T> > processedMap(const T &t)
+		    {
 		      Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return BfsWizard<SetProcessedMapBase<T> >(*this);
+		    }
 		    template<class T>
 		    struct SetPathBase : public Base {
 		      typedef T Path;
 		      SetPathBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-func-param "Named parameter"
 		    ///for getting the shortest path to the target node.
 		    ///
 		    ///\ref named-func-param "Named parameter"
 		    ///for getting the shortest path to the target node.
 		    template<class T>
 		    BfsWizard<SetPathBase<T> > path(const T &t)
+		    {
 		      Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return BfsWizard<SetPathBase<T> >(*this);
+		    }
 		    ///\brief \ref named-func-param "Named parameter"
 		    ///for getting the distance of the target node.
 		    ///
 		    ///\ref named-func-param "Named parameter"
 		    ///for getting the distance of the target node.
 		    BfsWizard dist(const int &d)
+		    {
 		      Base::_di=const_cast<int*>(&d);
 		      return *this;
+		    }
 		  };
 		  ///Function-type interface for BFS algorithm.
 		  /// \ingroup search
 		  ///Function-type interface for BFS algorithm.
 		  ///
 		  ///This function also has several \ref named-func-param "named parameters",
 		  ///they are declared as the members of class \ref BfsWizard.
 		  ///The following examples show how to use these parameters.
 		  ///\code
 		  ///  // Compute shortest path from node s to each node
 		  ///  bfs(g).predMap(preds).distMap(dists).run(s);
 		  ///
 		  ///  // Compute shortest path from s to t
 		  ///  bool reached = bfs(g).path(p).dist(d).run(s,t);
 		  ///\endcode
 		  ///\warning Don't forget to put the \ref BfsWizard::run(Node) "run()"
 		  ///to the end of the parameter list.
 		  ///\sa BfsWizard
 		  ///\sa Bfs
 		  template<class GR>
 		  BfsWizard<BfsWizardBase<GR> >
 		  bfs(const GR &digraph)
+		  {
 		    return BfsWizard<BfsWizardBase<GR> >(digraph);
+		  }
 		#ifdef DOXYGEN
 		  /// \brief Visitor class for BFS.
 		  ///
 		  /// This class defines the interface of the BfsVisit events, and
 		  /// it could be the base of a real visitor class.
 		  template <typename GR>
 		  struct BfsVisitor {
 		    typedef GR Digraph;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::Node Node;
 		    /// \brief Called for the source node(s) of the BFS.
 		    ///
 		    /// This function is called for the source node(s) of the BFS.
 		    void start(const Node& node) {}
 		    /// \brief Called when a node is reached first time.
 		    ///
 		    /// This function is called when a node is reached first time.
 		    void reach(const Node& node) {}
 		    /// \brief Called when a node is processed.
 		    ///
 		    /// This function is called when a node is processed.
 		    void process(const Node& node) {}
 		    /// \brief Called when an arc reaches a new node.
 		    ///
 		    /// This function is called when the BFS finds an arc whose target node
 		    /// is not reached yet.
 		    void discover(const Arc& arc) {}
 		    /// \brief Called when an arc is examined but its target node is
 		    /// already discovered.
 		    ///
 		    /// This function is called when an arc is examined but its target node is
 		    /// already discovered.
 		    void examine(const Arc& arc) {}
 		  };
 		#else
 		  template <typename GR>
 		  struct BfsVisitor {
 		    typedef GR Digraph;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::Node Node;
 		    void start(const Node&) {}
 		    void reach(const Node&) {}
 		    void process(const Node&) {}
 		    void discover(const Arc&) {}
 		    void examine(const Arc&) {}
 		    template <typename _Visitor>
 		    struct Constraints {
 		      void constraints() {
 		        Arc arc;
 		        Node node;
 		        visitor.start(node);
 		        visitor.reach(node);
 		        visitor.process(node);
 		        visitor.discover(arc);
 		        visitor.examine(arc);
+		      }
 		      _Visitor& visitor;
 		    };
 		  };
 		#endif
 		  /// \brief Default traits class of BfsVisit class.
 		  ///
 		  /// Default traits class of BfsVisit class.
 		  /// \tparam GR The type of the digraph the algorithm runs on.
 		  template<class GR>
 		  struct BfsVisitDefaultTraits {
 		    /// \brief The type of the digraph the algorithm runs on.
 		    typedef GR Digraph;
 		    /// \brief The type of the map that indicates which nodes are reached.
 		    ///
 		    /// The type of the map that indicates which nodes are reached.
 		    /// It must conform to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
 		    typedef typename Digraph::template NodeMap<bool> ReachedMap;
 		    /// \brief Instantiates a ReachedMap.
 		    ///
 		    /// This function instantiates a ReachedMap.
 		    /// \param digraph is the digraph, to which
 		    /// we would like to define the ReachedMap.
 		    static ReachedMap *createReachedMap(const Digraph &digraph) {
 		      return new ReachedMap(digraph);
+		    }
 		  };
 		  /// \ingroup search
 		  ///
 		  /// \brief BFS algorithm class with visitor interface.
 		  ///
 		  /// This class provides an efficient implementation of the BFS algorithm
 		  /// with visitor interface.
 		  ///
 		  /// The BfsVisit class provides an alternative interface to the Bfs
 		  /// class. It works with callback mechanism, the BfsVisit object calls
 		  /// the member functions of the \c Visitor class on every BFS event.
 		  ///
 		  /// This interface of the BFS algorithm should be used in special cases
 		  /// when extra actions have to be performed in connection with certain
 		  /// events of the BFS algorithm. Otherwise consider to use Bfs or bfs()
 		  /// instead.
 		  ///
 		  /// \tparam GR The type of the digraph the algorithm runs on.
 		  /// The default type is \ref ListDigraph.
 		  /// The value of GR is not used directly by \ref BfsVisit,
 		  /// it is only passed to \ref BfsVisitDefaultTraits.
 		  /// \tparam VS The Visitor type that is used by the algorithm.
 		  /// \ref BfsVisitor "BfsVisitor<GR>" is an empty visitor, which
 		  /// does not observe the BFS events. If you want to observe the BFS
 		  /// events, you should implement your own visitor class.
 		  /// \tparam TR Traits class to set various data types used by the
 		  /// algorithm. The default traits class is
 		  /// \ref BfsVisitDefaultTraits "BfsVisitDefaultTraits<GR>".
 		  /// See \ref BfsVisitDefaultTraits for the documentation of
-		  /// a BFS visit traits class.
+		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm. By default, it is \ref BfsVisitDefaultTraits
 		  /// "BfsVisitDefaultTraits<GR>".
 		  /// In most cases, this parameter should not be set directly,
 		  /// consider to use the named template parameters instead.
 		#ifdef DOXYGEN
 		  template <typename GR, typename VS, typename TR>
 		#else
 		  template <typename GR = ListDigraph,
 		            typename VS = BfsVisitor<GR>,
 		            typename TR = BfsVisitDefaultTraits<GR> >
 		#endif
 		  class BfsVisit {
 		  public:
 		    ///The traits class.
 		    typedef TR Traits;
 		    ///The type of the digraph the algorithm runs on.
 		    typedef typename Traits::Digraph Digraph;
 		    ///The visitor type used by the algorithm.
 		    typedef VS Visitor;
 		    ///The type of the map that indicates which nodes are reached.
 		    typedef typename Traits::ReachedMap ReachedMap;
 		  private:
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::OutArcIt OutArcIt;
 		    //Pointer to the underlying digraph.
 		    const Digraph *_digraph;
 		    //Pointer to the visitor object.
 		    Visitor *_visitor;
 		    //Pointer to the map of reached status of the nodes.
 		    ReachedMap *_reached;
 		    //Indicates if _reached is locally allocated (true) or not.
 		    bool local_reached;
 		    std::vector<typename Digraph::Node> _list;
 		    int _list_front, _list_back;
 		    //Creates the maps if necessary.
 		    void create_maps() {
 		      if(!_reached) {
 		        local_reached = true;
 		        _reached = Traits::createReachedMap(*_digraph);
+		      }
+		    }
 		  protected:
 		    BfsVisit() {}
 		  public:
 		    typedef BfsVisit Create;
 		    /// \name Named Template Parameters
 		    ///@{
 		    template <class T>
 		    struct SetReachedMapTraits : public Traits {
 		      typedef T ReachedMap;
 		      static ReachedMap *createReachedMap(const Digraph &digraph) {
 		        LEMON_ASSERT(false, "ReachedMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// ReachedMap type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting ReachedMap type.
 		    template <class T>
 		    struct SetReachedMap : public BfsVisit< Digraph, Visitor,
 		                                            SetReachedMapTraits<T> > {
 		      typedef BfsVisit< Digraph, Visitor, SetReachedMapTraits<T> > Create;
 		    };
 		    ///@}
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// Constructor.
 		    ///
 		    /// \param digraph The digraph the algorithm runs on.
 		    /// \param visitor The visitor object of the algorithm.
 		    BfsVisit(const Digraph& digraph, Visitor& visitor)
 		      : _digraph(&digraph), _visitor(&visitor),
 		        _reached(0), local_reached(false) {}
 		    /// \brief Destructor.
 		    ~BfsVisit() {
 		      if(local_reached) delete _reached;
+		    }
 		    /// \brief Sets the map that indicates which nodes are reached.
 		    ///
 		    /// Sets the map that indicates which nodes are reached.
 		    /// If you don't use this function before calling \ref run(Node) "run()"
 		    /// or \ref init(), an instance will be allocated automatically.
 		    /// The destructor deallocates this automatically allocated map,
 		    /// of course.
 		    /// \return <tt> (*this) </tt>
 		    BfsVisit &reachedMap(ReachedMap &m) {
 		      if(local_reached) {
 		        delete _reached;
 		        local_reached = false;
+		      }
 		      _reached = &m;
 		      return *this;
+		    }
 		  public:
 		    /// \name Execution Control
 		    /// The simplest way to execute the BFS algorithm is to use one of the
 		    /// member functions called \ref run(Node) "run()".\n
 		    /// If you need better control on the execution, you have to call
 		    /// \ref init() first, then you can add several source nodes with
 		    /// \ref addSource(). Finally the actual path computation can be
 		    /// performed with one of the \ref start() functions.
 		    /// @{
 		    /// \brief Initializes the internal data structures.
 		    ///
 		    /// Initializes the internal data structures.
 		    void init() {
 		      create_maps();
 		      _list.resize(countNodes(*_digraph));
 		      _list_front = _list_back = -1;
 		      for (NodeIt u(*_digraph) ; u != INVALID ; ++u) {
 		        _reached->set(u, false);
+		      }
+		    }
 		    /// \brief Adds a new source node.
 		    ///
 		    /// Adds a new source node to the set of nodes to be processed.
 		    void addSource(Node s) {
 		      if(!(*_reached)[s]) {
 		          _reached->set(s,true);
 		          _visitor->start(s);
 		          _visitor->reach(s);
 		          _list[++_list_back] = s;
+		        }
+		    }
 		    /// \brief Processes the next node.
 		    ///
 		    /// Processes the next node.
 		    ///
 		    /// \return The processed node.
 		    ///
 		    /// \pre The queue must not be empty.
 		    Node processNextNode() {
 		      Node n = _list[++_list_front];
 		      _visitor->process(n);
 		      Arc e;
 		      for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
 		        Node m = _digraph->target(e);
 		        if (!(*_reached)[m]) {
 		          _visitor->discover(e);
 		          _visitor->reach(m);
 		          _reached->set(m, true);
 		          _list[++_list_back] = m;
 		        } else {
 		          _visitor->examine(e);
+		        }
+		      }
 		      return n;
+		    }
 		    /// \brief Processes the next node.
 		    ///
 		    /// Processes the next node and checks if the given target node
 		    /// is reached. If the target node is reachable from the processed
 		    /// node, then the \c reach parameter will be set to \c true.
 		    ///
 		    /// \param target The target node.
 		    /// \retval reach Indicates if the target node is reached.
 		    /// It should be initially \c false.
 		    ///
 		    /// \return The processed node.
 		    ///
 		    /// \pre The queue must not be empty.
 		    Node processNextNode(Node target, bool& reach) {
 		      Node n = _list[++_list_front];
 		      _visitor->process(n);
 		      Arc e;
 		      for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
 		        Node m = _digraph->target(e);
 		        if (!(*_reached)[m]) {
 		          _visitor->discover(e);
 		          _visitor->reach(m);
 		          _reached->set(m, true);
 		          _list[++_list_back] = m;
 		          reach = reach || (target == m);
 		        } else {
 		          _visitor->examine(e);
+		        }
+		      }
 		      return n;
+		    }
 		    /// \brief Processes the next node.
 		    ///
 		    /// Processes the next node and checks if at least one of reached
 		    /// nodes has \c true value in the \c nm node map. If one node
 		    /// with \c true value is reachable from the processed node, then the
 		    /// \c rnode parameter will be set to the first of such nodes.
 		    ///
 		    /// \param nm A \c bool (or convertible) node map that indicates the
 		    /// possible targets.
 		    /// \retval rnode The reached target node.
 		    /// It should be initially \c INVALID.
 		    ///
 		    /// \return The processed node.
 		    ///
 		    /// \pre The queue must not be empty.
 		    template <typename NM>
 		    Node processNextNode(const NM& nm, Node& rnode) {
 		      Node n = _list[++_list_front];
 		      _visitor->process(n);
 		      Arc e;
 		      for (_digraph->firstOut(e, n); e != INVALID; _digraph->nextOut(e)) {
 		        Node m = _digraph->target(e);
 		        if (!(*_reached)[m]) {
 		          _visitor->discover(e);
 		          _visitor->reach(m);
 		          _reached->set(m, true);
 		          _list[++_list_back] = m;
 		          if (nm[m] && rnode == INVALID) rnode = m;
 		        } else {
 		          _visitor->examine(e);
+		        }
+		      }
 		      return n;
+		    }
 		    /// \brief The next node to be processed.
 		    ///
 		    /// Returns the next node to be processed or \c INVALID if the queue
 		    /// is empty.
 		    Node nextNode() const {
 		      return _list_front != _list_back ? _list[_list_front + 1] : 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.
 		    bool emptyQueue() const { return _list_front == _list_back; }
 		    /// \brief Returns the number of the nodes to be processed.
 		    ///
 		    /// Returns the number of the nodes to be processed in the queue.
 		    int queueSize() const { return _list_back - _list_front; }
 		    /// \brief Executes the algorithm.
 		    ///
 		    /// Executes the algorithm.
 		    ///
 		    /// This method runs the %BFS algorithm from the root node(s)
 		    /// in order to compute the shortest path to each node.
 		    ///
 		    /// The algorithm computes
 		    /// - the shortest path tree (forest),
 		    /// - the distance of each node from the root(s).
 		    ///
 		    /// \pre init() must be called and at least one root node should be added
 		    /// with addSource() before using this function.
 		    ///
 		    /// \note <tt>b.start()</tt> is just a shortcut of the following code.
 		    /// \code
 		    ///   while ( !b.emptyQueue() ) {
 		    ///     b.processNextNode();
 		    ///   }
 		    /// \endcode
 		    void start() {
 		      while ( !emptyQueue() ) processNextNode();
+		    }
 		    /// \brief Executes the algorithm until the given target node is reached.
 		    ///
 		    /// Executes the algorithm until the given target node is reached.
 		    ///
 		    /// This method runs the %BFS algorithm from the root node(s)
 		    /// in order to compute the shortest path to \c t.
 		    ///
 		    /// The algorithm computes
 		    /// - the shortest path to \c t,
 		    /// - the distance of \c t from the root(s).
 		    ///
 		    /// \pre init() must be called and at least one root node should be
 		    /// added with addSource() before using this function.
 		    ///
 		    /// \note <tt>b.start(t)</tt> is just a shortcut of the following code.
 		    /// \code
 		    ///   bool reach = false;
 		    ///   while ( !b.emptyQueue() && !reach ) {
 		    ///     b.processNextNode(t, reach);
 		    ///   }
 		    /// \endcode
 		    void start(Node t) {
 		      bool reach = false;
 		      while ( !emptyQueue() && !reach ) processNextNode(t, reach);
+		    }
 		    /// \brief Executes the algorithm until a condition is met.
 		    ///
 		    /// Executes the algorithm until a condition is met.
 		    ///
 		    /// This method runs the %BFS algorithm from the root node(s) in
 		    /// order to compute the shortest path to a node \c v with
 		    /// <tt>nm[v]</tt> true, if such a node can be found.
 		    ///
 		    /// \param nm must be a bool (or convertible) node map. The
 		    /// algorithm will stop when it reaches a node \c v with
 		    /// <tt>nm[v]</tt> true.
 		    ///
 		    /// \return The reached node \c v with <tt>nm[v]</tt> true or
 		    /// \c INVALID if no such node was found.
 		    ///
 		    /// \pre init() must be called and at least one root node should be
 		    /// added with addSource() before using this function.
 		    ///
 		    /// \note <tt>b.start(nm)</tt> is just a shortcut of the following code.
 		    /// \code
 		    ///   Node rnode = INVALID;
 		    ///   while ( !b.emptyQueue() && rnode == INVALID ) {
 		    ///     b.processNextNode(nm, rnode);
 		    ///   }
 		    ///   return rnode;
 		    /// \endcode
 		    template <typename NM>
 		    Node start(const NM &nm) {
 		      Node rnode = INVALID;
 		      while ( !emptyQueue() && rnode == INVALID ) {
 		        processNextNode(nm, rnode);
+		      }
 		      return rnode;
+		    }
 		    /// \brief Runs the algorithm from the given source node.
 		    ///
 		    /// This method runs the %BFS algorithm from node \c s
 		    /// in order to compute the shortest path to each node.
 		    ///
 		    /// The algorithm computes
 		    /// - the shortest path tree,
 		    /// - the distance of each node from the root.
 		    ///
 		    /// \note <tt>b.run(s)</tt> is just a shortcut of the following code.
 		    ///\code
 		    ///   b.init();
 		    ///   b.addSource(s);
 		    ///   b.start();
 		    ///\endcode
 		    void run(Node s) {
 		      init();
 		      addSource(s);
 		      start();
+		    }
 		    /// \brief Finds the shortest path between \c s and \c t.
 		    ///
 		    /// This method runs the %BFS algorithm from node \c s
 		    /// in order to compute the shortest 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>b.run(s,t)</tt> is just a
 		    /// shortcut of the following code.
 		    ///\code
 		    ///   b.init();
 		    ///   b.addSource(s);
 		    ///   b.start(t);
 		    ///\endcode
 		    bool run(Node s,Node t) {
 		      init();
 		      addSource(s);
 		      start(t);
 		      return reached(t);
+		    }
 		    /// \brief Runs the algorithm to visit all nodes in the digraph.
 		    ///
 		    /// This method runs the %BFS algorithm in order to visit all nodes
 		    /// in the digraph.
 		    ///
 		    /// \note <tt>b.run(s)</tt> is just a shortcut of the following code.
 		    ///\code
 		    ///  b.init();
 		    ///  for (NodeIt n(gr); n != INVALID; ++n) {
 		    ///    if (!b.reached(n)) {
 		    ///      b.addSource(n);
 		    ///      b.start();
 		    ///    }
 		    ///  }
 		    ///\endcode
 		    void run() {
 		      init();
 		      for (NodeIt it(*_digraph); it != INVALID; ++it) {
 		        if (!reached(it)) {
 		          addSource(it);
 		          start();
+		        }
+		      }
+		    }
 		    ///@}
 		    /// \name Query Functions
 		    /// The results of the BFS algorithm can be obtained using these
 		    /// functions.\n
 		    /// Either \ref run(Node) "run()" or \ref start() should be called
 		    /// before using them.
 		    ///@{
 		    /// \brief Checks if the given node is reached from the root(s).
 		    ///
 		    /// Returns \c true if \c v is reached from the root(s).
 		    ///
 		    /// \pre Either \ref run(Node) "run()" or \ref init()
 		    /// must be called before using this function.
 		    bool reached(Node v) const { return (*_reached)[v]; }
 		    ///@}
 		  };
 		} //END OF NAMESPACE LEMON
 		#endif

lemon/capacity_scaling.h

Show inline comments

 		/* -*- 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_CAPACITY_SCALING_H
 		#define LEMON_CAPACITY_SCALING_H
 		/// \ingroup min_cost_flow_algs
 		///
 		/// \file
 		/// \brief Capacity Scaling algorithm for finding a minimum cost flow.
 		#include <vector>
 		#include <limits>
 		#include <lemon/core.h>
 		#include <lemon/bin_heap.h>
 		namespace lemon {
 		  /// \brief Default traits class of CapacityScaling algorithm.
 		  ///
 		  /// Default traits class of CapacityScaling algorithm.
 		  /// \tparam GR Digraph type.
 		  /// \tparam V The number type used for flow amounts, capacity bounds
 		  /// and supply values. By default it is \c int.
 		  /// \tparam C The number type used for costs and potentials.
 		  /// By default it is the same as \c V.
 		  template <typename GR, typename V = int, typename C = V>
 		  struct CapacityScalingDefaultTraits
+		  {
 		    /// The type of the digraph
 		    typedef GR Digraph;
 		    /// The type of the flow amounts, capacity bounds and supply values
 		    typedef V Value;
 		    /// The type of the arc costs
 		    typedef C Cost;
 		    /// \brief The type of the heap used for internal Dijkstra computations.
 		    ///
 		    /// The type of the heap used for internal Dijkstra computations.
 		    /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,
 		    /// its priority type must be \c Cost and its cross reference type
 		    /// must be \ref RangeMap "RangeMap<int>".
 		    typedef BinHeap<Cost, RangeMap<int> > Heap;
 		  };
 		  /// \addtogroup min_cost_flow_algs
 		  /// @{
 		  /// \brief Implementation of the Capacity Scaling algorithm for
 		  /// finding a \ref min_cost_flow "minimum cost flow".
 		  ///
 		  /// \ref CapacityScaling implements the capacity scaling version
 		  /// of the successive shortest path algorithm for finding a
 		  /// \ref min_cost_flow "minimum cost flow" \ref amo93networkflows,
 		  /// \ref edmondskarp72theoretical. It is an efficient dual
 		  /// solution method.
 		  ///
 		  /// Most of the parameters of the problem (except for the digraph)
 		  /// can be given using separate functions, and the algorithm can be
 		  /// executed using the \ref run() function. If some parameters are not
 		  /// specified, then default values will be used.
 		  ///
 		  /// \tparam GR The digraph type the algorithm runs on.
 		  /// \tparam V The number type used for flow amounts, capacity bounds
 		  /// and supply values in the algorithm. By default it is \c int.
+		  /// and supply values in the algorithm. By default, it is \c int.
 		  /// \tparam C The number type used for costs and potentials in the
 		  /// algorithm. By default it is the same as \c V.
+		  /// algorithm. By default, it is the same as \c V.
 		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm. By default, it is \ref CapacityScalingDefaultTraits
 		  /// "CapacityScalingDefaultTraits<GR, V, C>".
 		  /// In most cases, this parameter should not be set directly,
 		  /// consider to use the named template parameters instead.
 		  ///
 		  /// \warning Both number types must be signed and all input data must
 		  /// be integer.
 		  /// \warning This algorithm does not support negative costs for such
 		  /// arcs that have infinite upper bound.
 		#ifdef DOXYGEN
 		  template <typename GR, typename V, typename C, typename TR>
 		#else
 		  template < typename GR, typename V = int, typename C = V,
 		             typename TR = CapacityScalingDefaultTraits<GR, V, C> >
 		#endif
 		  class CapacityScaling
+		  {
 		  public:
 		    /// The type of the digraph
 		    typedef typename TR::Digraph Digraph;
 		    /// The type of the flow amounts, capacity bounds and supply values
 		    typedef typename TR::Value Value;
 		    /// The type of the arc costs
 		    typedef typename TR::Cost Cost;
 		    /// The type of the heap used for internal Dijkstra computations
 		    typedef typename TR::Heap Heap;
 		    /// The \ref CapacityScalingDefaultTraits "traits class" of the algorithm
 		    typedef TR Traits;
 		  public:
 		    /// \brief Problem type constants for the \c run() function.
 		    ///
 		    /// Enum type containing the problem type constants that can be
 		    /// returned by the \ref run() function of the algorithm.
 		    enum ProblemType {
 		      /// The problem has no feasible solution (flow).
 		      INFEASIBLE,
 		      /// The problem has optimal solution (i.e. it is feasible and
 		      /// bounded), and the algorithm has found optimal flow and node
 		      /// potentials (primal and dual solutions).
 		      OPTIMAL,
 		      /// The digraph contains an arc of negative cost and infinite
 		      /// upper bound. It means that the objective function is unbounded
 		      /// on that arc, however, note that it could actually be bounded
 		      /// over the feasible flows, but this algroithm cannot handle
 		      /// these cases.
 		      UNBOUNDED
 		    };
 		  private:
 		    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
 		    typedef std::vector<int> IntVector;
 		    typedef std::vector<char> BoolVector;
 		    typedef std::vector<Value> ValueVector;
 		    typedef std::vector<Cost> CostVector;
 		  private:
 		    // Data related to the underlying digraph
 		    const GR &_graph;
 		    int _node_num;
 		    int _arc_num;
 		    int _res_arc_num;
 		    int _root;
 		    // Parameters of the problem
 		    bool _have_lower;
 		    Value _sum_supply;
 		    // Data structures for storing the digraph
 		    IntNodeMap _node_id;
 		    IntArcMap _arc_idf;
 		    IntArcMap _arc_idb;
 		    IntVector _first_out;
 		    BoolVector _forward;
 		    IntVector _source;
 		    IntVector _target;
 		    IntVector _reverse;
 		    // Node and arc data
 		    ValueVector _lower;
 		    ValueVector _upper;
 		    CostVector _cost;
 		    ValueVector _supply;
 		    ValueVector _res_cap;
 		    CostVector _pi;
 		    ValueVector _excess;
 		    IntVector _excess_nodes;
 		    IntVector _deficit_nodes;
 		    Value _delta;
 		    int _factor;
 		    IntVector _pred;
 		  public:
 		    /// \brief Constant for infinite upper bounds (capacities).
 		    ///
 		    /// Constant for infinite upper bounds (capacities).
 		    /// It is \c std::numeric_limits<Value>::infinity() if available,
 		    /// \c std::numeric_limits<Value>::max() otherwise.
 		    const Value INF;
 		  private:
 		    // Special implementation of the Dijkstra algorithm for finding
 		    // shortest paths in the residual network of the digraph with
 		    // respect to the reduced arc costs and modifying the node
 		    // potentials according to the found distance labels.
 		    class ResidualDijkstra
+		    {
 		    private:
 		      int _node_num;
 		      bool _geq;
 		      const IntVector &_first_out;
 		      const IntVector &_target;
 		      const CostVector &_cost;
 		      const ValueVector &_res_cap;
 		      const ValueVector &_excess;
 		      CostVector &_pi;
 		      IntVector &_pred;
 		      IntVector _proc_nodes;
 		      CostVector _dist;
 		    public:
 		      ResidualDijkstra(CapacityScaling& cs) :
 		        _node_num(cs._node_num), _geq(cs._sum_supply < 0),
 		        _first_out(cs._first_out), _target(cs._target), _cost(cs._cost),
 		        _res_cap(cs._res_cap), _excess(cs._excess), _pi(cs._pi),
 		        _pred(cs._pred), _dist(cs._node_num)
 		      {}
 		      int run(int s, Value delta = 1) {
 		        RangeMap<int> heap_cross_ref(_node_num, Heap::PRE_HEAP);
 		        Heap heap(heap_cross_ref);
 		        heap.push(s, 0);
 		        _pred[s] = -1;
 		        _proc_nodes.clear();
 		        // Process nodes
 		        while (!heap.empty() && _excess[heap.top()] > -delta) {
 		          int u = heap.top(), v;
 		          Cost d = heap.prio() + _pi[u], dn;
 		          _dist[u] = heap.prio();
 		          _proc_nodes.push_back(u);
 		          heap.pop();
 		          // Traverse outgoing residual arcs
 		          int last_out = _geq ? _first_out[u+1] : _first_out[u+1] - 1;
 		          for (int a = _first_out[u]; a != last_out; ++a) {
 		            if (_res_cap[a] < delta) continue;
 		            v = _target[a];
 		            switch (heap.state(v)) {
 		              case Heap::PRE_HEAP:
 		                heap.push(v, d + _cost[a] - _pi[v]);
 		                _pred[v] = a;
 		                break;
 		              case Heap::IN_HEAP:
 		                dn = d + _cost[a] - _pi[v];
 		                if (dn < heap[v]) {
 		                  heap.decrease(v, dn);
 		                  _pred[v] = a;
+		                }
 		                break;
 		              case Heap::POST_HEAP:
 		                break;
+		            }
+		          }
+		        }
 		        if (heap.empty()) return -1;
 		        // Update potentials of processed nodes
 		        int t = heap.top();
 		        Cost dt = heap.prio();
 		        for (int i = 0; i < int(_proc_nodes.size()); ++i) {
 		          _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - dt;
+		        }
 		        return t;
+		      }
 		    }; //class ResidualDijkstra
 		  public:
 		    /// \name Named Template Parameters
 		    /// @{
 		    template <typename T>
 		    struct SetHeapTraits : public Traits {
 		      typedef T Heap;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c Heap type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting \c Heap
 		    /// type, which is used for internal Dijkstra computations.
 		    /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,
 		    /// its priority type must be \c Cost and its cross reference type
 		    /// must be \ref RangeMap "RangeMap<int>".
 		    template <typename T>
 		    struct SetHeap
 		      : public CapacityScaling<GR, V, C, SetHeapTraits<T> > {
 		      typedef  CapacityScaling<GR, V, C, SetHeapTraits<T> > Create;
 		    };
 		    /// @}
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// The constructor of the class.
 		    ///
 		    /// \param graph The digraph the algorithm runs on.
 		    CapacityScaling(const GR& graph) :
 		      _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
 		      INF(std::numeric_limits<Value>::has_infinity ?
 		          std::numeric_limits<Value>::infinity() :
 		          std::numeric_limits<Value>::max())
+		    {
 		      // Check the number types
 		      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
 		        "The flow type of CapacityScaling must be signed");
 		      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
 		        "The cost type of CapacityScaling must be signed");
 		      // Resize vectors
 		      _node_num = countNodes(_graph);
 		      _arc_num = countArcs(_graph);
 		      _res_arc_num = 2 * (_arc_num + _node_num);
 		      _root = _node_num;
 		      ++_node_num;
 		      _first_out.resize(_node_num + 1);
 		      _forward.resize(_res_arc_num);
 		      _source.resize(_res_arc_num);
 		      _target.resize(_res_arc_num);
 		      _reverse.resize(_res_arc_num);
 		      _lower.resize(_res_arc_num);
 		      _upper.resize(_res_arc_num);
 		      _cost.resize(_res_arc_num);
 		      _supply.resize(_node_num);
 		      _res_cap.resize(_res_arc_num);
 		      _pi.resize(_node_num);
 		      _excess.resize(_node_num);
 		      _pred.resize(_node_num);
 		      // Copy the graph
 		      int i = 0, j = 0, k = 2 * _arc_num + _node_num - 1;
 		      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
 		        _node_id[n] = i;
+		      }
 		      i = 0;
 		      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
 		        _first_out[i] = j;
 		        for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
 		          _arc_idf[a] = j;
 		          _forward[j] = true;
 		          _source[j] = i;
 		          _target[j] = _node_id[_graph.runningNode(a)];
+		        }
 		        for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
 		          _arc_idb[a] = j;
 		          _forward[j] = false;
 		          _source[j] = i;
 		          _target[j] = _node_id[_graph.runningNode(a)];
+		        }
 		        _forward[j] = false;
 		        _source[j] = i;
 		        _target[j] = _root;
 		        _reverse[j] = k;
 		        _forward[k] = true;
 		        _source[k] = _root;
 		        _target[k] = i;
 		        _reverse[k] = j;
 		        ++j; ++k;
+		      }
 		      _first_out[i] = j;
 		      _first_out[_node_num] = k;
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        int fi = _arc_idf[a];
 		        int bi = _arc_idb[a];
 		        _reverse[fi] = bi;
 		        _reverse[bi] = fi;
+		      }
 		      // Reset parameters
 		      reset();
+		    }
 		    /// \name Parameters
 		    /// The parameters of the algorithm can be specified using these
 		    /// functions.
 		    /// @{
 		    /// \brief Set the lower bounds on the arcs.
 		    ///
 		    /// This function sets the lower bounds on the arcs.
 		    /// If it is not used before calling \ref run(), the lower bounds
 		    /// will be set to zero on all arcs.
 		    ///
 		    /// \param map An arc map storing the lower bounds.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template <typename LowerMap>
 		    CapacityScaling& lowerMap(const LowerMap& map) {
 		      _have_lower = true;
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _lower[_arc_idf[a]] = map[a];
 		        _lower[_arc_idb[a]] = map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the upper bounds (capacities) on the arcs.
 		    ///
 		    /// This function sets the upper bounds (capacities) on the arcs.
 		    /// If it is not used before calling \ref run(), the upper bounds
 		    /// will be set to \ref INF on all arcs (i.e. the flow value will be
 		    /// unbounded from above).
 		    ///
 		    /// \param map An arc map storing the upper bounds.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename UpperMap>
 		    CapacityScaling& upperMap(const UpperMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _upper[_arc_idf[a]] = map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the costs of the arcs.
 		    ///
 		    /// This function sets the costs of the arcs.
 		    /// If it is not used before calling \ref run(), the costs
 		    /// will be set to \c 1 on all arcs.
 		    ///
 		    /// \param map An arc map storing the costs.
 		    /// Its \c Value type must be convertible to the \c Cost type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename CostMap>
 		    CapacityScaling& costMap(const CostMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _cost[_arc_idf[a]] =  map[a];
 		        _cost[_arc_idb[a]] = -map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the supply values of the nodes.
 		    ///
 		    /// This function sets the supply values of the nodes.
 		    /// If neither this function nor \ref stSupply() is used before
 		    /// calling \ref run(), the supply of each node will be set to zero.
 		    ///
 		    /// \param map A node map storing the supply values.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename SupplyMap>
 		    CapacityScaling& supplyMap(const SupplyMap& map) {
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
 		        _supply[_node_id[n]] = map[n];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set single source and target nodes and a supply value.
 		    ///
 		    /// This function sets a single source node and a single target node
 		    /// and the required flow value.
 		    /// If neither this function nor \ref supplyMap() is used before
 		    /// calling \ref run(), the supply of each node will be set to zero.
 		    ///
 		    /// Using this function has the same effect as using \ref supplyMap()
 		    /// with such a map in which \c k is assigned to \c s, \c -k is
 		    /// assigned to \c t and all other nodes have zero supply value.
 		    ///
 		    /// \param s The source node.
 		    /// \param t The target node.
 		    /// \param k The required amount of flow from node \c s to node \c t
 		    /// (i.e. the supply of \c s and the demand of \c t).
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    CapacityScaling& stSupply(const Node& s, const Node& t, Value k) {
 		      for (int i = 0; i != _node_num; ++i) {
 		        _supply[i] = 0;
+		      }
 		      _supply[_node_id[s]] =  k;
 		      _supply[_node_id[t]] = -k;
 		      return *this;
+		    }
 		    /// @}
 		    /// \name Execution control
 		    /// The algorithm can be executed using \ref run().
 		    /// @{
 		    /// \brief Run the algorithm.
 		    ///
 		    /// This function runs the algorithm.
 		    /// The paramters can be specified using functions \ref lowerMap(),
 		    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
 		    /// For example,
 		    /// \code
 		    ///   CapacityScaling<ListDigraph> cs(graph);
 		    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    /// \endcode
 		    ///
 		    /// This function can be called more than once. All the parameters
 		    /// that have been given are kept for the next call, unless
 		    /// \ref reset() is called, thus only the modified parameters
 		    /// have to be set again. See \ref reset() for examples.
 		    /// However, the underlying digraph must not be modified after this
 		    /// class have been constructed, since it copies and extends the graph.
 		    ///
 		    /// \param factor The capacity scaling factor. It must be larger than
 		    /// one to use scaling. If it is less or equal to one, then scaling
 		    /// will be disabled.
 		    ///
 		    /// \return \c INFEASIBLE if no feasible flow exists,
 		    /// \n \c OPTIMAL if the problem has optimal solution
 		    /// (i.e. it is feasible and bounded), and the algorithm has found
 		    /// optimal flow and node potentials (primal and dual solutions),
 		    /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
 		    /// and infinite upper bound. It means that the objective function
 		    /// is unbounded on that arc, however, note that it could actually be
 		    /// bounded over the feasible flows, but this algroithm cannot handle
 		    /// these cases.
 		    ///
 		    /// \see ProblemType
 		    ProblemType run(int factor = 4) {
 		      _factor = factor;
 		      ProblemType pt = init();
 		      if (pt != OPTIMAL) return pt;
 		      return start();
+		    }
 		    /// \brief Reset all the parameters that have been given before.
 		    ///
 		    /// This function resets all the paramaters that have been given
 		    /// before using functions \ref lowerMap(), \ref upperMap(),
 		    /// \ref costMap(), \ref supplyMap(), \ref stSupply().
 		    ///
 		    /// It is useful for multiple run() calls. If this function is not
 		    /// used, all the parameters given before are kept for the next
 		    /// \ref run() call.
 		    /// However, the underlying digraph must not be modified after this
 		    /// class have been constructed, since it copies and extends the graph.
 		    ///
 		    /// For example,
 		    /// \code
 		    ///   CapacityScaling<ListDigraph> cs(graph);
 		    ///
 		    ///   // First run
 		    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    ///
 		    ///   // Run again with modified cost map (reset() is not called,
 		    ///   // so only the cost map have to be set again)
 		    ///   cost[e] += 100;
 		    ///   cs.costMap(cost).run();
 		    ///
 		    ///   // Run again from scratch using reset()
 		    ///   // (the lower bounds will be set to zero on all arcs)
 		    ///   cs.reset();
 		    ///   cs.upperMap(capacity).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    /// \endcode
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    CapacityScaling& reset() {
 		      for (int i = 0; i != _node_num; ++i) {
 		        _supply[i] = 0;
+		      }
 		      for (int j = 0; j != _res_arc_num; ++j) {
 		        _lower[j] = 0;
 		        _upper[j] = INF;
 		        _cost[j] = _forward[j] ? 1 : -1;
+		      }
 		      _have_lower = false;
 		      return *this;
+		    }
 		    /// @}
 		    /// \name Query Functions
 		    /// The results of the algorithm can be obtained using these
 		    /// functions.\n
 		    /// The \ref run() function must be called before using them.
 		    /// @{
 		    /// \brief Return the total cost of the found flow.
 		    ///
 		    /// This function returns the total cost of the found flow.
 		    /// Its complexity is O(e).
 		    ///
 		    /// \note The return type of the function can be specified as a
 		    /// template parameter. For example,
 		    /// \code
 		    ///   cs.totalCost<double>();
 		    /// \endcode
 		    /// It is useful if the total cost cannot be stored in the \c Cost
 		    /// type of the algorithm, which is the default return type of the
 		    /// function.
 		    ///
 		    /// \pre \ref run() must be called before using this function.
 		    template <typename Number>
 		    Number totalCost() const {
 		      Number c = 0;
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        int i = _arc_idb[a];
 		        c += static_cast<Number>(_res_cap[i]) *
 		             (-static_cast<Number>(_cost[i]));
+		      }
 		      return c;
+		    }
 		#ifndef DOXYGEN
 		    Cost totalCost() const {
 		      return totalCost<Cost>();
+		    }
 		#endif
 		    /// \brief Return the flow on the given arc.
 		    ///
 		    /// This function returns the flow on the given arc.
 		    ///
 		    /// \pre \ref run() must be called before using this function.
 		    Value flow(const Arc& a) const {
 		      return _res_cap[_arc_idb[a]];
+		    }
 		    /// \brief Return the flow map (the primal solution).
 		    ///
 		    /// This function copies the flow value on each arc into the given
 		    /// map. The \c Value type of the algorithm must be convertible to
 		    /// the \c Value type of the map.
 		    ///
 		    /// \pre \ref run() must be called before using this function.
 		    template <typename FlowMap>
 		    void flowMap(FlowMap &map) const {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        map.set(a, _res_cap[_arc_idb[a]]);
+		      }
+		    }
 		    /// \brief Return the potential (dual value) of the given node.
 		    ///
 		    /// This function returns the potential (dual value) of the
 		    /// given node.
 		    ///
 		    /// \pre \ref run() must be called before using this function.
 		    Cost potential(const Node& n) const {
 		      return _pi[_node_id[n]];
+		    }
 		    /// \brief Return the potential map (the dual solution).
 		    ///
 		    /// This function copies the potential (dual value) of each node
 		    /// into the given map.
 		    /// The \c Cost type of the algorithm must be convertible to the
 		    /// \c Value type of the map.
 		    ///
 		    /// \pre \ref run() must be called before using this function.
 		    template <typename PotentialMap>
 		    void potentialMap(PotentialMap &map) const {
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
 		        map.set(n, _pi[_node_id[n]]);
+		      }
+		    }
 		    /// @}
 		  private:
 		    // Initialize the algorithm
 		    ProblemType init() {
 		      if (_node_num <= 1) return INFEASIBLE;
 		      // Check the sum of supply values
 		      _sum_supply = 0;
 		      for (int i = 0; i != _root; ++i) {
 		        _sum_supply += _supply[i];
+		      }
 		      if (_sum_supply > 0) return INFEASIBLE;
 		      // Initialize vectors
 		      for (int i = 0; i != _root; ++i) {
 		        _pi[i] = 0;
 		        _excess[i] = _supply[i];
+		      }
 		      // Remove non-zero lower bounds
 		      const Value MAX = std::numeric_limits<Value>::max();
 		      int last_out;
 		      if (_have_lower) {
 		        for (int i = 0; i != _root; ++i) {
 		          last_out = _first_out[i+1];
 		          for (int j = _first_out[i]; j != last_out; ++j) {
 		            if (_forward[j]) {
 		              Value c = _lower[j];
 		              if (c >= 0) {
 		                _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF;
 		              } else {
 		                _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF;
+		              }
 		              _excess[i] -= c;
 		              _excess[_target[j]] += c;
 		            } else {
 		              _res_cap[j] = 0;
+		            }
+		          }
+		        }
 		      } else {
 		        for (int j = 0; j != _res_arc_num; ++j) {
 		          _res_cap[j] = _forward[j] ? _upper[j] : 0;
+		        }
+		      }
 		      // Handle negative costs
 		      for (int i = 0; i != _root; ++i) {
 		        last_out = _first_out[i+1] - 1;
 		        for (int j = _first_out[i]; j != last_out; ++j) {
 		          Value rc = _res_cap[j];
 		          if (_cost[j] < 0 && rc > 0) {
 		            if (rc >= MAX) return UNBOUNDED;
 		            _excess[i] -= rc;
 		            _excess[_target[j]] += rc;
 		            _res_cap[j] = 0;
 		            _res_cap[_reverse[j]] += rc;
+		          }
+		        }
+		      }
 		      // Handle GEQ supply type
 		      if (_sum_supply < 0) {
 		        _pi[_root] = 0;
 		        _excess[_root] = -_sum_supply;
 		        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
 		          int ra = _reverse[a];
 		          _res_cap[a] = -_sum_supply + 1;
 		          _res_cap[ra] = 0;
 		          _cost[a] = 0;
 		          _cost[ra] = 0;
+		        }
 		      } else {
 		        _pi[_root] = 0;
 		        _excess[_root] = 0;
 		        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
 		          int ra = _reverse[a];
 		          _res_cap[a] = 1;
 		          _res_cap[ra] = 0;
 		          _cost[a] = 0;
 		          _cost[ra] = 0;
+		        }
+		      }
 		      // Initialize delta value
 		      if (_factor > 1) {
 		        // With scaling
 		        Value max_sup = 0, max_dem = 0;
 		        for (int i = 0; i != _node_num; ++i) {
 		          Value ex = _excess[i];
 		          if ( ex > max_sup) max_sup =  ex;
 		          if (-ex > max_dem) max_dem = -ex;
+		        }
 		        Value max_cap = 0;
 		        for (int j = 0; j != _res_arc_num; ++j) {
 		          if (_res_cap[j] > max_cap) max_cap = _res_cap[j];
+		        }
 		        max_sup = std::min(std::min(max_sup, max_dem), max_cap);
 		        for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ;
 		      } else {
 		        // Without scaling
 		        _delta = 1;
+		      }
 		      return OPTIMAL;
+		    }
 		    ProblemType start() {
 		      // Execute the algorithm
 		      ProblemType pt;
 		      if (_delta > 1)
 		        pt = startWithScaling();
 		      else
 		        pt = startWithoutScaling();
 		      // Handle non-zero lower bounds
 		      if (_have_lower) {
 		        int limit = _first_out[_root];
 		        for (int j = 0; j != limit; ++j) {
 		          if (!_forward[j]) _res_cap[j] += _lower[j];
+		        }
+		      }
 		      // Shift potentials if necessary
 		      Cost pr = _pi[_root];
 		      if (_sum_supply < 0 || pr > 0) {
 		        for (int i = 0; i != _node_num; ++i) {
 		          _pi[i] -= pr;
+		        }
+		      }
 		      return pt;
+		    }
 		    // Execute the capacity scaling algorithm
 		    ProblemType startWithScaling() {
 		      // Perform capacity scaling phases
 		      int s, t;
 		      ResidualDijkstra _dijkstra(*this);
 		      while (true) {
 		        // Saturate all arcs not satisfying the optimality condition
 		        int last_out;
 		        for (int u = 0; u != _node_num; ++u) {
 		          last_out = _sum_supply < 0 ?
 		            _first_out[u+1] : _first_out[u+1] - 1;
 		          for (int a = _first_out[u]; a != last_out; ++a) {
 		            int v = _target[a];
 		            Cost c = _cost[a] + _pi[u] - _pi[v];
 		            Value rc = _res_cap[a];
 		            if (c < 0 && rc >= _delta) {
 		              _excess[u] -= rc;
 		              _excess[v] += rc;
 		              _res_cap[a] = 0;
 		              _res_cap[_reverse[a]] += rc;
+		            }
+		          }
+		        }
 		        // Find excess nodes and deficit nodes
 		        _excess_nodes.clear();
 		        _deficit_nodes.clear();
 		        for (int u = 0; u != _node_num; ++u) {
 		          Value ex = _excess[u];
 		          if (ex >=  _delta) _excess_nodes.push_back(u);
 		          if (ex <= -_delta) _deficit_nodes.push_back(u);
+		        }
 		        int next_node = 0, next_def_node = 0;
 		        // Find augmenting shortest paths
 		        while (next_node < int(_excess_nodes.size())) {
 		          // Check deficit nodes

