lemon/euler.h
author Alpar Juttner <alpar@cs.elte.hu>
Mon, 23 Feb 2009 12:33:40 +0000
changeset 530 1c5d6e47921f
parent 521 3af83b6be1df
child 559 c5fd2d996909
permissions -rw-r--r--
Merge
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2009
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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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_EULER_H
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#define LEMON_EULER_H
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#include<lemon/core.h>
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#include<lemon/adaptors.h>
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#include<lemon/connectivity.h>
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#include <list>
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/// \ingroup graph_prop
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/// \file
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/// \brief Euler tour
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///
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///This file provides an Euler tour iterator and ways to check
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///if a digraph is euler.
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namespace lemon {
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  ///Euler iterator for digraphs.
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  /// \ingroup graph_prop
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  ///This iterator converts to the \c Arc type of the digraph and using
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  ///operator ++, it provides an Euler tour of a \e directed
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  ///graph (if there exists).
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  ///
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  ///For example
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  ///if the given digraph is Euler (i.e it has only one nontrivial component
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  ///and the in-degree is equal to the out-degree for all nodes),
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  ///the following code will put the arcs of \c g
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  ///to the vector \c et according to an
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  ///Euler tour of \c g.
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  ///\code
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  ///  std::vector<ListDigraph::Arc> et;
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  ///  for(DiEulerIt<ListDigraph> e(g),e!=INVALID;++e)
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  ///    et.push_back(e);
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  ///\endcode
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  ///If \c g is not Euler then the resulted tour will not be full or closed.
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  ///\sa EulerIt
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  template<class Digraph>
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  class DiEulerIt
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  {
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    typedef typename Digraph::Node Node;
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    typedef typename Digraph::NodeIt NodeIt;
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    typedef typename Digraph::Arc Arc;
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    typedef typename Digraph::ArcIt ArcIt;
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    typedef typename Digraph::OutArcIt OutArcIt;
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    typedef typename Digraph::InArcIt InArcIt;
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    const Digraph &g;
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    typename Digraph::template NodeMap<OutArcIt> nedge;
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    std::list<Arc> euler;
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  public:
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    ///Constructor
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    ///\param _g A digraph.
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    ///\param start The starting point of the tour. If it is not given
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    ///       the tour will start from the first node.
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    DiEulerIt(const Digraph &_g,typename Digraph::Node start=INVALID)
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      : g(_g), nedge(g)
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    {
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      if(start==INVALID) start=NodeIt(g);
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      for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n);
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      while(nedge[start]!=INVALID) {
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        euler.push_back(nedge[start]);
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        Node next=g.target(nedge[start]);
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        ++nedge[start];
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        start=next;
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      }
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    }
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    ///Arc Conversion
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    operator Arc() { return euler.empty()?INVALID:euler.front(); }
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    bool operator==(Invalid) { return euler.empty(); }
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    bool operator!=(Invalid) { return !euler.empty(); }
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    ///Next arc of the tour
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    DiEulerIt &operator++() {
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      Node s=g.target(euler.front());
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      euler.pop_front();
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      //This produces a warning.Strange.
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      //std::list<Arc>::iterator next=euler.begin();
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      typename std::list<Arc>::iterator next=euler.begin();
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      while(nedge[s]!=INVALID) {
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        euler.insert(next,nedge[s]);
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        Node n=g.target(nedge[s]);
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        ++nedge[s];
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        s=n;
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      }
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      return *this;
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    }
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    ///Postfix incrementation
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    ///\warning This incrementation
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    ///returns an \c Arc, not an \ref DiEulerIt, as one may
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    ///expect.
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    Arc operator++(int)
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    {
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      Arc e=*this;
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      ++(*this);
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      return e;
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    }
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  };
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  ///Euler iterator for graphs.
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  /// \ingroup graph_prop
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  ///This iterator converts to the \c Arc (or \c Edge)
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  ///type of the digraph and using
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  ///operator ++, it provides an Euler tour of an undirected
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  ///digraph (if there exists).
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  ///
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  ///For example
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  ///if the given digraph if Euler (i.e it has only one nontrivial component
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  ///and the degree of each node is even),
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  ///the following code will print the arc IDs according to an
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  ///Euler tour of \c g.
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  ///\code
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  ///  for(EulerIt<ListGraph> e(g),e!=INVALID;++e) {
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  ///    std::cout << g.id(Edge(e)) << std::eol;
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  ///  }
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  ///\endcode
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  ///Although the iterator provides an Euler tour of an graph,
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  ///it still returns Arcs in order to indicate the direction of the tour.
