RhodeCode

/* -*- 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_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 Value>

  struct DijkstraDefaultOperationTraits {

    /// \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 LM The type of the length map.

  template<class GR, class LM>

  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 meet the \ref concepts::ReadMap "ReadMap" concept.

    typedef LM LengthMap;

    ///The type of the length of the arcs.

    typedef typename LM::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

    /// \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 LM::Value, HeapCrossRef, std::less<Value> > Heap;

    ///Instantiates a \ref 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 meet 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 meet 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 meet the \ref concepts::WriteMap "WriteMap" concept.

    typedef typename Digraph::template NodeMap<typename LM::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);

    }

  };

  ///%Dijkstra algorithm class.

  /// \ingroup shortest_path

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

  ///

  ///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 value is \ref ListDigraph.

  ///The value of GR is not used directly by \ref Dijkstra, it is only

  ///passed to \ref DijkstraDefaultTraits.

  ///\tparam LM A readable arc map that determines 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 "Digraph::ArcMap<int>".

  ///The value of LM is not used directly by \ref Dijkstra, it is only

  ///passed to \ref DijkstraDefaultTraits.

  ///\tparam TR Traits class to set various data types used by the algorithm.

  ///The default traits class is \ref DijkstraDefaultTraits

  ///"DijkstraDefaultTraits<GR,LM>". See \ref DijkstraDefaultTraits

  ///for the documentation of a Dijkstra traits class.

#ifdef DOXYGEN

  template <typename GR, typename LM, typename TR>

#else

  template <typename GR=ListDigraph,

            typename LM=typename GR::template ArcMap<int>,

            typename TR=DijkstraDefaultTraits<GR,LM> >

#endif

  class Dijkstra {

  public:

    ///The type of the digraph the algorithm runs on.

    typedef typename TR::Digraph Digraph;

    ///The type of the length of the arcs.

    typedef typename TR::LengthMap::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;

    ///The operation traits class.

    typedef typename TR::OperationTraits OperationTraits;

    ///The traits class.

    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

    ///PredMap type.

    ///

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

    ///PredMap type.

    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

    ///DistMap type.

    ///

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

    ///DistMap type.

    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

    ///ProcessedMap type.

    ///

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

    ///ProcessedMap type.

    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

    ///ProcessedMap type to be <tt>Digraph::NodeMap<bool></tt>.

    ///

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

    ///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 type

    ///

    ///\ref named-templ-param "Named parameter" for setting heap and cross

    ///reference type.

    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 type with automatic allocation

    ///

    ///\ref named-templ-param "Named parameter" for setting heap and cross

    ///reference type. It can allocate the heap and the cross reference

    ///object if the cross reference's constructor waits for the digraph as

    ///parameter and the heap's constructor waits for the cross reference.

    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

    ///\ref OperationTraits type.

    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(),

    ///it will allocate one. 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(),

    ///it will allocate one. 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(),

    ///it will allocate one. 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(),

    ///it will allocate one. The destructor deallocates this

    ///automatically allocated heap and cross reference, 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:

/* -*- 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.

 *

 */

#include <lemon/concepts/digraph.h>

#include <lemon/smart_graph.h>

#include <lemon/list_graph.h>

#include <lemon/lgf_reader.h>

#include <lemon/dijkstra.h>

#include <lemon/path.h>

#include <lemon/bin_heap.h>

#include "graph_test.h"

#include "test_tools.h"

using namespace lemon;

char test_lgf[] =

  "@nodes\n"

  "label\n"

  "0\n"

  "1\n"

  "2\n"

  "3\n"

  "4\n"

  "@arcs\n"

  "     label length\n"

  "0 1  0     1\n"

  "1 2  1     1\n"

  "2 3  2     1\n"

  "0 3  4     5\n"

  "0 3  5     10\n"

  "0 3  6     7\n"

  "4 2  7     1\n"

  "@attributes\n"

  "source 0\n"

  "target 3\n";

void checkDijkstraCompile()

{

  typedef int VType;

  typedef concepts::Digraph Digraph;

  typedef concepts::ReadMap<Digraph::Arc,VType> LengthMap;

  typedef Dijkstra<Digraph, LengthMap> DType;

  typedef Digraph::Node Node;

  typedef Digraph::Arc Arc;

