lemon/bellman_ford.h
changeset 696 c9b9da1a90a0
child 697 9496ed797f20
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/lemon/bellman_ford.h	Fri Jul 24 23:19:43 2009 +0200
     1.3 @@ -0,0 +1,1042 @@
     1.4 +/* -*- C++ -*-
     1.5 + *
     1.6 + * This file is a part of LEMON, a generic C++ optimization library
     1.7 + *
     1.8 + * Copyright (C) 2003-2008
     1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
    1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
    1.11 + *
    1.12 + * Permission to use, modify and distribute this software is granted
    1.13 + * provided that this copyright notice appears in all copies. For
    1.14 + * precise terms see the accompanying LICENSE file.
    1.15 + *
    1.16 + * This software is provided "AS IS" with no warranty of any kind,
    1.17 + * express or implied, and with no claim as to its suitability for any
    1.18 + * purpose.
    1.19 + *
    1.20 + */
    1.21 +
    1.22 +#ifndef LEMON_BELMANN_FORD_H
    1.23 +#define LEMON_BELMANN_FORD_H
    1.24 +
    1.25 +/// \ingroup shortest_path
    1.26 +/// \file
    1.27 +/// \brief Bellman-Ford algorithm.
    1.28 +///
    1.29 +
    1.30 +#include <lemon/bits/path_dump.h>
    1.31 +#include <lemon/core.h>
    1.32 +#include <lemon/error.h>
    1.33 +#include <lemon/maps.h>
    1.34 +
    1.35 +#include <limits>
    1.36 +
    1.37 +namespace lemon {
    1.38 +
    1.39 +  /// \brief Default OperationTraits for the BellmanFord algorithm class.
    1.40 +  ///  
    1.41 +  /// It defines all computational operations and constants which are
    1.42 +  /// used in the Bellman-Ford algorithm. The default implementation
    1.43 +  /// is based on the numeric_limits class. If the numeric type does not
    1.44 +  /// have infinity value then the maximum value is used as extremal
    1.45 +  /// infinity value.
    1.46 +  template <
    1.47 +    typename Value, 
    1.48 +    bool has_infinity = std::numeric_limits<Value>::has_infinity>
    1.49 +  struct BellmanFordDefaultOperationTraits {
    1.50 +    /// \brief Gives back the zero value of the type.
    1.51 +    static Value zero() {
    1.52 +      return static_cast<Value>(0);
    1.53 +    }
    1.54 +    /// \brief Gives back the positive infinity value of the type.
    1.55 +    static Value infinity() {
    1.56 +      return std::numeric_limits<Value>::infinity();
    1.57 +    }
    1.58 +    /// \brief Gives back the sum of the given two elements.
    1.59 +    static Value plus(const Value& left, const Value& right) {
    1.60 +      return left + right;
    1.61 +    }
    1.62 +    /// \brief Gives back true only if the first value less than the second.
    1.63 +    static bool less(const Value& left, const Value& right) {
    1.64 +      return left < right;
    1.65 +    }
    1.66 +  };
    1.67 +
    1.68 +  template <typename Value>
    1.69 +  struct BellmanFordDefaultOperationTraits<Value, false> {
    1.70 +    static Value zero() {
    1.71 +      return static_cast<Value>(0);
    1.72 +    }
    1.73 +    static Value infinity() {
    1.74 +      return std::numeric_limits<Value>::max();
    1.75 +    }
    1.76 +    static Value plus(const Value& left, const Value& right) {
    1.77 +      if (left == infinity() || right == infinity()) return infinity();
    1.78 +      return left + right;
    1.79 +    }
    1.80 +    static bool less(const Value& left, const Value& right) {
    1.81 +      return left < right;
    1.82 +    }
    1.83 +  };
    1.84 +  
    1.85 +  /// \brief Default traits class of BellmanFord class.
    1.86 +  ///
    1.87 +  /// Default traits class of BellmanFord class.
    1.88 +  /// \param _Digraph Digraph type.
    1.89 +  /// \param _LegthMap Type of length map.
    1.90 +  template<class _Digraph, class _LengthMap>
    1.91 +  struct BellmanFordDefaultTraits {
    1.92 +    /// The digraph type the algorithm runs on. 
    1.93 +    typedef _Digraph Digraph;
    1.94 +
    1.95 +    /// \brief The type of the map that stores the arc lengths.
    1.96 +    ///
    1.97 +    /// The type of the map that stores the arc lengths.
    1.98 +    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
    1.99 +    typedef _LengthMap LengthMap;
   1.100 +
   1.101 +    // The type of the length of the arcs.
   1.102 +    typedef typename _LengthMap::Value Value;
   1.103 +
   1.104 +    /// \brief Operation traits for Bellman-Ford algorithm.
   1.105 +    ///
   1.106 +    /// It defines the infinity type on the given Value type
   1.107 +    /// and the used operation.
   1.108 +    /// \see BellmanFordDefaultOperationTraits
   1.109 +    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
   1.110 + 
   1.111 +    /// \brief The type of the map that stores the last arcs of the 
   1.112 +    /// shortest paths.
   1.113 +    /// 
   1.114 +    /// The type of the map that stores the last
   1.115 +    /// arcs of the shortest paths.
   1.116 +    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
   1.117 +    ///
   1.118 +    typedef typename Digraph::template NodeMap<typename _Digraph::Arc> PredMap;
   1.119 +
   1.120 +    /// \brief Instantiates a PredMap.
   1.121 +    /// 
   1.122 +    /// This function instantiates a \ref PredMap. 
   1.123 +    /// \param digraph is the digraph, to which we would like to define the PredMap.
   1.124 +    static PredMap *createPredMap(const _Digraph& digraph) {
   1.125 +      return new PredMap(digraph);
   1.126 +    }
   1.127 +
   1.128 +    /// \brief The type of the map that stores the dists of the nodes.
   1.129 +    ///
   1.130 +    /// The type of the map that stores the dists of the nodes.
   1.131 +    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
   1.132 +    ///
   1.133 +    typedef typename Digraph::template NodeMap<typename _LengthMap::Value> 
   1.134 +    DistMap;
   1.135 +
   1.136 +    /// \brief Instantiates a DistMap.
   1.137 +    ///
   1.138 +    /// This function instantiates a \ref DistMap. 