lemon/circulation.h

Show inline comments

 		/* -*- 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_CIRCULATION_H
 		#define LEMON_CIRCULATION_H
 		#include <lemon/tolerance.h>
 		#include <lemon/elevator.h>
 		#include <limits>
 		///\ingroup max_flow
 		///\file
 		///\brief Push-relabel algorithm for finding a feasible circulation.
 		///
 		namespace lemon {
 		  /// \brief Default traits class of Circulation class.
 		  ///
 		  /// Default traits class of Circulation class.
 		  ///
 		  /// \tparam GR Type of the digraph the algorithm runs on.
 		  /// \tparam LM The type of the lower bound map.
 		  /// \tparam UM The type of the upper bound (capacity) map.
 		  /// \tparam SM The type of the supply map.
 		  template <typename GR, typename LM,
 		            typename UM, typename SM>
 		  struct CirculationDefaultTraits {
 		    /// \brief The type of the digraph the algorithm runs on.
 		    typedef GR Digraph;
 		    /// \brief The type of the lower bound map.
 		    ///
 		    /// The type of the map that stores the lower bounds on the arcs.
 		    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
 		    typedef LM LowerMap;
 		    /// \brief The type of the upper bound (capacity) map.
 		    ///
 		    /// The type of the map that stores the upper bounds (capacities)
 		    /// on the arcs.
 		    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
 		    typedef UM UpperMap;
 		    /// \brief The type of supply map.
 		    ///
 		    /// The type of the map that stores the signed supply values of the
 		    /// nodes.
 		    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
 		    typedef SM SupplyMap;
 		    /// \brief The type of the flow and supply values.
 		    typedef typename SupplyMap::Value Value;
 		    /// \brief The type of the map that stores the flow values.
 		    ///
 		    /// The type of the map that stores the flow values.
 		    /// It must conform to the \ref concepts::ReadWriteMap "ReadWriteMap"
 		    /// concept.
 		#ifdef DOXYGEN
 		    typedef GR::ArcMap<Value> FlowMap;
 		#else
 		    typedef typename Digraph::template ArcMap<Value> FlowMap;
 		#endif
 		    /// \brief Instantiates a FlowMap.
 		    ///
 		    /// This function instantiates a \ref FlowMap.
 		    /// \param digraph The digraph for which we would like to define
 		    /// the flow map.
 		    static FlowMap* createFlowMap(const Digraph& digraph) {
 		      return new FlowMap(digraph);
+		    }
 		    /// \brief The elevator type used by the algorithm.
 		    ///
 		    /// The elevator type used by the algorithm.
 		    ///
 		    /// \sa Elevator, LinkedElevator
 		#ifdef DOXYGEN
 		    typedef lemon::Elevator<GR, GR::Node> Elevator;
 		#else
 		    typedef lemon::Elevator<Digraph, typename Digraph::Node> Elevator;
 		#endif
 		    /// \brief Instantiates an Elevator.
 		    ///
 		    /// This function instantiates an \ref Elevator.
 		    /// \param digraph The digraph for which we would like to define
 		    /// the elevator.
 		    /// \param max_level The maximum level of the elevator.
 		    static Elevator* createElevator(const Digraph& digraph, int max_level) {
 		      return new Elevator(digraph, max_level);
+		    }
 		    /// \brief The tolerance used by the algorithm
 		    ///
 		    /// The tolerance used by the algorithm to handle inexact computation.
 		    typedef lemon::Tolerance<Value> Tolerance;
 		  };
 		  /**
 		     \brief Push-relabel algorithm for the network circulation problem.
 		     \ingroup max_flow
 		     This class implements a push-relabel algorithm for the \e network
 		     \e circulation problem.
 		     It is to find a feasible circulation when lower and upper bounds
 		     are given for the flow values on the arcs and lower bounds are
 		     given for the difference between the outgoing and incoming flow
 		     at the nodes.
 		     The exact formulation of this problem is the following.
 		     Let \f$G=(V,A)\f$ be a digraph, \f$lower: A\rightarrow\mathbf{R}\f$
 		     \f$upper: A\rightarrow\mathbf{R}\cup\{\infty\}\f$ denote the lower and
 		     upper bounds on the arcs, for which \f$lower(uv) \leq upper(uv)\f$
 		     holds for all \f$uv\in A\f$, and \f$sup: V\rightarrow\mathbf{R}\f$
 		     denotes the signed supply values of the nodes.
 		     If \f$sup(u)>0\f$, then \f$u\f$ is a supply node with \f$sup(u)\f$
 		     supply, if \f$sup(u)<0\f$, then \f$u\f$ is a demand node with
 		     \f$-sup(u)\f$ demand.
 		     A feasible circulation is an \f$f: A\rightarrow\mathbf{R}\f$
 		     solution of the following problem.
 		     \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu)
 		     \geq sup(u) \quad \forall u\in V, \f]
 		     \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A. \f]
 		     The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be
 		     zero or negative in order to have a feasible solution (since the sum
 		     of the expressions on the left-hand side of the inequalities is zero).
 		     It means that the total demand must be greater or equal to the total
 		     supply and all the supplies have to be carried out from the supply nodes,
 		     but there could be demands that are not satisfied.
 		     If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand
 		     constraints have to be satisfied with equality, i.e. all demands
 		     have to be satisfied and all supplies have to be used.
 		     If you need the opposite inequalities in the supply/demand constraints
 		     (i.e. the total demand is less than the total supply and all the demands
 		     have to be satisfied while there could be supplies that are not used),
 		     then you could easily transform the problem to the above form by reversing
 		     the direction of the arcs and taking the negative of the supply values
 		     (e.g. using \ref ReverseDigraph and \ref NegMap adaptors).
 		     This algorithm either calculates a feasible circulation, or provides
 		     a \ref barrier() "barrier", which prooves that a feasible soultion
 		     cannot exist.
 		     Note that this algorithm also provides a feasible solution for the
 		     \ref min_cost_flow "minimum cost flow problem".
 		     \tparam GR The type of the digraph the algorithm runs on.
 		     \tparam LM The type of the lower bound map. The default
 		     map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
 		     \tparam UM The type of the upper bound (capacity) map.
 		     The default map type is \c LM.
 		     \tparam SM The type of the supply map. The default map type is
 		     \ref concepts::Digraph::NodeMap "GR::NodeMap<UM::Value>".
 		     \tparam TR The traits class that defines various types used by the
 		     algorithm. By default, it is \ref CirculationDefaultTraits
 		     "CirculationDefaultTraits<GR, LM, UM, SM>".
 		     In most cases, this parameter should not be set directly,
 		     consider to use the named template parameters instead.
 		  */
 		#ifdef DOXYGEN
 		template< typename GR,
 		          typename LM,
 		          typename UM,
 		          typename SM,
 		          typename TR >
 		#else
 		template< typename GR,
 		          typename LM = typename GR::template ArcMap<int>,
 		          typename UM = LM,
 		          typename SM = typename GR::template NodeMap<typename UM::Value>,
 		          typename TR = CirculationDefaultTraits<GR, LM, UM, SM> >
 		#endif
 		  class Circulation {
 		  public:
 		    ///The \ref CirculationDefaultTraits "traits class" of the algorithm.
 		    typedef TR Traits;
 		    ///The type of the digraph the algorithm runs on.
 		    typedef typename Traits::Digraph Digraph;
 		    ///The type of the flow and supply values.
 		    typedef typename Traits::Value Value;
 		    ///The type of the lower bound map.
 		    typedef typename Traits::LowerMap LowerMap;
 		    ///The type of the upper bound (capacity) map.
 		    typedef typename Traits::UpperMap UpperMap;
 		    ///The type of the supply map.
 		    typedef typename Traits::SupplyMap SupplyMap;
 		    ///The type of the flow map.
 		    typedef typename Traits::FlowMap FlowMap;
 		    ///The type of the elevator.
 		    typedef typename Traits::Elevator Elevator;
 		    ///The type of the tolerance.
 		    typedef typename Traits::Tolerance Tolerance;
 		  private:
 		    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
 		    const Digraph &_g;
 		    int _node_num;
 		    const LowerMap *_lo;
 		    const UpperMap *_up;
 		    const SupplyMap *_supply;
 		    FlowMap *_flow;
 		    bool _local_flow;
 		    Elevator* _level;
 		    bool _local_level;
 		    typedef typename Digraph::template NodeMap<Value> ExcessMap;
 		    ExcessMap* _excess;
 		    Tolerance _tol;
 		    int _el;
 		  public:
 		    typedef Circulation Create;
 		    ///\name Named Template Parameters
 		    ///@{
 		    template <typename T>
 		    struct SetFlowMapTraits : public Traits {
 		      typedef T FlowMap;
 		      static FlowMap *createFlowMap(const Digraph&) {
 		        LEMON_ASSERT(false, "FlowMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// FlowMap type
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting FlowMap
 		    /// type.
 		    template <typename T>
 		    struct SetFlowMap
 		      : public Circulation<Digraph, LowerMap, UpperMap, SupplyMap,
 		                           SetFlowMapTraits<T> > {
 		      typedef Circulation<Digraph, LowerMap, UpperMap, SupplyMap,
 		                          SetFlowMapTraits<T> > Create;
 		    };
 		    template <typename T>
 		    struct SetElevatorTraits : public Traits {
 		      typedef T Elevator;
 		      static Elevator *createElevator(const Digraph&, int) {
 		        LEMON_ASSERT(false, "Elevator is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// Elevator type
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting Elevator
 		    /// type. If this named parameter is used, then an external
 		    /// elevator object must be passed to the algorithm using the
 		    /// \ref elevator(Elevator&) "elevator()" function before calling
 		    /// \ref run() or \ref init().
 		    /// \sa SetStandardElevator
 		    template <typename T>
 		    struct SetElevator
 		      : public Circulation<Digraph, LowerMap, UpperMap, SupplyMap,
 		                           SetElevatorTraits<T> > {
 		      typedef Circulation<Digraph, LowerMap, UpperMap, SupplyMap,
 		                          SetElevatorTraits<T> > Create;
 		    };
 		    template <typename T>
 		    struct SetStandardElevatorTraits : public Traits {
 		      typedef T Elevator;
 		      static Elevator *createElevator(const Digraph& digraph, int max_level) {
 		        return new Elevator(digraph, max_level);
+		      }
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// Elevator type with automatic allocation
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting Elevator
 		    /// type with automatic allocation.
 		    /// The Elevator should have standard constructor interface to be
 		    /// able to automatically created by the algorithm (i.e. the
 		    /// digraph and the maximum level should be passed to it).
 		    /// However, an external elevator object could also be passed to the
 		    /// algorithm with the \ref elevator(Elevator&) "elevator()" function
 		    /// before calling \ref run() or \ref init().
 		    /// \sa SetElevator
 		    template <typename T>
 		    struct SetStandardElevator
 		      : public Circulation<Digraph, LowerMap, UpperMap, SupplyMap,
 		                       SetStandardElevatorTraits<T> > {
 		      typedef Circulation<Digraph, LowerMap, UpperMap, SupplyMap,
 		                      SetStandardElevatorTraits<T> > Create;
 		    };
 		    /// @}
 		  protected:
 		    Circulation() {}
 		  public:
 		    /// Constructor.
 		    /// The constructor of the class.
 		    ///
 		    /// \param graph The digraph the algorithm runs on.
 		    /// \param lower The lower bounds for the flow values on the arcs.
 		    /// \param upper The upper bounds (capacities) for the flow values
 		    /// on the arcs.
 		    /// \param supply The signed supply values of the nodes.
 		    Circulation(const Digraph &graph, const LowerMap &lower,
 		                const UpperMap &upper, const SupplyMap &supply)
 		      : _g(graph), _lo(&lower), _up(&upper), _supply(&supply),
 		        _flow(NULL), _local_flow(false), _level(NULL), _local_level(false),
 		        _excess(NULL) {}
 		    /// Destructor.
 		    ~Circulation() {
 		      destroyStructures();
+		    }
 		  private:
 		    bool checkBoundMaps() {
 		      for (ArcIt e(_g);e!=INVALID;++e) {
 		        if (_tol.less((*_up)[e], (*_lo)[e])) return false;
+		      }
 		      return true;
+		    }
 		    void createStructures() {
 		      _node_num = _el = countNodes(_g);
 		      if (!_flow) {
 		        _flow = Traits::createFlowMap(_g);
 		        _local_flow = true;
+		      }
 		      if (!_level) {
 		        _level = Traits::createElevator(_g, _node_num);
 		        _local_level = true;
+		      }
 		      if (!_excess) {
 		        _excess = new ExcessMap(_g);
+		      }
+		    }
 		    void destroyStructures() {
 		      if (_local_flow) {
 		        delete _flow;
+		      }
 		      if (_local_level) {
 		        delete _level;
+		      }
 		      if (_excess) {
 		        delete _excess;
+		      }
+		    }
 		  public:
 		    /// Sets the lower bound map.
 		    /// Sets the lower bound map.
 		    /// \return <tt>(*this)</tt>
 		    Circulation& lowerMap(const LowerMap& map) {
 		      _lo = &map;
 		      return *this;
+		    }
 		    /// Sets the upper bound (capacity) map.
 		    /// Sets the upper bound (capacity) map.
 		    /// \return <tt>(*this)</tt>
 		    Circulation& upperMap(const UpperMap& map) {
 		      _up = &map;
 		      return *this;
+		    }
 		    /// Sets the supply map.
 		    /// Sets the supply map.
 		    /// \return <tt>(*this)</tt>
 		    Circulation& supplyMap(const SupplyMap& map) {
 		      _supply = &map;
 		      return *this;
+		    }
 		    /// \brief Sets the flow map.
 		    ///
 		    /// Sets the flow map.
 		    /// If you don't use this function before calling \ref run() or
 		    /// \ref init(), an instance will be allocated automatically.
 		    /// The destructor deallocates this automatically allocated map,
 		    /// of course.
 		    /// \return <tt>(*this)</tt>
 		    Circulation& flowMap(FlowMap& map) {
 		      if (_local_flow) {
 		        delete _flow;
 		        _local_flow = false;
+		      }
 		      _flow = &map;
 		      return *this;
+		    }
 		    /// \brief Sets the elevator used by algorithm.
 		    ///
 		    /// Sets the elevator used by algorithm.
 		    /// If you don't use this function before calling \ref run() or
 		    /// \ref init(), an instance will be allocated automatically.
 		    /// The destructor deallocates this automatically allocated elevator,
 		    /// of course.
 		    /// \return <tt>(*this)</tt>
 		    Circulation& elevator(Elevator& elevator) {
 		      if (_local_level) {
 		        delete _level;
 		        _local_level = false;
+		      }
 		      _level = &elevator;
 		      return *this;
+		    }
 		    /// \brief Returns a const reference to the elevator.
 		    ///
 		    /// Returns a const reference to the elevator.
 		    ///
 		    /// \pre Either \ref run() or \ref init() must be called before
 		    /// using this function.
 		    const Elevator& elevator() const {
 		      return *_level;
+		    }
 		    /// \brief Sets the tolerance used by the algorithm.
 		    ///
 		    /// Sets the tolerance object used by the algorithm.
 		    /// \return <tt>(*this)</tt>
 		    Circulation& tolerance(const Tolerance& tolerance) {
 		      _tol = tolerance;
 		      return *this;
+		    }
 		    /// \brief Returns a const reference to the tolerance.
 		    ///
 		    /// Returns a const reference to the tolerance object used by
 		    /// the algorithm.
 		    const Tolerance& tolerance() const {
 		      return _tol;
+		    }
 		    /// \name Execution Control
 		    /// The simplest way to execute the algorithm is to call \ref run().\n
 		    /// If you need better control on the initial solution or the execution,
 		    /// you have to call one of the \ref init() functions first, then
 		    /// the \ref start() function.
 		    ///@{
 		    /// Initializes the internal data structures.
 		    /// Initializes the internal data structures and sets all flow values
 		    /// to the lower bound.
 		    void init()
+		    {
 		      LEMON_DEBUG(checkBoundMaps(),
 		        "Upper bounds must be greater or equal to the lower bounds");
 		      createStructures();
 		      for(NodeIt n(_g);n!=INVALID;++n) {
 		        (*_excess)[n] = (*_supply)[n];
+		      }
 		      for (ArcIt e(_g);e!=INVALID;++e) {
 		        _flow->set(e, (*_lo)[e]);
 		        (*_excess)[_g.target(e)] += (*_flow)[e];
 		        (*_excess)[_g.source(e)] -= (*_flow)[e];
+		      }
 		      // global relabeling tested, but in general case it provides
 		      // worse performance for random digraphs
 		      _level->initStart();
 		      for(NodeIt n(_g);n!=INVALID;++n)
 		        _level->initAddItem(n);
 		      _level->initFinish();
 		      for(NodeIt n(_g);n!=INVALID;++n)
 		        if(_tol.positive((*_excess)[n]))
 		          _level->activate(n);
+		    }
 		    /// Initializes the internal data structures using a greedy approach.
 		    /// Initializes the internal data structures using a greedy approach
 		    /// to construct the initial solution.
 		    void greedyInit()
+		    {
 		      LEMON_DEBUG(checkBoundMaps(),
 		        "Upper bounds must be greater or equal to the lower bounds");
 		      createStructures();
 		      for(NodeIt n(_g);n!=INVALID;++n) {
 		        (*_excess)[n] = (*_supply)[n];
+		      }
 		      for (ArcIt e(_g);e!=INVALID;++e) {
 		        if (!_tol.less(-(*_excess)[_g.target(e)], (*_up)[e])) {
 		          _flow->set(e, (*_up)[e]);
 		          (*_excess)[_g.target(e)] += (*_up)[e];
 		          (*_excess)[_g.source(e)] -= (*_up)[e];
 		        } else if (_tol.less(-(*_excess)[_g.target(e)], (*_lo)[e])) {
 		          _flow->set(e, (*_lo)[e]);
 		          (*_excess)[_g.target(e)] += (*_lo)[e];
 		          (*_excess)[_g.source(e)] -= (*_lo)[e];
 		        } else {
 		          Value fc = -(*_excess)[_g.target(e)];
 		          _flow->set(e, fc);
 		          (*_excess)[_g.target(e)] = 0;
 		          (*_excess)[_g.source(e)] -= fc;
+		        }
+		      }
 		      _level->initStart();
 		      for(NodeIt n(_g);n!=INVALID;++n)
 		        _level->initAddItem(n);
 		      _level->initFinish();
 		      for(NodeIt n(_g);n!=INVALID;++n)
 		        if(_tol.positive((*_excess)[n]))
 		          _level->activate(n);
+		    }
 		    ///Executes the algorithm
 		    ///This function executes the algorithm.
 		    ///
 		    ///\return \c true if a feasible circulation is found.
 		    ///
 		    ///\sa barrier()
 		    ///\sa barrierMap()
 		    bool start()
+		    {
 		      Node act;
 		      Node bact=INVALID;
 		      Node last_activated=INVALID;
 		      while((act=_level->highestActive())!=INVALID) {
 		        int actlevel=(*_level)[act];
 		        int mlevel=_node_num;
 		        Value exc=(*_excess)[act];
 		        for(OutArcIt e(_g,act);e!=INVALID; ++e) {
 		          Node v = _g.target(e);
 		          Value fc=(*_up)[e]-(*_flow)[e];
 		          if(!_tol.positive(fc)) continue;
 		          if((*_level)[v]<actlevel) {
 		            if(!_tol.less(fc, exc)) {
 		              _flow->set(e, (*_flow)[e] + exc);
 		              (*_excess)[v] += exc;
 		              if(!_level->active(v) && _tol.positive((*_excess)[v]))
 		                _level->activate(v);
 		              (*_excess)[act] = 0;
 		              _level->deactivate(act);
 		              goto next_l;
+		            }
 		            else {
 		              _flow->set(e, (*_up)[e]);
 		              (*_excess)[v] += fc;
 		              if(!_level->active(v) && _tol.positive((*_excess)[v]))
 		                _level->activate(v);
 		              exc-=fc;
+		            }
+		          }
 		          else if((*_level)[v]<mlevel) mlevel=(*_level)[v];
+		        }
 		        for(InArcIt e(_g,act);e!=INVALID; ++e) {
 		          Node v = _g.source(e);
 		          Value fc=(*_flow)[e]-(*_lo)[e];
 		          if(!_tol.positive(fc)) continue;
 		          if((*_level)[v]<actlevel) {
 		            if(!_tol.less(fc, exc)) {
 		              _flow->set(e, (*_flow)[e] - exc);
 		              (*_excess)[v] += exc;
 		              if(!_level->active(v) && _tol.positive((*_excess)[v]))
 		                _level->activate(v);
 		              (*_excess)[act] = 0;
 		              _level->deactivate(act);
 		              goto next_l;
+		            }
 		            else {
 		              _flow->set(e, (*_lo)[e]);
 		              (*_excess)[v] += fc;
 		              if(!_level->active(v) && _tol.positive((*_excess)[v]))
 		                _level->activate(v);
 		              exc-=fc;
+		            }
+		          }
 		          else if((*_level)[v]<mlevel) mlevel=(*_level)[v];
+		        }
 		        (*_excess)[act] = exc;
 		        if(!_tol.positive(exc)) _level->deactivate(act);
 		        else if(mlevel==_node_num) {
 		          _level->liftHighestActiveToTop();
 		          _el = _node_num;
 		          return false;
+		        }
 		        else {
 		          _level->liftHighestActive(mlevel+1);
 		          if(_level->onLevel(actlevel)==0) {
 		            _el = actlevel;
 		            return false;
+		          }
+		        }
 		      next_l:
+		        ;
+		      }
 		      return true;
+		    }
 		    /// Runs the algorithm.
 		    /// This function runs the algorithm.
 		    ///
 		    /// \return \c true if a feasible circulation is found.
 		    ///
 		    /// \note Apart from the return value, c.run() is just a shortcut of
 		    /// the following code.
 		    /// \code
 		    ///   c.greedyInit();
 		    ///   c.start();
 		    /// \endcode
 		    bool run() {
 		      greedyInit();
 		      return start();
+		    }
 		    /// @}
 		    /// \name Query Functions
 		    /// The results of the circulation algorithm can be obtained using
 		    /// these functions.\n
 		    /// Either \ref run() or \ref start() should be called before
 		    /// using them.
 		    ///@{
 		    /// \brief Returns the flow value on the given arc.
 		    ///
 		    /// Returns the flow value on the given arc.
 		    ///
 		    /// \pre Either \ref run() or \ref init() must be called before
 		    /// using this function.
 		    Value flow(const Arc& arc) const {
 		      return (*_flow)[arc];
+		    }
 		    /// \brief Returns a const reference to the flow map.
 		    ///
 		    /// Returns a const reference to the arc map storing the found flow.
 		    ///
 		    /// \pre Either \ref run() or \ref init() must be called before
 		    /// using this function.
 		    const FlowMap& flowMap() const {
 		      return *_flow;
+		    }
 		    /**
 		       \brief Returns \c true if the given node is in a barrier.
 		       Barrier is a set \e B of nodes for which
 		       \f[ \sum_{uv\in A: u\in B} upper(uv) -
 		           \sum_{uv\in A: v\in B} lower(uv) < \sum_{v\in B} sup(v) \f]
 		       holds. The existence of a set with this property prooves that a
 		       feasible circualtion cannot exist.
 		       This function returns \c true if the given node is in the found
 		       barrier. If a feasible circulation is found, the function
 		       gives back \c false for every node.
 		       \pre Either \ref run() or \ref init() must be called before
 		       using this function.
 		       \sa barrierMap()
 		       \sa checkBarrier()
 		    */
 		    bool barrier(const Node& node) const
+		    {
 		      return (*_level)[node] >= _el;
+		    }
 		    /// \brief Gives back a barrier.
 		    ///
 		    /// This function sets \c bar to the characteristic vector of the
 		    /// found barrier. \c bar should be a \ref concepts::WriteMap "writable"
 		    /// node map with \c bool (or convertible) value type.
 		    ///
 		    /// If a feasible circulation is found, the function gives back an
 		    /// empty set, so \c bar[v] will be \c false for all nodes \c v.
 		    ///
 		    /// \note This function calls \ref barrier() for each node,
 		    /// so it runs in O(n) time.
 		    ///
 		    /// \pre Either \ref run() or \ref init() must be called before
 		    /// using this function.
 		    ///
 		    /// \sa barrier()
 		    /// \sa checkBarrier()
 		    template<class BarrierMap>
 		    void barrierMap(BarrierMap &bar) const
+		    {
 		      for(NodeIt n(_g);n!=INVALID;++n)
 		        bar.set(n, (*_level)[n] >= _el);
+		    }
 		    /// @}
 		    /// \name Checker Functions
 		    /// The feasibility of the results can be checked using
 		    /// these functions.\n
 		    /// Either \ref run() or \ref start() should be called before
 		    /// using them.
 		    ///@{
 		    ///Check if the found flow is a feasible circulation
 		    ///Check if the found flow is a feasible circulation,
 		    ///
 		    bool checkFlow() const {
 		      for(ArcIt e(_g);e!=INVALID;++e)
 		        if((*_flow)[e]<(*_lo)[e]||(*_flow)[e]>(*_up)[e]) return false;
 		      for(NodeIt n(_g);n!=INVALID;++n)
+		        {
 		          Value dif=-(*_supply)[n];
 		          for(InArcIt e(_g,n);e!=INVALID;++e) dif-=(*_flow)[e];
 		          for(OutArcIt e(_g,n);e!=INVALID;++e) dif+=(*_flow)[e];
 		          if(_tol.negative(dif)) return false;
+		        }
 		      return true;
+		    }
 		    ///Check whether or not the last execution provides a barrier
 		    ///Check whether or not the last execution provides a barrier.
 		    ///\sa barrier()
 		    ///\sa barrierMap()
 		    bool checkBarrier() const
+		    {
 		      Value delta=0;
 		      Value inf_cap = std::numeric_limits<Value>::has_infinity ?
 		        std::numeric_limits<Value>::infinity() :
 		        std::numeric_limits<Value>::max();
 		      for(NodeIt n(_g);n!=INVALID;++n)
 		        if(barrier(n))
 		          delta-=(*_supply)[n];
 		      for(ArcIt e(_g);e!=INVALID;++e)
+		        {
 		          Node s=_g.source(e);
 		          Node t=_g.target(e);
 		          if(barrier(s)&&!barrier(t)) {
 		            if (_tol.less(inf_cap - (*_up)[e], delta)) return false;
 		            delta+=(*_up)[e];
+		          }
 		          else if(barrier(t)&&!barrier(s)) delta-=(*_lo)[e];
+		        }
 		      return _tol.negative(delta);
+		    }
 		    /// @}
 		  };
+		}
 		#endif

