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alpar (Alpar Juttner)
alpar@cs.elte.hu
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#ifndef LEMON_DIJKSTRA_H
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#define LEMON_DIJKSTRA_H
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///\ingroup shortest_path
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///\file
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///\brief Dijkstra algorithm.
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#include <limits>
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#include <lemon/list_graph.h>
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#include <lemon/bin_heap.h>
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#include <lemon/bits/path_dump.h>
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#include <lemon/core.h>
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#include <lemon/error.h>
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#include <lemon/maps.h>
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#include <lemon/path.h>
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namespace lemon {
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  /// \brief Default operation traits for the Dijkstra algorithm class.
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  ///
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  /// This operation traits class defines all computational operations and
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  /// constants which are used in the Dijkstra algorithm.
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  template <typename Value>
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  struct DijkstraDefaultOperationTraits {
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    /// \brief Gives back the zero value of the type.
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    static Value zero() {
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      return static_cast<Value>(0);
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    }
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    /// \brief Gives back the sum of the given two elements.
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    static Value plus(const Value& left, const Value& right) {
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      return left + right;
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    }
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    /// \brief Gives back true only if the first value is less than the second.
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    static bool less(const Value& left, const Value& right) {
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      return left < right;
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    }
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  };
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  /// \brief Widest path operation traits for the Dijkstra algorithm class.
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  ///
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  /// This operation traits class defines all computational operations and
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  /// constants which are used in the Dijkstra algorithm for widest path
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  /// computation.
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  ///
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  /// \see DijkstraDefaultOperationTraits
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  template <typename Value>
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  struct DijkstraWidestPathOperationTraits {
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    /// \brief Gives back the maximum value of the type.
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    static Value zero() {
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      return std::numeric_limits<Value>::max();
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    }
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    /// \brief Gives back the minimum of the given two elements.
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    static Value plus(const Value& left, const Value& right) {
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      return std::min(left, right);
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    }
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    /// \brief Gives back true only if the first value is less than the second.
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    static bool less(const Value& left, const Value& right) {
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      return left < right;
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    }
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  };
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  ///Default traits class of Dijkstra class.
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  ///Default traits class of Dijkstra class.
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  ///\tparam GR The type of the digraph.
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  ///\tparam LM The type of the length map.
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  template<class GR, class LM>
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  struct DijkstraDefaultTraits
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  {
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    ///The type of the digraph the algorithm runs on.
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    typedef GR Digraph;
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    ///The type of the map that stores the arc lengths.
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    ///The type of the map that stores the arc lengths.
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    ///It must meet the \ref concepts::ReadMap "ReadMap" concept.
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    typedef LM LengthMap;
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    ///The type of the length of the arcs.
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    typedef typename LM::Value Value;
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    /// Operation traits for Dijkstra algorithm.
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    /// This class defines the operations that are used in the algorithm.
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    /// \see DijkstraDefaultOperationTraits
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    typedef DijkstraDefaultOperationTraits<Value> OperationTraits;
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    /// The cross reference type used by the heap.
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    /// The cross reference type used by the heap.
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    /// Usually it is \c Digraph::NodeMap<int>.
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    typedef typename Digraph::template NodeMap<int> HeapCrossRef;
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    ///Instantiates a \ref HeapCrossRef.
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    ///This function instantiates a \ref HeapCrossRef.
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    /// \param g is the digraph, to which we would like to define the
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    /// \ref HeapCrossRef.
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    static HeapCrossRef *createHeapCrossRef(const Digraph &g)
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    {
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      return new HeapCrossRef(g);
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    }
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    ///The heap type used by the Dijkstra algorithm.
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    ///The heap type used by the Dijkstra algorithm.
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    ///
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    ///\sa BinHeap
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    ///\sa Dijkstra
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    typedef BinHeap<typename LM::Value, HeapCrossRef, std::less<Value> > Heap;
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    ///Instantiates a \ref Heap.
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  "2 3  2     1\n"
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  "0 3  4     5\n"
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  "0 3  5     10\n"
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  "0 3  6     7\n"
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  "4 2  7     1\n"
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  "@attributes\n"
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  "source 0\n"
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  "target 3\n";
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void checkDijkstraCompile()
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{
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  typedef int VType;
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  typedef concepts::Digraph Digraph;
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  typedef concepts::ReadMap<Digraph::Arc,VType> LengthMap;
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  typedef Dijkstra<Digraph, LengthMap> DType;
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  typedef Digraph::Node Node;
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  typedef Digraph::Arc Arc;
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  Digraph G;
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  Node s, t;
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  Arc e;
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  VType l;
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  bool b;
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  DType::DistMap d(G);
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  DType::PredMap p(G);
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  LengthMap length;
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  Path<Digraph> pp;
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  {
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    DType dijkstra_test(G,length);
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    dijkstra_test.run(s);
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    dijkstra_test.run(s,t);
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    l  = dijkstra_test.dist(t);
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    e  = dijkstra_test.predArc(t);
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    s  = dijkstra_test.predNode(t);
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    b  = dijkstra_test.reached(t);
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    d  = dijkstra_test.distMap();
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    p  = dijkstra_test.predMap();
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    pp = dijkstra_test.path(t);
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  }
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  {
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    DType
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      ::SetPredMap<concepts::ReadWriteMap<Node,Arc> >
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      ::SetDistMap<concepts::ReadWriteMap<Node,VType> >
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      ::SetProcessedMap<concepts::WriteMap<Node,bool> >
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      ::SetStandardProcessedMap
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      ::SetOperationTraits<DijkstraWidestPathOperationTraits<VType> >
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      ::SetOperationTraits<DijkstraDefaultOperationTraits<VType> >
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      ::SetHeap<BinHeap<VType, concepts::ReadWriteMap<Node,int> > >
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      ::SetStandardHeap<BinHeap<VType, concepts::ReadWriteMap<Node,int> > >
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      ::Create dijkstra_test(G,length);
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    dijkstra_test.run(s);
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    dijkstra_test.run(s,t);
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    l  = dijkstra_test.dist(t);
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    e  = dijkstra_test.predArc(t);
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    s  = dijkstra_test.predNode(t);
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    b  = dijkstra_test.reached(t);
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    pp = dijkstra_test.path(t);
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  }
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}
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void checkDijkstraFunctionCompile()
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{
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  typedef int VType;
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  typedef concepts::Digraph Digraph;
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  typedef Digraph::Arc Arc;
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  typedef Digraph::Node Node;
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  typedef concepts::ReadMap<Digraph::Arc,VType> LengthMap;
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  Digraph g;
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  bool b;
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  dijkstra(g,LengthMap()).run(Node());
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  b=dijkstra(g,LengthMap()).run(Node(),Node());
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  dijkstra(g,LengthMap())
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    .predMap(concepts::ReadWriteMap<Node,Arc>())
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    .distMap(concepts::ReadWriteMap<Node,VType>())
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    .processedMap(concepts::WriteMap<Node,bool>())
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    .run(Node());
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  b=dijkstra(g,LengthMap())
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    .predMap(concepts::ReadWriteMap<Node,Arc>())
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    .distMap(concepts::ReadWriteMap<Node,VType>())
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    .processedMap(concepts::WriteMap<Node,bool>())
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    .path(concepts::Path<Digraph>())
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    .dist(VType())
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    .run(Node(),Node());
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}
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template <class Digraph>
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void checkDijkstra() {
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  TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
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  typedef typename Digraph::template ArcMap<int> LengthMap;
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  Digraph G;
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