   1.139 +    /// \param digraph is the digraph, to which we would like to define the 
   1.140 +    /// \ref DistMap
   1.141 +    static DistMap *createDistMap(const _Digraph& digraph) {
   1.142 +      return new DistMap(digraph);
   1.143 +    }
   1.144 +
   1.145 +  };
   1.146 +  
   1.147 +  /// \brief %BellmanFord algorithm class.
   1.148 +  ///
   1.149 +  /// \ingroup shortest_path
   1.150 +  /// This class provides an efficient implementation of \c Bellman-Ford 
   1.151 +  /// algorithm. The arc lengths are passed to the algorithm using a
   1.152 +  /// \ref concepts::ReadMap "ReadMap", so it is easy to change it to any 
   1.153 +  /// kind of length.
   1.154 +  ///
   1.155 +  /// The Bellman-Ford algorithm solves the shortest path from one node
   1.156 +  /// problem when the arcs can have negative length but the digraph should
   1.157 +  /// not contain cycles with negative sum of length. If we can assume
   1.158 +  /// that all arc is non-negative in the digraph then the dijkstra algorithm
   1.159 +  /// should be used rather.
   1.160 +  ///
   1.161 +  /// The maximal time complexity of the algorithm is \f$ O(ne) \f$.
   1.162 +  ///
   1.163 +  /// The type of the length is determined by the
   1.164 +  /// \ref concepts::ReadMap::Value "Value" of the length map.
   1.165 +  ///
   1.166 +  /// \param _Digraph The digraph type the algorithm runs on. The default value
   1.167 +  /// is \ref ListDigraph. The value of _Digraph is not used directly by
   1.168 +  /// BellmanFord, it is only passed to \ref BellmanFordDefaultTraits.
   1.169 +  /// \param _LengthMap This read-only ArcMap determines the lengths of the
   1.170 +  /// arcs. The default map type is \ref concepts::Digraph::ArcMap 
   1.171 +  /// "Digraph::ArcMap<int>".  The value of _LengthMap is not used directly 
   1.172 +  /// by BellmanFord, it is only passed to \ref BellmanFordDefaultTraits.  
   1.173 +  /// \param _Traits Traits class to set various data types used by the 
   1.174 +  /// algorithm.  The default traits class is \ref BellmanFordDefaultTraits
   1.175 +  /// "BellmanFordDefaultTraits<_Digraph,_LengthMap>".  See \ref
   1.176 +  /// BellmanFordDefaultTraits for the documentation of a BellmanFord traits
   1.177 +  /// class.
   1.178 +#ifdef DOXYGEN
   1.179 +  template <typename _Digraph, typename _LengthMap, typename _Traits>
   1.180 +#else
   1.181 +  template <typename _Digraph,
   1.182 +	    typename _LengthMap=typename _Digraph::template ArcMap<int>,
   1.183 +	    typename _Traits=BellmanFordDefaultTraits<_Digraph,_LengthMap> >
   1.184 +#endif
   1.185 +  class BellmanFord {
   1.186 +  public:
   1.187 +
   1.188 +    typedef _Traits Traits;
   1.189 +    ///The type of the underlying digraph.
   1.190 +    typedef typename _Traits::Digraph Digraph;
   1.191 +
   1.192 +    typedef typename Digraph::Node Node;
   1.193 +    typedef typename Digraph::NodeIt NodeIt;
   1.194 +    typedef typename Digraph::Arc Arc;
   1.195 +    typedef typename Digraph::OutArcIt OutArcIt;
   1.196 +    
   1.197 +    /// \brief The type of the length of the arcs.
   1.198 +    typedef typename _Traits::LengthMap::Value Value;
   1.199 +    /// \brief The type of the map that stores the arc lengths.
   1.200 +    typedef typename _Traits::LengthMap LengthMap;
   1.201 +    /// \brief The type of the map that stores the last
   1.202 +    /// arcs of the shortest paths.
   1.203 +    typedef typename _Traits::PredMap PredMap;
   1.204 +    /// \brief The type of the map that stores the dists of the nodes.
   1.205 +    typedef typename _Traits::DistMap DistMap;
   1.206 +    /// \brief The operation traits.
   1.207 +    typedef typename _Traits::OperationTraits OperationTraits;
   1.208 +  private:
   1.209 +    /// Pointer to the underlying digraph.
   1.210 +    const Digraph *digraph;
   1.211 +    /// Pointer to the length map
   1.212 +    const LengthMap *length;
   1.213 +    ///Pointer to the map of predecessors arcs.
   1.214 +    PredMap *_pred;
   1.215 +    ///Indicates if \ref _pred is locally allocated (\c true) or not.
   1.216 +    bool local_pred;
   1.217 +    ///Pointer to the map of distances.
   1.218 +    DistMap *_dist;
   1.219 +    ///Indicates if \ref _dist is locally allocated (\c true) or not.
   1.220 +    bool local_dist;
   1.221 +
   1.222 +    typedef typename Digraph::template NodeMap<bool> MaskMap;
   1.223 +    MaskMap *_mask;
   1.224 +
   1.225 +    std::vector<Node> _process;
   1.226 +
   1.227 +    /// Creates the maps if necessary.