lemon/cost_scaling.h

Show inline comments

 		/* -*- 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_COST_SCALING_H
 		#define LEMON_COST_SCALING_H
 		/// \ingroup min_cost_flow_algs
 		/// \file
 		/// \brief Cost scaling algorithm for finding a minimum cost flow.
 		#include <vector>
 		#include <deque>
 		#include <limits>
 		#include <lemon/core.h>
 		#include <lemon/maps.h>
 		#include <lemon/math.h>
 		#include <lemon/static_graph.h>
 		#include <lemon/circulation.h>
 		#include <lemon/bellman_ford.h>
 		namespace lemon {
 		  /// \brief Default traits class of CostScaling algorithm.
 		  ///
 		  /// Default traits class of CostScaling algorithm.
 		  /// \tparam GR Digraph type.
 		  /// \tparam V The number type used for flow amounts, capacity bounds
 		  /// and supply values. By default it is \c int.
 		  /// \tparam C The number type used for costs and potentials.
 		  /// By default it is the same as \c V.
 		#ifdef DOXYGEN
 		  template <typename GR, typename V = int, typename C = V>
 		#else
 		  template < typename GR, typename V = int, typename C = V,
 		             bool integer = std::numeric_limits<C>::is_integer >
 		#endif
 		  struct CostScalingDefaultTraits
+		  {
 		    /// The type of the digraph
 		    typedef GR Digraph;
 		    /// The type of the flow amounts, capacity bounds and supply values
 		    typedef V Value;
 		    /// The type of the arc costs
 		    typedef C Cost;
 		    /// \brief The large cost type used for internal computations
 		    ///
 		    /// The large cost type used for internal computations.
 		    /// It is \c long \c long if the \c Cost type is integer,
 		    /// otherwise it is \c double.
 		    /// \c Cost must be convertible to \c LargeCost.
 		    typedef double LargeCost;
 		  };
 		  // Default traits class for integer cost types
 		  template <typename GR, typename V, typename C>
 		  struct CostScalingDefaultTraits<GR, V, C, true>
+		  {
 		    typedef GR Digraph;
 		    typedef V Value;
 		    typedef C Cost;
 		#ifdef LEMON_HAVE_LONG_LONG
 		    typedef long long LargeCost;
 		#else
 		    typedef long LargeCost;
 		#endif
 		  };
 		  /// \addtogroup min_cost_flow_algs
 		  /// @{
 		  /// \brief Implementation of the Cost Scaling algorithm for
 		  /// finding a \ref min_cost_flow "minimum cost flow".
 		  ///
 		  /// \ref CostScaling implements a cost scaling algorithm that performs
 		  /// push/augment and relabel operations for finding a \ref min_cost_flow
 		  /// "minimum cost flow" \ref amo93networkflows, \ref goldberg90approximation,
 		  /// \ref goldberg97efficient, \ref bunnagel98efficient.
 		  /// It is a highly efficient primal-dual solution method, which
 		  /// can be viewed as the generalization of the \ref Preflow
 		  /// "preflow push-relabel" algorithm for the maximum flow problem.
 		  ///
 		  /// Most of the parameters of the problem (except for the digraph)
 		  /// can be given using separate functions, and the algorithm can be
 		  /// executed using the \ref run() function. If some parameters are not
 		  /// specified, then default values will be used.
 		  ///
 		  /// \tparam GR The digraph type the algorithm runs on.
 		  /// \tparam V The number type used for flow amounts, capacity bounds
 		  /// and supply values in the algorithm. By default it is \c int.
+		  /// and supply values in the algorithm. By default, it is \c int.
 		  /// \tparam C The number type used for costs and potentials in the
 		  /// algorithm. By default it is the same as \c V.
+		  /// algorithm. By default, it is the same as \c V.
 		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm. By default, it is \ref CostScalingDefaultTraits
 		  /// "CostScalingDefaultTraits<GR, V, C>".
 		  /// In most cases, this parameter should not be set directly,
 		  /// consider to use the named template parameters instead.
 		  ///
 		  /// \warning Both number types must be signed and all input data must
 		  /// be integer.
 		  /// \warning This algorithm does not support negative costs for such
 		  /// arcs that have infinite upper bound.
 		  ///
 		  /// \note %CostScaling provides three different internal methods,
 		  /// from which the most efficient one is used by default.
 		  /// For more information, see \ref Method.
 		#ifdef DOXYGEN
 		  template <typename GR, typename V, typename C, typename TR>
 		#else
 		  template < typename GR, typename V = int, typename C = V,
 		             typename TR = CostScalingDefaultTraits<GR, V, C> >
 		#endif
 		  class CostScaling
+		  {
 		  public:
 		    /// The type of the digraph
 		    typedef typename TR::Digraph Digraph;
 		    /// The type of the flow amounts, capacity bounds and supply values
 		    typedef typename TR::Value Value;
 		    /// The type of the arc costs
 		    typedef typename TR::Cost Cost;
 		    /// \brief The large cost type
 		    ///
 		    /// The large cost type used for internal computations.
 		    /// Using the \ref CostScalingDefaultTraits "default traits class",
 		    /// it is \c long \c long if the \c Cost type is integer,
 		    /// By default, it is \c long \c long if the \c Cost type is integer,
 		    /// otherwise it is \c double.
 		    typedef typename TR::LargeCost LargeCost;
 		    /// The \ref CostScalingDefaultTraits "traits class" of the algorithm
 		    typedef TR Traits;
 		  public:
 		    /// \brief Problem type constants for the \c run() function.
 		    ///
 		    /// Enum type containing the problem type constants that can be
 		    /// returned by the \ref run() function of the algorithm.
 		    enum ProblemType {
 		      /// The problem has no feasible solution (flow).
 		      INFEASIBLE,
 		      /// The problem has optimal solution (i.e. it is feasible and
 		      /// bounded), and the algorithm has found optimal flow and node
 		      /// potentials (primal and dual solutions).
 		      OPTIMAL,
 		      /// The digraph contains an arc of negative cost and infinite
 		      /// upper bound. It means that the objective function is unbounded
 		      /// on that arc, however, note that it could actually be bounded
 		      /// over the feasible flows, but this algroithm cannot handle
 		      /// these cases.
 		      UNBOUNDED
 		    };
 		    /// \brief Constants for selecting the internal method.
 		    ///
 		    /// Enum type containing constants for selecting the internal method
 		    /// for the \ref run() function.
 		    ///
 		    /// \ref CostScaling provides three internal methods that differ mainly
 		    /// in their base operations, which are used in conjunction with the
 		    /// relabel operation.
 		    /// By default, the so called \ref PARTIAL_AUGMENT
 		    /// "Partial Augment-Relabel" method is used, which proved to be
 		    /// the most efficient and the most robust on various test inputs.
 		    /// However, the other methods can be selected using the \ref run()
 		    /// function with the proper parameter.
 		    enum Method {
 		      /// Local push operations are used, i.e. flow is moved only on one
 		      /// admissible arc at once.
 		      PUSH,
 		      /// Augment operations are used, i.e. flow is moved on admissible
 		      /// paths from a node with excess to a node with deficit.
 		      AUGMENT,
 		      /// Partial augment operations are used, i.e. flow is moved on
 		      /// admissible paths started from a node with excess, but the
 		      /// lengths of these paths are limited. This method can be viewed
 		      /// as a combined version of the previous two operations.
 		      PARTIAL_AUGMENT
 		    };
 		  private:
 		    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
 		    typedef std::vector<int> IntVector;
 		    typedef std::vector<char> BoolVector;
 		    typedef std::vector<Value> ValueVector;
 		    typedef std::vector<Cost> CostVector;
 		    typedef std::vector<LargeCost> LargeCostVector;
 		  private:
 		    template <typename KT, typename VT>
 		    class StaticVectorMap {
 		    public:
 		      typedef KT Key;
 		      typedef VT Value;
 		      StaticVectorMap(std::vector<Value>& v) : _v(v) {}
 		      const Value& operator[](const Key& key) const {
 		        return _v[StaticDigraph::id(key)];
+		      }
 		      Value& operator[](const Key& key) {
 		        return _v[StaticDigraph::id(key)];
+		      }
 		      void set(const Key& key, const Value& val) {
 		        _v[StaticDigraph::id(key)] = val;
+		      }
 		    private:
 		      std::vector<Value>& _v;
 		    };
 		    typedef StaticVectorMap<StaticDigraph::Node, LargeCost> LargeCostNodeMap;
 		    typedef StaticVectorMap<StaticDigraph::Arc, LargeCost> LargeCostArcMap;
 		  private:
 		    // Data related to the underlying digraph
 		    const GR &_graph;
 		    int _node_num;
 		    int _arc_num;
 		    int _res_node_num;
 		    int _res_arc_num;
 		    int _root;
 		    // Parameters of the problem
 		    bool _have_lower;
 		    Value _sum_supply;
 		    // Data structures for storing the digraph
 		    IntNodeMap _node_id;
 		    IntArcMap _arc_idf;
 		    IntArcMap _arc_idb;
 		    IntVector _first_out;
 		    BoolVector _forward;
 		    IntVector _source;
 		    IntVector _target;
 		    IntVector _reverse;
 		    // Node and arc data
 		    ValueVector _lower;
 		    ValueVector _upper;
 		    CostVector _scost;
 		    ValueVector _supply;
 		    ValueVector _res_cap;
 		    LargeCostVector _cost;
 		    LargeCostVector _pi;
 		    ValueVector _excess;
 		    IntVector _next_out;
 		    std::deque<int> _active_nodes;
 		    // Data for scaling
 		    LargeCost _epsilon;
 		    int _alpha;
 		    // Data for a StaticDigraph structure
 		    typedef std::pair<int, int> IntPair;
 		    StaticDigraph _sgr;
 		    std::vector<IntPair> _arc_vec;
 		    std::vector<LargeCost> _cost_vec;
 		    LargeCostArcMap _cost_map;
 		    LargeCostNodeMap _pi_map;
 		  public:
 		    /// \brief Constant for infinite upper bounds (capacities).
 		    ///
 		    /// Constant for infinite upper bounds (capacities).
 		    /// It is \c std::numeric_limits<Value>::infinity() if available,
 		    /// \c std::numeric_limits<Value>::max() otherwise.
 		    const Value INF;
 		  public:
 		    /// \name Named Template Parameters
 		    /// @{
 		    template <typename T>
 		    struct SetLargeCostTraits : public Traits {
 		      typedef T LargeCost;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c LargeCost type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting \c LargeCost
 		    /// type, which is used for internal computations in the algorithm.
 		    /// \c Cost must be convertible to \c LargeCost.
 		    template <typename T>
 		    struct SetLargeCost
 		      : public CostScaling<GR, V, C, SetLargeCostTraits<T> > {
 		      typedef  CostScaling<GR, V, C, SetLargeCostTraits<T> > Create;
 		    };
 		    /// @}
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// The constructor of the class.
 		    ///
 		    /// \param graph The digraph the algorithm runs on.
 		    CostScaling(const GR& graph) :
 		      _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
 		      _cost_map(_cost_vec), _pi_map(_pi),
 		      INF(std::numeric_limits<Value>::has_infinity ?
 		          std::numeric_limits<Value>::infinity() :
 		          std::numeric_limits<Value>::max())
+		    {
 		      // Check the number types
 		      LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
 		        "The flow type of CostScaling must be signed");
 		      LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
 		        "The cost type of CostScaling must be signed");
 		      // Resize vectors
 		      _node_num = countNodes(_graph);
 		      _arc_num = countArcs(_graph);
 		      _res_node_num = _node_num + 1;
 		      _res_arc_num = 2 * (_arc_num + _node_num);
 		      _root = _node_num;
 		      _first_out.resize(_res_node_num + 1);
 		      _forward.resize(_res_arc_num);
 		      _source.resize(_res_arc_num);
 		      _target.resize(_res_arc_num);
 		      _reverse.resize(_res_arc_num);
 		      _lower.resize(_res_arc_num);
 		      _upper.resize(_res_arc_num);
 		      _scost.resize(_res_arc_num);
 		      _supply.resize(_res_node_num);
 		      _res_cap.resize(_res_arc_num);
 		      _cost.resize(_res_arc_num);
 		      _pi.resize(_res_node_num);
 		      _excess.resize(_res_node_num);
 		      _next_out.resize(_res_node_num);
 		      _arc_vec.reserve(_res_arc_num);
 		      _cost_vec.reserve(_res_arc_num);
 		      // Copy the graph
 		      int i = 0, j = 0, k = 2 * _arc_num + _node_num;
 		      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
 		        _node_id[n] = i;
+		      }
 		      i = 0;
 		      for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
 		        _first_out[i] = j;
 		        for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
 		          _arc_idf[a] = j;
 		          _forward[j] = true;
 		          _source[j] = i;
 		          _target[j] = _node_id[_graph.runningNode(a)];
+		        }
 		        for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
 		          _arc_idb[a] = j;
 		          _forward[j] = false;
 		          _source[j] = i;
 		          _target[j] = _node_id[_graph.runningNode(a)];
+		        }
 		        _forward[j] = false;
 		        _source[j] = i;
 		        _target[j] = _root;
 		        _reverse[j] = k;
 		        _forward[k] = true;
 		        _source[k] = _root;
 		        _target[k] = i;
 		        _reverse[k] = j;
 		        ++j; ++k;
+		      }
 		      _first_out[i] = j;
 		      _first_out[_res_node_num] = k;
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        int fi = _arc_idf[a];
 		        int bi = _arc_idb[a];
 		        _reverse[fi] = bi;
 		        _reverse[bi] = fi;
+		      }
 		      // Reset parameters
 		      reset();
+		    }
 		    /// \name Parameters
 		    /// The parameters of the algorithm can be specified using these
 		    /// functions.
 		    /// @{
 		    /// \brief Set the lower bounds on the arcs.
 		    ///
 		    /// This function sets the lower bounds on the arcs.
 		    /// If it is not used before calling \ref run(), the lower bounds
 		    /// will be set to zero on all arcs.
 		    ///
 		    /// \param map An arc map storing the lower bounds.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template <typename LowerMap>
 		    CostScaling& lowerMap(const LowerMap& map) {
 		      _have_lower = true;
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _lower[_arc_idf[a]] = map[a];
 		        _lower[_arc_idb[a]] = map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the upper bounds (capacities) on the arcs.
 		    ///
 		    /// This function sets the upper bounds (capacities) on the arcs.
 		    /// If it is not used before calling \ref run(), the upper bounds
 		    /// will be set to \ref INF on all arcs (i.e. the flow value will be
 		    /// unbounded from above).
 		    ///
 		    /// \param map An arc map storing the upper bounds.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename UpperMap>
 		    CostScaling& upperMap(const UpperMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _upper[_arc_idf[a]] = map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the costs of the arcs.
 		    ///
 		    /// This function sets the costs of the arcs.
 		    /// If it is not used before calling \ref run(), the costs
 		    /// will be set to \c 1 on all arcs.
 		    ///
 		    /// \param map An arc map storing the costs.
 		    /// Its \c Value type must be convertible to the \c Cost type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename CostMap>
 		    CostScaling& costMap(const CostMap& map) {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        _scost[_arc_idf[a]] =  map[a];
 		        _scost[_arc_idb[a]] = -map[a];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set the supply values of the nodes.
 		    ///
 		    /// This function sets the supply values of the nodes.
 		    /// If neither this function nor \ref stSupply() is used before
 		    /// calling \ref run(), the supply of each node will be set to zero.
 		    ///
 		    /// \param map A node map storing the supply values.
 		    /// Its \c Value type must be convertible to the \c Value type
 		    /// of the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    template<typename SupplyMap>
 		    CostScaling& supplyMap(const SupplyMap& map) {
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
 		        _supply[_node_id[n]] = map[n];
+		      }
 		      return *this;
+		    }
 		    /// \brief Set single source and target nodes and a supply value.
 		    ///
 		    /// This function sets a single source node and a single target node
 		    /// and the required flow value.
 		    /// If neither this function nor \ref supplyMap() is used before
 		    /// calling \ref run(), the supply of each node will be set to zero.
 		    ///
 		    /// Using this function has the same effect as using \ref supplyMap()
 		    /// with such a map in which \c k is assigned to \c s, \c -k is
 		    /// assigned to \c t and all other nodes have zero supply value.
 		    ///
 		    /// \param s The source node.
 		    /// \param t The target node.
 		    /// \param k The required amount of flow from node \c s to node \c t
 		    /// (i.e. the supply of \c s and the demand of \c t).
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    CostScaling& stSupply(const Node& s, const Node& t, Value k) {
 		      for (int i = 0; i != _res_node_num; ++i) {
 		        _supply[i] = 0;
+		      }
 		      _supply[_node_id[s]] =  k;
 		      _supply[_node_id[t]] = -k;
 		      return *this;
+		    }
 		    /// @}
 		    /// \name Execution control
 		    /// The algorithm can be executed using \ref run().
 		    /// @{
 		    /// \brief Run the algorithm.
 		    ///
 		    /// This function runs the algorithm.
 		    /// The paramters can be specified using functions \ref lowerMap(),
 		    /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
 		    /// For example,
 		    /// \code
 		    ///   CostScaling<ListDigraph> cs(graph);
 		    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    /// \endcode
 		    ///
 		    /// This function can be called more than once. All the parameters
 		    /// that have been given are kept for the next call, unless
 		    /// \ref reset() is called, thus only the modified parameters
 		    /// have to be set again. See \ref reset() for examples.
 		    /// However, the underlying digraph must not be modified after this
 		    /// class have been constructed, since it copies and extends the graph.
 		    ///
 		    /// \param method The internal method that will be used in the
 		    /// algorithm. For more information, see \ref Method.
 		    /// \param factor The cost scaling factor. It must be larger than one.
 		    ///
 		    /// \return \c INFEASIBLE if no feasible flow exists,
 		    /// \n \c OPTIMAL if the problem has optimal solution
 		    /// (i.e. it is feasible and bounded), and the algorithm has found
 		    /// optimal flow and node potentials (primal and dual solutions),
 		    /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
 		    /// and infinite upper bound. It means that the objective function
 		    /// is unbounded on that arc, however, note that it could actually be
 		    /// bounded over the feasible flows, but this algroithm cannot handle
 		    /// these cases.
 		    ///
 		    /// \see ProblemType, Method
 		    ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 8) {
 		      _alpha = factor;
 		      ProblemType pt = init();
 		      if (pt != OPTIMAL) return pt;
 		      start(method);
 		      return OPTIMAL;
+		    }
 		    /// \brief Reset all the parameters that have been given before.
 		    ///
 		    /// This function resets all the paramaters that have been given
 		    /// before using functions \ref lowerMap(), \ref upperMap(),
 		    /// \ref costMap(), \ref supplyMap(), \ref stSupply().
 		    ///
 		    /// It is useful for multiple run() calls. If this function is not
 		    /// used, all the parameters given before are kept for the next
 		    /// \ref run() call.
 		    /// However, the underlying digraph must not be modified after this
 		    /// class have been constructed, since it copies and extends the graph.
 		    ///
 		    /// For example,
 		    /// \code
 		    ///   CostScaling<ListDigraph> cs(graph);
 		    ///
 		    ///   // First run
 		    ///   cs.lowerMap(lower).upperMap(upper).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    ///
 		    ///   // Run again with modified cost map (reset() is not called,
 		    ///   // so only the cost map have to be set again)
 		    ///   cost[e] += 100;
 		    ///   cs.costMap(cost).run();
 		    ///
 		    ///   // Run again from scratch using reset()
 		    ///   // (the lower bounds will be set to zero on all arcs)
 		    ///   cs.reset();
 		    ///   cs.upperMap(capacity).costMap(cost)
 		    ///     .supplyMap(sup).run();
 		    /// \endcode
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    CostScaling& reset() {
 		      for (int i = 0; i != _res_node_num; ++i) {
 		        _supply[i] = 0;
+		      }
 		      int limit = _first_out[_root];
 		      for (int j = 0; j != limit; ++j) {
 		        _lower[j] = 0;
 		        _upper[j] = INF;
 		        _scost[j] = _forward[j] ? 1 : -1;
+		      }
 		      for (int j = limit; j != _res_arc_num; ++j) {
 		        _lower[j] = 0;
 		        _upper[j] = INF;
 		        _scost[j] = 0;
 		        _scost[_reverse[j]] = 0;
+		      }
 		      _have_lower = false;
 		      return *this;
+		    }
 		    /// @}
 		    /// \name Query Functions
 		    /// The results of the algorithm can be obtained using these
 		    /// functions.\n
 		    /// The \ref run() function must be called before using them.
 		    /// @{
 		    /// \brief Return the total cost of the found flow.
 		    ///
 		    /// This function returns the total cost of the found flow.
 		    /// Its complexity is O(e).
 		    ///
 		    /// \note The return type of the function can be specified as a
 		    /// template parameter. For example,
 		    /// \code
 		    ///   cs.totalCost<double>();
 		    /// \endcode
 		    /// It is useful if the total cost cannot be stored in the \c Cost
 		    /// type of the algorithm, which is the default return type of the
 		    /// function.
 		    ///
 		    /// \pre \ref run() must be called before using this function.
 		    template <typename Number>
 		    Number totalCost() const {
 		      Number c = 0;
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        int i = _arc_idb[a];
 		        c += static_cast<Number>(_res_cap[i]) *
 		             (-static_cast<Number>(_scost[i]));
+		      }
 		      return c;
+		    }
 		#ifndef DOXYGEN
 		    Cost totalCost() const {
 		      return totalCost<Cost>();
+		    }
 		#endif
 		    /// \brief Return the flow on the given arc.
 		    ///
 		    /// This function returns the flow on the given arc.
 		    ///
 		    /// \pre \ref run() must be called before using this function.
 		    Value flow(const Arc& a) const {
 		      return _res_cap[_arc_idb[a]];
+		    }
 		    /// \brief Return the flow map (the primal solution).
 		    ///
 		    /// This function copies the flow value on each arc into the given
 		    /// map. The \c Value type of the algorithm must be convertible to
 		    /// the \c Value type of the map.
 		    ///
 		    /// \pre \ref run() must be called before using this function.
 		    template <typename FlowMap>
 		    void flowMap(FlowMap &map) const {
 		      for (ArcIt a(_graph); a != INVALID; ++a) {
 		        map.set(a, _res_cap[_arc_idb[a]]);
+		      }
+		    }
 		    /// \brief Return the potential (dual value) of the given node.
 		    ///
 		    /// This function returns the potential (dual value) of the
 		    /// given node.
 		    ///
 		    /// \pre \ref run() must be called before using this function.
 		    Cost potential(const Node& n) const {
 		      return static_cast<Cost>(_pi[_node_id[n]]);
+		    }
 		    /// \brief Return the potential map (the dual solution).
 		    ///
 		    /// This function copies the potential (dual value) of each node
 		    /// into the given map.
 		    /// The \c Cost type of the algorithm must be convertible to the
 		    /// \c Value type of the map.
 		    ///
 		    /// \pre \ref run() must be called before using this function.
 		    template <typename PotentialMap>
 		    void potentialMap(PotentialMap &map) const {
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
 		        map.set(n, static_cast<Cost>(_pi[_node_id[n]]));
+		      }
+		    }
 		    /// @}
 		  private:
 		    // Initialize the algorithm
 		    ProblemType init() {
 		      if (_res_node_num <= 1) return INFEASIBLE;
 		      // Check the sum of supply values
 		      _sum_supply = 0;
 		      for (int i = 0; i != _root; ++i) {
 		        _sum_supply += _supply[i];
+		      }
 		      if (_sum_supply > 0) return INFEASIBLE;
 		      // Initialize vectors
 		      for (int i = 0; i != _res_node_num; ++i) {
 		        _pi[i] = 0;
 		        _excess[i] = _supply[i];
+		      }
 		      // Remove infinite upper bounds and check negative arcs
 		      const Value MAX = std::numeric_limits<Value>::max();
 		      int last_out;
 		      if (_have_lower) {
 		        for (int i = 0; i != _root; ++i) {
 		          last_out = _first_out[i+1];
 		          for (int j = _first_out[i]; j != last_out; ++j) {
 		            if (_forward[j]) {
 		              Value c = _scost[j] < 0 ? _upper[j] : _lower[j];
 		              if (c >= MAX) return UNBOUNDED;
 		              _excess[i] -= c;
 		              _excess[_target[j]] += c;
+		            }
+		          }
+		        }
 		      } else {
 		        for (int i = 0; i != _root; ++i) {
 		          last_out = _first_out[i+1];
 		          for (int j = _first_out[i]; j != last_out; ++j) {
 		            if (_forward[j] && _scost[j] < 0) {
 		              Value c = _upper[j];
 		              if (c >= MAX) return UNBOUNDED;
 		              _excess[i] -= c;
 		              _excess[_target[j]] += c;
+		            }
+		          }
+		        }
+		      }
 		      Value ex, max_cap = 0;
 		      for (int i = 0; i != _res_node_num; ++i) {
 		        ex = _excess[i];
 		        _excess[i] = 0;
 		        if (ex < 0) max_cap -= ex;
+		      }
 		      for (int j = 0; j != _res_arc_num; ++j) {
 		        if (_upper[j] >= MAX) _upper[j] = max_cap;
+		      }
 		      // Initialize the large cost vector and the epsilon parameter
 		      _epsilon = 0;
 		      LargeCost lc;
 		      for (int i = 0; i != _root; ++i) {
 		        last_out = _first_out[i+1];
 		        for (int j = _first_out[i]; j != last_out; ++j) {
 		          lc = static_cast<LargeCost>(_scost[j]) * _res_node_num * _alpha;
 		          _cost[j] = lc;
 		          if (lc > _epsilon) _epsilon = lc;
+		        }
+		      }
 		      _epsilon /= _alpha;
 		      // Initialize maps for Circulation and remove non-zero lower bounds
 		      ConstMap<Arc, Value> low(0);
 		      typedef typename Digraph::template ArcMap<Value> ValueArcMap;
 		      typedef typename Digraph::template NodeMap<Value> ValueNodeMap;
 		      ValueArcMap cap(_graph), flow(_graph);
 		      ValueNodeMap sup(_graph);
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
 		        sup[n] = _supply[_node_id[n]];
+		      }
 		      if (_have_lower) {
 		        for (ArcIt a(_graph); a != INVALID; ++a) {
 		          int j = _arc_idf[a];
 		          Value c = _lower[j];
 		          cap[a] = _upper[j] - c;
 		          sup[_graph.source(a)] -= c;
 		          sup[_graph.target(a)] += c;
+		        }
 		      } else {
 		        for (ArcIt a(_graph); a != INVALID; ++a) {
 		          cap[a] = _upper[_arc_idf[a]];
+		        }
+		      }
 		      // Find a feasible flow using Circulation
 		      Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap>
 		        circ(_graph, low, cap, sup);
 		      if (!circ.flowMap(flow).run()) return INFEASIBLE;
 		      // Set residual capacities and handle GEQ supply type
 		      if (_sum_supply < 0) {
 		        for (ArcIt a(_graph); a != INVALID; ++a) {
 		          Value fa = flow[a];
 		          _res_cap[_arc_idf[a]] = cap[a] - fa;
 		          _res_cap[_arc_idb[a]] = fa;
 		          sup[_graph.source(a)] -= fa;
 		          sup[_graph.target(a)] += fa;
+		        }
 		        for (NodeIt n(_graph); n != INVALID; ++n) {
 		          _excess[_node_id[n]] = sup[n];
+		        }
 		        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
 		          int u = _target[a];
 		          int ra = _reverse[a];
 		          _res_cap[a] = -_sum_supply + 1;
 		          _res_cap[ra] = -_excess[u];
 		          _cost[a] = 0;
 		          _cost[ra] = 0;
 		          _excess[u] = 0;
+		        }
 		      } else {
 		        for (ArcIt a(_graph); a != INVALID; ++a) {
 		          Value fa = flow[a];
 		          _res_cap[_arc_idf[a]] = cap[a] - fa;
 		          _res_cap[_arc_idb[a]] = fa;
+		        }
 		        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
 		          int ra = _reverse[a];
 		          _res_cap[a] = 1;
 		          _res_cap[ra] = 0;
 		          _cost[a] = 0;
 		          _cost[ra] = 0;
+		        }
+		      }
 		      return OPTIMAL;
+		    }
 		    // Execute the algorithm and transform the results
 		    void start(Method method) {
 		      // Maximum path length for partial augment
 		      const int MAX_PATH_LENGTH = 4;
 		      // Execute the algorithm
 		      switch (method) {
 		        case PUSH:
 		          startPush();
 		          break;
 		        case AUGMENT:
 		          startAugment();
 		          break;
 		        case PARTIAL_AUGMENT:
 		          startAugment(MAX_PATH_LENGTH);
 		          break;
+		      }
 		      // Compute node potentials for the original costs
 		      _arc_vec.clear();
 		      _cost_vec.clear();
 		      for (int j = 0; j != _res_arc_num; ++j) {
 		        if (_res_cap[j] > 0) {
 		          _arc_vec.push_back(IntPair(_source[j], _target[j]));
 		          _cost_vec.push_back(_scost[j]);
+		        }
+		      }
 		      _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
 		      typename BellmanFord<StaticDigraph, LargeCostArcMap>
 		        ::template SetDistMap<LargeCostNodeMap>::Create bf(_sgr, _cost_map);
 		      bf.distMap(_pi_map);
 		      bf.init(0);
 		      bf.start();
 		      // Handle non-zero lower bounds
 		      if (_have_lower) {
 		        int limit = _first_out[_root];
 		        for (int j = 0; j != limit; ++j) {
 		          if (!_forward[j]) _res_cap[j] += _lower[j];
+		        }
+		      }
+		    }
 		    /// Execute the algorithm performing augment and relabel operations
 		    void startAugment(int max_length = std::numeric_limits<int>::max()) {
 		      // Paramters for heuristics
 		      const int BF_HEURISTIC_EPSILON_BOUND = 1000;
 		      const int BF_HEURISTIC_BOUND_FACTOR  = 3;
 		      // Perform cost scaling phases
 		      IntVector pred_arc(_res_node_num);
 		      std::vector<int> path_nodes;
 		      for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
 : _epsilon / _alpha )
+		      {
 		        // "Early Termination" heuristic: use Bellman-Ford algorithm
 		        // to check if the current flow is optimal
 		        if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) {
 		          _arc_vec.clear();

