/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2009

 * 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_EULER_H

#define LEMON_EULER_H

#include<lemon/core.h>

#include<lemon/adaptors.h>

#include<lemon/connectivity.h>

#include <list>

/// \ingroup graph_properties

/// \file

/// \brief Euler tour iterators and a function for checking the \e Eulerian 

/// property.

///

///This file provides Euler tour iterators and a function to check

///if a (di)graph is \e Eulerian.

namespace lemon {

  ///Euler tour iterator for digraphs.

  /// \ingroup graph_prop

  ///This iterator provides an Euler tour (Eulerian circuit) of a \e directed

  ///graph (if there exists) and it converts to the \c Arc type of the digraph.

  ///

  ///For example, if the given digraph has an Euler tour (i.e it has only one

  ///non-trivial component and the in-degree is equal to the out-degree 

  ///for all nodes), then the following code will put the arcs of \c g

  ///to the vector \c et according to an Euler tour of \c g.

  ///\code

  ///  std::vector<ListDigraph::Arc> et;

  ///  for(DiEulerIt<ListDigraph> e(g); e!=INVALID; ++e)

  ///    et.push_back(e);

  ///\endcode

  ///If \c g has no Euler tour, then the resulted walk will not be closed

  ///or not contain all arcs.

  ///\sa EulerIt

  template<typename GR>

  class DiEulerIt

  {

    typedef typename GR::Node Node;

    typedef typename GR::NodeIt NodeIt;

    typedef typename GR::Arc Arc;

    typedef typename GR::ArcIt ArcIt;

    typedef typename GR::OutArcIt OutArcIt;

    typedef typename GR::InArcIt InArcIt;

    const GR &g;

    typename GR::template NodeMap<OutArcIt> narc;

    std::list<Arc> euler;

  public:

    ///Constructor

    ///Constructor.

    ///\param gr A digraph.

    ///\param start The starting point of the tour. If it is not given,

    ///the tour will start from the first node that has an outgoing arc.

    DiEulerIt(const GR &gr, typename GR::Node start = INVALID)

      : g(gr), narc(g)

    {

      if (start==INVALID) {

        NodeIt n(g);

        while (n!=INVALID && OutArcIt(g,n)==INVALID) ++n;

        start=n;

      }

      if (start!=INVALID) {

        for (NodeIt n(g); n!=INVALID; ++n) narc[n]=OutArcIt(g,n);

        while (narc[start]!=INVALID) {

          euler.push_back(narc[start]);

          Node next=g.target(narc[start]);

          ++narc[start];

          start=next;

        }

      }

    }

    ///Arc conversion

    operator Arc() { return euler.empty()?INVALID:euler.front(); }

    ///Compare with \c INVALID

    bool operator==(Invalid) { return euler.empty(); }

    ///Compare with \c INVALID

    bool operator!=(Invalid) { return !euler.empty(); }

    ///Next arc of the tour

    ///Next arc of the tour

    ///

    DiEulerIt &operator++() {

      Node s=g.target(euler.front());

      euler.pop_front();

      typename std::list<Arc>::iterator next=euler.begin();

      while(narc[s]!=INVALID) {

        euler.insert(next,narc[s]);

        Node n=g.target(narc[s]);

        ++narc[s];

        s=n;

      }

      return *this;

    }

    ///Postfix incrementation

    /// Postfix incrementation.

    ///

    ///\warning This incrementation

    ///returns an \c Arc, not a \ref DiEulerIt, as one may

    ///expect.

    Arc operator++(int)

    {

      Arc e=*this;

      ++(*this);

      return e;

    }

  };

  ///Euler tour iterator for graphs.

  /// \ingroup graph_properties

  ///This iterator provides an Euler tour (Eulerian circuit) of an

  ///\e undirected graph (if there exists) and it converts to the \c Arc

  ///and \c Edge types of the graph.

  ///

  ///For example, if the given graph has an Euler tour (i.e it has only one 

  ///non-trivial component and the degree of each node is even),

  ///the following code will print the arc IDs according to an

  ///Euler tour of \c g.