   1.228 +    void create_maps() {
   1.229 +      if(!_pred) {
   1.230 +	local_pred = true;
   1.231 +	_pred = Traits::createPredMap(*digraph);
   1.232 +      }
   1.233 +      if(!_dist) {
   1.234 +	local_dist = true;
   1.235 +	_dist = Traits::createDistMap(*digraph);
   1.236 +      }
   1.237 +      _mask = new MaskMap(*digraph, false);
   1.238 +    }
   1.239 +    
   1.240 +  public :
   1.241 + 
   1.242 +    typedef BellmanFord Create;
   1.243 +
   1.244 +    /// \name Named template parameters
   1.245 +
   1.246 +    ///@{
   1.247 +
   1.248 +    template <class T>
   1.249 +    struct DefPredMapTraits : public Traits {
   1.250 +      typedef T PredMap;
   1.251 +      static PredMap *createPredMap(const Digraph&) {
   1.252 +        LEMON_ASSERT(false, "PredMap is not initialized");
   1.253 +        return 0; // ignore warnings
   1.254 +      }
   1.255 +    };
   1.256 +
   1.257 +    /// \brief \ref named-templ-param "Named parameter" for setting PredMap 
   1.258 +    /// type
   1.259 +    /// \ref named-templ-param "Named parameter" for setting PredMap type
   1.260 +    ///
   1.261 +    template <class T>
   1.262 +    struct SetPredMap 
   1.263 +      : public BellmanFord< Digraph, LengthMap, DefPredMapTraits<T> > {
   1.264 +      typedef BellmanFord< Digraph, LengthMap, DefPredMapTraits<T> > Create;
   1.265 +    };
   1.266 +    
   1.267 +    template <class T>
   1.268 +    struct DefDistMapTraits : public Traits {
   1.269 +      typedef T DistMap;
   1.270 +      static DistMap *createDistMap(const Digraph&) {
   1.271 +        LEMON_ASSERT(false, "DistMap is not initialized");
   1.272 +        return 0; // ignore warnings
   1.273 +      }
   1.274 +    };
   1.275 +
   1.276 +    /// \brief \ref named-templ-param "Named parameter" for setting DistMap 
   1.277 +    /// type
   1.278 +    ///
   1.279 +    /// \ref named-templ-param "Named parameter" for setting DistMap type
   1.280 +    ///
   1.281 +    template <class T>
   1.282 +    struct SetDistMap 
   1.283 +      : public BellmanFord< Digraph, LengthMap, DefDistMapTraits<T> > {
   1.284 +      typedef BellmanFord< Digraph, LengthMap, DefDistMapTraits<T> > Create;
   1.285 +    };
   1.286 +    
   1.287 +    template <class T>
   1.288 +    struct DefOperationTraitsTraits : public Traits {
   1.289 +      typedef T OperationTraits;
   1.290 +    };
   1.291 +    
   1.292 +    /// \brief \ref named-templ-param "Named parameter" for setting 
   1.293 +    /// OperationTraits type
   1.294 +    ///
   1.295 +    /// \ref named-templ-param "Named parameter" for setting OperationTraits
   1.296 +    /// type
   1.297 +    template <class T>
   1.298 +    struct SetOperationTraits
   1.299 +      : public BellmanFord< Digraph, LengthMap, DefOperationTraitsTraits<T> > {
   1.300 +      typedef BellmanFord< Digraph, LengthMap, DefOperationTraitsTraits<T> >
   1.301 +      Create;
   1.302 +    };
   1.303 +    
   1.304 +    ///@}
   1.305 +
   1.306 +  protected:
   1.307 +    
   1.308 +    BellmanFord() {}
   1.309 +
   1.310 +  public:      
   1.311 +    
   1.312 +    /// \brief Constructor.
   1.313 +    ///
   1.314 +    /// \param _graph the digraph the algorithm will run on.
   1.315 +    /// \param _length the length map used by the algorithm.
   1.316 +    BellmanFord(const Digraph& _graph, const LengthMap& _length) :
   1.317 +      digraph(&_graph), length(&_length),
   1.318 +      _pred(0), local_pred(false),
   1.319 +      _dist(0), local_dist(false), _mask(0) {}
   1.320 +    
   1.321 +    ///Destructor.
   1.322 +    ~BellmanFord() {
   1.323 +      if(local_pred) delete _pred;
   1.324 +      if(local_dist) delete _dist;
   1.325 +      if(_mask) delete _mask;
   1.326 +    }
   1.327 +
   1.328 +    /// \brief Sets the length map.
   1.329 +    ///
   1.330 +    /// Sets the length map.
   1.331 +    /// \return \c (*this)
   1.332 +    BellmanFord &lengthMap(const LengthMap &m) {
   1.333 +      length = &m;
   1.334 +      return *this;
   1.335 +    }
   1.336 +
   1.337 +    /// \brief Sets the map storing the predecessor arcs.
   1.338 +    ///
   1.339 +    /// Sets the map storing the predecessor arcs.
   1.340 +    /// If you don't use this function before calling \ref run(),
   1.341 +    /// it will allocate one. The destuctor deallocates this
   1.342 +    /// automatically allocated map, of course.
   1.343 +    /// \return \c (*this)
   1.344 +    BellmanFord &predMap(PredMap &m) {
   1.345 +      if(local_pred) {
   1.346 +	delete _pred;
   1.347 +	local_pred=false;
   1.348 +      }
   1.349 +      _pred = &m;
   1.350 +      return *this;
   1.351 +    }
   1.352 +
   1.353 +    /// \brief Sets the map storing the distances calculated by the algorithm.
   1.354 +    ///
   1.355 +    /// Sets the map storing the distances calculated by the algorithm.
   1.356 +    /// If you don't use this function before calling \ref run(),
   1.357 +    /// it will allocate one. The destuctor deallocates this
   1.358 +    /// automatically allocated map, of course.
   1.359 +    /// \return \c (*this)
   1.360 +    BellmanFord &distMap(DistMap &m) {
   1.361 +      if(local_dist) {
   1.362 +	delete _dist;
   1.363 +	local_dist=false;
   1.364 +      }
   1.365 +      _dist = &m;
   1.366 +      return *this;
   1.367 +    }
   1.368 +
   1.369 +    /// \name Execution control
   1.370 +    /// The simplest way to execute the algorithm is to use
   1.371 +    /// one of the member functions called \c run(...).
   1.372 +    /// \n
   1.373 +    /// If you need more control on the execution,
   1.374 +    /// first you must call \ref init(), then you can add several source nodes
   1.375 +    /// with \ref addSource().
   1.376 +    /// Finally \ref start() will perform the actual path
   1.377 +    /// computation.
   1.378 +
   1.379 +    ///@{
   1.380 +
   1.381 +    /// \brief Initializes the internal data structures.
   1.382 +    /// 
   1.383 +    /// Initializes the internal data structures.
   1.384 +    void init(const Value value = OperationTraits::infinity()) {
   1.385 +      create_maps();
   1.386 +      for (NodeIt it(*digraph); it != INVALID; ++it) {
   1.387 +	_pred->set(it, INVALID);
   1.388 +	_dist->set(it, value);
   1.389 +      }
   1.390 +      _process.clear();
   1.391 +      if (OperationTraits::less(value, OperationTraits::infinity())) {
   1.392 +	for (NodeIt it(*digraph); it != INVALID; ++it) {
   1.393 +	  _process.push_back(it);
   1.394 +	  _mask->set(it, true);
   1.395 +	}
   1.396 +      }
   1.397 +    }
   1.398 +    
   1.399 +    /// \brief Adds a new source node.
   1.400 +    ///
   1.401 +    /// Adds a new source node. The optional second parameter is the 
   1.402 +    /// initial distance of the node. It just sets the distance of the 
   1.403 +    /// node to the given value.
