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 - For all \f$u\in V\f$ nodes:
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   - \f$\pi(u)<=0\f$;
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   - \f$\pi(u)\leq 0\f$;
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   - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,
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@@ -147,3 +147,3 @@
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 - For all \f$u\in V\f$ nodes:
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   - \f$\pi(u)>=0\f$;
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   - \f$\pi(u)\geq 0\f$;
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   - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,
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    /// \c OperationTraits type.
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    /// For more information see \ref BellmanFordDefaultOperationTraits.
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    /// For more information, see \ref BellmanFordDefaultOperationTraits.
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    template <class T>
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    /// The shortest path tree used here is equal to the shortest path
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    /// tree used in \ref predNode() and \predMap().
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    /// tree used in \ref predNode() and \ref predMap().
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    ///
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    /// The shortest path tree used here is equal to the shortest path
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    /// tree used in \ref predArc() and \predMap().
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    /// tree used in \ref predArc() and \ref predMap().
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    ///
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@@ -65,3 +65,3 @@
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    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
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    ///By default it is a NullMap.
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    ///By default, it is a NullMap.
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    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
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    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
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    ///By default it is a NullMap.
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    ///By default, it is a NullMap.
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    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
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    /// digraph and the maximum level should be passed to it).
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    /// However an external elevator object could also be passed to the
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    /// However, an external elevator object could also be passed to the
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    /// algorithm with the \ref elevator(Elevator&) "elevator()" function
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      /// This iterator goes through each node of the digraph.
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      /// Its usage is quite simple, for example you can count the number
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      /// Its usage is quite simple, for example, you can count the number
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      /// of nodes in a digraph \c g of type \c %Digraph like this:
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@@ -198,3 +198,3 @@
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      /// of a digraph.
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      /// Its usage is quite simple, for example you can count the number
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      /// Its usage is quite simple, for example, you can count the number
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      /// of outgoing arcs of a node \c n
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@@ -243,3 +243,3 @@
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      /// of a digraph.
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      /// Its usage is quite simple, for example you can count the number
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      /// Its usage is quite simple, for example, you can count the number
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      /// of incoming arcs of a node \c n
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@@ -287,3 +287,3 @@
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      /// This iterator goes through each arc of the digraph.
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      /// Its usage is quite simple, for example you can count the number
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      /// Its usage is quite simple, for example, you can count the number
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      /// of arcs in a digraph \c g of type \c %Digraph as follows:
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      /// This iterator goes through each node of the graph.
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      /// Its usage is quite simple, for example you can count the number
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      /// Its usage is quite simple, for example, you can count the number
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      /// of nodes in a graph \c g of type \c %Graph like this:
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      /// This iterator goes through each edge of the graph.
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      /// Its usage is quite simple, for example you can count the number
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      /// Its usage is quite simple, for example, you can count the number
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      /// of edges in a graph \c g of type \c %Graph as follows:
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      /// of a certain node of a graph.
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      /// Its usage is quite simple, for example you can compute the
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      /// Its usage is quite simple, for example, you can compute the
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      /// degree (i.e. the number of incident edges) of a node \c n
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      /// This iterator goes through each directed arc of the graph.
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      /// Its usage is quite simple, for example you can count the number
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      /// Its usage is quite simple, for example, you can count the number
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      /// of arcs in a graph \c g of type \c %Graph as follows:
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      /// certain node of a graph.
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      /// Its usage is quite simple, for example you can count the number
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      /// Its usage is quite simple, for example, you can count the number
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      /// of outgoing arcs of a node \c n
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      /// certain node of a graph.
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      /// Its usage is quite simple, for example you can count the number
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      /// Its usage is quite simple, for example, you can count the number
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      /// of incoming arcs of a node \c n
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      ///
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      /// Edges don't have source and target nodes, however methods
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      /// Edges don't have source and target nodes, however, methods
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      /// u() and v() are used to query the two end-nodes of an edge.
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      ///
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      /// Edges don't have source and target nodes, however methods
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      /// Edges don't have source and target nodes, however, methods
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      /// u() and v() are used to query the two end-nodes of an edge.
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///\file
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///\brief The concept of graph components.
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///\brief The concepts of graph components.
22 22