lemon/dfs.h

Show inline comments

 		/* -*- 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_DFS_H
 		#define LEMON_DFS_H
 		///\ingroup search
 		///\file
 		///\brief DFS algorithm.
 		#include <lemon/list_graph.h>
 		#include <lemon/bits/path_dump.h>
 		#include <lemon/core.h>
 		#include <lemon/error.h>
 		#include <lemon/maps.h>
 		#include <lemon/path.h>
 		namespace lemon {
 		  ///Default traits class of Dfs class.
 		  ///Default traits class of Dfs class.
 		  ///\tparam GR Digraph type.
 		  template<class GR>
 		  struct DfsDefaultTraits
+		  {
 		    ///The type of the digraph the algorithm runs on.
 		    typedef GR Digraph;
 		    ///\brief The type of the map that stores the predecessor
 		    ///arcs of the %DFS paths.
 		    ///
 		    ///The type of the map that stores the predecessor
 		    ///arcs of the %DFS paths.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
 		    ///Instantiates a \c PredMap.
 		    ///This function instantiates a \ref PredMap.
 		    ///\param g is the digraph, to which we would like to define the
 		    ///\ref PredMap.
 		    static PredMap *createPredMap(const Digraph &g)
+		    {
 		      return new PredMap(g);
+		    }
 		    ///The type of the map that indicates which nodes are processed.
 		    ///The type of the map that indicates which nodes are processed.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    ///By default, it is a NullMap.
 		    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
 		    ///Instantiates a \c ProcessedMap.
 		    ///This function instantiates a \ref ProcessedMap.
 		    ///\param g is the digraph, to which
 		    ///we would like to define the \ref ProcessedMap.
 		#ifdef DOXYGEN
 		    static ProcessedMap *createProcessedMap(const Digraph &g)
 		#else
 		    static ProcessedMap *createProcessedMap(const Digraph &)
 		#endif
+		    {
 		      return new ProcessedMap();
+		    }
 		    ///The type of the map that indicates which nodes are reached.
 		    ///The type of the map that indicates which nodes are reached.
 		    ///It must conform to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
 		    typedef typename Digraph::template NodeMap<bool> ReachedMap;
 		    ///Instantiates a \c ReachedMap.
 		    ///This function instantiates a \ref ReachedMap.
 		    ///\param g is the digraph, to which
 		    ///we would like to define the \ref ReachedMap.
 		    static ReachedMap *createReachedMap(const Digraph &g)
+		    {
 		      return new ReachedMap(g);
+		    }
 		    ///The type of the map that stores the distances of the nodes.
 		    ///The type of the map that stores the distances of the nodes.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename Digraph::template NodeMap<int> DistMap;
 		    ///Instantiates a \c DistMap.
 		    ///This function instantiates a \ref DistMap.
 		    ///\param g is the digraph, to which we would like to define the
 		    ///\ref DistMap.
 		    static DistMap *createDistMap(const Digraph &g)
+		    {
 		      return new DistMap(g);
+		    }
 		  };
 		  ///%DFS algorithm class.
 		  ///\ingroup search
 		  ///This class provides an efficient implementation of the %DFS algorithm.
 		  ///
 		  ///There is also a \ref dfs() "function-type interface" for the DFS
 		  ///algorithm, which is convenient in the simplier cases and it can be
 		  ///used easier.
 		  ///
 		  ///\tparam GR The type of the digraph the algorithm runs on.
 		  ///The default type is \ref ListDigraph.
 		  ///\tparam TR The traits class that defines various types used by the
 		  ///algorithm. By default, it is \ref DfsDefaultTraits
 		  ///"DfsDefaultTraits<GR>".
 		  ///In most cases, this parameter should not be set directly,
 		  ///consider to use the named template parameters instead.
 		#ifdef DOXYGEN
 		  template <typename GR,
 		            typename TR>
 		#else
 		  template <typename GR=ListDigraph,
 		            typename TR=DfsDefaultTraits<GR> >
 		#endif
 		  class Dfs {
 		  public:
 		    ///The type of the digraph the algorithm runs on.
 		    typedef typename TR::Digraph Digraph;
 		    ///\brief The type of the map that stores the predecessor arcs of the
 		    ///DFS paths.
 		    typedef typename TR::PredMap PredMap;
 		    ///The type of the map that stores the distances of the nodes.
 		    typedef typename TR::DistMap DistMap;
 		    ///The type of the map that indicates which nodes are reached.
 		    typedef typename TR::ReachedMap ReachedMap;
 		    ///The type of the map that indicates which nodes are processed.
 		    typedef typename TR::ProcessedMap ProcessedMap;
 		    ///The type of the paths.
 		    typedef PredMapPath<Digraph, PredMap> Path;
 		    ///The \ref DfsDefaultTraits "traits class" of the algorithm.
 		    typedef TR Traits;
 		  private:
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::OutArcIt OutArcIt;
 		    //Pointer to the underlying digraph.
 		    const Digraph *G;
 		    //Pointer to the map of predecessor arcs.
 		    PredMap *_pred;
 		    //Indicates if _pred is locally allocated (true) or not.
 		    bool local_pred;
 		    //Pointer to the map of distances.
 		    DistMap *_dist;
 		    //Indicates if _dist is locally allocated (true) or not.
 		    bool local_dist;
 		    //Pointer to the map of reached status of the nodes.
 		    ReachedMap *_reached;
 		    //Indicates if _reached is locally allocated (true) or not.
 		    bool local_reached;
 		    //Pointer to the map of processed status of the nodes.
 		    ProcessedMap *_processed;
 		    //Indicates if _processed is locally allocated (true) or not.
 		    bool local_processed;
 		    std::vector<typename Digraph::OutArcIt> _stack;
 		    int _stack_head;
 		    //Creates the maps if necessary.
 		    void create_maps()
+		    {
 		      if(!_pred) {
 		        local_pred = true;
 		        _pred = Traits::createPredMap(*G);
+		      }
 		      if(!_dist) {
 		        local_dist = true;
 		        _dist = Traits::createDistMap(*G);
+		      }
 		      if(!_reached) {
 		        local_reached = true;
 		        _reached = Traits::createReachedMap(*G);
+		      }
 		      if(!_processed) {
 		        local_processed = true;
 		        _processed = Traits::createProcessedMap(*G);
+		      }
+		    }
 		  protected:
 		    Dfs() {}
 		  public:
 		    typedef Dfs Create;
 		    ///\name Named Template Parameters
 		    ///@{
 		    template <class T>
 		    struct SetPredMapTraits : public Traits {
 		      typedef T PredMap;
 		      static PredMap *createPredMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "PredMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c PredMap type.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c PredMap type.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    template <class T>
 		    struct SetPredMap : public Dfs<Digraph, SetPredMapTraits<T> > {
 		      typedef Dfs<Digraph, SetPredMapTraits<T> > Create;
 		    };
 		    template <class T>
 		    struct SetDistMapTraits : public Traits {
 		      typedef T DistMap;
 		      static DistMap *createDistMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "DistMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c DistMap type.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c DistMap type.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    template <class T>
 		    struct SetDistMap : public Dfs< Digraph, SetDistMapTraits<T> > {
 		      typedef Dfs<Digraph, SetDistMapTraits<T> > Create;
 		    };
 		    template <class T>
 		    struct SetReachedMapTraits : public Traits {
 		      typedef T ReachedMap;
 		      static ReachedMap *createReachedMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "ReachedMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c ReachedMap type.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c ReachedMap type.
 		    ///It must conform to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
 		    template <class T>
 		    struct SetReachedMap : public Dfs< Digraph, SetReachedMapTraits<T> > {
 		      typedef Dfs< Digraph, SetReachedMapTraits<T> > Create;
 		    };
 		    template <class T>
 		    struct SetProcessedMapTraits : public Traits {
 		      typedef T ProcessedMap;
 		      static ProcessedMap *createProcessedMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "ProcessedMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c ProcessedMap type.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c ProcessedMap type.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    template <class T>
 		    struct SetProcessedMap : public Dfs< Digraph, SetProcessedMapTraits<T> > {
 		      typedef Dfs< Digraph, SetProcessedMapTraits<T> > Create;
 		    };
 		    struct SetStandardProcessedMapTraits : public Traits {
 		      typedef typename Digraph::template NodeMap<bool> ProcessedMap;
 		      static ProcessedMap *createProcessedMap(const Digraph &g)
+		      {
 		        return new ProcessedMap(g);
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
 		    ///If you don't set it explicitly, it will be automatically allocated.
 		    struct SetStandardProcessedMap :
 		      public Dfs< Digraph, SetStandardProcessedMapTraits > {
 		      typedef Dfs< Digraph, SetStandardProcessedMapTraits > Create;
 		    };
 		    ///@}
 		  public:
 		    ///Constructor.
 		    ///Constructor.
 		    ///\param g The digraph the algorithm runs on.
 		    Dfs(const Digraph &g) :
 		      G(&g),
 		      _pred(NULL), local_pred(false),
 		      _dist(NULL), local_dist(false),
 		      _reached(NULL), local_reached(false),
 		      _processed(NULL), local_processed(false)
 		    { }
 		    ///Destructor.
 		    ~Dfs()
+		    {
 		      if(local_pred) delete _pred;
 		      if(local_dist) delete _dist;
 		      if(local_reached) delete _reached;
 		      if(local_processed) delete _processed;
+		    }
 		    ///Sets the map that stores the predecessor arcs.
 		    ///Sets the map that stores the predecessor arcs.
 		    ///If you don't use this function before calling \ref run(Node) "run()"
 		    ///or \ref init(), an instance will be allocated automatically.
 		    ///The destructor deallocates this automatically allocated map,
 		    ///of course.
 		    ///\return <tt> (*this) </tt>
 		    Dfs &predMap(PredMap &m)
+		    {
 		      if(local_pred) {
 		        delete _pred;
 		        local_pred=false;
+		      }
 		      _pred = &m;
 		      return *this;
+		    }
 		    ///Sets the map that indicates which nodes are reached.
 		    ///Sets the map that indicates which nodes are reached.
 		    ///If you don't use this function before calling \ref run(Node) "run()"
 		    ///or \ref init(), an instance will be allocated automatically.
 		    ///The destructor deallocates this automatically allocated map,
 		    ///of course.
 		    ///\return <tt> (*this) </tt>
 		    Dfs &reachedMap(ReachedMap &m)
+		    {
 		      if(local_reached) {
 		        delete _reached;
 		        local_reached=false;
+		      }
 		      _reached = &m;
 		      return *this;
+		    }
 		    ///Sets the map that indicates which nodes are processed.
 		    ///Sets the map that indicates which nodes are processed.
 		    ///If you don't use this function before calling \ref run(Node) "run()"
 		    ///or \ref init(), an instance will be allocated automatically.
 		    ///The destructor deallocates this automatically allocated map,
 		    ///of course.
 		    ///\return <tt> (*this) </tt>
 		    Dfs &processedMap(ProcessedMap &m)
+		    {
 		      if(local_processed) {
 		        delete _processed;
 		        local_processed=false;
+		      }
 		      _processed = &m;
 		      return *this;
+		    }
 		    ///Sets the map that stores the distances of the nodes.
 		    ///Sets the map that stores the distances of the nodes calculated by
 		    ///the algorithm.
 		    ///If you don't use this function before calling \ref run(Node) "run()"
 		    ///or \ref init(), an instance will be allocated automatically.
 		    ///The destructor deallocates this automatically allocated map,
 		    ///of course.
 		    ///\return <tt> (*this) </tt>
 		    Dfs &distMap(DistMap &m)
+		    {
 		      if(local_dist) {
 		        delete _dist;
 		        local_dist=false;
+		      }
 		      _dist = &m;
 		      return *this;
+		    }
 		  public:
 		    ///\name Execution Control
 		    ///The simplest way to execute the DFS algorithm is to use one of the
 		    ///member functions called \ref run(Node) "run()".\n
 		    ///If you need better control on the execution, you have to call
 		    ///\ref init() first, then you can add a source node with \ref addSource()
 		    ///and perform the actual computation with \ref start().
 		    ///This procedure can be repeated if there are nodes that have not
 		    ///been reached.
 		    ///@{
 		    ///\brief Initializes the internal data structures.
 		    ///
 		    ///Initializes the internal data structures.
 		    void init()
+		    {
 		      create_maps();
 		      _stack.resize(countNodes(*G));
 		      _stack_head=-1;
 		      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
 		        _pred->set(u,INVALID);
 		        _reached->set(u,false);
 		        _processed->set(u,false);
+		      }
+		    }
 		    ///Adds a new source node.
 		    ///Adds a new source node to the set of nodes to be processed.
 		    ///
 		    ///\pre The stack must be empty. Otherwise the algorithm gives
 		    ///wrong results. (One of the outgoing arcs of all the source nodes
 		    ///except for the last one will not be visited and distances will
 		    ///also be wrong.)
 		    void addSource(Node s)
+		    {
 		      LEMON_DEBUG(emptyQueue(), "The stack is not empty.");
 		      if(!(*_reached)[s])
+		        {
 		          _reached->set(s,true);
 		          _pred->set(s,INVALID);
 		          OutArcIt e(*G,s);
 		          if(e!=INVALID) {
 		            _stack[++_stack_head]=e;
 		            _dist->set(s,_stack_head);
+		          }
 		          else {
 		            _processed->set(s,true);
 		            _dist->set(s,0);
+		          }
+		        }
+		    }
 		    ///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)
+		    {
 		      while ( !emptyQueue() && G->target(_stack[_stack_head])!=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 visit all nodes
 		    ///in the digraph.
 		    ///
 		    ///\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);
 		          start();
+		        }
+		      }
+		    }
 		    ///@}
 		    ///\name Query Functions
 		    ///The results of the DFS algorithm can be obtained using these
 		    ///functions.\n
 		    ///Either \ref run(Node) "run()" or \ref start() should be called
 		    ///before using them.
 		    ///@{
 		    ///The DFS path to the given node.
 		    ///Returns the DFS path to the given node from the root(s).
 		    ///
 		    ///\warning \c t should be reached from the root(s).
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    Path path(Node t) const { return Path(*G, *_pred, t); }
 		    ///The distance of the given node from the root(s).
 		    ///Returns the distance of the given node from the root(s).
 		    ///
 		    ///\warning If node \c v is not reached from the root(s), then
 		    ///the return value of this function is undefined.
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    int dist(Node v) const { return (*_dist)[v]; }
 		    ///Returns the 'previous arc' of the %DFS tree for the given node.
 		    ///This function returns the 'previous arc' of the %DFS tree for the
 		    ///node \c v, i.e. it returns the last arc of a %DFS path from a
 		    ///root to \c v. It is \c INVALID if \c v is not reached from the
 		    ///root(s) or if \c v is a root.
 		    ///
 		    ///The %DFS tree used here is equal to the %DFS tree used in
 		    ///\ref predNode() and \ref predMap().
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    Arc predArc(Node v) const { return (*_pred)[v];}
 		    ///Returns the 'previous node' of the %DFS tree for the given node.
 		    ///This function returns the 'previous node' of the %DFS
 		    ///tree for the node \c v, i.e. it returns the last but one node
 		    ///of a %DFS path from a root to \c v. It is \c INVALID
 		    ///if \c v is not reached from the root(s) or if \c v is a root.
 		    ///
 		    ///The %DFS tree used here is equal to the %DFS tree used in
 		    ///\ref predArc() and \ref predMap().
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
 		                                  G->source((*_pred)[v]); }
 		    ///\brief Returns a const reference to the node map that stores the
 		    ///distances of the nodes.
 		    ///
 		    ///Returns a const reference to the node map that stores the
 		    ///distances of the nodes calculated by the algorithm.
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    const DistMap &distMap() const { return *_dist;}
 		    ///\brief Returns a const reference to the node map that stores the
 		    ///predecessor arcs.
 		    ///
 		    ///Returns a const reference to the node map that stores the predecessor
 		    ///arcs, which form the DFS tree (forest).
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    const PredMap &predMap() const { return *_pred;}
 		    ///Checks if the given node. node is reached from the root(s).
 		    ///Returns \c true if \c v is reached from the root(s).
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    bool reached(Node v) const { return (*_reached)[v]; }
 		    ///@}
 		  };
 		  ///Default traits class of dfs() function.
 		  ///Default traits class of dfs() function.
 		  ///\tparam GR Digraph type.
 		  template<class GR>
 		  struct DfsWizardDefaultTraits
+		  {
 		    ///The type of the digraph the algorithm runs on.
 		    typedef GR Digraph;
 		    ///\brief The type of the map that stores the predecessor
 		    ///arcs of the %DFS paths.
 		    ///
 		    ///The type of the map that stores the predecessor
 		    ///arcs of the %DFS paths.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
 		    ///Instantiates a PredMap.
 		    ///This function instantiates a PredMap.
 		    ///\param g is the digraph, to which we would like to define the
 		    ///PredMap.
 		    static PredMap *createPredMap(const Digraph &g)
+		    {
 		      return new PredMap(g);
+		    }
 		    ///The type of the map that indicates which nodes are processed.
 		    ///The type of the map that indicates which nodes are processed.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    ///By default, it is a NullMap.
 		    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
 		    ///Instantiates a ProcessedMap.
 		    ///This function instantiates a ProcessedMap.
 		    ///\param g is the digraph, to which
 		    ///we would like to define the ProcessedMap.
 		#ifdef DOXYGEN
 		    static ProcessedMap *createProcessedMap(const Digraph &g)
 		#else
 		    static ProcessedMap *createProcessedMap(const Digraph &)
 		#endif
+		    {
 		      return new ProcessedMap();
+		    }
 		    ///The type of the map that indicates which nodes are reached.
 		    ///The type of the map that indicates which nodes are reached.
 		    ///It must conform to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
 		    typedef typename Digraph::template NodeMap<bool> ReachedMap;
 		    ///Instantiates a ReachedMap.
 		    ///This function instantiates a ReachedMap.
 		    ///\param g is the digraph, to which
 		    ///we would like to define the ReachedMap.
 		    static ReachedMap *createReachedMap(const Digraph &g)
+		    {
 		      return new ReachedMap(g);
+		    }
 		    ///The type of the map that stores the distances of the nodes.
 		    ///The type of the map that stores the distances of the nodes.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename Digraph::template NodeMap<int> DistMap;
 		    ///Instantiates a DistMap.
 		    ///This function instantiates a DistMap.
 		    ///\param g is the digraph, to which we would like to define
 		    ///the DistMap
 		    static DistMap *createDistMap(const Digraph &g)
+		    {
 		      return new DistMap(g);
+		    }
 		    ///The type of the DFS paths.
 		    ///The type of the DFS paths.
 		    ///It must conform to the \ref concepts::Path "Path" concept.
 		    typedef lemon::Path<Digraph> Path;
 		  };
 		  /// Default traits class used by DfsWizard
 		  /// Default traits class used by DfsWizard.
 		  /// \tparam GR The type of the digraph.
 		  template<class GR>
 		  class DfsWizardBase : public DfsWizardDefaultTraits<GR>
+		  {
 		    typedef DfsWizardDefaultTraits<GR> Base;
 		  protected:
 		    //The type of the nodes in the digraph.
 		    typedef typename Base::Digraph::Node Node;
 		    //Pointer to the digraph the algorithm runs on.
 		    void *_g;
 		    //Pointer to the map of reached nodes.
 		    void *_reached;
 		    //Pointer to the map of processed nodes.
 		    void *_processed;
 		    //Pointer to the map of predecessors arcs.
 		    void *_pred;
 		    //Pointer to the map of distances.
 		    void *_dist;
 		    //Pointer to the DFS path to the target node.
 		    void *_path;
 		    //Pointer to the distance of the target node.
 		    int *_di;
 		    public:
 		    /// Constructor.
 		    /// This constructor does not require parameters, it initiates
 		    /// all of the attributes to \c 0.
 		    DfsWizardBase() : _g(0), _reached(0), _processed(0), _pred(0),
 		                      _dist(0), _path(0), _di(0) {}
 		    /// Constructor.
 		    /// This constructor requires one parameter,
 		    /// others are initiated to \c 0.
 		    /// \param g The digraph the algorithm runs on.
 		    DfsWizardBase(const GR &g) :
 		      _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
 		      _reached(0), _processed(0), _pred(0), _dist(0),  _path(0), _di(0) {}
 		  };
 		  /// Auxiliary class for the function-type interface of DFS algorithm.
 		  /// This auxiliary class is created to implement the
 		  /// \ref dfs() "function-type interface" of \ref Dfs algorithm.
 		  /// It does not have own \ref run(Node) "run()" method, it uses the
 		  /// functions and features of the plain \ref Dfs.
 		  ///
 		  /// This class should only be used through the \ref dfs() function,
 		  /// which makes it easier to use the algorithm.
 		  ///
 		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm.
 		  template<class TR>
 		  class DfsWizard : public TR
+		  {
 		    typedef TR Base;
 		    typedef typename TR::Digraph Digraph;
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::OutArcIt OutArcIt;
 		    typedef typename TR::PredMap PredMap;
 		    typedef typename TR::DistMap DistMap;
 		    typedef typename TR::ReachedMap ReachedMap;
 		    typedef typename TR::ProcessedMap ProcessedMap;
 		    typedef typename TR::Path Path;
 		  public:
 		    /// Constructor.
 		    DfsWizard() : TR() {}
 		    /// Constructor that requires parameters.
 		    /// Constructor that requires parameters.
 		    /// These parameters will be the default values for the traits class.
 		    /// \param g The digraph the algorithm runs on.
 		    DfsWizard(const Digraph &g) :
 		      TR(g) {}
 		    ///Copy constructor
 		    DfsWizard(const TR &b) : TR(b) {}
 		    ~DfsWizard() {}
 		    ///Runs DFS algorithm from the given source node.
 		    ///This method runs DFS algorithm from node \c s
 		    ///in order to compute the DFS path to each node.
 		    void run(Node s)
+		    {
 		      Dfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
 		      if (Base::_pred)
 		        alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
 		      if (Base::_dist)
 		        alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
 		      if (Base::_reached)
 		        alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
 		      if (Base::_processed)
 		        alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
 		      if (s!=INVALID)
 		        alg.run(s);
 		      else
 		        alg.run();
+		    }
 		    ///Finds the DFS path between \c s and \c t.
 		    ///This method runs 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.
 		    bool run(Node s, Node t)
+		    {
 		      Dfs<Digraph,TR> alg(*reinterpret_cast<const Digraph*>(Base::_g));
 		      if (Base::_pred)
 		        alg.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
 		      if (Base::_dist)
 		        alg.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
 		      if (Base::_reached)
 		        alg.reachedMap(*reinterpret_cast<ReachedMap*>(Base::_reached));
 		      if (Base::_processed)
 		        alg.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
 		      alg.run(s,t);
 		      if (Base::_path)
 		        *reinterpret_cast<Path*>(Base::_path) = alg.path(t);
 		      if (Base::_di)
 		        *Base::_di = alg.dist(t);
 		      return alg.reached(t);
+		      }
 		    ///Runs DFS algorithm to visit all nodes in the digraph.
 		    ///This method runs DFS algorithm in order to visit all nodes
 		    ///in the digraph.
 		    void run()
+		    {
 		      run(INVALID);
+		    }
 		    template<class T>
 		    struct SetPredMapBase : public Base {
 		      typedef T PredMap;
 		      static PredMap *createPredMap(const Digraph &) { return 0; };
 		      SetPredMapBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///the predecessor map.
 		    ///
 		    ///\ref named-templ-param "Named parameter" function for setting
 		    ///the map that stores the predecessor arcs of the nodes.
 		    template<class T>
 		    DfsWizard<SetPredMapBase<T> > predMap(const T &t)
+		    {
 		      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return DfsWizard<SetPredMapBase<T> >(*this);
+		    }
 		    template<class T>
 		    struct SetReachedMapBase : public Base {
 		      typedef T ReachedMap;
 		      static ReachedMap *createReachedMap(const Digraph &) { return 0; };
 		      SetReachedMapBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///the reached map.
 		    ///
 		    ///\ref named-templ-param "Named parameter" function for setting
 		    ///the map that indicates which nodes are reached.
 		    template<class T>
 		    DfsWizard<SetReachedMapBase<T> > reachedMap(const T &t)
+		    {
 		      Base::_reached=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return DfsWizard<SetReachedMapBase<T> >(*this);
+		    }
 		    template<class T>
 		    struct SetDistMapBase : public Base {
 		      typedef T DistMap;
 		      static DistMap *createDistMap(const Digraph &) { return 0; };
 		      SetDistMapBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///the distance map.
 		    ///
 		    ///\ref named-templ-param "Named parameter" function for setting
 		    ///the map that stores the distances of the nodes calculated
 		    ///by the algorithm.
 		    template<class T>
 		    DfsWizard<SetDistMapBase<T> > distMap(const T &t)
+		    {
 		      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return DfsWizard<SetDistMapBase<T> >(*this);
+		    }
 		    template<class T>
 		    struct SetProcessedMapBase : public Base {
 		      typedef T ProcessedMap;
 		      static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
 		      SetProcessedMapBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-func-param "Named parameter" for setting
 		    ///the processed map.
 		    ///
 		    ///\ref named-templ-param "Named parameter" function for setting
 		    ///the map that indicates which nodes are processed.
 		    template<class T>
 		    DfsWizard<SetProcessedMapBase<T> > processedMap(const T &t)
+		    {
 		      Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return DfsWizard<SetProcessedMapBase<T> >(*this);
+		    }
 		    template<class T>
 		    struct SetPathBase : public Base {
 		      typedef T Path;
 		      SetPathBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-func-param "Named parameter"
 		    ///for getting the DFS path to the target node.
 		    ///
 		    ///\ref named-func-param "Named parameter"
 		    ///for getting the DFS path to the target node.
 		    template<class T>
 		    DfsWizard<SetPathBase<T> > path(const T &t)
+		    {
 		      Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return DfsWizard<SetPathBase<T> >(*this);
+		    }
 		    ///\brief \ref named-func-param "Named parameter"
 		    ///for getting the distance of the target node.
 		    ///
 		    ///\ref named-func-param "Named parameter"
 		    ///for getting the distance of the target node.
 		    DfsWizard dist(const int &d)
+		    {
 		      Base::_di=const_cast<int*>(&d);
 		      return *this;
+		    }
 		  };
 		  ///Function-type interface for DFS algorithm.
 		  ///\ingroup search
 		  ///Function-type interface for DFS algorithm.
 		  ///
 		  ///This function also has several \ref named-func-param "named parameters",
 		  ///they are declared as the members of class \ref DfsWizard.
 		  ///The following examples show how to use these parameters.
 		  ///\code
 		  ///  // Compute the DFS tree
 		  ///  dfs(g).predMap(preds).distMap(dists).run(s);
 		  ///
 		  ///  // Compute the DFS path from s to t
 		  ///  bool reached = dfs(g).path(p).dist(d).run(s,t);
 		  ///\endcode
 		  ///\warning Don't forget to put the \ref DfsWizard::run(Node) "run()"
 		  ///to the end of the parameter list.
 		  ///\sa DfsWizard
 		  ///\sa Dfs
 		  template<class GR>
 		  DfsWizard<DfsWizardBase<GR> >
 		  dfs(const GR &digraph)
+		  {
 		    return DfsWizard<DfsWizardBase<GR> >(digraph);
+		  }
 		#ifdef DOXYGEN
 		  /// \brief Visitor class for DFS.
 		  ///
 		  /// This class defines the interface of the DfsVisit events, and
 		  /// it could be the base of a real visitor class.
 		  template <typename GR>
 		  struct DfsVisitor {
 		    typedef GR Digraph;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::Node Node;
 		    /// \brief Called for the source node of the DFS.
 		    ///
 		    /// This function is called for the source node of the DFS.
 		    void start(const Node& node) {}
 		    /// \brief Called when the source node is leaved.
 		    ///
 		    /// This function is called when the source node is leaved.
 		    void stop(const Node& node) {}
 		    /// \brief Called when a node is reached first time.
 		    ///
 		    /// This function is called when a node is reached first time.
 		    void reach(const Node& node) {}
 		    /// \brief Called when an arc reaches a new node.
 		    ///
 		    /// This function is called when the DFS finds an arc whose target node
 		    /// is not reached yet.
 		    void discover(const Arc& arc) {}
 		    /// \brief Called when an arc is examined but its target node is
 		    /// already discovered.
 		    ///
 		    /// This function is called when an arc is examined but its target node is
 		    /// already discovered.
 		    void examine(const Arc& arc) {}
 		    /// \brief Called when the DFS steps back from a node.
 		    ///
 		    /// This function is called when the DFS steps back from a node.
 		    void leave(const Node& node) {}
 		    /// \brief Called when the DFS steps back on an arc.
 		    ///
 		    /// This function is called when the DFS steps back on an arc.
 		    void backtrack(const Arc& arc) {}
 		  };
 		#else
 		  template <typename GR>
 		  struct DfsVisitor {
 		    typedef GR Digraph;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::Node Node;
 		    void start(const Node&) {}
 		    void stop(const Node&) {}
 		    void reach(const Node&) {}
 		    void discover(const Arc&) {}
 		    void examine(const Arc&) {}
 		    void leave(const Node&) {}
 		    void backtrack(const Arc&) {}
 		    template <typename _Visitor>
 		    struct Constraints {
 		      void constraints() {
 		        Arc arc;
 		        Node node;
 		        visitor.start(node);
 		        visitor.stop(arc);
 		        visitor.reach(node);
 		        visitor.discover(arc);
 		        visitor.examine(arc);
 		        visitor.leave(node);
 		        visitor.backtrack(arc);
+		      }
 		      _Visitor& visitor;
 		    };
 		  };
 		#endif
 		  /// \brief Default traits class of DfsVisit class.
 		  ///
 		  /// Default traits class of DfsVisit class.
 		  /// \tparam _Digraph The type of the digraph the algorithm runs on.
 		  template<class GR>
 		  struct DfsVisitDefaultTraits {
 		    /// \brief The type of the digraph the algorithm runs on.
 		    typedef GR Digraph;
 		    /// \brief The type of the map that indicates which nodes are reached.
 		    ///
 		    /// The type of the map that indicates which nodes are reached.
 		    /// It must conform to the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
 		    typedef typename Digraph::template NodeMap<bool> ReachedMap;
 		    /// \brief Instantiates a ReachedMap.
 		    ///
 		    /// This function instantiates a ReachedMap.
 		    /// \param digraph is the digraph, to which
 		    /// we would like to define the ReachedMap.
 		    static ReachedMap *createReachedMap(const Digraph &digraph) {
 		      return new ReachedMap(digraph);
+		    }
 		  };
 		  /// \ingroup search
 		  ///
 		  /// \brief DFS algorithm class with visitor interface.
 		  ///
 		  /// 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
 		  /// the member functions of the \c Visitor class on every DFS event.
 		  ///
 		  /// This interface of the DFS algorithm should be used in special cases
 		  /// when extra actions have to be performed in connection with certain
 		  /// events of the DFS algorithm. Otherwise consider to use Dfs or dfs()
 		  /// instead.
 		  ///
 		  /// \tparam GR The type of the digraph the algorithm runs on.
 		  /// The default type is \ref ListDigraph.
 		  /// The value of GR is not used directly by \ref DfsVisit,
 		  /// it is only passed to \ref DfsVisitDefaultTraits.
 		  /// \tparam VS The Visitor type that is used by the algorithm.
 		  /// \ref DfsVisitor "DfsVisitor<GR>" 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 TR Traits class to set various data types used by the
 		  /// algorithm. The default traits class is
 		  /// \ref DfsVisitDefaultTraits "DfsVisitDefaultTraits<GR>".
 		  /// See \ref DfsVisitDefaultTraits for the documentation of
-		  /// a DFS visit traits class.
+		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm. By default, it is \ref DfsVisitDefaultTraits
 		  /// "DfsVisitDefaultTraits<GR>".
 		  /// In most cases, this parameter should not be set directly,
 		  /// consider to use the named template parameters instead.
 		#ifdef DOXYGEN
 		  template <typename GR, typename VS, typename TR>
 		#else
 		  template <typename GR = ListDigraph,
 		            typename VS = DfsVisitor<GR>,
 		            typename TR = DfsVisitDefaultTraits<GR> >
 		#endif
 		  class DfsVisit {
 		  public:
 		    ///The traits class.
 		    typedef TR Traits;
 		    ///The type of the digraph the algorithm runs on.
 		    typedef typename Traits::Digraph Digraph;
 		    ///The visitor type used by the algorithm.
 		    typedef VS Visitor;
 		    ///The type of the map that indicates which nodes are reached.
 		    typedef typename Traits::ReachedMap ReachedMap;
 		  private:
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::OutArcIt OutArcIt;
 		    //Pointer to the underlying digraph.
 		    const Digraph *_digraph;
 		    //Pointer to the visitor object.
 		    Visitor *_visitor;
 		    //Pointer to the map of reached status of the nodes.
 		    ReachedMap *_reached;
 		    //Indicates if _reached is locally allocated (true) or not.
 		    bool local_reached;
 		    std::vector<typename Digraph::Arc> _stack;
 		    int _stack_head;
 		    //Creates the maps if necessary.
 		    void create_maps() {
 		      if(!_reached) {
 		        local_reached = true;
 		        _reached = Traits::createReachedMap(*_digraph);
+		      }
+		    }
 		  protected:
 		    DfsVisit() {}
 		  public:
 		    typedef DfsVisit Create;
 		    /// \name Named Template Parameters
 		    ///@{
 		    template <class T>
 		    struct SetReachedMapTraits : public Traits {
 		      typedef T ReachedMap;
 		      static ReachedMap *createReachedMap(const Digraph &digraph) {
 		        LEMON_ASSERT(false, "ReachedMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// ReachedMap type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting ReachedMap type.
 		    template <class T>
 		    struct SetReachedMap : public DfsVisit< Digraph, Visitor,
 		                                            SetReachedMapTraits<T> > {
 		      typedef DfsVisit< Digraph, Visitor, SetReachedMapTraits<T> > Create;
 		    };
 		    ///@}
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// Constructor.
 		    ///
 		    /// \param digraph The digraph the algorithm runs on.
 		    /// \param visitor The visitor object of the algorithm.
 		    DfsVisit(const Digraph& digraph, Visitor& visitor)
 		      : _digraph(&digraph), _visitor(&visitor),
 		        _reached(0), local_reached(false) {}
 		    /// \brief Destructor.
 		    ~DfsVisit() {
 		      if(local_reached) delete _reached;
+		    }
 		    /// \brief Sets the map that indicates which nodes are reached.
 		    ///
 		    /// Sets the map that indicates which nodes are reached.
 		    /// If you don't use this function before calling \ref run(Node) "run()"
 		    /// or \ref init(), an instance will be allocated automatically.
 		    /// The destructor deallocates this automatically allocated map,
 		    /// of course.
 		    /// \return <tt> (*this) </tt>
 		    DfsVisit &reachedMap(ReachedMap &m) {
 		      if(local_reached) {
 		        delete _reached;
 		        local_reached=false;
+		      }
 		      _reached = &m;
 		      return *this;
+		    }
 		  public:
 		    /// \name Execution Control
 		    /// The simplest way to execute the DFS algorithm is to use one of the
 		    /// member functions called \ref run(Node) "run()".\n
 		    /// If you need better control on the execution, you have to call
 		    /// \ref init() first, then you can add a source node with \ref addSource()
 		    /// and perform the actual computation with \ref start().
 		    /// This procedure can be repeated if there are nodes that have not
 		    /// been reached.
 		    /// @{
 		    /// \brief Initializes the internal data structures.
 		    ///
 		    /// Initializes the internal data structures.
 		    void init() {
 		      create_maps();
 		      _stack.resize(countNodes(*_digraph));
 		      _stack_head = -1;
 		      for (NodeIt u(*_digraph) ; u != INVALID ; ++u) {
 		        _reached->set(u, false);
+		      }
+		    }
 		    /// \brief Adds a new source node.
 		    ///
 		    /// Adds a new source node to the set of nodes to be processed.
 		    ///
 		    /// \pre The stack must be empty. Otherwise the algorithm gives
 		    /// wrong results. (One of the outgoing arcs of all the source nodes
 		    /// except for the last one will not be visited and distances will
 		    /// also be wrong.)
 		    void addSource(Node s)
+		    {
 		      LEMON_DEBUG(emptyQueue(), "The stack is not empty.");
 		      if(!(*_reached)[s]) {
 		          _reached->set(s,true);
 		          _visitor->start(s);
 		          _visitor->reach(s);
 		          Arc e;
 		          _digraph->firstOut(e, s);
 		          if (e != INVALID) {
 		            _stack[++_stack_head] = e;
 		          } else {
 		            _visitor->leave(s);
 		            _visitor->stop(s);
+		          }
+		        }
+		    }
 		    /// \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.
 		    ///
 		    /// 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();
+		    }
 		    /// \brief 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) {
 		      while ( !emptyQueue() && _digraph->target(_stack[_stack_head]) != t )
 		        processNextArc();
+		    }
 		    /// \brief 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 <typename AM>
 		    Arc start(const AM &am) {
 		      while ( !emptyQueue() && !am[_stack[_stack_head]] )
 		        processNextArc();
 		      return emptyQueue() ? INVALID : _stack[_stack_head];
+		    }
 		    /// \brief 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();
+		    }
 		    /// \brief 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);
+		    }
 		    /// \brief Runs the algorithm to visit all nodes in the digraph.
 		    /// This method runs the %DFS algorithm in order to visit all nodes
 		    /// in the digraph.
 		    ///
 		    /// \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(*_digraph); it != INVALID; ++it) {
 		        if (!reached(it)) {
 		          addSource(it);
 		          start();
+		        }
+		      }
+		    }
 		    ///@}
 		    /// \name Query Functions
 		    /// The results of the DFS algorithm can be obtained using these
 		    /// functions.\n
 		    /// Either \ref run(Node) "run()" or \ref start() should be called
 		    /// before using them.
 		    ///@{
 		    /// \brief Checks if the given node is reached from the root(s).
 		    ///
 		    /// Returns \c true if \c v is reached from the root(s).
 		    ///
 		    /// \pre Either \ref run(Node) "run()" or \ref init()
 		    /// must be called before using this function.
 		    bool reached(Node v) const { return (*_reached)[v]; }
 		    ///@}
 		  };
 		} //END OF NAMESPACE LEMON
 		#endif