   1.404 +    void addSource(Node source, Value dst = OperationTraits::zero()) {
   1.405 +      _dist->set(source, dst);
   1.406 +      if (!(*_mask)[source]) {
   1.407 +	_process.push_back(source);
   1.408 +	_mask->set(source, true);
   1.409 +      }
   1.410 +    }
   1.411 +
   1.412 +    /// \brief Executes one round from the Bellman-Ford algorithm.
   1.413 +    ///
   1.414 +    /// If the algoritm calculated the distances in the previous round
   1.415 +    /// exactly for all at most \f$ k \f$ length path lengths then it will
   1.416 +    /// calculate the distances exactly for all at most \f$ k + 1 \f$
   1.417 +    /// length path lengths. With \f$ k \f$ iteration this function
   1.418 +    /// calculates the at most \f$ k \f$ length path lengths.
   1.419 +    ///
   1.420 +    /// \warning The paths with limited arc number cannot be retrieved
   1.421 +    /// easily with \ref path() or \ref predArc() functions. If you
   1.422 +    /// need the shortest path and not just the distance you should store
   1.423 +    /// after each iteration the \ref predMap() map and manually build
   1.424 +    /// the path.
   1.425 +    ///
   1.426 +    /// \return \c true when the algorithm have not found more shorter
   1.427 +    /// paths.
   1.428 +    bool processNextRound() {
   1.429 +      for (int i = 0; i < int(_process.size()); ++i) {
   1.430 +	_mask->set(_process[i], false);
   1.431 +      }
   1.432 +      std::vector<Node> nextProcess;
   1.433 +      std::vector<Value> values(_process.size());
   1.434 +      for (int i = 0; i < int(_process.size()); ++i) {
   1.435 +	values[i] = (*_dist)[_process[i]];
   1.436 +      }
   1.437 +      for (int i = 0; i < int(_process.size()); ++i) {
   1.438 +	for (OutArcIt it(*digraph, _process[i]); it != INVALID; ++it) {
   1.439 +	  Node target = digraph->target(it);
   1.440 +	  Value relaxed = OperationTraits::plus(values[i], (*length)[it]);
   1.441 +	  if (OperationTraits::less(relaxed, (*_dist)[target])) {
   1.442 +	    _pred->set(target, it);
   1.443 +	    _dist->set(target, relaxed);
   1.444 +	    if (!(*_mask)[target]) {
   1.445 +	      _mask->set(target, true);
   1.446 +	      nextProcess.push_back(target);
   1.447 +	    }
   1.448 +	  }	  
   1.449 +	}
   1.450 +      }
   1.451 +      _process.swap(nextProcess);
   1.452 +      return _process.empty();
   1.453 +    }
   1.454 +
   1.455 +    /// \brief Executes one weak round from the Bellman-Ford algorithm.
   1.456 +    ///
   1.457 +    /// If the algorithm calculated the distances in the
   1.458 +    /// previous round at least for all at most k length paths then it will
   1.459 +    /// calculate the distances at least for all at most k + 1 length paths.
   1.460 +    /// This function does not make it possible to calculate strictly the
   1.461 +    /// at most k length minimal paths, this is why it is
   1.462 +    /// called just weak round.
   1.463 +    /// \return \c true when the algorithm have not found more shorter paths.
   1.464 +    bool processNextWeakRound() {
   1.465 +      for (int i = 0; i < int(_process.size()); ++i) {
   1.466 +	_mask->set(_process[i], false);
   1.467 +      }
   1.468 +      std::vector<Node> nextProcess;
   1.469 +      for (int i = 0; i < int(_process.size()); ++i) {
   1.470 +	for (OutArcIt it(*digraph, _process[i]); it != INVALID; ++it) {
   1.471 +	  Node target = digraph->target(it);
   1.472 +	  Value relaxed = 
   1.473 +	    OperationTraits::plus((*_dist)[_process[i]], (*length)[it]);
   1.474 +	  if (OperationTraits::less(relaxed, (*_dist)[target])) {
   1.475 +	    _pred->set(target, it);
   1.476 +	    _dist->set(target, relaxed);
   1.477 +	    if (!(*_mask)[target]) {
   1.478 +	      _mask->set(target, true);
   1.479 +	      nextProcess.push_back(target);
   1.480 +	    }
   1.481 +	  }	  
   1.482 +	}
   1.483 +      }
   1.484 +      _process.swap(nextProcess);
   1.485 +      return _process.empty();
   1.486 +    }
   1.487 +
   1.488 +    /// \brief Executes the algorithm.
   1.489 +    ///
   1.490 +    /// \pre init() must be called and at least one node should be added
   1.491 +    /// with addSource() before using this function.
   1.492 +    ///
   1.493 +    /// This method runs the %BellmanFord algorithm from the root node(s)
   1.494 +    /// in order to compute the shortest path to each node. The algorithm 
   1.495 +    /// computes 
   1.496 +    /// - The shortest path tree.
   1.497 +    /// - The distance of each node from the root(s).
   1.498 +    void start() {
   1.499 +      int num = countNodes(*digraph) - 1;
   1.500 +      for (int i = 0; i < num; ++i) {
   1.501 +	if (processNextWeakRound()) break;
   1.502 +      }
   1.503 +    }
   1.504 +
   1.505 +    /// \brief Executes the algorithm and checks the negative cycles.
   1.506 +    ///
   1.507 +    /// \pre init() must be called and at least one node should be added
   1.508 +    /// with addSource() before using this function. 
   1.509 +    ///
   1.510 +    /// This method runs the %BellmanFord algorithm from the root node(s)
   1.511 +    /// in order to compute the shortest path to each node. The algorithm 
   1.512 +    /// computes 
   1.513 +    /// - The shortest path tree.
   1.514 +    /// - The distance of each node from the root(s).
   1.515 +    /// 
   1.516 +    /// \return \c false if there is a negative cycle in the digraph.
   1.517 +    bool checkedStart() {
   1.518 +      int num = countNodes(*digraph);
   1.519 +      for (int i = 0; i < num; ++i) {
   1.520 +	if (processNextWeakRound()) return true;
   1.521 +      }
   1.522 +      return _process.empty();
   1.523 +    }
   1.524 +
   1.525 +    /// \brief Executes the algorithm with path length limit.
   1.526 +    ///
   1.527 +    /// \pre init() must be called and at least one node should be added
   1.528 +    /// with addSource() before using this function.