	
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214 214

	
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  /// This class can be used in the same way as \ref Counter however it
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  /// This class can be used in the same way as \ref Counter, but it
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  /// does not count at all and does not print report on destruction.
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    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
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    ///By default it is a NullMap.
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    ///By default, it is a NullMap.
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    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
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    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
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    ///By default it is a NullMap.
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    ///By default, it is a NullMap.
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    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
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    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
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    ///By default it is a NullMap.
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    ///By default, it is a NullMap.
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    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
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    ///reference should be passed to the constructor of the heap).
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    ///However external heap and cross reference objects could also be
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    ///However, external heap and cross reference objects could also be
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    ///passed to the algorithm using the \ref heap() function before
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    ///\c OperationTraits type.
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    /// For more information see \ref DijkstraDefaultOperationTraits.
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    /// For more information, see \ref DijkstraDefaultOperationTraits.
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    template <class T>
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    ///It must conform to the \ref concepts::WriteMap "WriteMap" concept.
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    ///By default it is a NullMap.
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    ///By default, it is a NullMap.
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    typedef NullMap<typename Digraph::Node,bool> ProcessedMap;
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    template <typename CutMap>
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    Value minCutMap(const Node& s, ///< 
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    Value minCutMap(const Node& s,
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                    const Node& t,
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                    ///< 
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                    CutMap& cutMap
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                    ///< 
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                    ) const {
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                   /// does not necessarily give the same set of nodes.
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                   /// However it is ensured that
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                   /// However, it is ensured that
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                   /// \code
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  ///\param ost Reference to the output stream.
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  ///By default it is <tt>std::cout</tt>.
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  ///By default, it is <tt>std::cout</tt>.
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  ///\param pros If it is \c true, then the \c ostream referenced by \c os
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514 514

	
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  ///By default graphToEps() rescales the whole image in order to avoid
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  ///By default, graphToEps() rescales the whole image in order to avoid
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  ///very big or very small bounding boxes.
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///\param os Reference to the output stream.
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///By default it is <tt>std::cout</tt>.
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///By default, it is <tt>std::cout</tt>.
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///
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///
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///For more detailed examples see the \ref graph_to_eps_demo.cc demo file.
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///For more detailed examples, see the \ref graph_to_eps_demo.cc demo file.
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///
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  /// This class is completely static and it needs constant memory space.
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  /// Thus you can neither add nor delete nodes or edges, however 
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  /// Thus you can neither add nor delete nodes or edges, however,
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  /// the structure can be resized using resize().
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  ///
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  /// By default the reader uses the first section in the file of the
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  /// By default, the reader uses the first section in the file of the
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  /// proper type. If a section has an optional name, then it can be
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    ///
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    /// For example let's see a section, which contain several
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    /// For example, let's see a section, which contain several
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    /// integers, which should be inserted into a vector.
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    ///\note \c ArcIt and \c OutArcIt iterators referencing the changed
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    ///arc remain valid, however \c InArcIt iterators are invalidated.
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    ///arc remain valid, but \c InArcIt iterators are invalidated.
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    ///
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    ///\note \c InArcIt iterators referencing the changed arc remain
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    ///valid, however \c ArcIt and \c OutArcIt iterators are invalidated.
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    ///valid, but \c ArcIt and \c OutArcIt iterators are invalidated.
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    ///
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    /// restored. These events invalidate the snapshot.
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    /// However the arcs and nodes that were added to the digraph after
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    /// However, the arcs and nodes that were added to the digraph after
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    /// making the current snapshot can be removed without invalidating it.
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    ///\note \c EdgeIt iterators referencing the changed edge remain
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    ///valid, however \c ArcIt iterators referencing the changed edge and
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    ///valid, but \c ArcIt iterators referencing the changed edge and
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    ///all other iterators whose base node is the changed node are also
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    /// cannot be restored. These events invalidate the snapshot.
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    /// However the edges and nodes that were added to the graph after
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    /// However, the edges and nodes that were added to the graph after
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    /// making the current snapshot can be removed without invalidating it.
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148 148