lemon/dijkstra.h

Show inline comments

 		/* -*- 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_DIJKSTRA_H
 		#define LEMON_DIJKSTRA_H
 		///\ingroup shortest_path
 		///\file
 		///\brief Dijkstra algorithm.
 		#include <limits>
 		#include <lemon/list_graph.h>
 		#include <lemon/bin_heap.h>
 		#include <lemon/bits/path_dump.h>
 		#include <lemon/core.h>
 		#include <lemon/error.h>
 		#include <lemon/maps.h>
 		#include <lemon/path.h>
 		namespace lemon {
 		  /// \brief Default operation traits for the Dijkstra algorithm class.
 		  ///
 		  /// This operation traits class defines all computational operations and
 		  /// constants which are used in the Dijkstra algorithm.
 		  template <typename V>
 		  struct DijkstraDefaultOperationTraits {
 		    /// \e
 		    typedef V Value;
 		    /// \brief Gives back the zero value of the type.
 		    static Value zero() {
 		      return static_cast<Value>(0);
+		    }
 		    /// \brief Gives back the sum of the given two elements.
 		    static Value plus(const Value& left, const Value& right) {
 		      return left + right;
+		    }
 		    /// \brief Gives back true only if the first value is less than the second.
 		    static bool less(const Value& left, const Value& right) {
 		      return left < right;
+		    }
 		  };
 		  ///Default traits class of Dijkstra class.
 		  ///Default traits class of Dijkstra class.
 		  ///\tparam GR The type of the digraph.
 		  ///\tparam LEN The type of the length map.
 		  template<typename GR, typename LEN>
 		  struct DijkstraDefaultTraits
+		  {
 		    ///The type of the digraph the algorithm runs on.
 		    typedef GR Digraph;
 		    ///The type of the map that stores the arc lengths.
 		    ///The type of the map that stores the arc lengths.
 		    ///It must conform to the \ref concepts::ReadMap "ReadMap" concept.
 		    typedef LEN LengthMap;
 		    ///The type of the arc lengths.
 		    typedef typename LEN::Value Value;
 		    /// Operation traits for %Dijkstra algorithm.
 		    /// This class defines the operations that are used in the algorithm.
 		    /// \see DijkstraDefaultOperationTraits
 		    typedef DijkstraDefaultOperationTraits<Value> OperationTraits;
 		    /// The cross reference type used by the heap.
 		    /// The cross reference type used by the heap.
 		    /// Usually it is \c Digraph::NodeMap<int>.
 		    typedef typename Digraph::template NodeMap<int> HeapCrossRef;
 		    ///Instantiates a \c HeapCrossRef.
 		    ///This function instantiates a \ref HeapCrossRef.
 		    /// \param g is the digraph, to which we would like to define the
 		    /// \ref HeapCrossRef.
 		    static HeapCrossRef *createHeapCrossRef(const Digraph &g)
+		    {
 		      return new HeapCrossRef(g);
+		    }
 		    ///The heap type used by the %Dijkstra algorithm.
 		    ///The heap type used by the Dijkstra algorithm.
 		    ///
 		    ///\sa BinHeap
 		    ///\sa Dijkstra
 		    typedef BinHeap<typename LEN::Value, HeapCrossRef, std::less<Value> > Heap;
 		    ///Instantiates a \c Heap.
 		    ///This function instantiates a \ref Heap.
 		    static Heap *createHeap(HeapCrossRef& r)
+		    {
 		      return new Heap(r);
+		    }
 		    ///\brief The type of the map that stores the predecessor
 		    ///arcs of the shortest paths.
 		    ///
 		    ///The type of the map that stores the predecessor
 		    ///arcs of the shortest paths.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
 		    ///Instantiates a \c PredMap.
 		    ///This function instantiates a \ref PredMap.
 		    ///\param g is the digraph, to which we would like to define the
 		    ///\ref PredMap.
 		    static PredMap *createPredMap(const Digraph &g)
+		    {
 		      return new PredMap(g);
+		    }
 		    ///The type of the map that indicates which nodes are processed.
 		    ///The type of the map that indicates which nodes are processed.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    ///By default, it is a NullMap.
 		    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
 		    ///Instantiates a \c ProcessedMap.
 		    ///This function instantiates a \ref ProcessedMap.
 		    ///\param g is the digraph, to which
 		    ///we would like to define the \ref ProcessedMap.
 		#ifdef DOXYGEN
 		    static ProcessedMap *createProcessedMap(const Digraph &g)
 		#else
 		    static ProcessedMap *createProcessedMap(const Digraph &)
 		#endif
+		    {
 		      return new ProcessedMap();
+		    }
 		    ///The type of the map that stores the distances of the nodes.
 		    ///The type of the map that stores the distances of the nodes.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename Digraph::template NodeMap<typename LEN::Value> DistMap;
 		    ///Instantiates a \c DistMap.
 		    ///This function instantiates a \ref DistMap.
 		    ///\param g is the digraph, to which we would like to define
 		    ///the \ref DistMap.
 		    static DistMap *createDistMap(const Digraph &g)
+		    {
 		      return new DistMap(g);
+		    }
 		  };
 		  ///%Dijkstra algorithm class.
 		  /// \ingroup shortest_path
 		  ///This class provides an efficient implementation of the %Dijkstra algorithm.
 		  ///
 		  ///The %Dijkstra algorithm solves the single-source shortest path problem
 		  ///when all arc lengths are non-negative. If there are negative lengths,
 		  ///the BellmanFord algorithm should be used instead.
 		  ///
 		  ///The arc lengths are passed to the algorithm using a
 		  ///\ref concepts::ReadMap "ReadMap",
 		  ///so it is easy to change it to any kind of length.
 		  ///The type of the length is determined by the
 		  ///\ref concepts::ReadMap::Value "Value" of the length map.
 		  ///It is also possible to change the underlying priority heap.
 		  ///
 		  ///There is also a \ref dijkstra() "function-type interface" for the
 		  ///%Dijkstra algorithm, which is convenient in the simplier cases and
 		  ///it can be used easier.
 		  ///
 		  ///\tparam GR The type of the digraph the algorithm runs on.
 		  ///The default type is \ref ListDigraph.
 		  ///\tparam LEN A \ref concepts::ReadMap "readable" arc map that specifies
 		  ///the lengths of the arcs.
 		  ///It is read once for each arc, so the map may involve in
 		  ///relatively time consuming process to compute the arc lengths if
 		  ///it is necessary. The default map type is \ref
 		  ///concepts::Digraph::ArcMap "GR::ArcMap<int>".
 		  ///\tparam TR The traits class that defines various types used by the
 		  ///algorithm. By default, it is \ref DijkstraDefaultTraits
 		  ///"DijkstraDefaultTraits<GR, LEN>".
 		  ///In most cases, this parameter should not be set directly,
 		  ///consider to use the named template parameters instead.
 		#ifdef DOXYGEN
 		  template <typename GR, typename LEN, typename TR>
 		#else
 		  template <typename GR=ListDigraph,
 		            typename LEN=typename GR::template ArcMap<int>,
 		            typename TR=DijkstraDefaultTraits<GR,LEN> >
 		#endif
 		  class Dijkstra {
 		  public:
 		    ///The type of the digraph the algorithm runs on.
 		    typedef typename TR::Digraph Digraph;
 		    ///The type of the arc lengths.
 		    typedef typename TR::Value Value;
 		    ///The type of the map that stores the arc lengths.
 		    typedef typename TR::LengthMap LengthMap;
 		    ///\brief The type of the map that stores the predecessor arcs of the
 		    ///shortest paths.
 		    typedef typename TR::PredMap PredMap;
 		    ///The type of the map that stores the distances of the nodes.
 		    typedef typename TR::DistMap DistMap;
 		    ///The type of the map that indicates which nodes are processed.
 		    typedef typename TR::ProcessedMap ProcessedMap;
 		    ///The type of the paths.
 		    typedef PredMapPath<Digraph, PredMap> Path;
 		    ///The cross reference type used for the current heap.
 		    typedef typename TR::HeapCrossRef HeapCrossRef;
 		    ///The heap type used by the algorithm.
 		    typedef typename TR::Heap Heap;
 		    ///\brief The \ref DijkstraDefaultOperationTraits "operation traits class"
 		    ///of the algorithm.
 		    typedef typename TR::OperationTraits OperationTraits;
 		    ///The \ref DijkstraDefaultTraits "traits class" of the algorithm.
 		    typedef TR Traits;
 		  private:
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::OutArcIt OutArcIt;
 		    //Pointer to the underlying digraph.
 		    const Digraph *G;
 		    //Pointer to the length map.
 		    const LengthMap *_length;
 		    //Pointer to the map of predecessors arcs.
 		    PredMap *_pred;
 		    //Indicates if _pred is locally allocated (true) or not.
 		    bool local_pred;
 		    //Pointer to the map of distances.
 		    DistMap *_dist;
 		    //Indicates if _dist is locally allocated (true) or not.
 		    bool local_dist;
 		    //Pointer to the map of processed status of the nodes.
 		    ProcessedMap *_processed;
 		    //Indicates if _processed is locally allocated (true) or not.
 		    bool local_processed;
 		    //Pointer to the heap cross references.
 		    HeapCrossRef *_heap_cross_ref;
 		    //Indicates if _heap_cross_ref is locally allocated (true) or not.
 		    bool local_heap_cross_ref;
 		    //Pointer to the heap.
 		    Heap *_heap;
 		    //Indicates if _heap is locally allocated (true) or not.
 		    bool local_heap;
 		    //Creates the maps if necessary.
 		    void create_maps()
+		    {
 		      if(!_pred) {
 		        local_pred = true;
 		        _pred = Traits::createPredMap(*G);
+		      }
 		      if(!_dist) {
 		        local_dist = true;
 		        _dist = Traits::createDistMap(*G);
+		      }
 		      if(!_processed) {
 		        local_processed = true;
 		        _processed = Traits::createProcessedMap(*G);
+		      }
 		      if (!_heap_cross_ref) {
 		        local_heap_cross_ref = true;
 		        _heap_cross_ref = Traits::createHeapCrossRef(*G);
+		      }
 		      if (!_heap) {
 		        local_heap = true;
 		        _heap = Traits::createHeap(*_heap_cross_ref);
+		      }
+		    }
 		  public:
 		    typedef Dijkstra Create;
 		    ///\name Named Template Parameters
 		    ///@{
 		    template <class T>
 		    struct SetPredMapTraits : public Traits {
 		      typedef T PredMap;
 		      static PredMap *createPredMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "PredMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c PredMap type.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c PredMap type.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    template <class T>
 		    struct SetPredMap
 		      : public Dijkstra< Digraph, LengthMap, SetPredMapTraits<T> > {
 		      typedef Dijkstra< Digraph, LengthMap, SetPredMapTraits<T> > Create;
 		    };
 		    template <class T>
 		    struct SetDistMapTraits : public Traits {
 		      typedef T DistMap;
 		      static DistMap *createDistMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "DistMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c DistMap type.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c DistMap type.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    template <class T>
 		    struct SetDistMap
 		      : public Dijkstra< Digraph, LengthMap, SetDistMapTraits<T> > {
 		      typedef Dijkstra< Digraph, LengthMap, SetDistMapTraits<T> > Create;
 		    };
 		    template <class T>
 		    struct SetProcessedMapTraits : public Traits {
 		      typedef T ProcessedMap;
 		      static ProcessedMap *createProcessedMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "ProcessedMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c ProcessedMap type.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c ProcessedMap type.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    template <class T>
 		    struct SetProcessedMap
 		      : public Dijkstra< Digraph, LengthMap, SetProcessedMapTraits<T> > {
 		      typedef Dijkstra< Digraph, LengthMap, SetProcessedMapTraits<T> > Create;
 		    };
 		    struct SetStandardProcessedMapTraits : public Traits {
 		      typedef typename Digraph::template NodeMap<bool> ProcessedMap;
 		      static ProcessedMap *createProcessedMap(const Digraph &g)
+		      {
 		        return new ProcessedMap(g);
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.
 		    ///If you don't set it explicitly, it will be automatically allocated.
 		    struct SetStandardProcessedMap
 		      : public Dijkstra< Digraph, LengthMap, SetStandardProcessedMapTraits > {
 		      typedef Dijkstra< Digraph, LengthMap, SetStandardProcessedMapTraits >
 		      Create;
 		    };
 		    template <class H, class CR>
 		    struct SetHeapTraits : public Traits {
 		      typedef CR HeapCrossRef;
 		      typedef H Heap;
 		      static HeapCrossRef *createHeapCrossRef(const Digraph &) {
 		        LEMON_ASSERT(false, "HeapCrossRef is not initialized");
 		        return 0; // ignore warnings
+		      }
 		      static Heap *createHeap(HeapCrossRef &)
+		      {
 		        LEMON_ASSERT(false, "Heap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///heap and cross reference types
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting heap and cross
 		    ///reference types. If this named parameter is used, then external
 		    ///heap and cross reference objects must be passed to the algorithm
 		    ///using the \ref heap() function before calling \ref run(Node) "run()"
 		    ///or \ref init().
 		    ///\sa SetStandardHeap
 		    template <class H, class CR = typename Digraph::template NodeMap<int> >
 		    struct SetHeap
 		      : public Dijkstra< Digraph, LengthMap, SetHeapTraits<H, CR> > {
 		      typedef Dijkstra< Digraph, LengthMap, SetHeapTraits<H, CR> > Create;
 		    };
 		    template <class H, class CR>
 		    struct SetStandardHeapTraits : public Traits {
 		      typedef CR HeapCrossRef;
 		      typedef H Heap;
 		      static HeapCrossRef *createHeapCrossRef(const Digraph &G) {
 		        return new HeapCrossRef(G);
+		      }
 		      static Heap *createHeap(HeapCrossRef &R)
+		      {
 		        return new Heap(R);
+		      }
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///heap and cross reference types with automatic allocation
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting heap and cross
 		    ///reference types with automatic allocation.
 		    ///They should have standard constructor interfaces to be able to
 		    ///automatically created by the algorithm (i.e. the digraph should be
 		    ///passed to the constructor of the cross reference and the cross
 		    ///reference should be passed to the constructor of the heap).
 		    ///However, external heap and cross reference objects could also be
 		    ///passed to the algorithm using the \ref heap() function before
 		    ///calling \ref run(Node) "run()" or \ref init().
 		    ///\sa SetHeap
 		    template <class H, class CR = typename Digraph::template NodeMap<int> >
 		    struct SetStandardHeap
 		      : public Dijkstra< Digraph, LengthMap, SetStandardHeapTraits<H, CR> > {
 		      typedef Dijkstra< Digraph, LengthMap, SetStandardHeapTraits<H, CR> >
 		      Create;
 		    };
 		    template <class T>
 		    struct SetOperationTraitsTraits : public Traits {
 		      typedef T OperationTraits;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    ///\c OperationTraits type
 		    ///
 		    ///\ref named-templ-param "Named parameter" for setting
 		    ///\c OperationTraits type.
 		    /// For more information, see \ref DijkstraDefaultOperationTraits.
 		    template <class T>
 		    struct SetOperationTraits
 		      : public Dijkstra<Digraph, LengthMap, SetOperationTraitsTraits<T> > {
 		      typedef Dijkstra<Digraph, LengthMap, SetOperationTraitsTraits<T> >
 		      Create;
 		    };
 		    ///@}
 		  protected:
 		    Dijkstra() {}
 		  public:
 		    ///Constructor.
 		    ///Constructor.
 		    ///\param g The digraph the algorithm runs on.
 		    ///\param length The length map used by the algorithm.
 		    Dijkstra(const Digraph& g, const LengthMap& length) :
 		      G(&g), _length(&length),
 		      _pred(NULL), local_pred(false),
 		      _dist(NULL), local_dist(false),
 		      _processed(NULL), local_processed(false),
 		      _heap_cross_ref(NULL), local_heap_cross_ref(false),
 		      _heap(NULL), local_heap(false)
 		    { }
 		    ///Destructor.
 		    ~Dijkstra()
+		    {
 		      if(local_pred) delete _pred;
 		      if(local_dist) delete _dist;
 		      if(local_processed) delete _processed;
 		      if(local_heap_cross_ref) delete _heap_cross_ref;
 		      if(local_heap) delete _heap;
+		    }
 		    ///Sets the length map.
 		    ///Sets the length map.
 		    ///\return <tt> (*this) </tt>
 		    Dijkstra &lengthMap(const LengthMap &m)
+		    {
 		      _length = &m;
 		      return *this;
+		    }
 		    ///Sets the map that stores the predecessor arcs.
 		    ///Sets the map that stores the predecessor arcs.
 		    ///If you don't use this function before calling \ref run(Node) "run()"
 		    ///or \ref init(), an instance will be allocated automatically.
 		    ///The destructor deallocates this automatically allocated map,
 		    ///of course.
 		    ///\return <tt> (*this) </tt>
 		    Dijkstra &predMap(PredMap &m)
+		    {
 		      if(local_pred) {
 		        delete _pred;
 		        local_pred=false;
+		      }
 		      _pred = &m;
 		      return *this;
+		    }
 		    ///Sets the map that indicates which nodes are processed.
 		    ///Sets the map that indicates which nodes are processed.
 		    ///If you don't use this function before calling \ref run(Node) "run()"
 		    ///or \ref init(), an instance will be allocated automatically.
 		    ///The destructor deallocates this automatically allocated map,
 		    ///of course.
 		    ///\return <tt> (*this) </tt>
 		    Dijkstra &processedMap(ProcessedMap &m)
+		    {
 		      if(local_processed) {
 		        delete _processed;
 		        local_processed=false;
+		      }
 		      _processed = &m;
 		      return *this;
+		    }
 		    ///Sets the map that stores the distances of the nodes.
 		    ///Sets the map that stores the distances of the nodes calculated by the
 		    ///algorithm.
 		    ///If you don't use this function before calling \ref run(Node) "run()"
 		    ///or \ref init(), an instance will be allocated automatically.
 		    ///The destructor deallocates this automatically allocated map,
 		    ///of course.
 		    ///\return <tt> (*this) </tt>
 		    Dijkstra &distMap(DistMap &m)
+		    {
 		      if(local_dist) {
 		        delete _dist;
 		        local_dist=false;
+		      }
 		      _dist = &m;
 		      return *this;
+		    }
 		    ///Sets the heap and the cross reference used by algorithm.
 		    ///Sets the heap and the cross reference used by algorithm.
 		    ///If you don't use this function before calling \ref run(Node) "run()"
 		    ///or \ref init(), heap and cross reference instances will be
 		    ///allocated automatically.
 		    ///The destructor deallocates these automatically allocated objects,
 		    ///of course.
 		    ///\return <tt> (*this) </tt>
 		    Dijkstra &heap(Heap& hp, HeapCrossRef &cr)
+		    {
 		      if(local_heap_cross_ref) {
 		        delete _heap_cross_ref;
 		        local_heap_cross_ref=false;
+		      }
 		      _heap_cross_ref = &cr;
 		      if(local_heap) {
 		        delete _heap;
 		        local_heap=false;
+		      }
 		      _heap = &hp;
 		      return *this;
+		    }
 		  private:
 		    void finalizeNodeData(Node v,Value dst)
+		    {
 		      _processed->set(v,true);
 		      _dist->set(v, dst);
+		    }
 		  public:
 		    ///\name Execution Control
 		    ///The simplest way to execute the %Dijkstra algorithm is to use
 		    ///one of the member functions called \ref run(Node) "run()".\n
 		    ///If you need better control on the execution, you have to call
 		    ///\ref init() first, then you can add several source nodes with
 		    ///\ref addSource(). Finally the actual path computation can be
 		    ///performed with one of the \ref start() functions.
 		    ///@{
 		    ///\brief Initializes the internal data structures.
 		    ///
 		    ///Initializes the internal data structures.
 		    void init()
+		    {
 		      create_maps();
 		      _heap->clear();
 		      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
 		        _pred->set(u,INVALID);
 		        _processed->set(u,false);
 		        _heap_cross_ref->set(u,Heap::PRE_HEAP);
+		      }
+		    }
 		    ///Adds a new source node.
 		    ///Adds a new source node to the priority heap.
 		    ///The optional second parameter is the initial distance of the node.
 		    ///
 		    ///The function checks if the node has already been added to the heap and
 		    ///it is pushed to the heap only if either it was not in the heap
 		    ///or the shortest path found till then is shorter than \c dst.
 		    void addSource(Node s,Value dst=OperationTraits::zero())
+		    {
 		      if(_heap->state(s) != Heap::IN_HEAP) {
 		        _heap->push(s,dst);
 		      } else if(OperationTraits::less((*_heap)[s], dst)) {
 		        _heap->set(s,dst);
 		        _pred->set(s,INVALID);
+		      }
+		    }
 		    ///Processes the next node in the priority heap
 		    ///Processes the next node in the priority heap.
 		    ///
 		    ///\return The processed node.
 		    ///
 		    ///\warning The priority heap must not be empty.
 		    Node processNextNode()
+		    {
 		      Node v=_heap->top();
 		      Value oldvalue=_heap->prio();
 		      _heap->pop();
 		      finalizeNodeData(v,oldvalue);
 		      for(OutArcIt e(*G,v); e!=INVALID; ++e) {
 		        Node w=G->target(e);
 		        switch(_heap->state(w)) {
 		        case Heap::PRE_HEAP:
 		          _heap->push(w,OperationTraits::plus(oldvalue, (*_length)[e]));
 		          _pred->set(w,e);
 		          break;
 		        case Heap::IN_HEAP:
+		          {
 		            Value newvalue = OperationTraits::plus(oldvalue, (*_length)[e]);
 		            if ( OperationTraits::less(newvalue, (*_heap)[w]) ) {
 		              _heap->decrease(w, newvalue);
 		              _pred->set(w,e);
+		            }
+		          }
 		          break;
 		        case Heap::POST_HEAP:
 		          break;
+		        }
+		      }
 		      return v;
+		    }
 		    ///The next node to be processed.
 		    ///Returns the next node to be processed or \c INVALID if the
 		    ///priority heap is empty.
 		    Node nextNode() const
+		    {
 		      return !_heap->empty()?_heap->top():INVALID;
+		    }
 		    ///Returns \c false if there are nodes to be processed.
 		    ///Returns \c false if there are nodes to be processed
 		    ///in the priority heap.
 		    bool emptyQueue() const { return _heap->empty(); }
 		    ///Returns the number of the nodes to be processed.
 		    ///Returns the number of the nodes to be processed
 		    ///in the priority heap.
 		    int queueSize() const { return _heap->size(); }
 		    ///Executes the algorithm.
 		    ///Executes the algorithm.
 		    ///
 		    ///This method runs the %Dijkstra algorithm from the root node(s)
 		    ///in order to compute the shortest path to each node.
 		    ///
 		    ///The algorithm computes
 		    ///- the shortest path tree (forest),
 		    ///- the distance of each node from the root(s).
 		    ///
 		    ///\pre init() must be called and at least one 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.processNextNode();
 		    ///  }
 		    ///\endcode
 		    void start()
+		    {
 		      while ( !emptyQueue() ) processNextNode();
+		    }
 		    ///Executes the algorithm until the given target node is processed.
 		    ///Executes the algorithm until the given target node is processed.
 		    ///
 		    ///This method runs the %Dijkstra algorithm from the root node(s)
 		    ///in order to compute the shortest path to \c t.
 		    ///
 		    ///The algorithm computes
 		    ///- the shortest path to \c t,
 		    ///- the distance of \c t from the root(s).
 		    ///
 		    ///\pre init() must be called and at least one root node should be
 		    ///added with addSource() before using this function.
 		    void start(Node t)
+		    {
 		      while ( !_heap->empty() && _heap->top()!=t ) processNextNode();
 		      if ( !_heap->empty() ) {
 		        finalizeNodeData(_heap->top(),_heap->prio());
 		        _heap->pop();
+		      }
+		    }
 		    ///Executes the algorithm until a condition is met.
 		    ///Executes the algorithm until a condition is met.
 		    ///
 		    ///This method runs the %Dijkstra algorithm from the root node(s) in
 		    ///order to compute the shortest path to a node \c v with
 		    /// <tt>nm[v]</tt> true, if such a node can be found.
 		    ///
 		    ///\param nm A \c bool (or convertible) node map. The algorithm
 		    ///will stop when it reaches a node \c v with <tt>nm[v]</tt> true.
 		    ///
 		    ///\return The reached node \c v with <tt>nm[v]</tt> true or
 		    ///\c INVALID if no such node was found.
 		    ///
 		    ///\pre init() must be called and at least one root node should be
 		    ///added with addSource() before using this function.
 		    template<class NodeBoolMap>
 		    Node start(const NodeBoolMap &nm)
+		    {
 		      while ( !_heap->empty() && !nm[_heap->top()] ) processNextNode();
 		      if ( _heap->empty() ) return INVALID;
 		      finalizeNodeData(_heap->top(),_heap->prio());
 		      return _heap->top();
+		    }
 		    ///Runs the algorithm from the given source node.
 		    ///This method runs the %Dijkstra algorithm from node \c s
 		    ///in order to compute the shortest path to each node.
 		    ///
 		    ///The algorithm computes
 		    ///- the shortest path tree,
 		    ///- the distance of each node from the root.
 		    ///
 		    ///\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 shortest path between \c s and \c t.
 		    ///This method runs the %Dijkstra algorithm from node \c s
 		    ///in order to compute the shortest 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 (*_heap_cross_ref)[t] == Heap::POST_HEAP;
+		    }
 		    ///@}
 		    ///\name Query Functions
 		    ///The results of the %Dijkstra algorithm can be obtained using these
 		    ///functions.\n
 		    ///Either \ref run(Node) "run()" or \ref init() should be called
 		    ///before using them.
 		    ///@{
 		    ///The shortest path to the given node.
 		    ///Returns the shortest path to the given node from the root(s).
 		    ///
 		    ///\warning \c t should be reached from the root(s).
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    Path path(Node t) const { return Path(*G, *_pred, t); }
 		    ///The distance of the given node from the root(s).
 		    ///Returns the distance of the given node from the root(s).
 		    ///
 		    ///\warning If node \c v is not reached from the root(s), then
 		    ///the return value of this function is undefined.
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    Value dist(Node v) const { return (*_dist)[v]; }
 		    ///\brief Returns the 'previous arc' of the shortest path tree for
 		    ///the given node.
 		    ///
 		    ///This function returns the 'previous arc' of the shortest path
 		    ///tree for the node \c v, i.e. it returns the last arc of a
 		    ///shortest path from a root to \c v. It is \c INVALID if \c v
 		    ///is not reached from the root(s) or if \c v is a root.
 		    ///
 		    ///The shortest path tree used here is equal to the shortest path
 		    ///tree used in \ref predNode() and \ref predMap().
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    Arc predArc(Node v) const { return (*_pred)[v]; }
 		    ///\brief Returns the 'previous node' of the shortest path tree for
 		    ///the given node.
 		    ///
 		    ///This function returns the 'previous node' of the shortest path
 		    ///tree for the node \c v, i.e. it returns the last but one node
 		    ///of a shortest path from a root to \c v. It is \c INVALID
 		    ///if \c v is not reached from the root(s) or if \c v is a root.
 		    ///
 		    ///The shortest path tree used here is equal to the shortest path
 		    ///tree used in \ref predArc() and \ref predMap().
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    Node predNode(Node v) const { return (*_pred)[v]==INVALID ? INVALID:
 		                                  G->source((*_pred)[v]); }
 		    ///\brief Returns a const reference to the node map that stores the
 		    ///distances of the nodes.
 		    ///
 		    ///Returns a const reference to the node map that stores the distances
 		    ///of the nodes calculated by the algorithm.
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    const DistMap &distMap() const { return *_dist;}
 		    ///\brief Returns a const reference to the node map that stores the
 		    ///predecessor arcs.
 		    ///
 		    ///Returns a const reference to the node map that stores the predecessor
 		    ///arcs, which form the shortest path tree (forest).
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    const PredMap &predMap() const { return *_pred;}
 		    ///Checks if the given node is reached from the root(s).
 		    ///Returns \c true if \c v is reached from the root(s).
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    bool reached(Node v) const { return (*_heap_cross_ref)[v] !=
 		                                        Heap::PRE_HEAP; }
 		    ///Checks if a node is processed.
 		    ///Returns \c true if \c v is processed, i.e. the shortest
 		    ///path to \c v has already found.
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function.
 		    bool processed(Node v) const { return (*_heap_cross_ref)[v] ==
 		                                          Heap::POST_HEAP; }
 		    ///The current distance of the given node from the root(s).
 		    ///Returns the current distance of the given node from the root(s).
 		    ///It may be decreased in the following processes.
 		    ///
 		    ///\pre Either \ref run(Node) "run()" or \ref init()
 		    ///must be called before using this function and
 		    ///node \c v must be reached but not necessarily processed.
 		    Value currentDist(Node v) const {
 		      return processed(v) ? (*_dist)[v] : (*_heap)[v];
+		    }
 		    ///@}
 		  };
 		  ///Default traits class of dijkstra() function.
 		  ///Default traits class of dijkstra() function.
 		  ///\tparam GR The type of the digraph.
 		  ///\tparam LEN The type of the length map.
 		  template<class GR, class LEN>
 		  struct DijkstraWizardDefaultTraits
+		  {
 		    ///The type of the digraph the algorithm runs on.
 		    typedef GR Digraph;
 		    ///The type of the map that stores the arc lengths.
 		    ///The type of the map that stores the arc lengths.
 		    ///It must conform to the \ref concepts::ReadMap "ReadMap" concept.
 		    typedef LEN LengthMap;
 		    ///The type of the arc lengths.
 		    typedef typename LEN::Value Value;
 		    /// Operation traits for Dijkstra algorithm.
 		    /// This class defines the operations that are used in the algorithm.
 		    /// \see DijkstraDefaultOperationTraits
 		    typedef DijkstraDefaultOperationTraits<Value> OperationTraits;
 		    /// The cross reference type used by the heap.
 		    /// The cross reference type used by the heap.
 		    /// Usually it is \c Digraph::NodeMap<int>.
 		    typedef typename Digraph::template NodeMap<int> HeapCrossRef;
 		    ///Instantiates a \ref HeapCrossRef.
 		    ///This function instantiates a \ref HeapCrossRef.
 		    /// \param g is the digraph, to which we would like to define the
 		    /// HeapCrossRef.
 		    static HeapCrossRef *createHeapCrossRef(const Digraph &g)
+		    {
 		      return new HeapCrossRef(g);
+		    }
 		    ///The heap type used by the Dijkstra algorithm.
 		    ///The heap type used by the Dijkstra algorithm.
 		    ///
 		    ///\sa BinHeap
 		    ///\sa Dijkstra
 		    typedef BinHeap<Value, typename Digraph::template NodeMap<int>,
 		                    std::less<Value> > Heap;
 		    ///Instantiates a \ref Heap.
 		    ///This function instantiates a \ref Heap.
 		    /// \param r is the HeapCrossRef which is used.
 		    static Heap *createHeap(HeapCrossRef& r)
+		    {
 		      return new Heap(r);
+		    }
 		    ///\brief The type of the map that stores the predecessor
 		    ///arcs of the shortest paths.
 		    ///
 		    ///The type of the map that stores the predecessor
 		    ///arcs of the shortest paths.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
 		    ///Instantiates a PredMap.
 		    ///This function instantiates a PredMap.
 		    ///\param g is the digraph, to which we would like to define the
 		    ///PredMap.
 		    static PredMap *createPredMap(const Digraph &g)
+		    {
 		      return new PredMap(g);
+		    }
 		    ///The type of the map that indicates which nodes are processed.
 		    ///The type of the map that indicates which nodes are processed.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    ///By default, it is a NullMap.
 		    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
 		    ///Instantiates a ProcessedMap.
 		    ///This function instantiates a ProcessedMap.
 		    ///\param g is the digraph, to which
 		    ///we would like to define the ProcessedMap.
 		#ifdef DOXYGEN
 		    static ProcessedMap *createProcessedMap(const Digraph &g)
 		#else
 		    static ProcessedMap *createProcessedMap(const Digraph &)
 		#endif
+		    {
 		      return new ProcessedMap();
+		    }
 		    ///The type of the map that stores the distances of the nodes.
 		    ///The type of the map that stores the distances of the nodes.
 		    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
 		    typedef typename Digraph::template NodeMap<typename LEN::Value> DistMap;
 		    ///Instantiates a DistMap.
 		    ///This function instantiates a DistMap.
 		    ///\param g is the digraph, to which we would like to define
 		    ///the DistMap
 		    static DistMap *createDistMap(const Digraph &g)
+		    {
 		      return new DistMap(g);
+		    }
 		    ///The type of the shortest paths.
 		    ///The type of the shortest paths.
 		    ///It must conform to the \ref concepts::Path "Path" concept.
 		    typedef lemon::Path<Digraph> Path;
 		  };
 		  /// Default traits class used by DijkstraWizard
 		  /// Default traits class used by DijkstraWizard.
 		  /// \tparam GR The type of the digraph.
 		  /// \tparam LEN The type of the length map.
 		  template<typename GR, typename LEN>
 		  class DijkstraWizardBase : public DijkstraWizardDefaultTraits<GR,LEN>
+		  {
 		    typedef DijkstraWizardDefaultTraits<GR,LEN> Base;
 		  protected:
 		    //The type of the nodes in the digraph.
 		    typedef typename Base::Digraph::Node Node;
 		    //Pointer to the digraph the algorithm runs on.
 		    void *_g;
 		    //Pointer to the length map.
 		    void *_length;
 		    //Pointer to the map of processed nodes.
 		    void *_processed;
 		    //Pointer to the map of predecessors arcs.
 		    void *_pred;
 		    //Pointer to the map of distances.
 		    void *_dist;
 		    //Pointer to the shortest path to the target node.
 		    void *_path;
 		    //Pointer to the distance of the target node.
 		    void *_di;
 		  public:
 		    /// Constructor.
 		    /// This constructor does not require parameters, therefore it initiates
 		    /// all of the attributes to \c 0.
 		    DijkstraWizardBase() : _g(0), _length(0), _processed(0), _pred(0),
 		                           _dist(0), _path(0), _di(0) {}
 		    /// Constructor.
 		    /// This constructor requires two parameters,
 		    /// others are initiated to \c 0.
 		    /// \param g The digraph the algorithm runs on.
 		    /// \param l The length map.
 		    DijkstraWizardBase(const GR &g,const LEN &l) :
 		      _g(reinterpret_cast<void*>(const_cast<GR*>(&g))),
 		      _length(reinterpret_cast<void*>(const_cast<LEN*>(&l))),
 		      _processed(0), _pred(0), _dist(0), _path(0), _di(0) {}
 		  };
 		  /// Auxiliary class for the function-type interface of Dijkstra algorithm.
 		  /// This auxiliary class is created to implement the
 		  /// \ref dijkstra() "function-type interface" of \ref Dijkstra algorithm.
 		  /// It does not have own \ref run(Node) "run()" method, it uses the
 		  /// functions and features of the plain \ref Dijkstra.
 		  ///
 		  /// This class should only be used through the \ref dijkstra() function,
 		  /// which makes it easier to use the algorithm.
 		  ///
 		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm.
 		  template<class TR>
 		  class DijkstraWizard : public TR
+		  {
 		    typedef TR Base;
 		    typedef typename TR::Digraph Digraph;
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::OutArcIt OutArcIt;
 		    typedef typename TR::LengthMap LengthMap;
 		    typedef typename LengthMap::Value Value;
 		    typedef typename TR::PredMap PredMap;
 		    typedef typename TR::DistMap DistMap;
 		    typedef typename TR::ProcessedMap ProcessedMap;
 		    typedef typename TR::Path Path;
 		    typedef typename TR::Heap Heap;
 		  public:
 		    /// Constructor.
 		    DijkstraWizard() : TR() {}
 		    /// Constructor that requires parameters.
 		    /// Constructor that requires parameters.
 		    /// These parameters will be the default values for the traits class.
 		    /// \param g The digraph the algorithm runs on.
 		    /// \param l The length map.
 		    DijkstraWizard(const Digraph &g, const LengthMap &l) :
 		      TR(g,l) {}
 		    ///Copy constructor
 		    DijkstraWizard(const TR &b) : TR(b) {}
 		    ~DijkstraWizard() {}
 		    ///Runs Dijkstra algorithm from the given source node.
 		    ///This method runs %Dijkstra algorithm from the given source node
 		    ///in order to compute the shortest path to each node.
 		    void run(Node s)
+		    {
 		      Dijkstra<Digraph,LengthMap,TR>
 		        dijk(*reinterpret_cast<const Digraph*>(Base::_g),
 		             *reinterpret_cast<const LengthMap*>(Base::_length));
 		      if (Base::_pred)
 		        dijk.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
 		      if (Base::_dist)
 		        dijk.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
 		      if (Base::_processed)
 		        dijk.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
 		      dijk.run(s);
+		    }
 		    ///Finds the shortest path between \c s and \c t.
 		    ///This method runs the %Dijkstra algorithm from node \c s
 		    ///in order to compute the shortest path to node \c t
 		    ///(it stops searching when \c t is processed).
 		    ///
 		    ///\return \c true if \c t is reachable form \c s.
 		    bool run(Node s, Node t)
+		    {
 		      Dijkstra<Digraph,LengthMap,TR>
 		        dijk(*reinterpret_cast<const Digraph*>(Base::_g),
 		             *reinterpret_cast<const LengthMap*>(Base::_length));
 		      if (Base::_pred)
 		        dijk.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
 		      if (Base::_dist)
 		        dijk.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
 		      if (Base::_processed)
 		        dijk.processedMap(*reinterpret_cast<ProcessedMap*>(Base::_processed));
 		      dijk.run(s,t);
 		      if (Base::_path)
 		        *reinterpret_cast<Path*>(Base::_path) = dijk.path(t);
 		      if (Base::_di)
 		        *reinterpret_cast<Value*>(Base::_di) = dijk.dist(t);
 		      return dijk.reached(t);
+		    }
 		    template<class T>
 		    struct SetPredMapBase : public Base {
 		      typedef T PredMap;
 		      static PredMap *createPredMap(const Digraph &) { return 0; };
 		      SetPredMapBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///the predecessor map.
 		    ///
 		    ///\ref named-templ-param "Named parameter" function for setting
 		    ///the map that stores the predecessor arcs of the nodes.
 		    template<class T>
 		    DijkstraWizard<SetPredMapBase<T> > predMap(const T &t)
+		    {
 		      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return DijkstraWizard<SetPredMapBase<T> >(*this);
+		    }
 		    template<class T>
 		    struct SetDistMapBase : public Base {
 		      typedef T DistMap;
 		      static DistMap *createDistMap(const Digraph &) { return 0; };
 		      SetDistMapBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-templ-param "Named parameter" for setting
 		    ///the distance map.
 		    ///
 		    ///\ref named-templ-param "Named parameter" function for setting
 		    ///the map that stores the distances of the nodes calculated
 		    ///by the algorithm.
 		    template<class T>
 		    DijkstraWizard<SetDistMapBase<T> > distMap(const T &t)
+		    {
 		      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return DijkstraWizard<SetDistMapBase<T> >(*this);
+		    }
 		    template<class T>
 		    struct SetProcessedMapBase : public Base {
 		      typedef T ProcessedMap;
 		      static ProcessedMap *createProcessedMap(const Digraph &) { return 0; };
 		      SetProcessedMapBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-func-param "Named parameter" for setting
 		    ///the processed map.
 		    ///
 		    ///\ref named-templ-param "Named parameter" function for setting
 		    ///the map that indicates which nodes are processed.
 		    template<class T>
 		    DijkstraWizard<SetProcessedMapBase<T> > processedMap(const T &t)
+		    {
 		      Base::_processed=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return DijkstraWizard<SetProcessedMapBase<T> >(*this);
+		    }
 		    template<class T>
 		    struct SetPathBase : public Base {
 		      typedef T Path;
 		      SetPathBase(const TR &b) : TR(b) {}
 		    };
 		    ///\brief \ref named-func-param "Named parameter"
 		    ///for getting the shortest path to the target node.
 		    ///
 		    ///\ref named-func-param "Named parameter"
 		    ///for getting the shortest path to the target node.
 		    template<class T>
 		    DijkstraWizard<SetPathBase<T> > path(const T &t)
+		    {
 		      Base::_path=reinterpret_cast<void*>(const_cast<T*>(&t));
 		      return DijkstraWizard<SetPathBase<T> >(*this);
+		    }
 		    ///\brief \ref named-func-param "Named parameter"
 		    ///for getting the distance of the target node.
 		    ///
 		    ///\ref named-func-param "Named parameter"
 		    ///for getting the distance of the target node.
 		    DijkstraWizard dist(const Value &d)
+		    {
 		      Base::_di=reinterpret_cast<void*>(const_cast<Value*>(&d));
 		      return *this;
+		    }
 		  };
 		  ///Function-type interface for Dijkstra algorithm.
 		  /// \ingroup shortest_path
 		  ///Function-type interface for Dijkstra algorithm.
 		  ///
 		  ///This function also has several \ref named-func-param "named parameters",
 		  ///they are declared as the members of class \ref DijkstraWizard.
 		  ///The following examples show how to use these parameters.
 		  ///\code
 		  ///  // Compute shortest path from node s to each node
 		  ///  dijkstra(g,length).predMap(preds).distMap(dists).run(s);
 		  ///
 		  ///  // Compute shortest path from s to t
 		  ///  bool reached = dijkstra(g,length).path(p).dist(d).run(s,t);
 		  ///\endcode
 		  ///\warning Don't forget to put the \ref DijkstraWizard::run(Node) "run()"
 		  ///to the end of the parameter list.
 		  ///\sa DijkstraWizard
 		  ///\sa Dijkstra
 		  template<typename GR, typename LEN>
 		  DijkstraWizard<DijkstraWizardBase<GR,LEN> >
 		  dijkstra(const GR &digraph, const LEN &length)
+		  {
 		    return DijkstraWizard<DijkstraWizardBase<GR,LEN> >(digraph,length);
+		  }
 		} //END OF NAMESPACE LEMON
 		#endif