   1.529 +    ///
   1.530 +    /// This method runs the %BellmanFord algorithm from the root
   1.531 +    /// node(s) in order to compute the shortest path lengths with at
   1.532 +    /// most \c num arc.
   1.533 +    ///
   1.534 +    /// \warning The paths with limited arc number cannot be retrieved
   1.535 +    /// easily with \ref path() or \ref predArc() functions. If you
   1.536 +    /// need the shortest path and not just the distance you should store
   1.537 +    /// after each iteration the \ref predMap() map and manually build
   1.538 +    /// the path.
   1.539 +    ///
   1.540 +    /// The algorithm computes
   1.541 +    /// - The predecessor arc from each node.
   1.542 +    /// - The limited distance of each node from the root(s).
   1.543 +    void limitedStart(int num) {
   1.544 +      for (int i = 0; i < num; ++i) {
   1.545 +	if (processNextRound()) break;
   1.546 +      }
   1.547 +    }
   1.548 +    
   1.549 +    /// \brief Runs %BellmanFord algorithm from node \c s.
   1.550 +    ///    
   1.551 +    /// This method runs the %BellmanFord algorithm from a root node \c s
   1.552 +    /// in order to compute the shortest path to each node. The algorithm 
   1.553 +    /// computes
   1.554 +    /// - The shortest path tree.
   1.555 +    /// - The distance of each node from the root.
   1.556 +    ///
   1.557 +    /// \note d.run(s) is just a shortcut of the following code.
   1.558 +    ///\code
   1.559 +    ///  d.init();
   1.560 +    ///  d.addSource(s);
   1.561 +    ///  d.start();
   1.562 +    ///\endcode
   1.563 +    void run(Node s) {
   1.564 +      init();
   1.565 +      addSource(s);
   1.566 +      start();
   1.567 +    }
   1.568 +    
   1.569 +    /// \brief Runs %BellmanFord algorithm with limited path length 
   1.570 +    /// from node \c s.
   1.571 +    ///    
   1.572 +    /// This method runs the %BellmanFord algorithm from a root node \c s
   1.573 +    /// in order to compute the shortest path with at most \c len arcs 
   1.574 +    /// to each node. The algorithm computes
   1.575 +    /// - The shortest path tree.
   1.576 +    /// - The distance of each node from the root.
   1.577 +    ///
   1.578 +    /// \note d.run(s, num) is just a shortcut of the following code.
   1.579 +    ///\code
   1.580 +    ///  d.init();
   1.581 +    ///  d.addSource(s);
   1.582 +    ///  d.limitedStart(num);
   1.583 +    ///\endcode
   1.584 +    void run(Node s, int num) {
   1.585 +      init();
   1.586 +      addSource(s);
   1.587 +      limitedStart(num);
   1.588 +    }
   1.589 +    
   1.590 +    ///@}
   1.591 +
   1.592 +    /// \name Query Functions
   1.593 +    /// The result of the %BellmanFord algorithm can be obtained using these
   1.594 +    /// functions.\n
   1.595 +    /// Before the use of these functions,
   1.596 +    /// either run() or start() must be called.
   1.597 +    
   1.598 +    ///@{
   1.599 +
   1.600 +    /// \brief Lemon iterator for get the active nodes.
   1.601 +    ///
   1.602 +    /// Lemon iterator for get the active nodes. This class provides a
   1.603 +    /// common style lemon iterator which gives back a subset of the
   1.604 +    /// nodes. The iterated nodes are active in the algorithm after
   1.605 +    /// the last phase so these should be checked in the next phase to
   1.606 +    /// find augmenting arcs from these.
   1.607 +    class ActiveIt {
   1.608 +    public:
   1.609 +
   1.610 +      /// \brief Constructor.
   1.611 +      ///
   1.612 +      /// Constructor for get the nodeset of the variable. 
   1.613 +      ActiveIt(const BellmanFord& algorithm) : _algorithm(&algorithm)
   1.614 +      {
   1.615 +        _index = _algorithm->_process.size() - 1;
   1.616 +      }
   1.617 +
   1.618 +      /// \brief Invalid constructor.
   1.619 +      ///
   1.620 +      /// Invalid constructor.
   1.621 +      ActiveIt(Invalid) : _algorithm(0), _index(-1) {}
   1.622 +
   1.623 +      /// \brief Conversion to node.
   1.624 +      ///
   1.625 +      /// Conversion to node.
   1.626 +      operator Node() const { 
   1.627 +        return _index >= 0 ? _algorithm->_process[_index] : INVALID;
   1.628 +      }
   1.629 +
   1.630 +      /// \brief Increment operator.
   1.631 +      ///
   1.632 +      /// Increment operator.
   1.633 +      ActiveIt& operator++() {
   1.634 +        --_index;
   1.635 +        return *this; 
   1.636 +      }
   1.637 +
   1.638 +      bool operator==(const ActiveIt& it) const { 
   1.639 +        return static_cast<Node>(*this) == static_cast<Node>(it); 
   1.640 +      }
   1.641 +      bool operator!=(const ActiveIt& it) const { 
   1.642 +        return static_cast<Node>(*this) != static_cast<Node>(it); 
   1.643 +      }
   1.644 +      bool operator<(const ActiveIt& it) const { 
   1.645 +        return static_cast<Node>(*this) < static_cast<Node>(it); 
   1.646 +      }
   1.647 +      
   1.648 +    private:
   1.649 +      const BellmanFord* _algorithm;
   1.650 +      int _index;
   1.651 +    };
   1.652 +
   1.653 +    typedef PredMapPath<Digraph, PredMap> Path;
   1.654 +
   1.655 +    /// \brief Gives back the shortest path.
   1.656 +    ///    
   1.657 +    /// Gives back the shortest path.
   1.658 +    /// \pre The \c t should be reachable from the source.
   1.659 +    Path path(Node t) 
   1.660 +    {
   1.661 +      return Path(*digraph, *_pred, t);
   1.662 +    }
   1.663 +
   1.664 +
   1.665 +    // TODO : implement negative cycle
   1.666 +//     /// \brief Gives back a negative cycle.
   1.667 +//     ///    
   1.668 +//     /// This function gives back a negative cycle.
   1.669 +//     /// If the algorithm have not found yet negative cycle it will give back
   1.670 +//     /// an empty path.