  Digraph G;

  Node s, t;

  Arc e;

  VType l;

  bool b;

  DType::DistMap d(G);

  DType::PredMap p(G);

  LengthMap length;

  Path<Digraph> pp;

  {

    DType dijkstra_test(G,length);

    dijkstra_test.run(s);

    dijkstra_test.run(s,t);

    l  = dijkstra_test.dist(t);

    e  = dijkstra_test.predArc(t);

    s  = dijkstra_test.predNode(t);

    b  = dijkstra_test.reached(t);

    d  = dijkstra_test.distMap();

    p  = dijkstra_test.predMap();

    pp = dijkstra_test.path(t);

  }

  {

    DType

      ::SetPredMap<concepts::ReadWriteMap<Node,Arc> >

      ::SetDistMap<concepts::ReadWriteMap<Node,VType> >

      ::SetProcessedMap<concepts::WriteMap<Node,bool> >

      ::SetStandardProcessedMap

      ::SetHeap<BinHeap<VType, concepts::ReadWriteMap<Node,int> > >

      ::SetStandardHeap<BinHeap<VType, concepts::ReadWriteMap<Node,int> > >

      ::Create dijkstra_test(G,length);

    dijkstra_test.run(s);

    dijkstra_test.run(s,t);

    l  = dijkstra_test.dist(t);

    e  = dijkstra_test.predArc(t);

    s  = dijkstra_test.predNode(t);

    b  = dijkstra_test.reached(t);

    pp = dijkstra_test.path(t);

  }

}

void checkDijkstraFunctionCompile()

{

  typedef int VType;

  typedef concepts::Digraph Digraph;

  typedef Digraph::Arc Arc;

  typedef Digraph::Node Node;

  typedef concepts::ReadMap<Digraph::Arc,VType> LengthMap;

  Digraph g;

  bool b;

  dijkstra(g,LengthMap()).run(Node());

  b=dijkstra(g,LengthMap()).run(Node(),Node());

  dijkstra(g,LengthMap())

    .predMap(concepts::ReadWriteMap<Node,Arc>())

    .distMap(concepts::ReadWriteMap<Node,VType>())

    .processedMap(concepts::WriteMap<Node,bool>())

    .run(Node());

  b=dijkstra(g,LengthMap())

    .predMap(concepts::ReadWriteMap<Node,Arc>())

    .distMap(concepts::ReadWriteMap<Node,VType>())

    .processedMap(concepts::WriteMap<Node,bool>())

    .path(concepts::Path<Digraph>())

    .dist(VType())

    .run(Node(),Node());

}

template <class Digraph>

void checkDijkstra() {

  TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

  typedef typename Digraph::template ArcMap<int> LengthMap;

  Digraph G;

  Node s, t;

  LengthMap length(G);

  std::istringstream input(test_lgf);

  digraphReader(G, input).

    arcMap("length", length).

    node("source", s).

    node("target", t).

    run();

  Dijkstra<Digraph, LengthMap>

        dijkstra_test(G, length);

  dijkstra_test.run(s);

  check(dijkstra_test.dist(t)==3,"Dijkstra found a wrong path.");

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

  check(p.length()==3,"path() found a wrong path.");

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

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

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

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

    Node u=G.source(e);

    Node v=G.target(e);

    check( !dijkstra_test.reached(u) ||

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

           "Wrong output. dist(target)-dist(source)-arc_length=" <<

           dijkstra_test.dist(v) - dijkstra_test.dist(u) - length[e]);

  }

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

    if (dijkstra_test.reached(v)) {

      check(v==s || dijkstra_test.predArc(v)!=INVALID, "Wrong tree.");

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

        Arc e=dijkstra_test.predArc(v);

        Node u=G.source(e);

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

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

              "Wrong distance! Difference: " <<

              std::abs(dijkstra_test.dist(v)-dijkstra_test.dist(u)-length[e]));

      }

    }

  }

  {

    NullMap<Node,Arc> myPredMap;

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

  }

}

int main() {

  checkDijkstra<ListDigraph>();

  checkDijkstra<SmartDigraph>();

  return 0;

}