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  ///(But Arc will convert to Edges, of course).
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  ///
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  ///If \c g is not Euler then the resulted tour will not be full or closed.
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  ///\sa EulerIt
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  template<class Digraph>
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  class EulerIt
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  {
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    typedef typename Digraph::Node Node;
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    typedef typename Digraph::NodeIt NodeIt;
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    typedef typename Digraph::Arc Arc;
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    typedef typename Digraph::Edge Edge;
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    typedef typename Digraph::ArcIt ArcIt;
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    typedef typename Digraph::OutArcIt OutArcIt;
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    typedef typename Digraph::InArcIt InArcIt;
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    const Digraph &g;
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    typename Digraph::template NodeMap<OutArcIt> nedge;
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    typename Digraph::template EdgeMap<bool> visited;
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    std::list<Arc> euler;
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  public:
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    ///Constructor
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    ///\param _g An graph.
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    ///\param start The starting point of the tour. If it is not given
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    ///       the tour will start from the first node.
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    EulerIt(const Digraph &_g,typename Digraph::Node start=INVALID)
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      : g(_g), nedge(g), visited(g,false)
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    {
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      if(start==INVALID) start=NodeIt(g);
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      for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n);
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      while(nedge[start]!=INVALID) {
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        euler.push_back(nedge[start]);
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        visited[nedge[start]]=true;
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        Node next=g.target(nedge[start]);
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        ++nedge[start];
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        start=next;
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        while(nedge[start]!=INVALID && visited[nedge[start]]) ++nedge[start];
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      }
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    }
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    ///Arc Conversion
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    operator Arc() const { return euler.empty()?INVALID:euler.front(); }
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    ///Arc Conversion
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    operator Edge() const { return euler.empty()?INVALID:euler.front(); }
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    ///\e
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    bool operator==(Invalid) const { return euler.empty(); }
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    ///\e
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    bool operator!=(Invalid) const { return !euler.empty(); }
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    ///Next arc of the tour
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    EulerIt &operator++() {
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      Node s=g.target(euler.front());
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      euler.pop_front();
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      typename std::list<Arc>::iterator next=euler.begin();
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      while(nedge[s]!=INVALID) {
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        while(nedge[s]!=INVALID && visited[nedge[s]]) ++nedge[s];
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        if(nedge[s]==INVALID) break;
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        else {
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          euler.insert(next,nedge[s]);
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          visited[nedge[s]]=true;
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          Node n=g.target(nedge[s]);
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          ++nedge[s];
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          s=n;
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        }
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      }
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      return *this;
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    }
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    ///Postfix incrementation
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    ///\warning This incrementation
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    ///returns an \c Arc, not an \ref EulerIt, as one may
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    ///expect.
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    Arc operator++(int)
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    {
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      Arc e=*this;
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      ++(*this);
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      return e;
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    }
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  };
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  ///Checks if the graph is Eulerian
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  /// \ingroup graph_prop
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  ///Checks if the graph is Eulerian. It works for both directed and undirected
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  ///graphs.
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  ///\note By definition, a digraph is called \e Eulerian if
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  ///and only if it is connected and the number of its incoming and outgoing
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  ///arcs are the same for each node.
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  ///Similarly, an undirected graph is called \e Eulerian if
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  ///and only if it is connected and the number of incident arcs is even
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  ///for each node. <em>Therefore, there are digraphs which are not Eulerian,
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  ///but still have an Euler tour</em>.
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  template<class Digraph>
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#ifdef DOXYGEN
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  bool
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#else
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  typename enable_if<UndirectedTagIndicator<Digraph>,bool>::type
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  eulerian(const Digraph &g)
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  {
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    for(typename Digraph::NodeIt n(g);n!=INVALID;++n)
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      if(countIncEdges(g,n)%2) return false;
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    return connected(g);
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  }
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  template<class Digraph>
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  typename disable_if<UndirectedTagIndicator<Digraph>,bool>::type
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#endif
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  eulerian(const Digraph &g)
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  {
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    for(typename Digraph::NodeIt n(g);n!=INVALID;++n)
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      if(countInArcs(g,n)!=countOutArcs(g,n)) return false;
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    return connected(Undirector<const Digraph>(g));
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  }
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}
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#endif