   1.671 +//     Path negativeCycle() {
   1.672 +//       typename Digraph::template NodeMap<int> state(*digraph, 0);
   1.673 +//       for (ActiveIt it(*this); it != INVALID; ++it) {
   1.674 +//         if (state[it] == 0) {
   1.675 +//           for (Node t = it; predArc(t) != INVALID; t = predNode(t)) {
   1.676 +//             if (state[t] == 0) {
   1.677 +//               state[t] = 1;
   1.678 +//             } else if (state[t] == 2) {
   1.679 +//               break;
   1.680 +//             } else {
   1.681 +//               p.clear();
   1.682 +//               typename Path::Builder b(p);
   1.683 +//               b.setStartNode(t);
   1.684 +//               b.pushFront(predArc(t));
   1.685 +//               for(Node s = predNode(t); s != t; s = predNode(s)) {
   1.686 +//                 b.pushFront(predArc(s));
   1.687 +//               }
   1.688 +//               b.commit();
   1.689 +//               return true;
   1.690 +//             }
   1.691 +//           }
   1.692 +//           for (Node t = it; predArc(t) != INVALID; t = predNode(t)) {
   1.693 +//             if (state[t] == 1) {
   1.694 +//               state[t] = 2;
   1.695 +//             } else {
   1.696 +//               break;
   1.697 +//             }
   1.698 +//           }
   1.699 +//         }
   1.700 +//       }
   1.701 +//       return false;
   1.702 +//     }
   1.703 +	  
   1.704 +    /// \brief The distance of a node from the root.
   1.705 +    ///
   1.706 +    /// Returns the distance of a node from the root.
   1.707 +    /// \pre \ref run() must be called before using this function.
   1.708 +    /// \warning If node \c v in unreachable from the root the return value
   1.709 +    /// of this funcion is undefined.
   1.710 +    Value dist(Node v) const { return (*_dist)[v]; }
   1.711 +
   1.712 +    /// \brief Returns the 'previous arc' of the shortest path tree.
   1.713 +    ///
   1.714 +    /// For a node \c v it returns the 'previous arc' of the shortest path 
   1.715 +    /// tree, i.e. it returns the last arc of a shortest path from the root 
   1.716 +    /// to \c v. It is \ref INVALID if \c v is unreachable from the root or 
   1.717 +    /// if \c v=s. The shortest path tree used here is equal to the shortest 
   1.718 +    /// path tree used in \ref predNode(). 
   1.719 +    /// \pre \ref run() must be called before using
   1.720 +    /// this function.
   1.721 +    Arc predArc(Node v) const { return (*_pred)[v]; }
   1.722 +
   1.723 +    /// \brief Returns the 'previous node' of the shortest path tree.
   1.724 +    ///
   1.725 +    /// For a node \c v it returns the 'previous node' of the shortest path 
   1.726 +    /// tree, i.e. it returns the last but one node from a shortest path from 
   1.727 +    /// the root to \c /v. It is INVALID if \c v is unreachable from the root 
   1.728 +    /// or if \c v=s. The shortest path tree used here is equal to the 
   1.729 +    /// shortest path tree used in \ref predArc().  \pre \ref run() must be 
   1.730 +    /// called before using this function.
   1.731 +    Node predNode(Node v) const { 
   1.732 +      return (*_pred)[v] == INVALID ? INVALID : digraph->source((*_pred)[v]); 
   1.733 +    }
   1.734 +    
   1.735 +    /// \brief Returns a reference to the NodeMap of distances.
   1.736 +    ///
   1.737 +    /// Returns a reference to the NodeMap of distances. \pre \ref run() must
   1.738 +    /// be called before using this function.
   1.739 +    const DistMap &distMap() const { return *_dist;}
   1.740 + 
   1.741 +    /// \brief Returns a reference to the shortest path tree map.
   1.742 +    ///
   1.743 +    /// Returns a reference to the NodeMap of the arcs of the
   1.744 +    /// shortest path tree.
   1.745 +    /// \pre \ref run() must be called before using this function.
   1.746 +    const PredMap &predMap() const { return *_pred; }
   1.747 + 
   1.748 +    /// \brief Checks if a node is reachable from the root.
   1.749 +    ///
   1.750 +    /// Returns \c true if \c v is reachable from the root.
   1.751 +    /// \pre \ref run() must be called before using this function.
   1.752 +    ///
   1.753 +    bool reached(Node v) { return (*_dist)[v] != OperationTraits::infinity(); }
   1.754 +    
   1.755 +    ///@}
   1.756 +  };
   1.757 + 
   1.758 +  /// \brief Default traits class of BellmanFord function.
   1.759 +  ///
   1.760 +  /// Default traits class of BellmanFord function.
   1.761 +  /// \param _Digraph Digraph type.
   1.762 +  /// \param _LengthMap Type of length map.
   1.763 +  template <typename _Digraph, typename _LengthMap>
   1.764 +  struct BellmanFordWizardDefaultTraits {
   1.765 +    /// \brief The digraph type the algorithm runs on. 
   1.766 +    typedef _Digraph Digraph;
   1.767 +
   1.768 +    /// \brief The type of the map that stores the arc lengths.
   1.769 +    ///
   1.770 +    /// The type of the map that stores the arc lengths.
   1.771 +    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
   1.772 +    typedef _LengthMap LengthMap;
   1.773 +
   1.774 +    /// \brief The value type of the length map.
   1.775 +    typedef typename _LengthMap::Value Value;
   1.776 +
   1.777 +    /// \brief Operation traits for Bellman-Ford algorithm.
   1.778 +    ///
   1.779 +    /// It defines the infinity type on the given Value type
   1.780 +    /// and the used operation.
   1.781 +    /// \see BellmanFordDefaultOperationTraits
   1.782 +    typedef BellmanFordDefaultOperationTraits<Value> OperationTraits;
   1.783 +
   1.784 +    /// \brief The type of the map that stores the last
   1.785 +    /// arcs of the shortest paths.
   1.786 +    /// 
   1.787 +    /// The type of the map that stores the last
   1.788 +    /// arcs of the shortest paths.
   1.789 +    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
   1.790 +    typedef NullMap <typename _Digraph::Node,typename _Digraph::Arc> PredMap;
   1.791 +
   1.792 +    /// \brief Instantiates a PredMap.
   1.793 +    /// 
   1.794 +    /// This function instantiates a \ref PredMap. 
   1.795 +    static PredMap *createPredMap(const _Digraph &) {
   1.796 +      return new PredMap();
   1.797 +    }
   1.798 +    /// \brief The type of the map that stores the dists of the nodes.