lemon/hartmann_orlin.h

Show inline comments

 		/* -*- 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_HARTMANN_ORLIN_H
 		#define LEMON_HARTMANN_ORLIN_H
 		/// \ingroup min_mean_cycle
 		///
 		/// \file
 		/// \brief Hartmann-Orlin's algorithm for finding a minimum mean cycle.
 		#include <vector>
 		#include <limits>
 		#include <lemon/core.h>
 		#include <lemon/path.h>
 		#include <lemon/tolerance.h>
 		#include <lemon/connectivity.h>
 		namespace lemon {
 		  /// \brief Default traits class of HartmannOrlin algorithm.
 		  ///
 		  /// Default traits class of HartmannOrlin algorithm.
 		  /// \tparam GR The type of the digraph.
 		  /// \tparam LEN The type of the length map.
 		  /// It must conform to the \ref concepts::Rea_data "Rea_data" concept.
 		#ifdef DOXYGEN
 		  template <typename GR, typename LEN>
 		#else
 		  template <typename GR, typename LEN,
 		    bool integer = std::numeric_limits<typename LEN::Value>::is_integer>
 		#endif
 		  struct HartmannOrlinDefaultTraits
+		  {
 		    /// The type of the digraph
 		    typedef GR Digraph;
 		    /// The type of the length map
 		    typedef LEN LengthMap;
 		    /// The type of the arc lengths
 		    typedef typename LengthMap::Value Value;
 		    /// \brief The large value type used for internal computations
 		    ///
 		    /// The large value type used for internal computations.
 		    /// It is \c long \c long if the \c Value type is integer,
 		    /// otherwise it is \c double.
 		    /// \c Value must be convertible to \c LargeValue.
 		    typedef double LargeValue;
 		    /// The tolerance type used for internal computations
 		    typedef lemon::Tolerance<LargeValue> Tolerance;
 		    /// \brief The path type of the found cycles
 		    ///
 		    /// The path type of the found cycles.
 		    /// It must conform to the \ref lemon::concepts::Path "Path" concept
 		    /// and it must have an \c addFront() function.
 		    typedef lemon::Path<Digraph> Path;
 		  };
 		  // Default traits class for integer value types
 		  template <typename GR, typename LEN>
 		  struct HartmannOrlinDefaultTraits<GR, LEN, true>
+		  {
 		    typedef GR Digraph;
 		    typedef LEN LengthMap;
 		    typedef typename LengthMap::Value Value;
 		#ifdef LEMON_HAVE_LONG_LONG
 		    typedef long long LargeValue;
 		#else
 		    typedef long LargeValue;
 		#endif
 		    typedef lemon::Tolerance<LargeValue> Tolerance;
 		    typedef lemon::Path<Digraph> Path;
 		  };
 		  /// \addtogroup min_mean_cycle
 		  /// @{
 		  /// \brief Implementation of the Hartmann-Orlin algorithm for finding
 		  /// a minimum mean cycle.
 		  ///
 		  /// This class implements the Hartmann-Orlin algorithm for finding
 		  /// a directed cycle of minimum mean length (cost) in a digraph
 		  /// \ref amo93networkflows, \ref dasdan98minmeancycle.
 		  /// It is an improved version of \ref Karp "Karp"'s original algorithm,
 		  /// it applies an efficient early termination scheme.
 		  /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
 		  ///
 		  /// \tparam GR The type of the digraph the algorithm runs on.
 		  /// \tparam LEN The type of the length map. The default
 		  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
 		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm. By default, it is \ref HartmannOrlinDefaultTraits
 		  /// "HartmannOrlinDefaultTraits<GR, LEN>".
 		  /// In most cases, this parameter should not be set directly,
 		  /// consider to use the named template parameters instead.
 		#ifdef DOXYGEN
 		  template <typename GR, typename LEN, typename TR>
 		#else
 		  template < typename GR,
 		             typename LEN = typename GR::template ArcMap<int>,
 		             typename TR = HartmannOrlinDefaultTraits<GR, LEN> >
 		#endif
 		  class HartmannOrlin
+		  {
 		  public:
 		    /// The type of the digraph
 		    typedef typename TR::Digraph Digraph;
 		    /// The type of the length map
 		    typedef typename TR::LengthMap LengthMap;
 		    /// The type of the arc lengths
 		    typedef typename TR::Value Value;
 		    /// \brief The large value type
 		    ///
 		    /// The large value type used for internal computations.
 		    /// Using the \ref HartmannOrlinDefaultTraits "default traits class",
 		    /// it is \c long \c long if the \c Value type is integer,
 		    /// By default, it is \c long \c long if the \c Value type is integer,
 		    /// otherwise it is \c double.
 		    typedef typename TR::LargeValue LargeValue;
 		    /// The tolerance type
 		    typedef typename TR::Tolerance Tolerance;
 		    /// \brief The path type of the found cycles
 		    ///
 		    /// The path type of the found cycles.
 		    /// Using the \ref HartmannOrlinDefaultTraits "default traits class",
 		    /// it is \ref lemon::Path "Path<Digraph>".
 		    typedef typename TR::Path Path;
 		    /// The \ref HartmannOrlinDefaultTraits "traits class" of the algorithm
 		    typedef TR Traits;
 		  private:
 		    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
 		    // Data sturcture for path data
 		    struct PathData
+		    {
 		      LargeValue dist;
 		      Arc pred;
 		      PathData(LargeValue d, Arc p = INVALID) :
 		        dist(d), pred(p) {}
 		    };
 		    typedef typename Digraph::template NodeMap<std::vector<PathData> >
 		      PathDataNodeMap;
 		  private:
 		    // The digraph the algorithm runs on
 		    const Digraph &_gr;
 		    // The length of the arcs
 		    const LengthMap &_length;
 		    // Data for storing the strongly connected components
 		    int _comp_num;
 		    typename Digraph::template NodeMap<int> _comp;
 		    std::vector<std::vector<Node> > _comp_nodes;
 		    std::vector<Node>* _nodes;
 		    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
 		    // Data for the found cycles
 		    bool _curr_found, _best_found;
 		    LargeValue _curr_length, _best_length;
 		    int _curr_size, _best_size;
 		    Node _curr_node, _best_node;
 		    int _curr_level, _best_level;
 		    Path *_cycle_path;
 		    bool _local_path;
 		    // Node map for storing path data
 		    PathDataNodeMap _data;
 		    // The processed nodes in the last round
 		    std::vector<Node> _process;
 		    Tolerance _tolerance;
 		    // Infinite constant
 		    const LargeValue INF;
 		  public:
 		    /// \name Named Template Parameters
 		    /// @{
 		    template <typename T>
 		    struct SetLargeValueTraits : public Traits {
 		      typedef T LargeValue;
 		      typedef lemon::Tolerance<T> Tolerance;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c LargeValue type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
 		    /// type. It is used for internal computations in the algorithm.
 		    template <typename T>
 		    struct SetLargeValue
 		      : public HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > {
 		      typedef HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > Create;
 		    };
 		    template <typename T>
 		    struct SetPathTraits : public Traits {
 		      typedef T Path;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c %Path type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting the \c %Path
 		    /// type of the found cycles.
 		    /// It must conform to the \ref lemon::concepts::Path "Path" concept
 		    /// and it must have an \c addFront() function.
 		    template <typename T>
 		    struct SetPath
 		      : public HartmannOrlin<GR, LEN, SetPathTraits<T> > {
 		      typedef HartmannOrlin<GR, LEN, SetPathTraits<T> > Create;
 		    };
 		    /// @}
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// The constructor of the class.
 		    ///
 		    /// \param digraph The digraph the algorithm runs on.
 		    /// \param length The lengths (costs) of the arcs.
 		    HartmannOrlin( const Digraph &digraph,
 		                   const LengthMap &length ) :
 		      _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
 		      _best_found(false), _best_length(0), _best_size(1),
 		      _cycle_path(NULL), _local_path(false), _data(digraph),
 		      INF(std::numeric_limits<LargeValue>::has_infinity ?
 		          std::numeric_limits<LargeValue>::infinity() :
 		          std::numeric_limits<LargeValue>::max())
 		    {}
 		    /// Destructor.
 		    ~HartmannOrlin() {
 		      if (_local_path) delete _cycle_path;
+		    }
 		    /// \brief Set the path structure for storing the found cycle.
 		    ///
 		    /// This function sets an external path structure for storing the
 		    /// found cycle.
 		    ///
 		    /// If you don't call this function before calling \ref run() or
 		    /// \ref findMinMean(), it will allocate a local \ref Path "path"
 		    /// structure. The destuctor deallocates this automatically
 		    /// allocated object, of course.
 		    ///
 		    /// \note The algorithm calls only the \ref lemon::Path::addFront()
 		    /// "addFront()" function of the given path structure.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    HartmannOrlin& cycle(Path &path) {
 		      if (_local_path) {
 		        delete _cycle_path;
 		        _local_path = false;
+		      }
 		      _cycle_path = &path;
 		      return *this;
+		    }
 		    /// \brief Set the tolerance used by the algorithm.
 		    ///
 		    /// This function sets the tolerance object used by the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    HartmannOrlin& tolerance(const Tolerance& tolerance) {
 		      _tolerance = tolerance;
 		      return *this;
+		    }
 		    /// \brief Return a const reference to the tolerance.
 		    ///
 		    /// This function returns a const reference to the tolerance object
 		    /// used by the algorithm.
 		    const Tolerance& tolerance() const {
 		      return _tolerance;
+		    }
 		    /// \name Execution control
 		    /// The simplest way to execute the algorithm is to call the \ref run()
 		    /// function.\n
 		    /// If you only need the minimum mean length, you may call
 		    /// \ref findMinMean().
 		    /// @{
 		    /// \brief Run the algorithm.
 		    ///
 		    /// This function runs the algorithm.
 		    /// It can be called more than once (e.g. if the underlying digraph
 		    /// and/or the arc lengths have been modified).
 		    ///
 		    /// \return \c true if a directed cycle exists in the digraph.
 		    ///
 		    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
 		    /// \code
 		    ///   return mmc.findMinMean() && mmc.findCycle();
 		    /// \endcode
 		    bool run() {
 		      return findMinMean() && findCycle();
+		    }
 		    /// \brief Find the minimum cycle mean.
 		    ///
 		    /// This function finds the minimum mean length of the directed
 		    /// cycles in the digraph.
 		    ///
 		    /// \return \c true if a directed cycle exists in the digraph.
 		    bool findMinMean() {
 		      // Initialization and find strongly connected components
 		      init();
 		      findComponents();
 		      // Find the minimum cycle mean in the components
 		      for (int comp = 0; comp < _comp_num; ++comp) {
 		        if (!initComponent(comp)) continue;
 		        processRounds();
 		        // Update the best cycle (global minimum mean cycle)
 		        if ( _curr_found && (!_best_found ||
 		             _curr_length * _best_size < _best_length * _curr_size) ) {
 		          _best_found = true;
 		          _best_length = _curr_length;
 		          _best_size = _curr_size;
 		          _best_node = _curr_node;
 		          _best_level = _curr_level;
+		        }
+		      }
 		      return _best_found;
+		    }
 		    /// \brief Find a minimum mean directed cycle.
 		    ///
 		    /// This function finds a directed cycle of minimum mean length
 		    /// in the digraph using the data computed by findMinMean().
 		    ///
 		    /// \return \c true if a directed cycle exists in the digraph.
 		    ///
 		    /// \pre \ref findMinMean() must be called before using this function.
 		    bool findCycle() {
 		      if (!_best_found) return false;
 		      IntNodeMap reached(_gr, -1);
 		      int r = _best_level + 1;
 		      Node u = _best_node;
 		      while (reached[u] < 0) {
 		        reached[u] = --r;
 		        u = _gr.source(_data[u][r].pred);
+		      }
 		      r = reached[u];
 		      Arc e = _data[u][r].pred;
 		      _cycle_path->addFront(e);
 		      _best_length = _length[e];
 		      _best_size = 1;
 		      Node v;
 		      while ((v = _gr.source(e)) != u) {
 		        e = _data[v][--r].pred;
 		        _cycle_path->addFront(e);
 		        _best_length += _length[e];
 		        ++_best_size;
+		      }
 		      return true;
+		    }
 		    /// @}
 		    /// \name Query Functions
 		    /// The results of the algorithm can be obtained using these
 		    /// functions.\n
 		    /// The algorithm should be executed before using them.
 		    /// @{
 		    /// \brief Return the total length of the found cycle.
 		    ///
 		    /// This function returns the total length of the found cycle.
 		    ///
 		    /// \pre \ref run() or \ref findMinMean() must be called before
 		    /// using this function.
 		    LargeValue cycleLength() const {
 		      return _best_length;
+		    }
 		    /// \brief Return the number of arcs on the found cycle.
 		    ///
 		    /// This function returns the number of arcs on the found cycle.
 		    ///
 		    /// \pre \ref run() or \ref findMinMean() must be called before
 		    /// using this function.
 		    int cycleArcNum() const {
 		      return _best_size;
+		    }
 		    /// \brief Return the mean length of the found cycle.
 		    ///
 		    /// This function returns the mean length of the found cycle.
 		    ///
 		    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
 		    /// following code.
 		    /// \code
 		    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
 		    /// \endcode
 		    ///
 		    /// \pre \ref run() or \ref findMinMean() must be called before
 		    /// using this function.
 		    double cycleMean() const {
 		      return static_cast<double>(_best_length) / _best_size;
+		    }
 		    /// \brief Return the found cycle.
 		    ///
 		    /// This function returns a const reference to the path structure
 		    /// storing the found cycle.
 		    ///
 		    /// \pre \ref run() or \ref findCycle() must be called before using
 		    /// this function.
 		    const Path& cycle() const {
 		      return *_cycle_path;
+		    }
 		    ///@}
 		  private:
 		    // Initialization
 		    void init() {
 		      if (!_cycle_path) {
 		        _local_path = true;
 		        _cycle_path = new Path;
+		      }
 		      _cycle_path->clear();
 		      _best_found = false;
 		      _best_length = 0;
 		      _best_size = 1;
 		      _cycle_path->clear();
 		      for (NodeIt u(_gr); u != INVALID; ++u)
 		        _data[u].clear();
+		    }
 		    // Find strongly connected components and initialize _comp_nodes
 		    // and _out_arcs
 		    void findComponents() {
 		      _comp_num = stronglyConnectedComponents(_gr, _comp);
 		      _comp_nodes.resize(_comp_num);
 		      if (_comp_num == 1) {
 		        _comp_nodes[0].clear();
 		        for (NodeIt n(_gr); n != INVALID; ++n) {
 		          _comp_nodes[0].push_back(n);
 		          _out_arcs[n].clear();
 		          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
 		            _out_arcs[n].push_back(a);
+		          }
+		        }
 		      } else {
 		        for (int i = 0; i < _comp_num; ++i)
 		          _comp_nodes[i].clear();
 		        for (NodeIt n(_gr); n != INVALID; ++n) {
 		          int k = _comp[n];
 		          _comp_nodes[k].push_back(n);
 		          _out_arcs[n].clear();
 		          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
 		            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
+		          }
+		        }
+		      }
+		    }
 		    // Initialize path data for the current component
 		    bool initComponent(int comp) {
 		      _nodes = &(_comp_nodes[comp]);
 		      int n = _nodes->size();
 		      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
 		        return false;
+		      }
 		      for (int i = 0; i < n; ++i) {
 		        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
+		      }
 		      return true;
+		    }
 		    // Process all rounds of computing path data for the current component.
 		    // _data[v][k] is the length of a shortest directed walk from the root
 		    // node to node v containing exactly k arcs.
 		    void processRounds() {
 		      Node start = (*_nodes)[0];
 		      _data[start][0] = PathData(0);
 		      _process.clear();
 		      _process.push_back(start);
 		      int k, n = _nodes->size();
 		      int next_check = 4;
 		      bool terminate = false;
 		      for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
 		        processNextBuildRound(k);
 		        if (k == next_check || k == n) {
 		          terminate = checkTermination(k);
 		          next_check = next_check * 3 / 2;
+		        }
+		      }
 		      for ( ; k <= n && !terminate; ++k) {
 		        processNextFullRound(k);
 		        if (k == next_check || k == n) {
 		          terminate = checkTermination(k);
 		          next_check = next_check * 3 / 2;
+		        }
+		      }
+		    }
 		    // Process one round and rebuild _process
 		    void processNextBuildRound(int k) {
 		      std::vector<Node> next;
 		      Node u, v;
 		      Arc e;
 		      LargeValue d;
 		      for (int i = 0; i < int(_process.size()); ++i) {
 		        u = _process[i];
 		        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
 		          e = _out_arcs[u][j];
 		          v = _gr.target(e);
 		          d = _data[u][k-1].dist + _length[e];
 		          if (_tolerance.less(d, _data[v][k].dist)) {
 		            if (_data[v][k].dist == INF) next.push_back(v);
 		            _data[v][k] = PathData(d, e);
+		          }
+		        }
+		      }
 		      _process.swap(next);
+		    }
 		    // Process one round using _nodes instead of _process
 		    void processNextFullRound(int k) {
 		      Node u, v;
 		      Arc e;
 		      LargeValue d;
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        u = (*_nodes)[i];
 		        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
 		          e = _out_arcs[u][j];
 		          v = _gr.target(e);
 		          d = _data[u][k-1].dist + _length[e];
 		          if (_tolerance.less(d, _data[v][k].dist)) {
 		            _data[v][k] = PathData(d, e);
+		          }
+		        }
+		      }
+		    }
 		    // Check early termination
 		    bool checkTermination(int k) {
 		      typedef std::pair<int, int> Pair;
 		      typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
 		      typename GR::template NodeMap<LargeValue> pi(_gr);
 		      int n = _nodes->size();
 		      LargeValue length;
 		      int size;
 		      Node u;
 		      // Search for cycles that are already found
 		      _curr_found = false;
 		      for (int i = 0; i < n; ++i) {
 		        u = (*_nodes)[i];
 		        if (_data[u][k].dist == INF) continue;
 		        for (int j = k; j >= 0; --j) {
 		          if (level[u].first == i && level[u].second > 0) {
 		            // A cycle is found
 		            length = _data[u][level[u].second].dist - _data[u][j].dist;
 		            size = level[u].second - j;
 		            if (!_curr_found || length * _curr_size < _curr_length * size) {
 		              _curr_length = length;
 		              _curr_size = size;
 		              _curr_node = u;
 		              _curr_level = level[u].second;
 		              _curr_found = true;
+		            }
+		          }
 		          level[u] = Pair(i, j);
 		          if (j != 0) {
 			    u = _gr.source(_data[u][j].pred);
+			  }
+		        }
+		      }
 		      // If at least one cycle is found, check the optimality condition
 		      LargeValue d;
 		      if (_curr_found && k < n) {
 		        // Find node potentials
 		        for (int i = 0; i < n; ++i) {
 		          u = (*_nodes)[i];
 		          pi[u] = INF;
 		          for (int j = 0; j <= k; ++j) {
 		            if (_data[u][j].dist < INF) {
 		              d = _data[u][j].dist * _curr_size - j * _curr_length;
 		              if (_tolerance.less(d, pi[u])) pi[u] = d;
+		            }
+		          }
+		        }
 		        // Check the optimality condition for all arcs
 		        bool done = true;
 		        for (ArcIt a(_gr); a != INVALID; ++a) {
 		          if (_tolerance.less(_length[a] * _curr_size - _curr_length,
 		                              pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
 		            done = false;
 		            break;
+		          }
+		        }
 		        return done;
+		      }
 		      return (k == n);
+		    }
 		  }; //class HartmannOrlin
 		  ///@}
 		} //namespace lemon
 		#endif //LEMON_HARTMANN_ORLIN_H

lemon/howard.h

Show inline comments

 		/* -*- 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_HOWARD_H
 		#define LEMON_HOWARD_H
 		/// \ingroup min_mean_cycle
 		///
 		/// \file
 		/// \brief Howard's algorithm for finding a minimum mean cycle.
 		#include <vector>
 		#include <limits>
 		#include <lemon/core.h>
 		#include <lemon/path.h>
 		#include <lemon/tolerance.h>
 		#include <lemon/connectivity.h>
 		namespace lemon {
 		  /// \brief Default traits class of Howard class.
 		  ///
 		  /// Default traits class of Howard class.
 		  /// \tparam GR The type of the digraph.
 		  /// \tparam LEN The type of the length map.
 		  /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
 		#ifdef DOXYGEN
 		  template <typename GR, typename LEN>
 		#else
 		  template <typename GR, typename LEN,
 		    bool integer = std::numeric_limits<typename LEN::Value>::is_integer>
 		#endif
 		  struct HowardDefaultTraits
+		  {
 		    /// The type of the digraph
 		    typedef GR Digraph;
 		    /// The type of the length map
 		    typedef LEN LengthMap;
 		    /// The type of the arc lengths
 		    typedef typename LengthMap::Value Value;
 		    /// \brief The large value type used for internal computations
 		    ///
 		    /// The large value type used for internal computations.
 		    /// It is \c long \c long if the \c Value type is integer,
 		    /// otherwise it is \c double.
 		    /// \c Value must be convertible to \c LargeValue.
 		    typedef double LargeValue;
 		    /// The tolerance type used for internal computations
 		    typedef lemon::Tolerance<LargeValue> Tolerance;
 		    /// \brief The path type of the found cycles
 		    ///
 		    /// The path type of the found cycles.
 		    /// It must conform to the \ref lemon::concepts::Path "Path" concept
 		    /// and it must have an \c addBack() function.
 		    typedef lemon::Path<Digraph> Path;
 		  };
 		  // Default traits class for integer value types
 		  template <typename GR, typename LEN>
 		  struct HowardDefaultTraits<GR, LEN, true>
+		  {
 		    typedef GR Digraph;
 		    typedef LEN LengthMap;
 		    typedef typename LengthMap::Value Value;
 		#ifdef LEMON_HAVE_LONG_LONG
 		    typedef long long LargeValue;
 		#else
 		    typedef long LargeValue;
 		#endif
 		    typedef lemon::Tolerance<LargeValue> Tolerance;
 		    typedef lemon::Path<Digraph> Path;
 		  };
 		  /// \addtogroup min_mean_cycle
 		  /// @{
 		  /// \brief Implementation of Howard's algorithm for finding a minimum
 		  /// mean cycle.
 		  ///
 		  /// This class implements Howard's policy iteration algorithm for finding
 		  /// a directed cycle of minimum mean length (cost) in a digraph
 		  /// \ref amo93networkflows, \ref dasdan98minmeancycle.
 		  /// This class provides the most efficient algorithm for the
 		  /// minimum mean cycle problem, though the best known theoretical
 		  /// bound on its running time is exponential.
 		  ///
 		  /// \tparam GR The type of the digraph the algorithm runs on.
 		  /// \tparam LEN The type of the length map. The default
 		  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
 		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm. By default, it is \ref HowardDefaultTraits
 		  /// "HowardDefaultTraits<GR, LEN>".
 		  /// In most cases, this parameter should not be set directly,
 		  /// consider to use the named template parameters instead.
 		#ifdef DOXYGEN
 		  template <typename GR, typename LEN, typename TR>
 		#else
 		  template < typename GR,
 		             typename LEN = typename GR::template ArcMap<int>,
 		             typename TR = HowardDefaultTraits<GR, LEN> >
 		#endif
 		  class Howard
+		  {
 		  public:
 		    /// The type of the digraph
 		    typedef typename TR::Digraph Digraph;
 		    /// The type of the length map
 		    typedef typename TR::LengthMap LengthMap;
 		    /// The type of the arc lengths
 		    typedef typename TR::Value Value;
 		    /// \brief The large value type
 		    ///
 		    /// The large value type used for internal computations.
 		    /// Using the \ref HowardDefaultTraits "default traits class",
 		    /// it is \c long \c long if the \c Value type is integer,
 		    /// By default, it is \c long \c long if the \c Value type is integer,
 		    /// otherwise it is \c double.
 		    typedef typename TR::LargeValue LargeValue;
 		    /// The tolerance type
 		    typedef typename TR::Tolerance Tolerance;
 		    /// \brief The path type of the found cycles
 		    ///
 		    /// The path type of the found cycles.
 		    /// Using the \ref HowardDefaultTraits "default traits class",
 		    /// it is \ref lemon::Path "Path<Digraph>".
 		    typedef typename TR::Path Path;
 		    /// The \ref HowardDefaultTraits "traits class" of the algorithm
 		    typedef TR Traits;
 		  private:
 		    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
 		    // The digraph the algorithm runs on
 		    const Digraph &_gr;
 		    // The length of the arcs
 		    const LengthMap &_length;
 		    // Data for the found cycles
 		    bool _curr_found, _best_found;
 		    LargeValue _curr_length, _best_length;
 		    int _curr_size, _best_size;
 		    Node _curr_node, _best_node;
 		    Path *_cycle_path;
 		    bool _local_path;
 		    // Internal data used by the algorithm
 		    typename Digraph::template NodeMap<Arc> _policy;
 		    typename Digraph::template NodeMap<bool> _reached;
 		    typename Digraph::template NodeMap<int> _level;
 		    typename Digraph::template NodeMap<LargeValue> _dist;
 		    // Data for storing the strongly connected components
 		    int _comp_num;
 		    typename Digraph::template NodeMap<int> _comp;
 		    std::vector<std::vector<Node> > _comp_nodes;
 		    std::vector<Node>* _nodes;
 		    typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs;
 		    // Queue used for BFS search
 		    std::vector<Node> _queue;
 		    int _qfront, _qback;
 		    Tolerance _tolerance;
 		    // Infinite constant
 		    const LargeValue INF;
 		  public:
 		    /// \name Named Template Parameters
 		    /// @{
 		    template <typename T>
 		    struct SetLargeValueTraits : public Traits {
 		      typedef T LargeValue;
 		      typedef lemon::Tolerance<T> Tolerance;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c LargeValue type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
 		    /// type. It is used for internal computations in the algorithm.
 		    template <typename T>
 		    struct SetLargeValue
 		      : public Howard<GR, LEN, SetLargeValueTraits<T> > {
 		      typedef Howard<GR, LEN, SetLargeValueTraits<T> > Create;
 		    };
 		    template <typename T>
 		    struct SetPathTraits : public Traits {
 		      typedef T Path;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c %Path type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting the \c %Path
 		    /// type of the found cycles.
 		    /// It must conform to the \ref lemon::concepts::Path "Path" concept
 		    /// and it must have an \c addBack() function.
 		    template <typename T>
 		    struct SetPath
 		      : public Howard<GR, LEN, SetPathTraits<T> > {
 		      typedef Howard<GR, LEN, SetPathTraits<T> > Create;
 		    };
 		    /// @}
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// The constructor of the class.
 		    ///
 		    /// \param digraph The digraph the algorithm runs on.
 		    /// \param length The lengths (costs) of the arcs.
 		    Howard( const Digraph &digraph,
 		            const LengthMap &length ) :
 		      _gr(digraph), _length(length), _best_found(false),
 		      _best_length(0), _best_size(1), _cycle_path(NULL), _local_path(false),
 		      _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph),
 		      _comp(digraph), _in_arcs(digraph),
 		      INF(std::numeric_limits<LargeValue>::has_infinity ?
 		          std::numeric_limits<LargeValue>::infinity() :
 		          std::numeric_limits<LargeValue>::max())
 		    {}
 		    /// Destructor.
 		    ~Howard() {
 		      if (_local_path) delete _cycle_path;
+		    }
 		    /// \brief Set the path structure for storing the found cycle.
 		    ///
 		    /// This function sets an external path structure for storing the
 		    /// found cycle.
 		    ///
 		    /// If you don't call this function before calling \ref run() or
 		    /// \ref findMinMean(), it will allocate a local \ref Path "path"
 		    /// structure. The destuctor deallocates this automatically
 		    /// allocated object, of course.
 		    ///
 		    /// \note The algorithm calls only the \ref lemon::Path::addBack()
 		    /// "addBack()" function of the given path structure.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    Howard& cycle(Path &path) {
 		      if (_local_path) {
 		        delete _cycle_path;
 		        _local_path = false;
+		      }
 		      _cycle_path = &path;
 		      return *this;
+		    }
 		    /// \brief Set the tolerance used by the algorithm.
 		    ///
 		    /// This function sets the tolerance object used by the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    Howard& tolerance(const Tolerance& tolerance) {
 		      _tolerance = tolerance;
 		      return *this;
+		    }
 		    /// \brief Return a const reference to the tolerance.
 		    ///
 		    /// This function returns a const reference to the tolerance object
 		    /// used by the algorithm.
 		    const Tolerance& tolerance() const {
 		      return _tolerance;
+		    }
 		    /// \name Execution control
 		    /// The simplest way to execute the algorithm is to call the \ref run()
 		    /// function.\n
 		    /// If you only need the minimum mean length, you may call
 		    /// \ref findMinMean().
 		    /// @{
 		    /// \brief Run the algorithm.
 		    ///
 		    /// This function runs the algorithm.
 		    /// It can be called more than once (e.g. if the underlying digraph
 		    /// and/or the arc lengths have been modified).
 		    ///
 		    /// \return \c true if a directed cycle exists in the digraph.
 		    ///
 		    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
 		    /// \code
 		    ///   return mmc.findMinMean() && mmc.findCycle();
 		    /// \endcode
 		    bool run() {
 		      return findMinMean() && findCycle();
+		    }
 		    /// \brief Find the minimum cycle mean.
 		    ///
 		    /// This function finds the minimum mean length of the directed
 		    /// cycles in the digraph.
 		    ///
 		    /// \return \c true if a directed cycle exists in the digraph.
 		    bool findMinMean() {
 		      // Initialize and find strongly connected components
 		      init();
 		      findComponents();
 		      // Find the minimum cycle mean in the components
 		      for (int comp = 0; comp < _comp_num; ++comp) {
 		        // Find the minimum mean cycle in the current component
 		        if (!buildPolicyGraph(comp)) continue;
 		        while (true) {
 		          findPolicyCycle();
 		          if (!computeNodeDistances()) break;
+		        }
 		        // Update the best cycle (global minimum mean cycle)
 		        if ( _curr_found && (!_best_found ||
 		             _curr_length * _best_size < _best_length * _curr_size) ) {
 		          _best_found = true;
 		          _best_length = _curr_length;
 		          _best_size = _curr_size;
 		          _best_node = _curr_node;
+		        }
+		      }
 		      return _best_found;
+		    }
 		    /// \brief Find a minimum mean directed cycle.
 		    ///
 		    /// This function finds a directed cycle of minimum mean length
 		    /// in the digraph using the data computed by findMinMean().
 		    ///
 		    /// \return \c true if a directed cycle exists in the digraph.
 		    ///
 		    /// \pre \ref findMinMean() must be called before using this function.
 		    bool findCycle() {
 		      if (!_best_found) return false;
 		      _cycle_path->addBack(_policy[_best_node]);
 		      for ( Node v = _best_node;
 		            (v = _gr.target(_policy[v])) != _best_node; ) {
 		        _cycle_path->addBack(_policy[v]);
+		      }
 		      return true;
+		    }
 		    /// @}
 		    /// \name Query Functions
 		    /// The results of the algorithm can be obtained using these
 		    /// functions.\n
 		    /// The algorithm should be executed before using them.
 		    /// @{
 		    /// \brief Return the total length of the found cycle.
 		    ///
 		    /// This function returns the total length of the found cycle.
 		    ///
 		    /// \pre \ref run() or \ref findMinMean() must be called before
 		    /// using this function.
 		    LargeValue cycleLength() const {
 		      return _best_length;
+		    }
 		    /// \brief Return the number of arcs on the found cycle.
 		    ///
 		    /// This function returns the number of arcs on the found cycle.
 		    ///
 		    /// \pre \ref run() or \ref findMinMean() must be called before
 		    /// using this function.
 		    int cycleArcNum() const {
 		      return _best_size;
+		    }
 		    /// \brief Return the mean length of the found cycle.
 		    ///
 		    /// This function returns the mean length of the found cycle.
 		    ///
 		    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
 		    /// following code.
 		    /// \code
 		    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
 		    /// \endcode
 		    ///
 		    /// \pre \ref run() or \ref findMinMean() must be called before
 		    /// using this function.
 		    double cycleMean() const {
 		      return static_cast<double>(_best_length) / _best_size;
+		    }
 		    /// \brief Return the found cycle.
 		    ///
 		    /// This function returns a const reference to the path structure
 		    /// storing the found cycle.
 		    ///
 		    /// \pre \ref run() or \ref findCycle() must be called before using
 		    /// this function.
 		    const Path& cycle() const {
 		      return *_cycle_path;
+		    }
 		    ///@}
 		  private:
 		    // Initialize
 		    void init() {
 		      if (!_cycle_path) {
 		        _local_path = true;
 		        _cycle_path = new Path;
+		      }
 		      _queue.resize(countNodes(_gr));
 		      _best_found = false;
 		      _best_length = 0;
 		      _best_size = 1;
 		      _cycle_path->clear();
+		    }
 		    // Find strongly connected components and initialize _comp_nodes
 		    // and _in_arcs
 		    void findComponents() {
 		      _comp_num = stronglyConnectedComponents(_gr, _comp);
 		      _comp_nodes.resize(_comp_num);
 		      if (_comp_num == 1) {
 		        _comp_nodes[0].clear();
 		        for (NodeIt n(_gr); n != INVALID; ++n) {
 		          _comp_nodes[0].push_back(n);
 		          _in_arcs[n].clear();
 		          for (InArcIt a(_gr, n); a != INVALID; ++a) {
 		            _in_arcs[n].push_back(a);
+		          }
+		        }
 		      } else {
 		        for (int i = 0; i < _comp_num; ++i)
 		          _comp_nodes[i].clear();
 		        for (NodeIt n(_gr); n != INVALID; ++n) {
 		          int k = _comp[n];
 		          _comp_nodes[k].push_back(n);
 		          _in_arcs[n].clear();
 		          for (InArcIt a(_gr, n); a != INVALID; ++a) {
 		            if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);
+		          }
+		        }
+		      }
+		    }
 		    // Build the policy graph in the given strongly connected component
 		    // (the out-degree of every node is 1)
 		    bool buildPolicyGraph(int comp) {
 		      _nodes = &(_comp_nodes[comp]);
 		      if (_nodes->size() < 1 ||
 		          (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {
 		        return false;
+		      }
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        _dist[(*_nodes)[i]] = INF;
+		      }
 		      Node u, v;
 		      Arc e;
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        v = (*_nodes)[i];
 		        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
 		          e = _in_arcs[v][j];
 		          u = _gr.source(e);
 		          if (_length[e] < _dist[u]) {
 		            _dist[u] = _length[e];
 		            _policy[u] = e;
+		          }
+		        }
+		      }
 		      return true;
+		    }
 		    // Find the minimum mean cycle in the policy graph
 		    void findPolicyCycle() {
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        _level[(*_nodes)[i]] = -1;
+		      }
 		      LargeValue clength;
 		      int csize;
 		      Node u, v;
 		      _curr_found = false;
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        u = (*_nodes)[i];
 		        if (_level[u] >= 0) continue;
 		        for (; _level[u] < 0; u = _gr.target(_policy[u])) {
 		          _level[u] = i;
+		        }
 		        if (_level[u] == i) {
 		          // A cycle is found
 		          clength = _length[_policy[u]];
 		          csize = 1;
 		          for (v = u; (v = _gr.target(_policy[v])) != u; ) {
 		            clength += _length[_policy[v]];
 		            ++csize;
+		          }
 		          if ( !_curr_found ||
 		               (clength * _curr_size < _curr_length * csize) ) {
 		            _curr_found = true;
 		            _curr_length = clength;
 		            _curr_size = csize;
 		            _curr_node = u;
+		          }
+		        }
+		      }
+		    }
 		    // Contract the policy graph and compute node distances
 		    bool computeNodeDistances() {
 		      // Find the component of the main cycle and compute node distances
 		      // using reverse BFS
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        _reached[(*_nodes)[i]] = false;
+		      }
 		      _qfront = _qback = 0;
 		      _queue[0] = _curr_node;
 		      _reached[_curr_node] = true;
 		      _dist[_curr_node] = 0;
 		      Node u, v;
 		      Arc e;
 		      while (_qfront <= _qback) {
 		        v = _queue[_qfront++];
 		        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
 		          e = _in_arcs[v][j];
 		          u = _gr.source(e);
 		          if (_policy[u] == e && !_reached[u]) {
 		            _reached[u] = true;
 		            _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
 		            _queue[++_qback] = u;
+		          }
+		        }
+		      }
 		      // Connect all other nodes to this component and compute node
 		      // distances using reverse BFS
 		      _qfront = 0;
 		      while (_qback < int(_nodes->size())-1) {
 		        v = _queue[_qfront++];
 		        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
 		          e = _in_arcs[v][j];
 		          u = _gr.source(e);
 		          if (!_reached[u]) {
 		            _reached[u] = true;
 		            _policy[u] = e;
 		            _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
 		            _queue[++_qback] = u;
+		          }
+		        }
+		      }
 		      // Improve node distances
 		      bool improved = false;
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        v = (*_nodes)[i];
 		        for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
 		          e = _in_arcs[v][j];
 		          u = _gr.source(e);
 		          LargeValue delta = _dist[v] + _length[e] * _curr_size - _curr_length;
 		          if (_tolerance.less(delta, _dist[u])) {
 		            _dist[u] = delta;
 		            _policy[u] = e;
 		            improved = true;
+		          }
+		        }
+		      }
 		      return improved;
+		    }
 		  }; //class Howard
 		  ///@}
 		} //namespace lemon
 		#endif //LEMON_HOWARD_H