	
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    /// Its usage is quite simple, for example you can count the number
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    /// Its usage is quite simple, for example, you can count the number
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    /// of columns in an LP \c lp:
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    /// Its usage is quite simple, for example you can count the number
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    /// Its usage is quite simple, for example, you can count the number
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    /// of rows in an LP \c lp:
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  /// values to integer keys from the range <tt>[0..size-1]</tt>.
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  /// It can be used with some data structures, for example
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  /// \c UnionFind, \c BinHeap, when the used items are small
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  /// It can be used together with some data structures, e.g.
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  /// heap types and \c UnionFind, when the used items are small
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  /// integers. This map conforms to the \ref concepts::ReferenceMap
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  /// "ReferenceMap" concept.
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  /// "ReferenceMap" concept. 
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  ///
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  ///
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  /// Apart form that this map can be used in many other cases since it
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  /// Apart form that, this map can be used in many other cases since it
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  /// is based on \c std::map, which is a general associative container.
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  /// However keep in mind that it is usually not as efficient as other
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  /// However, keep in mind that it is usually not as efficient as other
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  /// maps.
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  /// that were marked \c true by an algorithm.
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  /// For example it makes easier to store the nodes in the processing
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  /// For example, it makes easier to store the nodes in the processing
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  /// order of Dfs algorithm, as the following examples show.
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  /// \note LoggerBoolMap is just \ref concepts::WriteMap "writable", so
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  /// it cannot be used when a readable map is needed, for example as
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  /// it cannot be used when a readable map is needed, for example, as
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  /// \c ReachedMap for \c Bfs, \c Dfs and \c Dijkstra algorithms.
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  /// suitable and more efficient for such cases. It provides iterators
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  /// to traverse the items with the same associated value, however
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  /// to traverse the items with the same associated value, but
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  /// it does not have \c InverseMap.
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3468 3468
  /// The correct behavior of InDegMap is not guarantied if these additional
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  /// features are used. For example the functions
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  /// features are used. For example, the functions
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  /// \ref ListDigraph::changeSource() "changeSource()",
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  /// The correct behavior of OutDegMap is not guarantied if these additional
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  /// features are used. For example the functions
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  /// features are used. For example, the functions
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  /// \ref ListDigraph::changeSource() "changeSource()",
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  /// Moreover it supports both directions of the supply/demand inequality
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  /// constraints. For more information see \ref SupplyType.
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  /// constraints. For more information, see \ref SupplyType.
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  ///
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  /// \tparam V The value type used for flow amounts, capacity bounds
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  /// and supply values in the algorithm. By default it is \c int.
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  /// and supply values in the algorithm. By default, it is \c int.
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  /// \tparam C The value type used for costs and potentials in the
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  /// algorithm. By default it is the same as \c V.
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  /// algorithm. By default, it is the same as \c V.
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  ///
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  /// implementations, from which the most efficient one is used
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  /// by default. For more information see \ref PivotRule.
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  /// by default. For more information, see \ref PivotRule.
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  template <typename GR, typename V = int, typename C = V>
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    /// of the algorithm.
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    /// By default \ref BLOCK_SEARCH "Block Search" is used, which
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    /// By default, \ref BLOCK_SEARCH "Block Search" is used, which
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    /// proved to be the most efficient and the most robust on various
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    /// test inputs according to our benchmark tests.
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    /// However another pivot rule can be selected using the \ref run()
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    /// However, another pivot rule can be selected using the \ref run()
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    /// function with the proper parameter.
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131 131

	
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      /// The First Eligible pivot rule.
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      /// The \e First \e Eligible pivot rule.
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      /// The next eligible arc is selected in a wraparound fashion
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136 136

	
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      /// The Best Eligible pivot rule.
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      /// The \e Best \e Eligible pivot rule.
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      /// The best eligible arc is selected in every iteration.
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140 140

	
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      /// The Block Search pivot rule.
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      /// The \e Block \e Search pivot rule.
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      /// A specified number of arcs are examined in every iteration
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146 146

	
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      /// The Candidate List pivot rule.
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      /// The \e Candidate \e List pivot rule.
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      /// In a major iteration a candidate list is built from eligible arcs
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152 152

	
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      /// The Altering Candidate List pivot rule.
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      /// The \e Altering \e Candidate \e List pivot rule.
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      /// It is a modified version of the Candidate List method.
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    ///
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    /// For more information see \ref SupplyType.
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    /// For more information, see \ref SupplyType.
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    ///
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844 844
    /// have to be set again. See \ref reset() for examples.
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    /// However the underlying digraph must not be modified after this
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    /// However, the underlying digraph must not be modified after this
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    /// class have been constructed, since it copies and extends the graph.
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848 848
    /// \param pivot_rule The pivot rule that will be used during the
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    /// algorithm. For more information see \ref PivotRule.
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    /// algorithm. For more information, see \ref PivotRule.
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    ///
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    /// \ref run() call.
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    /// However the underlying digraph must not be modified after this
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    /// However, the underlying digraph must not be modified after this
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    /// class have been constructed, since it copies and extends the graph.
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266 266
    /// digraph and the maximum level should be passed to it).
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    /// However an external elevator object could also be passed to the
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    /// However, an external elevator object could also be passed to the
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    /// algorithm with the \ref elevator(Elevator&) "elevator()" function
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377 377
    ///necessary to really stop the timer.
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    ///For example the timer
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    ///For example, the timer
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    ///is running if and only if the return value is \c true
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45 45
  /// only four methods: join (union), find, insert and size.
46
  /// For more features see the \ref UnionFindEnum class.
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  /// For more features, see the \ref UnionFindEnum class.
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  ///
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