   1.799 +    ///
   1.800 +    /// The type of the map that stores the dists of the nodes.
   1.801 +    /// It must meet the \ref concepts::WriteMap "WriteMap" concept.
   1.802 +    typedef NullMap<typename Digraph::Node, Value> DistMap;
   1.803 +    /// \brief Instantiates a DistMap.
   1.804 +    ///
   1.805 +    /// This function instantiates a \ref DistMap. 
   1.806 +    static DistMap *createDistMap(const _Digraph &) {
   1.807 +      return new DistMap();
   1.808 +    }
   1.809 +  };
   1.810 +  
   1.811 +  /// \brief Default traits used by \ref BellmanFordWizard
   1.812 +  ///
   1.813 +  /// To make it easier to use BellmanFord algorithm
   1.814 +  /// we have created a wizard class.
   1.815 +  /// This \ref BellmanFordWizard class needs default traits,
   1.816 +  /// as well as the \ref BellmanFord class.
   1.817 +  /// The \ref BellmanFordWizardBase is a class to be the default traits of the
   1.818 +  /// \ref BellmanFordWizard class.
   1.819 +  /// \todo More named parameters are required...
   1.820 +  template<class _Digraph,class _LengthMap>
   1.821 +  class BellmanFordWizardBase 
   1.822 +    : public BellmanFordWizardDefaultTraits<_Digraph,_LengthMap> {
   1.823 +
   1.824 +    typedef BellmanFordWizardDefaultTraits<_Digraph,_LengthMap> Base;
   1.825 +  protected:
   1.826 +    /// Type of the nodes in the digraph.
   1.827 +    typedef typename Base::Digraph::Node Node;
   1.828 +
   1.829 +    /// Pointer to the underlying digraph.
   1.830 +    void *_graph;
   1.831 +    /// Pointer to the length map
   1.832 +    void *_length;
   1.833 +    ///Pointer to the map of predecessors arcs.
   1.834 +    void *_pred;
   1.835 +    ///Pointer to the map of distances.
   1.836 +    void *_dist;
   1.837 +    ///Pointer to the source node.
   1.838 +    Node _source;
   1.839 +
   1.840 +    public:
   1.841 +    /// Constructor.
   1.842 +    
   1.843 +    /// This constructor does not require parameters, therefore it initiates
   1.844 +    /// all of the attributes to default values (0, INVALID).
   1.845 +    BellmanFordWizardBase() : _graph(0), _length(0), _pred(0),
   1.846 +			   _dist(0), _source(INVALID) {}
   1.847 +
   1.848 +    /// Constructor.
   1.849 +    
   1.850 +    /// This constructor requires some parameters,
   1.851 +    /// listed in the parameters list.
   1.852 +    /// Others are initiated to 0.
   1.853 +    /// \param digraph is the initial value of  \ref _graph
   1.854 +    /// \param length is the initial value of  \ref _length
   1.855 +    /// \param source is the initial value of  \ref _source
   1.856 +    BellmanFordWizardBase(const _Digraph& digraph, 
   1.857 +			  const _LengthMap& length, 
   1.858 +			  Node source = INVALID) :
   1.859 +      _graph(reinterpret_cast<void*>(const_cast<_Digraph*>(&digraph))), 
   1.860 +      _length(reinterpret_cast<void*>(const_cast<_LengthMap*>(&length))), 
   1.861 +      _pred(0), _dist(0), _source(source) {}
   1.862 +
   1.863 +  };
   1.864 +  
   1.865 +  /// A class to make the usage of BellmanFord algorithm easier
   1.866 +
   1.867 +  /// This class is created to make it easier to use BellmanFord algorithm.
   1.868 +  /// It uses the functions and features of the plain \ref BellmanFord,
   1.869 +  /// but it is much simpler to use it.
   1.870 +  ///
   1.871 +  /// Simplicity means that the way to change the types defined
   1.872 +  /// in the traits class is based on functions that returns the new class
   1.873 +  /// and not on templatable built-in classes.
   1.874 +  /// When using the plain \ref BellmanFord
   1.875 +  /// the new class with the modified type comes from
   1.876 +  /// the original class by using the ::
   1.877 +  /// operator. In the case of \ref BellmanFordWizard only
   1.878 +  /// a function have to be called and it will
   1.879 +  /// return the needed class.
   1.880 +  ///
   1.881 +  /// It does not have own \ref run method. When its \ref run method is called
   1.882 +  /// it initiates a plain \ref BellmanFord class, and calls the \ref 
   1.883 +  /// BellmanFord::run method of it.
   1.884 +  template<class _Traits>
   1.885 +  class BellmanFordWizard : public _Traits {
   1.886 +    typedef _Traits Base;
   1.887 +
   1.888 +    ///The type of the underlying digraph.
   1.889 +    typedef typename _Traits::Digraph Digraph;
   1.890 +
   1.891 +    typedef typename Digraph::Node Node;
   1.892 +    typedef typename Digraph::NodeIt NodeIt;
   1.893 +    typedef typename Digraph::Arc Arc;
   1.894 +    typedef typename Digraph::OutArcIt ArcIt;
   1.895 +    
   1.896 +    ///The type of the map that stores the arc lengths.
   1.897 +    typedef typename _Traits::LengthMap LengthMap;
   1.898 +
   1.899 +    ///The type of the length of the arcs.
   1.900 +    typedef typename LengthMap::Value Value;
   1.901 +
   1.902 +    ///\brief The type of the map that stores the last
   1.903 +    ///arcs of the shortest paths.
   1.904 +    typedef typename _Traits::PredMap PredMap;
   1.905 +
   1.906 +    ///The type of the map that stores the dists of the nodes.
   1.907 +    typedef typename _Traits::DistMap DistMap;
   1.908 +
   1.909 +  public:
   1.910 +    /// Constructor.
   1.911 +    BellmanFordWizard() : _Traits() {}
   1.912 +
   1.913 +    /// \brief Constructor that requires parameters.
   1.914 +    ///
   1.915 +    /// Constructor that requires parameters.
   1.916 +    /// These parameters will be the default values for the traits class.
   1.917 +    BellmanFordWizard(const Digraph& digraph, const LengthMap& length, 
   1.918 +		      Node src = INVALID) 
   1.919 +      : _Traits(digraph, length, src) {}
   1.920 +
   1.921 +    /// \brief Copy constructor
   1.922 +    BellmanFordWizard(const _Traits &b) : _Traits(b) {}
   1.923 +
   1.924 +    ~BellmanFordWizard() {}
   1.925 +
   1.926 +    /// \brief Runs BellmanFord algorithm from a given node.