lemon/karp.h

Show inline comments

 		/* -*- 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_KARP_H
 		#define LEMON_KARP_H
 		/// \ingroup min_mean_cycle
 		///
 		/// \file
 		/// \brief Karp's algorithm for finding a minimum mean cycle.
 		#include <vector>
 		#include <limits>
 		#include <lemon/core.h>
 		#include <lemon/path.h>
 		#include <lemon/tolerance.h>
 		#include <lemon/connectivity.h>
 		namespace lemon {
 		  /// \brief Default traits class of Karp algorithm.
 		  ///
 		  /// Default traits class of Karp algorithm.
 		  /// \tparam GR The type of the digraph.
 		  /// \tparam LEN The type of the length map.
 		  /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
 		#ifdef DOXYGEN
 		  template <typename GR, typename LEN>
 		#else
 		  template <typename GR, typename LEN,
 		    bool integer = std::numeric_limits<typename LEN::Value>::is_integer>
 		#endif
 		  struct KarpDefaultTraits
+		  {
 		    /// The type of the digraph
 		    typedef GR Digraph;
 		    /// The type of the length map
 		    typedef LEN LengthMap;
 		    /// The type of the arc lengths
 		    typedef typename LengthMap::Value Value;
 		    /// \brief The large value type used for internal computations
 		    ///
 		    /// The large value type used for internal computations.
 		    /// It is \c long \c long if the \c Value type is integer,
 		    /// otherwise it is \c double.
 		    /// \c Value must be convertible to \c LargeValue.
 		    typedef double LargeValue;
 		    /// The tolerance type used for internal computations
 		    typedef lemon::Tolerance<LargeValue> Tolerance;
 		    /// \brief The path type of the found cycles
 		    ///
 		    /// The path type of the found cycles.
 		    /// It must conform to the \ref lemon::concepts::Path "Path" concept
 		    /// and it must have an \c addFront() function.
 		    typedef lemon::Path<Digraph> Path;
 		  };
 		  // Default traits class for integer value types
 		  template <typename GR, typename LEN>
 		  struct KarpDefaultTraits<GR, LEN, true>
+		  {
 		    typedef GR Digraph;
 		    typedef LEN LengthMap;
 		    typedef typename LengthMap::Value Value;
 		#ifdef LEMON_HAVE_LONG_LONG
 		    typedef long long LargeValue;
 		#else
 		    typedef long LargeValue;
 		#endif
 		    typedef lemon::Tolerance<LargeValue> Tolerance;
 		    typedef lemon::Path<Digraph> Path;
 		  };
 		  /// \addtogroup min_mean_cycle
 		  /// @{
 		  /// \brief Implementation of Karp's algorithm for finding a minimum
 		  /// mean cycle.
 		  ///
 		  /// This class implements Karp's algorithm for finding a directed
 		  /// cycle of minimum mean length (cost) in a digraph
 		  /// \ref amo93networkflows, \ref dasdan98minmeancycle.
 		  /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).
 		  ///
 		  /// \tparam GR The type of the digraph the algorithm runs on.
 		  /// \tparam LEN The type of the length map. The default
 		  /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
 		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm. By default, it is \ref KarpDefaultTraits
 		  /// "KarpDefaultTraits<GR, LEN>".
 		  /// In most cases, this parameter should not be set directly,
 		  /// consider to use the named template parameters instead.
 		#ifdef DOXYGEN
 		  template <typename GR, typename LEN, typename TR>
 		#else
 		  template < typename GR,
 		             typename LEN = typename GR::template ArcMap<int>,
 		             typename TR = KarpDefaultTraits<GR, LEN> >
 		#endif
 		  class Karp
+		  {
 		  public:
 		    /// The type of the digraph
 		    typedef typename TR::Digraph Digraph;
 		    /// The type of the length map
 		    typedef typename TR::LengthMap LengthMap;
 		    /// The type of the arc lengths
 		    typedef typename TR::Value Value;
 		    /// \brief The large value type
 		    ///
 		    /// The large value type used for internal computations.
 		    /// Using the \ref KarpDefaultTraits "default traits class",
 		    /// it is \c long \c long if the \c Value type is integer,
 		    /// By default, it is \c long \c long if the \c Value type is integer,
 		    /// otherwise it is \c double.
 		    typedef typename TR::LargeValue LargeValue;
 		    /// The tolerance type
 		    typedef typename TR::Tolerance Tolerance;
 		    /// \brief The path type of the found cycles
 		    ///
 		    /// The path type of the found cycles.
 		    /// Using the \ref KarpDefaultTraits "default traits class",
 		    /// it is \ref lemon::Path "Path<Digraph>".
 		    typedef typename TR::Path Path;
 		    /// The \ref KarpDefaultTraits "traits class" of the algorithm
 		    typedef TR Traits;
 		  private:
 		    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
 		    // Data sturcture for path data
 		    struct PathData
+		    {
 		      LargeValue dist;
 		      Arc pred;
 		      PathData(LargeValue d, Arc p = INVALID) :
 		        dist(d), pred(p) {}
 		    };
 		    typedef typename Digraph::template NodeMap<std::vector<PathData> >
 		      PathDataNodeMap;
 		  private:
 		    // The digraph the algorithm runs on
 		    const Digraph &_gr;
 		    // The length of the arcs
 		    const LengthMap &_length;
 		    // Data for storing the strongly connected components
 		    int _comp_num;
 		    typename Digraph::template NodeMap<int> _comp;
 		    std::vector<std::vector<Node> > _comp_nodes;
 		    std::vector<Node>* _nodes;
 		    typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
 		    // Data for the found cycle
 		    LargeValue _cycle_length;
 		    int _cycle_size;
 		    Node _cycle_node;
 		    Path *_cycle_path;
 		    bool _local_path;
 		    // Node map for storing path data
 		    PathDataNodeMap _data;
 		    // The processed nodes in the last round
 		    std::vector<Node> _process;
 		    Tolerance _tolerance;
 		    // Infinite constant
 		    const LargeValue INF;
 		  public:
 		    /// \name Named Template Parameters
 		    /// @{
 		    template <typename T>
 		    struct SetLargeValueTraits : public Traits {
 		      typedef T LargeValue;
 		      typedef lemon::Tolerance<T> Tolerance;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c LargeValue type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting \c LargeValue
 		    /// type. It is used for internal computations in the algorithm.
 		    template <typename T>
 		    struct SetLargeValue
 		      : public Karp<GR, LEN, SetLargeValueTraits<T> > {
 		      typedef Karp<GR, LEN, SetLargeValueTraits<T> > Create;
 		    };
 		    template <typename T>
 		    struct SetPathTraits : public Traits {
 		      typedef T Path;
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// \c %Path type.
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting the \c %Path
 		    /// type of the found cycles.
 		    /// It must conform to the \ref lemon::concepts::Path "Path" concept
 		    /// and it must have an \c addFront() function.
 		    template <typename T>
 		    struct SetPath
 		      : public Karp<GR, LEN, SetPathTraits<T> > {
 		      typedef Karp<GR, LEN, SetPathTraits<T> > Create;
 		    };
 		    /// @}
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// The constructor of the class.
 		    ///
 		    /// \param digraph The digraph the algorithm runs on.
 		    /// \param length The lengths (costs) of the arcs.
 		    Karp( const Digraph &digraph,
 		          const LengthMap &length ) :
 		      _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
 		      _cycle_length(0), _cycle_size(1), _cycle_node(INVALID),
 		      _cycle_path(NULL), _local_path(false), _data(digraph),
 		      INF(std::numeric_limits<LargeValue>::has_infinity ?
 		          std::numeric_limits<LargeValue>::infinity() :
 		          std::numeric_limits<LargeValue>::max())
 		    {}
 		    /// Destructor.
 		    ~Karp() {
 		      if (_local_path) delete _cycle_path;
+		    }
 		    /// \brief Set the path structure for storing the found cycle.
 		    ///
 		    /// This function sets an external path structure for storing the
 		    /// found cycle.
 		    ///
 		    /// If you don't call this function before calling \ref run() or
 		    /// \ref findMinMean(), it will allocate a local \ref Path "path"
 		    /// structure. The destuctor deallocates this automatically
 		    /// allocated object, of course.
 		    ///
 		    /// \note The algorithm calls only the \ref lemon::Path::addFront()
 		    /// "addFront()" function of the given path structure.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    Karp& cycle(Path &path) {
 		      if (_local_path) {
 		        delete _cycle_path;
 		        _local_path = false;
+		      }
 		      _cycle_path = &path;
 		      return *this;
+		    }
 		    /// \brief Set the tolerance used by the algorithm.
 		    ///
 		    /// This function sets the tolerance object used by the algorithm.
 		    ///
 		    /// \return <tt>(*this)</tt>
 		    Karp& tolerance(const Tolerance& tolerance) {
 		      _tolerance = tolerance;
 		      return *this;
+		    }
 		    /// \brief Return a const reference to the tolerance.
 		    ///
 		    /// This function returns a const reference to the tolerance object
 		    /// used by the algorithm.
 		    const Tolerance& tolerance() const {
 		      return _tolerance;
+		    }
 		    /// \name Execution control
 		    /// The simplest way to execute the algorithm is to call the \ref run()
 		    /// function.\n
 		    /// If you only need the minimum mean length, you may call
 		    /// \ref findMinMean().
 		    /// @{
 		    /// \brief Run the algorithm.
 		    ///
 		    /// This function runs the algorithm.
 		    /// It can be called more than once (e.g. if the underlying digraph
 		    /// and/or the arc lengths have been modified).
 		    ///
 		    /// \return \c true if a directed cycle exists in the digraph.
 		    ///
 		    /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
 		    /// \code
 		    ///   return mmc.findMinMean() && mmc.findCycle();
 		    /// \endcode
 		    bool run() {
 		      return findMinMean() && findCycle();
+		    }
 		    /// \brief Find the minimum cycle mean.
 		    ///
 		    /// This function finds the minimum mean length of the directed
 		    /// cycles in the digraph.
 		    ///
 		    /// \return \c true if a directed cycle exists in the digraph.
 		    bool findMinMean() {
 		      // Initialization and find strongly connected components
 		      init();
 		      findComponents();
 		      // Find the minimum cycle mean in the components
 		      for (int comp = 0; comp < _comp_num; ++comp) {
 		        if (!initComponent(comp)) continue;
 		        processRounds();
 		        updateMinMean();
+		      }
 		      return (_cycle_node != INVALID);
+		    }
 		    /// \brief Find a minimum mean directed cycle.
 		    ///
 		    /// This function finds a directed cycle of minimum mean length
 		    /// in the digraph using the data computed by findMinMean().
 		    ///
 		    /// \return \c true if a directed cycle exists in the digraph.
 		    ///
 		    /// \pre \ref findMinMean() must be called before using this function.
 		    bool findCycle() {
 		      if (_cycle_node == INVALID) return false;
 		      IntNodeMap reached(_gr, -1);
 		      int r = _data[_cycle_node].size();
 		      Node u = _cycle_node;
 		      while (reached[u] < 0) {
 		        reached[u] = --r;
 		        u = _gr.source(_data[u][r].pred);
+		      }
 		      r = reached[u];
 		      Arc e = _data[u][r].pred;
 		      _cycle_path->addFront(e);
 		      _cycle_length = _length[e];
 		      _cycle_size = 1;
 		      Node v;
 		      while ((v = _gr.source(e)) != u) {
 		        e = _data[v][--r].pred;
 		        _cycle_path->addFront(e);
 		        _cycle_length += _length[e];
 		        ++_cycle_size;
+		      }
 		      return true;
+		    }
 		    /// @}
 		    /// \name Query Functions
 		    /// The results of the algorithm can be obtained using these
 		    /// functions.\n
 		    /// The algorithm should be executed before using them.
 		    /// @{
 		    /// \brief Return the total length of the found cycle.
 		    ///
 		    /// This function returns the total length of the found cycle.
 		    ///
 		    /// \pre \ref run() or \ref findMinMean() must be called before
 		    /// using this function.
 		    LargeValue cycleLength() const {
 		      return _cycle_length;
+		    }
 		    /// \brief Return the number of arcs on the found cycle.
 		    ///
 		    /// This function returns the number of arcs on the found cycle.
 		    ///
 		    /// \pre \ref run() or \ref findMinMean() must be called before
 		    /// using this function.
 		    int cycleArcNum() const {
 		      return _cycle_size;
+		    }
 		    /// \brief Return the mean length of the found cycle.
 		    ///
 		    /// This function returns the mean length of the found cycle.
 		    ///
 		    /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
 		    /// following code.
 		    /// \code
 		    ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
 		    /// \endcode
 		    ///
 		    /// \pre \ref run() or \ref findMinMean() must be called before
 		    /// using this function.
 		    double cycleMean() const {
 		      return static_cast<double>(_cycle_length) / _cycle_size;
+		    }
 		    /// \brief Return the found cycle.
 		    ///
 		    /// This function returns a const reference to the path structure
 		    /// storing the found cycle.
 		    ///
 		    /// \pre \ref run() or \ref findCycle() must be called before using
 		    /// this function.
 		    const Path& cycle() const {
 		      return *_cycle_path;
+		    }
 		    ///@}
 		  private:
 		    // Initialization
 		    void init() {
 		      if (!_cycle_path) {
 		        _local_path = true;
 		        _cycle_path = new Path;
+		      }
 		      _cycle_path->clear();
 		      _cycle_length = 0;
 		      _cycle_size = 1;
 		      _cycle_node = INVALID;
 		      for (NodeIt u(_gr); u != INVALID; ++u)
 		        _data[u].clear();
+		    }
 		    // Find strongly connected components and initialize _comp_nodes
 		    // and _out_arcs
 		    void findComponents() {
 		      _comp_num = stronglyConnectedComponents(_gr, _comp);
 		      _comp_nodes.resize(_comp_num);
 		      if (_comp_num == 1) {
 		        _comp_nodes[0].clear();
 		        for (NodeIt n(_gr); n != INVALID; ++n) {
 		          _comp_nodes[0].push_back(n);
 		          _out_arcs[n].clear();
 		          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
 		            _out_arcs[n].push_back(a);
+		          }
+		        }
 		      } else {
 		        for (int i = 0; i < _comp_num; ++i)
 		          _comp_nodes[i].clear();
 		        for (NodeIt n(_gr); n != INVALID; ++n) {
 		          int k = _comp[n];
 		          _comp_nodes[k].push_back(n);
 		          _out_arcs[n].clear();
 		          for (OutArcIt a(_gr, n); a != INVALID; ++a) {
 		            if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
+		          }
+		        }
+		      }
+		    }
 		    // Initialize path data for the current component
 		    bool initComponent(int comp) {
 		      _nodes = &(_comp_nodes[comp]);
 		      int n = _nodes->size();
 		      if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
 		        return false;
+		      }
 		      for (int i = 0; i < n; ++i) {
 		        _data[(*_nodes)[i]].resize(n + 1, PathData(INF));
+		      }
 		      return true;
+		    }
 		    // Process all rounds of computing path data for the current component.
 		    // _data[v][k] is the length of a shortest directed walk from the root
 		    // node to node v containing exactly k arcs.
 		    void processRounds() {
 		      Node start = (*_nodes)[0];
 		      _data[start][0] = PathData(0);
 		      _process.clear();
 		      _process.push_back(start);
 		      int k, n = _nodes->size();
 		      for (k = 1; k <= n && int(_process.size()) < n; ++k) {
 		        processNextBuildRound(k);
+		      }
 		      for ( ; k <= n; ++k) {
 		        processNextFullRound(k);
+		      }
+		    }
 		    // Process one round and rebuild _process
 		    void processNextBuildRound(int k) {
 		      std::vector<Node> next;
 		      Node u, v;
 		      Arc e;
 		      LargeValue d;
 		      for (int i = 0; i < int(_process.size()); ++i) {
 		        u = _process[i];
 		        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
 		          e = _out_arcs[u][j];
 		          v = _gr.target(e);
 		          d = _data[u][k-1].dist + _length[e];
 		          if (_tolerance.less(d, _data[v][k].dist)) {
 		            if (_data[v][k].dist == INF) next.push_back(v);
 		            _data[v][k] = PathData(d, e);
+		          }
+		        }
+		      }
 		      _process.swap(next);
+		    }
 		    // Process one round using _nodes instead of _process
 		    void processNextFullRound(int k) {
 		      Node u, v;
 		      Arc e;
 		      LargeValue d;
 		      for (int i = 0; i < int(_nodes->size()); ++i) {
 		        u = (*_nodes)[i];
 		        for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
 		          e = _out_arcs[u][j];
 		          v = _gr.target(e);
 		          d = _data[u][k-1].dist + _length[e];
 		          if (_tolerance.less(d, _data[v][k].dist)) {
 		            _data[v][k] = PathData(d, e);
+		          }
+		        }
+		      }
+		    }
 		    // Update the minimum cycle mean
 		    void updateMinMean() {
 		      int n = _nodes->size();
 		      for (int i = 0; i < n; ++i) {
 		        Node u = (*_nodes)[i];
 		        if (_data[u][n].dist == INF) continue;
 		        LargeValue length, max_length = 0;
 		        int size, max_size = 1;
 		        bool found_curr = false;
 		        for (int k = 0; k < n; ++k) {
 		          if (_data[u][k].dist == INF) continue;
 		          length = _data[u][n].dist - _data[u][k].dist;
 		          size = n - k;
 		          if (!found_curr || length * max_size > max_length * size) {
 		            found_curr = true;
 		            max_length = length;
 		            max_size = size;
+		          }
+		        }
 		        if ( found_curr && (_cycle_node == INVALID ||
 		             max_length * _cycle_size < _cycle_length * max_size) ) {
 		          _cycle_length = max_length;
 		          _cycle_size = max_size;
 		          _cycle_node = u;
+		        }
+		      }
+		    }
 		  }; //class Karp
 		  ///@}
 		} //namespace lemon
 		#endif //LEMON_KARP_H

lemon/min_cost_arborescence.h

Show inline comments

 		/* -*- mode: C++; indent-tabs-mode: nil; -*-
+		 *
 		 * 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_MIN_COST_ARBORESCENCE_H
 		#define LEMON_MIN_COST_ARBORESCENCE_H
 		///\ingroup spantree
 		///\file
 		///\brief Minimum Cost Arborescence algorithm.
 		#include <vector>
 		#include <lemon/list_graph.h>
 		#include <lemon/bin_heap.h>
 		#include <lemon/assert.h>
 		namespace lemon {
 		  /// \brief Default traits class for MinCostArborescence class.
 		  ///
 		  /// Default traits class for MinCostArborescence class.
 		  /// \param GR Digraph type.
 		  /// \param CM Type of the cost map.
 		  template <class GR, class CM>
 		  struct MinCostArborescenceDefaultTraits{
 		    /// \brief The digraph type the algorithm runs on.
 		    typedef GR Digraph;
 		    /// \brief The type of the map that stores the arc costs.
 		    ///
 		    /// The type of the map that stores the arc costs.
 		    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
 		    typedef CM CostMap;
 		    /// \brief The value type of the costs.
 		    ///
 		    /// The value type of the costs.
 		    typedef typename CostMap::Value Value;
 		    /// \brief The type of the map that stores which arcs are in the
 		    /// arborescence.
 		    ///
 		    /// The type of the map that stores which arcs are in the
 		    /// arborescence.  It must conform to the \ref concepts::WriteMap
 		    /// "WriteMap" concept, and its value type must be \c bool
 		    /// (or convertible). Initially it will be set to \c false on each
 		    /// arc, then it will be set on each arborescence arc once.
 		    typedef typename Digraph::template ArcMap<bool> ArborescenceMap;
 		    /// \brief Instantiates a \c ArborescenceMap.
 		    ///
 		    /// This function instantiates a \c ArborescenceMap.
 		    /// \param digraph The digraph to which we would like to calculate
 		    /// the \c ArborescenceMap.
 		    static ArborescenceMap *createArborescenceMap(const Digraph &digraph){
 		      return new ArborescenceMap(digraph);
+		    }
 		    /// \brief The type of the \c PredMap
 		    ///
 		    /// The type of the \c PredMap. It must confrom to the
 		    /// \ref concepts::WriteMap "WriteMap" concept, and its value type
 		    /// must be the \c Arc type of the digraph.
 		    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;
 		    /// \brief Instantiates a \c PredMap.
 		    ///
 		    /// This function instantiates a \c PredMap.
 		    /// \param digraph The digraph to which we would like to define the
 		    /// \c PredMap.
 		    static PredMap *createPredMap(const Digraph &digraph){
 		      return new PredMap(digraph);
+		    }
 		  };
 		  /// \ingroup spantree
 		  ///
 		  /// \brief Minimum Cost Arborescence algorithm class.
 		  ///
 		  /// This class provides an efficient implementation of the
 		  /// Minimum Cost Arborescence algorithm. The arborescence is a tree
 		  /// which is directed from a given source node of the digraph. One or
 		  /// more sources should be given to the algorithm and it will calculate
 		  /// the minimum cost subgraph that is the union of arborescences with the
 		  /// given sources and spans all the nodes which are reachable from the
 		  /// sources. The time complexity of the algorithm is O(n<sup>2</sup>+e).
 		  ///
 		  /// The algorithm also provides an optimal dual solution, therefore
 		  /// the optimality of the solution can be checked.
 		  ///
 		  /// \param GR The digraph type the algorithm runs on.
 		  /// \param CM A read-only arc map storing the costs of the
 		  /// arcs. It is read once for each arc, so the map may involve in
 		  /// relatively time consuming process to compute the arc costs if
 		  /// it is necessary. The default map type is \ref
 		  /// concepts::Digraph::ArcMap "Digraph::ArcMap<int>".
 		  /// \param TR Traits class to set various data types used
 		  /// by the algorithm. The default traits class is
-		  /// \ref MinCostArborescenceDefaultTraits
+		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm. By default, it is \ref MinCostArborescenceDefaultTraits
 		  /// "MinCostArborescenceDefaultTraits<GR, CM>".
 		  /// In most cases, this parameter should not be set directly,
 		  /// consider to use the named template parameters instead.
 		#ifndef DOXYGEN
 		  template <typename GR,
 		            typename CM = typename GR::template ArcMap<int>,
 		            typename TR =
 		              MinCostArborescenceDefaultTraits<GR, CM> >
 		#else
-		  template <typename GR, typename CM, typedef TR>
+		  template <typename GR, typename CM, typename TR>
 		#endif
 		  class MinCostArborescence {
 		  public:
 		    /// \brief The \ref MinCostArborescenceDefaultTraits "traits class"
 		    /// of the algorithm.
 		    typedef TR Traits;
 		    /// The type of the underlying digraph.
 		    typedef typename Traits::Digraph Digraph;
 		    /// The type of the map that stores the arc costs.
 		    typedef typename Traits::CostMap CostMap;
 		    ///The type of the costs of the arcs.
 		    typedef typename Traits::Value Value;
 		    ///The type of the predecessor map.
 		    typedef typename Traits::PredMap PredMap;
 		    ///The type of the map that stores which arcs are in the arborescence.
 		    typedef typename Traits::ArborescenceMap ArborescenceMap;
 		    typedef MinCostArborescence Create;
 		  private:
 		    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
 		    struct CostArc {
 		      Arc arc;
 		      Value value;
 		      CostArc() {}
 		      CostArc(Arc _arc, Value _value) : arc(_arc), value(_value) {}
 		    };
 		    const Digraph *_digraph;
 		    const CostMap *_cost;
 		    PredMap *_pred;
 		    bool local_pred;
 		    ArborescenceMap *_arborescence;
 		    bool local_arborescence;
 		    typedef typename Digraph::template ArcMap<int> ArcOrder;
 		    ArcOrder *_arc_order;
 		    typedef typename Digraph::template NodeMap<int> NodeOrder;
 		    NodeOrder *_node_order;
 		    typedef typename Digraph::template NodeMap<CostArc> CostArcMap;
 		    CostArcMap *_cost_arcs;
 		    struct StackLevel {
 		      std::vector<CostArc> arcs;
 		      int node_level;
 		    };
 		    std::vector<StackLevel> level_stack;
 		    std::vector<Node> queue;
 		    typedef std::vector<typename Digraph::Node> DualNodeList;
 		    DualNodeList _dual_node_list;
 		    struct DualVariable {
 		      int begin, end;
 		      Value value;
 		      DualVariable(int _begin, int _end, Value _value)
 		        : begin(_begin), end(_end), value(_value) {}
 		    };
 		    typedef std::vector<DualVariable> DualVariables;
 		    DualVariables _dual_variables;
 		    typedef typename Digraph::template NodeMap<int> HeapCrossRef;
 		    HeapCrossRef *_heap_cross_ref;
 		    typedef BinHeap<int, HeapCrossRef> Heap;
 		    Heap *_heap;
 		  protected:
 		    MinCostArborescence() {}
 		  private:
 		    void createStructures() {
 		      if (!_pred) {
 		        local_pred = true;
 		        _pred = Traits::createPredMap(*_digraph);
+		      }
 		      if (!_arborescence) {
 		        local_arborescence = true;
 		        _arborescence = Traits::createArborescenceMap(*_digraph);
+		      }
 		      if (!_arc_order) {
 		        _arc_order = new ArcOrder(*_digraph);
+		      }
 		      if (!_node_order) {
 		        _node_order = new NodeOrder(*_digraph);
+		      }
 		      if (!_cost_arcs) {
 		        _cost_arcs = new CostArcMap(*_digraph);
+		      }
 		      if (!_heap_cross_ref) {
 		        _heap_cross_ref = new HeapCrossRef(*_digraph, -1);
+		      }
 		      if (!_heap) {
 		        _heap = new Heap(*_heap_cross_ref);
+		      }
+		    }
 		    void destroyStructures() {
 		      if (local_arborescence) {
 		        delete _arborescence;
+		      }
 		      if (local_pred) {
 		        delete _pred;
+		      }
 		      if (_arc_order) {
 		        delete _arc_order;
+		      }
 		      if (_node_order) {
 		        delete _node_order;
+		      }
 		      if (_cost_arcs) {
 		        delete _cost_arcs;
+		      }
 		      if (_heap) {
 		        delete _heap;
+		      }
 		      if (_heap_cross_ref) {
 		        delete _heap_cross_ref;
+		      }
+		    }
 		    Arc prepare(Node node) {
 		      std::vector<Node> nodes;
 		      (*_node_order)[node] = _dual_node_list.size();
 		      StackLevel level;
 		      level.node_level = _dual_node_list.size();
 		      _dual_node_list.push_back(node);
 		      for (InArcIt it(*_digraph, node); it != INVALID; ++it) {
 		        Arc arc = it;
 		        Node source = _digraph->source(arc);
 		        Value value = (*_cost)[it];
 		        if (source == node || (*_node_order)[source] == -3) continue;
 		        if ((*_cost_arcs)[source].arc == INVALID) {
 		          (*_cost_arcs)[source].arc = arc;
 		          (*_cost_arcs)[source].value = value;
 		          nodes.push_back(source);
 		        } else {
 		          if ((*_cost_arcs)[source].value > value) {
 		            (*_cost_arcs)[source].arc = arc;
 		            (*_cost_arcs)[source].value = value;
+		          }
+		        }
+		      }
 		      CostArc minimum = (*_cost_arcs)[nodes[0]];
 		      for (int i = 1; i < int(nodes.size()); ++i) {
 		        if ((*_cost_arcs)[nodes[i]].value < minimum.value) {
 		          minimum = (*_cost_arcs)[nodes[i]];
+		        }
+		      }
 		      (*_arc_order)[minimum.arc] = _dual_variables.size();
 		      DualVariable var(_dual_node_list.size() - 1,
 		                       _dual_node_list.size(), minimum.value);
 		      _dual_variables.push_back(var);
 		      for (int i = 0; i < int(nodes.size()); ++i) {
 		        (*_cost_arcs)[nodes[i]].value -= minimum.value;
 		        level.arcs.push_back((*_cost_arcs)[nodes[i]]);
 		        (*_cost_arcs)[nodes[i]].arc = INVALID;
+		      }
 		      level_stack.push_back(level);
 		      return minimum.arc;
+		    }
 		    Arc contract(Node node) {
 		      int node_bottom = bottom(node);
 		      std::vector<Node> nodes;
 		      while (!level_stack.empty() &&
 		             level_stack.back().node_level >= node_bottom) {
 		        for (int i = 0; i < int(level_stack.back().arcs.size()); ++i) {
 		          Arc arc = level_stack.back().arcs[i].arc;
 		          Node source = _digraph->source(arc);
 		          Value value = level_stack.back().arcs[i].value;
 		          if ((*_node_order)[source] >= node_bottom) continue;
 		          if ((*_cost_arcs)[source].arc == INVALID) {
 		            (*_cost_arcs)[source].arc = arc;
 		            (*_cost_arcs)[source].value = value;
 		            nodes.push_back(source);
 		          } else {
 		            if ((*_cost_arcs)[source].value > value) {
 		              (*_cost_arcs)[source].arc = arc;
 		              (*_cost_arcs)[source].value = value;
+		            }
+		          }
+		        }
 		        level_stack.pop_back();
+		      }
 		      CostArc minimum = (*_cost_arcs)[nodes[0]];
 		      for (int i = 1; i < int(nodes.size()); ++i) {
 		        if ((*_cost_arcs)[nodes[i]].value < minimum.value) {
 		          minimum = (*_cost_arcs)[nodes[i]];
+		        }
+		      }
 		      (*_arc_order)[minimum.arc] = _dual_variables.size();
 		      DualVariable var(node_bottom, _dual_node_list.size(), minimum.value);
 		      _dual_variables.push_back(var);
 		      StackLevel level;
 		      level.node_level = node_bottom;
 		      for (int i = 0; i < int(nodes.size()); ++i) {
 		        (*_cost_arcs)[nodes[i]].value -= minimum.value;
 		        level.arcs.push_back((*_cost_arcs)[nodes[i]]);
 		        (*_cost_arcs)[nodes[i]].arc = INVALID;
+		      }
 		      level_stack.push_back(level);
 		      return minimum.arc;
+		    }
 		    int bottom(Node node) {
 		      int k = level_stack.size() - 1;
 		      while (level_stack[k].node_level > (*_node_order)[node]) {
 		        --k;
+		      }
 		      return level_stack[k].node_level;
+		    }
 		    void finalize(Arc arc) {
 		      Node node = _digraph->target(arc);
 		      _heap->push(node, (*_arc_order)[arc]);
 		      _pred->set(node, arc);
 		      while (!_heap->empty()) {
 		        Node source = _heap->top();
 		        _heap->pop();
 		        (*_node_order)[source] = -1;
 		        for (OutArcIt it(*_digraph, source); it != INVALID; ++it) {
 		          if ((*_arc_order)[it] < 0) continue;
 		          Node target = _digraph->target(it);
 		          switch(_heap->state(target)) {
 		          case Heap::PRE_HEAP:
 		            _heap->push(target, (*_arc_order)[it]);
 		            _pred->set(target, it);
 		            break;
 		          case Heap::IN_HEAP:
 		            if ((*_arc_order)[it] < (*_heap)[target]) {
 		              _heap->decrease(target, (*_arc_order)[it]);
 		              _pred->set(target, it);
+		            }
 		            break;
 		          case Heap::POST_HEAP:
 		            break;
+		          }
+		        }
 		        _arborescence->set((*_pred)[source], true);
+		      }
+		    }
 		  public:
 		    /// \name Named Template Parameters
 		    /// @{
 		    template <class T>
 		    struct SetArborescenceMapTraits : public Traits {
 		      typedef T ArborescenceMap;
 		      static ArborescenceMap *createArborescenceMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "ArborescenceMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for
 		    /// setting \c ArborescenceMap type
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting
 		    /// \c ArborescenceMap type.
 		    /// It must conform to the \ref concepts::WriteMap "WriteMap" concept,
 		    /// and its value type must be \c bool (or convertible).
 		    /// Initially it will be set to \c false on each arc,
 		    /// then it will be set on each arborescence arc once.
 		    template <class T>
 		    struct SetArborescenceMap
 		      : public MinCostArborescence<Digraph, CostMap,
 		                                   SetArborescenceMapTraits<T> > {
 		    };
 		    template <class T>
 		    struct SetPredMapTraits : public Traits {
 		      typedef T PredMap;
 		      static PredMap *createPredMap(const Digraph &)
+		      {
 		        LEMON_ASSERT(false, "PredMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for
 		    /// setting \c PredMap type
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting
 		    /// \c PredMap type.
 		    /// It must meet the \ref concepts::WriteMap "WriteMap" concept,
 		    /// and its value type must be the \c Arc type of the digraph.
 		    template <class T>
 		    struct SetPredMap
 		      : public MinCostArborescence<Digraph, CostMap, SetPredMapTraits<T> > {
 		    };
 		    /// @}
 		    /// \brief Constructor.
 		    ///
 		    /// \param digraph The digraph the algorithm will run on.
 		    /// \param cost The cost map used by the algorithm.
 		    MinCostArborescence(const Digraph& digraph, const CostMap& cost)
 		      : _digraph(&digraph), _cost(&cost), _pred(0), local_pred(false),
 		        _arborescence(0), local_arborescence(false),
 		        _arc_order(0), _node_order(0), _cost_arcs(0),
 		        _heap_cross_ref(0), _heap(0) {}
 		    /// \brief Destructor.
 		    ~MinCostArborescence() {
 		      destroyStructures();
+		    }
 		    /// \brief Sets the arborescence map.
 		    ///
 		    /// Sets the arborescence map.
 		    /// \return <tt>(*this)</tt>
 		    MinCostArborescence& arborescenceMap(ArborescenceMap& m) {
 		      if (local_arborescence) {
 		        delete _arborescence;
+		      }
 		      local_arborescence = false;
 		      _arborescence = &m;
 		      return *this;
+		    }
 		    /// \brief Sets the predecessor map.
 		    ///
 		    /// Sets the predecessor map.
 		    /// \return <tt>(*this)</tt>
 		    MinCostArborescence& predMap(PredMap& m) {
 		      if (local_pred) {
 		        delete _pred;
+		      }
 		      local_pred = false;
 		      _pred = &m;
 		      return *this;
+		    }
 		    /// \name Execution Control
 		    /// The simplest way to execute the algorithm is to use
 		    /// one of the member functions called \c run(...). \n
 		    /// If you need better control on the execution,
 		    /// you have to call \ref init() first, then you can add several
 		    /// source nodes with \ref addSource().
 		    /// Finally \ref start() will perform the arborescence
 		    /// computation.
 		    ///@{
 		    /// \brief Initializes the internal data structures.
 		    ///
 		    /// Initializes the internal data structures.
 		    ///
 		    void init() {
 		      createStructures();
 		      _heap->clear();
 		      for (NodeIt it(*_digraph); it != INVALID; ++it) {
 		        (*_cost_arcs)[it].arc = INVALID;
 		        (*_node_order)[it] = -3;
 		        (*_heap_cross_ref)[it] = Heap::PRE_HEAP;
 		        _pred->set(it, INVALID);
+		      }
 		      for (ArcIt it(*_digraph); it != INVALID; ++it) {
 		        _arborescence->set(it, false);
 		        (*_arc_order)[it] = -1;
+		      }
 		      _dual_node_list.clear();
 		      _dual_variables.clear();
+		    }
 		    /// \brief Adds a new source node.
 		    ///
 		    /// Adds a new source node to the algorithm.
 		    void addSource(Node source) {
 		      std::vector<Node> nodes;
 		      nodes.push_back(source);
 		      while (!nodes.empty()) {
 		        Node node = nodes.back();
 		        nodes.pop_back();
 		        for (OutArcIt it(*_digraph, node); it != INVALID; ++it) {
 		          Node target = _digraph->target(it);
 		          if ((*_node_order)[target] == -3) {
 		            (*_node_order)[target] = -2;
 		            nodes.push_back(target);
 		            queue.push_back(target);
+		          }
+		        }
+		      }
 		      (*_node_order)[source] = -1;
+		    }
 		    /// \brief Processes the next node in the priority queue.
 		    ///
 		    /// Processes the next node in the priority queue.
 		    ///
 		    /// \return The processed node.
 		    ///
 		    /// \warning The queue must not be empty.
 		    Node processNextNode() {
 		      Node node = queue.back();
 		      queue.pop_back();
 		      if ((*_node_order)[node] == -2) {
 		        Arc arc = prepare(node);
 		        Node source = _digraph->source(arc);
 		        while ((*_node_order)[source] != -1) {
 		          if ((*_node_order)[source] >= 0) {
 		            arc = contract(source);
 		          } else {
 		            arc = prepare(source);
+		          }
 		          source = _digraph->source(arc);
+		        }
 		        finalize(arc);
 		        level_stack.clear();
+		      }
 		      return node;
+		    }
 		    /// \brief Returns the number of the nodes to be processed.
 		    ///
 		    /// Returns the number of the nodes to be processed in the priority
 		    /// queue.
 		    int queueSize() const {
 		      return queue.size();
+		    }
 		    /// \brief Returns \c false if there are nodes to be processed.
 		    ///
 		    /// Returns \c false if there are nodes to be processed.
 		    bool emptyQueue() const {
 		      return queue.empty();
+		    }
 		    /// \brief Executes the algorithm.
 		    ///
 		    /// Executes the algorithm.
 		    ///
 		    /// \pre init() must be called and at least one node should be added
 		    /// with addSource() before using this function.
 		    ///
 		    ///\note mca.start() is just a shortcut of the following code.
 		    ///\code
 		    ///while (!mca.emptyQueue()) {
 		    ///  mca.processNextNode();
 		    ///}
 		    ///\endcode
 		    void start() {
 		      while (!emptyQueue()) {
 		        processNextNode();
+		      }
+		    }
 		    /// \brief Runs %MinCostArborescence algorithm from node \c s.
 		    ///
 		    /// This method runs the %MinCostArborescence algorithm from
 		    /// a root node \c s.
 		    ///
 		    /// \note mca.run(s) is just a shortcut of the following code.
 		    /// \code
 		    /// mca.init();
 		    /// mca.addSource(s);
 		    /// mca.start();
 		    /// \endcode
 		    void run(Node s) {
 		      init();
 		      addSource(s);
 		      start();
+		    }
 		    ///@}
 		    /// \name Query Functions
 		    /// The result of the %MinCostArborescence algorithm can be obtained
 		    /// using these functions.\n
 		    /// Either run() or start() must be called before using them.
 		    /// @{
 		    /// \brief Returns the cost of the arborescence.
 		    ///
 		    /// Returns the cost of the arborescence.
 		    Value arborescenceCost() const {
 		      Value sum = 0;
 		      for (ArcIt it(*_digraph); it != INVALID; ++it) {
 		        if (arborescence(it)) {
 		          sum += (*_cost)[it];
+		        }
+		      }
 		      return sum;
+		    }
 		    /// \brief Returns \c true if the arc is in the arborescence.
 		    ///
 		    /// Returns \c true if the given arc is in the arborescence.
 		    /// \param arc An arc of the digraph.
 		    /// \pre \ref run() must be called before using this function.
 		    bool arborescence(Arc arc) const {
 		      return (*_pred)[_digraph->target(arc)] == arc;
+		    }
 		    /// \brief Returns a const reference to the arborescence map.
 		    ///
 		    /// Returns a const reference to the arborescence map.
 		    /// \pre \ref run() must be called before using this function.
 		    const ArborescenceMap& arborescenceMap() const {
 		      return *_arborescence;
+		    }
 		    /// \brief Returns the predecessor arc of the given node.
 		    ///
 		    /// Returns the predecessor arc of the given node.
 		    /// \pre \ref run() must be called before using this function.
 		    Arc pred(Node node) const {
 		      return (*_pred)[node];
+		    }
 		    /// \brief Returns a const reference to the pred map.
 		    ///
 		    /// Returns a const reference to the pred map.
 		    /// \pre \ref run() must be called before using this function.
 		    const PredMap& predMap() const {
 		      return *_pred;
+		    }
 		    /// \brief Indicates that a node is reachable from the sources.
 		    ///
 		    /// Indicates that a node is reachable from the sources.
 		    bool reached(Node node) const {
 		      return (*_node_order)[node] != -3;
+		    }
 		    /// \brief Indicates that a node is processed.
 		    ///
 		    /// Indicates that a node is processed. The arborescence path exists
 		    /// from the source to the given node.
 		    bool processed(Node node) const {
 		      return (*_node_order)[node] == -1;
+		    }
 		    /// \brief Returns the number of the dual variables in basis.
 		    ///
 		    /// Returns the number of the dual variables in basis.
 		    int dualNum() const {
 		      return _dual_variables.size();
+		    }
 		    /// \brief Returns the value of the dual solution.
 		    ///
 		    /// Returns the value of the dual solution. It should be
 		    /// equal to the arborescence value.
 		    Value dualValue() const {
 		      Value sum = 0;
 		      for (int i = 0; i < int(_dual_variables.size()); ++i) {
 		        sum += _dual_variables[i].value;
+		      }
 		      return sum;
+		    }
 		    /// \brief Returns the number of the nodes in the dual variable.
 		    ///
 		    /// Returns the number of the nodes in the dual variable.
 		    int dualSize(int k) const {
 		      return _dual_variables[k].end - _dual_variables[k].begin;
+		    }
 		    /// \brief Returns the value of the dual variable.
 		    ///
 		    /// Returns the the value of the dual variable.
 		    Value dualValue(int k) const {
 		      return _dual_variables[k].value;
+		    }
 		    /// \brief LEMON iterator for getting a dual variable.
 		    ///
 		    /// This class provides a common style LEMON iterator for getting a
 		    /// dual variable of \ref MinCostArborescence algorithm.
 		    /// It iterates over a subset of the nodes.
 		    class DualIt {
 		    public:
 		      /// \brief Constructor.
 		      ///
 		      /// Constructor for getting the nodeset of the dual variable
 		      /// of \ref MinCostArborescence algorithm.
 		      DualIt(const MinCostArborescence& algorithm, int variable)
 		        : _algorithm(&algorithm)
+		      {
 		        _index = _algorithm->_dual_variables[variable].begin;
 		        _last = _algorithm->_dual_variables[variable].end;
+		      }
 		      /// \brief Conversion to \c Node.
 		      ///
 		      /// Conversion to \c Node.
 		      operator Node() const {
 		        return _algorithm->_dual_node_list[_index];
+		      }
 		      /// \brief Increment operator.
 		      ///
 		      /// Increment operator.
 		      DualIt& operator++() {
 		        ++_index;
 		        return *this;
+		      }
 		      /// \brief Validity checking
 		      ///
 		      /// Checks whether the iterator is invalid.
 		      bool operator==(Invalid) const {
 		        return _index == _last;
+		      }
 		      /// \brief Validity checking
 		      ///
 		      /// Checks whether the iterator is valid.
 		      bool operator!=(Invalid) const {
 		        return _index != _last;
+		      }
 		    private:
 		      const MinCostArborescence* _algorithm;
 		      int _index, _last;
 		    };
 		    /// @}
 		  };
 		  /// \ingroup spantree
 		  ///
 		  /// \brief Function type interface for MinCostArborescence algorithm.
 		  ///
 		  /// Function type interface for MinCostArborescence algorithm.
 		  /// \param digraph The digraph the algorithm runs on.
 		  /// \param cost An arc map storing the costs.
 		  /// \param source The source node of the arborescence.
 		  /// \retval arborescence An arc map with \c bool (or convertible) value
 		  /// type that stores the arborescence.
 		  /// \return The total cost of the arborescence.
 		  ///
 		  /// \sa MinCostArborescence
 		  template <typename Digraph, typename CostMap, typename ArborescenceMap>
 		  typename CostMap::Value minCostArborescence(const Digraph& digraph,
 		                                              const CostMap& cost,
 		                                              typename Digraph::Node source,
 		                                              ArborescenceMap& arborescence) {
 		    typename MinCostArborescence<Digraph, CostMap>
 		      ::template SetArborescenceMap<ArborescenceMap>
 		      ::Create mca(digraph, cost);
 		    mca.arborescenceMap(arborescence);
 		    mca.run(source);
 		    return mca.arborescenceCost();
+		  }
+		}
 		#endif

lemon/preflow.h

Show inline comments

 		/* -*- 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_PREFLOW_H
 		#define LEMON_PREFLOW_H
 		#include <lemon/tolerance.h>
 		#include <lemon/elevator.h>
 		/// \file
 		/// \ingroup max_flow
 		/// \brief Implementation of the preflow algorithm.
 		namespace lemon {
 		  /// \brief Default traits class of Preflow class.
 		  ///
 		  /// Default traits class of Preflow class.
 		  /// \tparam GR Digraph type.
 		  /// \tparam CAP Capacity map type.
 		  template <typename GR, typename CAP>
 		  struct PreflowDefaultTraits {
 		    /// \brief The type of the digraph the algorithm runs on.
 		    typedef GR Digraph;
 		    /// \brief The type of the map that stores the arc capacities.
 		    ///
 		    /// The type of the map that stores the arc capacities.
 		    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
 		    typedef CAP CapacityMap;
 		    /// \brief The type of the flow values.
 		    typedef typename CapacityMap::Value Value;
 		    /// \brief The type of the map that stores the flow values.
 		    ///
 		    /// The type of the map that stores the flow values.
 		    /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
 		#ifdef DOXYGEN
 		    typedef GR::ArcMap<Value> FlowMap;
 		#else
 		    typedef typename Digraph::template ArcMap<Value> FlowMap;
 		#endif
 		    /// \brief Instantiates a FlowMap.
 		    ///
 		    /// This function instantiates a \ref FlowMap.
 		    /// \param digraph The digraph for which we would like to define
 		    /// the flow map.
 		    static FlowMap* createFlowMap(const Digraph& digraph) {
 		      return new FlowMap(digraph);
+		    }
 		    /// \brief The elevator type used by Preflow algorithm.
 		    ///
 		    /// The elevator type used by Preflow algorithm.
 		    ///
 		    /// \sa Elevator, LinkedElevator
 		#ifdef DOXYGEN
 		    typedef lemon::Elevator<GR, GR::Node> Elevator;
 		#else
 		    typedef lemon::Elevator<Digraph, typename Digraph::Node> Elevator;
 		#endif
 		    /// \brief Instantiates an Elevator.
 		    ///
 		    /// This function instantiates an \ref Elevator.
 		    /// \param digraph The digraph for which we would like to define
 		    /// the elevator.
 		    /// \param max_level The maximum level of the elevator.
 		    static Elevator* createElevator(const Digraph& digraph, int max_level) {
 		      return new Elevator(digraph, max_level);
+		    }
 		    /// \brief The tolerance used by the algorithm
 		    ///
 		    /// The tolerance used by the algorithm to handle inexact computation.
 		    typedef lemon::Tolerance<Value> Tolerance;
 		  };
 		  /// \ingroup max_flow
 		  ///
 		  /// \brief %Preflow algorithm class.
 		  ///
 		  /// This class provides an implementation of Goldberg-Tarjan's \e preflow
 		  /// \e push-relabel algorithm producing a \ref max_flow
 		  /// "flow of maximum value" in a digraph \ref clrs01algorithms,
 		  /// \ref amo93networkflows, \ref goldberg88newapproach.
 		  /// The preflow algorithms are the fastest known maximum
 		  /// flow algorithms. The current implementation uses a mixture of the
 		  /// \e "highest label" and the \e "bound decrease" heuristics.
 		  /// The worst case time complexity of the algorithm is \f$O(n^2\sqrt{e})\f$.
 		  ///
 		  /// The algorithm consists of two phases. After the first phase
 		  /// the maximum flow value and the minimum cut is obtained. The
 		  /// second phase constructs a feasible maximum flow on each arc.
 		  ///
 		  /// \warning This implementation cannot handle infinite or very large
 		  /// capacities (e.g. the maximum value of \c CAP::Value).
 		  ///
 		  /// \tparam GR The type of the digraph the algorithm runs on.
 		  /// \tparam CAP The type of the capacity map. The default map
 		  /// type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
 		  /// \tparam TR The traits class that defines various types used by the
 		  /// algorithm. By default, it is \ref PreflowDefaultTraits
 		  /// "PreflowDefaultTraits<GR, CAP>".
 		  /// In most cases, this parameter should not be set directly,
 		  /// consider to use the named template parameters instead.
 		#ifdef DOXYGEN
 		  template <typename GR, typename CAP, typename TR>
 		#else
 		  template <typename GR,
 		            typename CAP = typename GR::template ArcMap<int>,
 		            typename TR = PreflowDefaultTraits<GR, CAP> >
 		#endif
 		  class Preflow {
 		  public:
 		    ///The \ref PreflowDefaultTraits "traits class" of the algorithm.
 		    typedef TR Traits;
 		    ///The type of the digraph the algorithm runs on.
 		    typedef typename Traits::Digraph Digraph;
 		    ///The type of the capacity map.
 		    typedef typename Traits::CapacityMap CapacityMap;
 		    ///The type of the flow values.
 		    typedef typename Traits::Value Value;
 		    ///The type of the flow map.
 		    typedef typename Traits::FlowMap FlowMap;
 		    ///The type of the elevator.
 		    typedef typename Traits::Elevator Elevator;
 		    ///The type of the tolerance.
 		    typedef typename Traits::Tolerance Tolerance;
 		  private:
 		    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
 		    const Digraph& _graph;
 		    const CapacityMap* _capacity;
 		    int _node_num;
 		    Node _source, _target;
 		    FlowMap* _flow;
 		    bool _local_flow;
 		    Elevator* _level;
 		    bool _local_level;
 		    typedef typename Digraph::template NodeMap<Value> ExcessMap;
 		    ExcessMap* _excess;
 		    Tolerance _tolerance;
 		    bool _phase;
 		    void createStructures() {
 		      _node_num = countNodes(_graph);
 		      if (!_flow) {
 		        _flow = Traits::createFlowMap(_graph);
 		        _local_flow = true;
+		      }
 		      if (!_level) {
 		        _level = Traits::createElevator(_graph, _node_num);
 		        _local_level = true;
+		      }
 		      if (!_excess) {
 		        _excess = new ExcessMap(_graph);
+		      }
+		    }
 		    void destroyStructures() {
 		      if (_local_flow) {
 		        delete _flow;
+		      }
 		      if (_local_level) {
 		        delete _level;
+		      }
 		      if (_excess) {
 		        delete _excess;
+		      }
+		    }
 		  public:
 		    typedef Preflow Create;
 		    ///\name Named Template Parameters
 		    ///@{
 		    template <typename T>
 		    struct SetFlowMapTraits : public Traits {
 		      typedef T FlowMap;
 		      static FlowMap *createFlowMap(const Digraph&) {
 		        LEMON_ASSERT(false, "FlowMap is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// FlowMap type
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting FlowMap
 		    /// type.
 		    template <typename T>
 		    struct SetFlowMap
 		      : public Preflow<Digraph, CapacityMap, SetFlowMapTraits<T> > {
 		      typedef Preflow<Digraph, CapacityMap,
 		                      SetFlowMapTraits<T> > Create;
 		    };
 		    template <typename T>
 		    struct SetElevatorTraits : public Traits {
 		      typedef T Elevator;
 		      static Elevator *createElevator(const Digraph&, int) {
 		        LEMON_ASSERT(false, "Elevator is not initialized");
 		        return 0; // ignore warnings
+		      }
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// Elevator type
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting Elevator
 		    /// type. If this named parameter is used, then an external
 		    /// elevator object must be passed to the algorithm using the
 		    /// \ref elevator(Elevator&) "elevator()" function before calling
 		    /// \ref run() or \ref init().
 		    /// \sa SetStandardElevator
 		    template <typename T>
 		    struct SetElevator
 		      : public Preflow<Digraph, CapacityMap, SetElevatorTraits<T> > {
 		      typedef Preflow<Digraph, CapacityMap,
 		                      SetElevatorTraits<T> > Create;
 		    };
 		    template <typename T>
 		    struct SetStandardElevatorTraits : public Traits {
 		      typedef T Elevator;
 		      static Elevator *createElevator(const Digraph& digraph, int max_level) {
 		        return new Elevator(digraph, max_level);
+		      }
 		    };
 		    /// \brief \ref named-templ-param "Named parameter" for setting
 		    /// Elevator type with automatic allocation
 		    ///
 		    /// \ref named-templ-param "Named parameter" for setting Elevator
 		    /// type with automatic allocation.
 		    /// The Elevator should have standard constructor interface to be
 		    /// able to automatically created by the algorithm (i.e. the
 		    /// digraph and the maximum level should be passed to it).
 		    /// However, an external elevator object could also be passed to the
 		    /// algorithm with the \ref elevator(Elevator&) "elevator()" function
 		    /// before calling \ref run() or \ref init().
 		    /// \sa SetElevator
 		    template <typename T>
 		    struct SetStandardElevator
 		      : public Preflow<Digraph, CapacityMap,
 		                       SetStandardElevatorTraits<T> > {
 		      typedef Preflow<Digraph, CapacityMap,
 		                      SetStandardElevatorTraits<T> > Create;
 		    };
 		    /// @}
 		  protected:
 		    Preflow() {}
 		  public:
 		    /// \brief The constructor of the class.
 		    ///
 		    /// The constructor of the class.
 		    /// \param digraph The digraph the algorithm runs on.
 		    /// \param capacity The capacity of the arcs.
 		    /// \param source The source node.
 		    /// \param target The target node.
 		    Preflow(const Digraph& digraph, const CapacityMap& capacity,
 		            Node source, Node target)
 		      : _graph(digraph), _capacity(&capacity),
 		        _node_num(0), _source(source), _target(target),
 		        _flow(0), _local_flow(false),
 		        _level(0), _local_level(false),
 		        _excess(0), _tolerance(), _phase() {}
 		    /// \brief Destructor.
 		    ///
 		    /// Destructor.
 		    ~Preflow() {
 		      destroyStructures();
+		    }
 		    /// \brief Sets the capacity map.
 		    ///
 		    /// Sets the capacity map.
 		    /// \return <tt>(*this)</tt>
 		    Preflow& capacityMap(const CapacityMap& map) {
 		      _capacity = &map;
 		      return *this;
+		    }
 		    /// \brief Sets the flow map.
 		    ///
 		    /// Sets the flow map.
 		    /// If you don't use this function before calling \ref run() or
 		    /// \ref init(), an instance will be allocated automatically.
 		    /// The destructor deallocates this automatically allocated map,
 		    /// of course.
 		    /// \return <tt>(*this)</tt>
 		    Preflow& flowMap(FlowMap& map) {
 		      if (_local_flow) {
 		        delete _flow;
 		        _local_flow = false;
+		      }
 		      _flow = &map;
 		      return *this;
+		    }
 		    /// \brief Sets the source node.
 		    ///
 		    /// Sets the source node.
 		    /// \return <tt>(*this)</tt>
 		    Preflow& source(const Node& node) {
 		      _source = node;
 		      return *this;
+		    }
 		    /// \brief Sets the target node.
 		    ///
 		    /// Sets the target node.
 		    /// \return <tt>(*this)</tt>
 		    Preflow& target(const Node& node) {
 		      _target = node;
 		      return *this;
+		    }
 		    /// \brief Sets the elevator used by algorithm.
 		    ///
 		    /// Sets the elevator used by algorithm.
 		    /// If you don't use this function before calling \ref run() or
 		    /// \ref init(), an instance will be allocated automatically.
 		    /// The destructor deallocates this automatically allocated elevator,
 		    /// of course.
 		    /// \return <tt>(*this)</tt>
 		    Preflow& elevator(Elevator& elevator) {
 		      if (_local_level) {
 		        delete _level;
 		        _local_level = false;
+		      }
 		      _level = &elevator;
 		      return *this;
+		    }
 		    /// \brief Returns a const reference to the elevator.
 		    ///
 		    /// Returns a const reference to the elevator.
 		    ///
 		    /// \pre Either \ref run() or \ref init() must be called before
 		    /// using this function.
 		    const Elevator& elevator() const {
 		      return *_level;
+		    }
 		    /// \brief Sets the tolerance used by the algorithm.
 		    ///
 		    /// Sets the tolerance object used by the algorithm.
 		    /// \return <tt>(*this)</tt>
 		    Preflow& tolerance(const Tolerance& tolerance) {
 		      _tolerance = tolerance;
 		      return *this;
+		    }
 		    /// \brief Returns a const reference to the tolerance.
 		    ///
 		    /// Returns a const reference to the tolerance object used by
 		    /// the algorithm.
 		    const Tolerance& tolerance() const {
 		      return _tolerance;
+		    }
 		    /// \name Execution Control
 		    /// The simplest way to execute the preflow algorithm is to use
 		    /// \ref run() or \ref runMinCut().\n
 		    /// If you need better control on the initial solution or the execution,
 		    /// you have to call one of the \ref init() functions first, then
 		    /// \ref startFirstPhase() and if you need it \ref startSecondPhase().
 		    ///@{
 		    /// \brief Initializes the internal data structures.
 		    ///
 		    /// Initializes the internal data structures and sets the initial
 		    /// flow to zero on each arc.
 		    void init() {
 		      createStructures();
 		      _phase = true;
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
 		        (*_excess)[n] = 0;
+		      }
 		      for (ArcIt e(_graph); e != INVALID; ++e) {
 		        _flow->set(e, 0);
+		      }
 		      typename Digraph::template NodeMap<bool> reached(_graph, false);
 		      _level->initStart();
 		      _level->initAddItem(_target);
 		      std::vector<Node> queue;
 		      reached[_source] = true;
 		      queue.push_back(_target);
 		      reached[_target] = true;
 		      while (!queue.empty()) {
 		        _level->initNewLevel();
 		        std::vector<Node> nqueue;
 		        for (int i = 0; i < int(queue.size()); ++i) {
 		          Node n = queue[i];
 		          for (InArcIt e(_graph, n); e != INVALID; ++e) {
 		            Node u = _graph.source(e);
 		            if (!reached[u] && _tolerance.positive((*_capacity)[e])) {
 		              reached[u] = true;
 		              _level->initAddItem(u);
 		              nqueue.push_back(u);
+		            }
+		          }
+		        }
 		        queue.swap(nqueue);
+		      }
 		      _level->initFinish();
 		      for (OutArcIt e(_graph, _source); e != INVALID; ++e) {
 		        if (_tolerance.positive((*_capacity)[e])) {
 		          Node u = _graph.target(e);
 		          if ((*_level)[u] == _level->maxLevel()) continue;
 		          _flow->set(e, (*_capacity)[e]);
 		          (*_excess)[u] += (*_capacity)[e];
 		          if (u != _target && !_level->active(u)) {
 		            _level->activate(u);
+		          }
+		        }
+		      }
+		    }
 		    /// \brief Initializes the internal data structures using the
 		    /// given flow map.
 		    ///
 		    /// Initializes the internal data structures and sets the initial
 		    /// flow to the given \c flowMap. The \c flowMap should contain a
 		    /// flow or at least a preflow, i.e. at each node excluding the
 		    /// source node the incoming flow should greater or equal to the
 		    /// outgoing flow.
 		    /// \return \c false if the given \c flowMap is not a preflow.
 		    template <typename FlowMap>
 		    bool init(const FlowMap& flowMap) {
 		      createStructures();
 		      for (ArcIt e(_graph); e != INVALID; ++e) {
 		        _flow->set(e, flowMap[e]);
+		      }
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
 		        Value excess = 0;
 		        for (InArcIt e(_graph, n); e != INVALID; ++e) {
 		          excess += (*_flow)[e];
+		        }
 		        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
 		          excess -= (*_flow)[e];
+		        }
 		        if (excess < 0 && n != _source) return false;
 		        (*_excess)[n] = excess;
+		      }
 		      typename Digraph::template NodeMap<bool> reached(_graph, false);
 		      _level->initStart();
 		      _level->initAddItem(_target);
 		      std::vector<Node> queue;
 		      reached[_source] = true;
 		      queue.push_back(_target);
 		      reached[_target] = true;
 		      while (!queue.empty()) {
 		        _level->initNewLevel();
 		        std::vector<Node> nqueue;
 		        for (int i = 0; i < int(queue.size()); ++i) {
 		          Node n = queue[i];
 		          for (InArcIt e(_graph, n); e != INVALID; ++e) {
 		            Node u = _graph.source(e);
 		            if (!reached[u] &&
 		                _tolerance.positive((*_capacity)[e] - (*_flow)[e])) {
 		              reached[u] = true;
 		              _level->initAddItem(u);
 		              nqueue.push_back(u);
+		            }
+		          }
 		          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
 		            Node v = _graph.target(e);
 		            if (!reached[v] && _tolerance.positive((*_flow)[e])) {
 		              reached[v] = true;
 		              _level->initAddItem(v);
 		              nqueue.push_back(v);
+		            }
+		          }
+		        }
 		        queue.swap(nqueue);
+		      }
 		      _level->initFinish();
 		      for (OutArcIt e(_graph, _source); e != INVALID; ++e) {
 		        Value rem = (*_capacity)[e] - (*_flow)[e];
 		        if (_tolerance.positive(rem)) {
 		          Node u = _graph.target(e);
 		          if ((*_level)[u] == _level->maxLevel()) continue;
 		          _flow->set(e, (*_capacity)[e]);
 		          (*_excess)[u] += rem;
 		          if (u != _target && !_level->active(u)) {
 		            _level->activate(u);
+		          }
+		        }
+		      }
 		      for (InArcIt e(_graph, _source); e != INVALID; ++e) {
 		        Value rem = (*_flow)[e];
 		        if (_tolerance.positive(rem)) {
 		          Node v = _graph.source(e);
 		          if ((*_level)[v] == _level->maxLevel()) continue;
 		          _flow->set(e, 0);
 		          (*_excess)[v] += rem;
 		          if (v != _target && !_level->active(v)) {
 		            _level->activate(v);
+		          }
+		        }
+		      }
 		      return true;
+		    }
 		    /// \brief Starts the first phase of the preflow algorithm.
 		    ///
 		    /// The preflow algorithm consists of two phases, this method runs
 		    /// the first phase. After the first phase the maximum flow value
 		    /// and a minimum value cut can already be computed, although a
 		    /// maximum flow is not yet obtained. So after calling this method
 		    /// \ref flowValue() returns the value of a maximum flow and \ref
 		    /// minCut() returns a minimum cut.
 		    /// \pre One of the \ref init() functions must be called before
 		    /// using this function.
 		    void startFirstPhase() {
 		      _phase = true;
 		      Node n = _level->highestActive();
 		      int level = _level->highestActiveLevel();
 		      while (n != INVALID) {
 		        int num = _node_num;
 		        while (num > 0 && n != INVALID) {
 		          Value excess = (*_excess)[n];
 		          int new_level = _level->maxLevel();
 		          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
 		            Value rem = (*_capacity)[e] - (*_flow)[e];
 		            if (!_tolerance.positive(rem)) continue;
 		            Node v = _graph.target(e);
 		            if ((*_level)[v] < level) {
 		              if (!_level->active(v) && v != _target) {
 		                _level->activate(v);
+		              }
 		              if (!_tolerance.less(rem, excess)) {
 		                _flow->set(e, (*_flow)[e] + excess);
 		                (*_excess)[v] += excess;
 		                excess = 0;
 		                goto no_more_push_1;
 		              } else {
 		                excess -= rem;
 		                (*_excess)[v] += rem;
 		                _flow->set(e, (*_capacity)[e]);
+		              }
 		            } else if (new_level > (*_level)[v]) {
 		              new_level = (*_level)[v];
+		            }
+		          }
 		          for (InArcIt e(_graph, n); e != INVALID; ++e) {
 		            Value rem = (*_flow)[e];
 		            if (!_tolerance.positive(rem)) continue;
 		            Node v = _graph.source(e);
 		            if ((*_level)[v] < level) {
 		              if (!_level->active(v) && v != _target) {
 		                _level->activate(v);
+		              }
 		              if (!_tolerance.less(rem, excess)) {
 		                _flow->set(e, (*_flow)[e] - excess);
 		                (*_excess)[v] += excess;
 		                excess = 0;
 		                goto no_more_push_1;
 		              } else {
 		                excess -= rem;
 		                (*_excess)[v] += rem;
 		                _flow->set(e, 0);
+		              }
 		            } else if (new_level > (*_level)[v]) {
 		              new_level = (*_level)[v];
+		            }
+		          }
 		        no_more_push_1:
 		          (*_excess)[n] = excess;
 		          if (excess != 0) {
 		            if (new_level + 1 < _level->maxLevel()) {
 		              _level->liftHighestActive(new_level + 1);
 		            } else {
 		              _level->liftHighestActiveToTop();
+		            }
 		            if (_level->emptyLevel(level)) {
 		              _level->liftToTop(level);
+		            }
 		          } else {
 		            _level->deactivate(n);
+		          }
 		          n = _level->highestActive();
 		          level = _level->highestActiveLevel();
 		          --num;
+		        }
 		        num = _node_num * 20;
 		        while (num > 0 && n != INVALID) {
 		          Value excess = (*_excess)[n];
 		          int new_level = _level->maxLevel();
 		          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
 		            Value rem = (*_capacity)[e] - (*_flow)[e];
 		            if (!_tolerance.positive(rem)) continue;
 		            Node v = _graph.target(e);
 		            if ((*_level)[v] < level) {
 		              if (!_level->active(v) && v != _target) {
 		                _level->activate(v);
+		              }
 		              if (!_tolerance.less(rem, excess)) {
 		                _flow->set(e, (*_flow)[e] + excess);
 		                (*_excess)[v] += excess;
 		                excess = 0;
 		                goto no_more_push_2;
 		              } else {
 		                excess -= rem;
 		                (*_excess)[v] += rem;
 		                _flow->set(e, (*_capacity)[e]);
+		              }
 		            } else if (new_level > (*_level)[v]) {
 		              new_level = (*_level)[v];
+		            }
+		          }
 		          for (InArcIt e(_graph, n); e != INVALID; ++e) {
 		            Value rem = (*_flow)[e];
 		            if (!_tolerance.positive(rem)) continue;
 		            Node v = _graph.source(e);
 		            if ((*_level)[v] < level) {
 		              if (!_level->active(v) && v != _target) {
 		                _level->activate(v);
+		              }
 		              if (!_tolerance.less(rem, excess)) {
 		                _flow->set(e, (*_flow)[e] - excess);
 		                (*_excess)[v] += excess;
 		                excess = 0;
 		                goto no_more_push_2;
 		              } else {
 		                excess -= rem;
 		                (*_excess)[v] += rem;
 		                _flow->set(e, 0);
+		              }
 		            } else if (new_level > (*_level)[v]) {
 		              new_level = (*_level)[v];
+		            }
+		          }
 		        no_more_push_2:
 		          (*_excess)[n] = excess;
 		          if (excess != 0) {
 		            if (new_level + 1 < _level->maxLevel()) {
 		              _level->liftActiveOn(level, new_level + 1);
 		            } else {
 		              _level->liftActiveToTop(level);
+		            }
 		            if (_level->emptyLevel(level)) {
 		              _level->liftToTop(level);
+		            }
 		          } else {
 		            _level->deactivate(n);
+		          }
 		          while (level >= 0 && _level->activeFree(level)) {
 		            --level;
+		          }
 		          if (level == -1) {
 		            n = _level->highestActive();
 		            level = _level->highestActiveLevel();
 		          } else {
 		            n = _level->activeOn(level);
+		          }
 		          --num;
+		        }
+		      }
+		    }
 		    /// \brief Starts the second phase of the preflow algorithm.
 		    ///
 		    /// The preflow algorithm consists of two phases, this method runs
 		    /// the second phase. After calling one of the \ref init() functions
 		    /// and \ref startFirstPhase() and then \ref startSecondPhase(),
 		    /// \ref flowMap() returns a maximum flow, \ref flowValue() returns the
 		    /// value of a maximum flow, \ref minCut() returns a minimum cut
 		    /// \pre One of the \ref init() functions and \ref startFirstPhase()
 		    /// must be called before using this function.
 		    void startSecondPhase() {
 		      _phase = false;
 		      typename Digraph::template NodeMap<bool> reached(_graph);
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
 		        reached[n] = (*_level)[n] < _level->maxLevel();
+		      }
 		      _level->initStart();
 		      _level->initAddItem(_source);
 		      std::vector<Node> queue;
 		      queue.push_back(_source);
 		      reached[_source] = true;
 		      while (!queue.empty()) {
 		        _level->initNewLevel();
 		        std::vector<Node> nqueue;
 		        for (int i = 0; i < int(queue.size()); ++i) {
 		          Node n = queue[i];
 		          for (OutArcIt e(_graph, n); e != INVALID; ++e) {
 		            Node v = _graph.target(e);
 		            if (!reached[v] && _tolerance.positive((*_flow)[e])) {
 		              reached[v] = true;
 		              _level->initAddItem(v);
 		              nqueue.push_back(v);
+		            }
+		          }
 		          for (InArcIt e(_graph, n); e != INVALID; ++e) {
 		            Node u = _graph.source(e);
 		            if (!reached[u] &&
 		                _tolerance.positive((*_capacity)[e] - (*_flow)[e])) {
 		              reached[u] = true;
 		              _level->initAddItem(u);
 		              nqueue.push_back(u);
+		            }
+		          }
+		        }
 		        queue.swap(nqueue);
+		      }
 		      _level->initFinish();
 		      for (NodeIt n(_graph); n != INVALID; ++n) {
 		        if (!reached[n]) {
 		          _level->dirtyTopButOne(n);
 		        } else if ((*_excess)[n] > 0 && _target != n) {
 		          _level->activate(n);
+		        }
+		      }
 		      Node n;
 		      while ((n = _level->highestActive()) != INVALID) {
 		        Value excess = (*_excess)[n];
 		        int level = _level->highestActiveLevel();
 		        int new_level = _level->maxLevel();
 		        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
 		          Value rem = (*_capacity)[e] - (*_flow)[e];
 		          if (!_tolerance.positive(rem)) continue;
 		          Node v = _graph.target(e);
 		          if ((*_level)[v] < level) {
 		            if (!_level->active(v) && v != _source) {
 		              _level->activate(v);
+		            }
 		            if (!_tolerance.less(rem, excess)) {
 		              _flow->set(e, (*_flow)[e] + excess);
 		              (*_excess)[v] += excess;
 		              excess = 0;
 		              goto no_more_push;
 		            } else {
 		              excess -= rem;
 		              (*_excess)[v] += rem;
 		              _flow->set(e, (*_capacity)[e]);
+		            }
 		          } else if (new_level > (*_level)[v]) {
 		            new_level = (*_level)[v];
+		          }
+		        }
 		        for (InArcIt e(_graph, n); e != INVALID; ++e) {
 		          Value rem = (*_flow)[e];
 		          if (!_tolerance.positive(rem)) continue;
 		          Node v = _graph.source(e);
 		          if ((*_level)[v] < level) {
 		            if (!_level->active(v) && v != _source) {
 		              _level->activate(v);
+		            }
 		            if (!_tolerance.less(rem, excess)) {
 		              _flow->set(e, (*_flow)[e] - excess);
 		              (*_excess)[v] += excess;
 		              excess = 0;
 		              goto no_more_push;
 		            } else {
 		              excess -= rem;
 		              (*_excess)[v] += rem;
 		              _flow->set(e, 0);
+		            }
 		          } else if (new_level > (*_level)[v]) {
 		            new_level = (*_level)[v];
+		          }
+		        }
 		      no_more_push:
 		        (*_excess)[n] = excess;
 		        if (excess != 0) {
 		          if (new_level + 1 < _level->maxLevel()) {
 		            _level->liftHighestActive(new_level + 1);
 		          } else {
 		            // Calculation error
 		            _level->liftHighestActiveToTop();
+		          }
 		          if (_level->emptyLevel(level)) {
 		            // Calculation error
 		            _level->liftToTop(level);
+		          }
 		        } else {
 		          _level->deactivate(n);
+		        }
+		      }
+		    }
 		    /// \brief Runs the preflow algorithm.
 		    ///
 		    /// Runs the preflow algorithm.
 		    /// \note pf.run() is just a shortcut of the following code.
 		    /// \code
 		    ///   pf.init();
 		    ///   pf.startFirstPhase();
 		    ///   pf.startSecondPhase();
 		    /// \endcode
 		    void run() {
 		      init();
 		      startFirstPhase();
 		      startSecondPhase();
+		    }
 		    /// \brief Runs the preflow algorithm to compute the minimum cut.
 		    ///
 		    /// Runs the preflow algorithm to compute the minimum cut.
 		    /// \note pf.runMinCut() is just a shortcut of the following code.
 		    /// \code
 		    ///   pf.init();
 		    ///   pf.startFirstPhase();
 		    /// \endcode
 		    void runMinCut() {

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