   1.927 +    ///    
   1.928 +    /// Runs BellmanFord algorithm from a given node.
   1.929 +    /// The node can be given by the \ref source function.
   1.930 +    void run() {
   1.931 +      LEMON_ASSERT(Base::_source != INVALID, "Source node is not given");
   1.932 +      BellmanFord<Digraph,LengthMap,_Traits> 
   1.933 +	bf(*reinterpret_cast<const Digraph*>(Base::_graph), 
   1.934 +           *reinterpret_cast<const LengthMap*>(Base::_length));
   1.935 +      if (Base::_pred) bf.predMap(*reinterpret_cast<PredMap*>(Base::_pred));
   1.936 +      if (Base::_dist) bf.distMap(*reinterpret_cast<DistMap*>(Base::_dist));
   1.937 +      bf.run(Base::_source);
   1.938 +    }
   1.939 +
   1.940 +    /// \brief Runs BellmanFord algorithm from the given node.
   1.941 +    ///
   1.942 +    /// Runs BellmanFord algorithm from the given node.
   1.943 +    /// \param src is the given source.
   1.944 +    void run(Node src) {
   1.945 +      Base::_source = src;
   1.946 +      run();
   1.947 +    }
   1.948 +
   1.949 +    template<class T>
   1.950 +    struct DefPredMapBase : public Base {
   1.951 +      typedef T PredMap;
   1.952 +      static PredMap *createPredMap(const Digraph &) { return 0; };
   1.953 +      DefPredMapBase(const _Traits &b) : _Traits(b) {}
   1.954 +    };
   1.955 +    
   1.956 +    ///\brief \ref named-templ-param "Named parameter"
   1.957 +    ///function for setting PredMap type
   1.958 +    ///
   1.959 +    /// \ref named-templ-param "Named parameter"
   1.960 +    ///function for setting PredMap type
   1.961 +    ///
   1.962 +    template<class T>
   1.963 +    BellmanFordWizard<DefPredMapBase<T> > predMap(const T &t) 
   1.964 +    {
   1.965 +      Base::_pred=reinterpret_cast<void*>(const_cast<T*>(&t));
   1.966 +      return BellmanFordWizard<DefPredMapBase<T> >(*this);
   1.967 +    }
   1.968 +    
   1.969 +    template<class T>
   1.970 +    struct DefDistMapBase : public Base {
   1.971 +      typedef T DistMap;
   1.972 +      static DistMap *createDistMap(const Digraph &) { return 0; };
   1.973 +      DefDistMapBase(const _Traits &b) : _Traits(b) {}
   1.974 +    };
   1.975 +    
   1.976 +    ///\brief \ref named-templ-param "Named parameter"
   1.977 +    ///function for setting DistMap type
   1.978 +    ///
   1.979 +    /// \ref named-templ-param "Named parameter"
   1.980 +    ///function for setting DistMap type
   1.981 +    ///
   1.982 +    template<class T>
   1.983 +    BellmanFordWizard<DefDistMapBase<T> > distMap(const T &t) {
   1.984 +      Base::_dist=reinterpret_cast<void*>(const_cast<T*>(&t));
   1.985 +      return BellmanFordWizard<DefDistMapBase<T> >(*this);
   1.986 +    }
   1.987 +
   1.988 +    template<class T>
   1.989 +    struct DefOperationTraitsBase : public Base {
   1.990 +      typedef T OperationTraits;
   1.991 +      DefOperationTraitsBase(const _Traits &b) : _Traits(b) {}
   1.992 +    };
   1.993 +    
   1.994 +    ///\brief \ref named-templ-param "Named parameter"
   1.995 +    ///function for setting OperationTraits type
   1.996 +    ///
   1.997 +    /// \ref named-templ-param "Named parameter"
   1.998 +    ///function for setting OperationTraits type
   1.999 +    ///
  1.1000 +    template<class T>
  1.1001 +    BellmanFordWizard<DefOperationTraitsBase<T> > distMap() {
  1.1002 +      return BellmanFordWizard<DefDistMapBase<T> >(*this);
  1.1003 +    }
  1.1004 +    
  1.1005 +    /// \brief Sets the source node, from which the BellmanFord algorithm runs.
  1.1006 +    ///
  1.1007 +    /// Sets the source node, from which the BellmanFord algorithm runs.
  1.1008 +    /// \param src is the source node.
  1.1009 +    BellmanFordWizard<_Traits>& source(Node src) {
  1.1010 +      Base::_source = src;
  1.1011 +      return *this;
  1.1012 +    }
  1.1013 +    
  1.1014 +  };
  1.1015 +  
  1.1016 +  /// \brief Function type interface for BellmanFord algorithm.
  1.1017 +  ///
  1.1018 +  /// \ingroup shortest_path
  1.1019 +  /// Function type interface for BellmanFord algorithm.
  1.1020 +  ///
  1.1021 +  /// This function also has several \ref named-templ-func-param 
  1.1022 +  /// "named parameters", they are declared as the members of class 
  1.1023 +  /// \ref BellmanFordWizard.
  1.1024 +  /// The following
  1.1025 +  /// example shows how to use these parameters.
  1.1026 +  ///\code
  1.1027 +  /// bellmanford(g,length,source).predMap(preds).run();
  1.1028 +  ///\endcode
  1.1029 +  /// \warning Don't forget to put the \ref BellmanFordWizard::run() "run()"
  1.1030 +  /// to the end of the parameter list.
  1.1031 +  /// \sa BellmanFordWizard
  1.1032 +  /// \sa BellmanFord
  1.1033 +  template<class _Digraph, class _LengthMap>
  1.1034 +  BellmanFordWizard<BellmanFordWizardBase<_Digraph,_LengthMap> >
  1.1035 +  bellmanFord(const _Digraph& digraph,
  1.1036 +	      const _LengthMap& length, 
  1.1037 +	      typename _Digraph::Node source = INVALID) {
  1.1038 +    return BellmanFordWizard<BellmanFordWizardBase<_Digraph,_LengthMap> >
  1.1039 +      (digraph, length, source);
  1.1040 +  }
  1.1041 +
  1.1042 +} //END OF NAMESPACE LEMON
  1.1043 +
  1.1044 +#endif
  1.1045 +