  ///\code

  ///  for(EulerIt<ListGraph> e(g); e!=INVALID; ++e) {

  ///    std::cout << g.id(Edge(e)) << std::eol;

  ///  }

  ///\endcode

  ///Although this iterator is for undirected graphs, it still returns 

  ///arcs in order to indicate the direction of the tour.

  ///(But arcs convert to edges, of course.)

  ///

  ///If \c g has no Euler tour, then the resulted walk will not be closed

  ///or not contain all edges.

  template<typename GR>

  class EulerIt

  {

    typedef typename GR::Node Node;

    typedef typename GR::NodeIt NodeIt;

    typedef typename GR::Arc Arc;

    typedef typename GR::Edge Edge;

    typedef typename GR::ArcIt ArcIt;

    typedef typename GR::OutArcIt OutArcIt;

    typedef typename GR::InArcIt InArcIt;

    const GR &g;

    typename GR::template NodeMap<OutArcIt> narc;

    typename GR::template EdgeMap<bool> visited;

    std::list<Arc> euler;

  public:

    ///Constructor

    ///Constructor.

    ///\param gr A graph.

    ///\param start The starting point of the tour. If it is not given,

    ///the tour will start from the first node that has an incident edge.

    EulerIt(const GR &gr, typename GR::Node start = INVALID)

      : g(gr), narc(g), visited(g, false)

    {

      if (start==INVALID) {

        NodeIt n(g);

        while (n!=INVALID && OutArcIt(g,n)==INVALID) ++n;

        start=n;

      }

      if (start!=INVALID) {

        for (NodeIt n(g); n!=INVALID; ++n) narc[n]=OutArcIt(g,n);

        while(narc[start]!=INVALID) {

          euler.push_back(narc[start]);

          visited[narc[start]]=true;

          Node next=g.target(narc[start]);

          ++narc[start];

          start=next;

          while(narc[start]!=INVALID && visited[narc[start]]) ++narc[start];

        }

      }

    }

    ///Arc conversion

    operator Arc() const { return euler.empty()?INVALID:euler.front(); }

    ///Edge conversion

    operator Edge() const { return euler.empty()?INVALID:euler.front(); }

    ///Compare with \c INVALID

    bool operator==(Invalid) const { return euler.empty(); }

    ///Compare with \c INVALID

    bool operator!=(Invalid) const { return !euler.empty(); }

    ///Next arc of the tour

    ///Next arc of the tour

    ///

    EulerIt &operator++() {

      Node s=g.target(euler.front());

      euler.pop_front();

      typename std::list<Arc>::iterator next=euler.begin();

      while(narc[s]!=INVALID) {

        while(narc[s]!=INVALID && visited[narc[s]]) ++narc[s];

        if(narc[s]==INVALID) break;

        else {

          euler.insert(next,narc[s]);

          visited[narc[s]]=true;

          Node n=g.target(narc[s]);

          ++narc[s];

          s=n;

        }

      }

      return *this;

    }

    ///Postfix incrementation

    /// Postfix incrementation.

    ///

    ///\warning This incrementation returns an \c Arc (which converts to 

    ///an \c Edge), not an \ref EulerIt, as one may expect.

    Arc operator++(int)

    {

      Arc e=*this;

      ++(*this);

      return e;

    }

  };

  ///Check if the given graph is Eulerian

  /// \ingroup graph_properties

  ///This function checks if the given graph is Eulerian.

  ///It works for both directed and undirected graphs.

  ///

  ///By definition, a digraph is called \e Eulerian if

  ///and only if it is connected and the number of incoming and outgoing

  ///arcs are the same for each node.

  ///Similarly, an undirected graph is called \e Eulerian if

  ///and only if it is connected and the number of incident edges is even

  ///for each node.

  ///

  ///\note There are (di)graphs that are not Eulerian, but still have an

  /// Euler tour, since they may contain isolated nodes.

  ///

  ///\sa DiEulerIt, EulerIt

  template<typename GR>

#ifdef DOXYGEN

  bool

#else

  typename enable_if<UndirectedTagIndicator<GR>,bool>::type

  eulerian(const GR &g)

  {

    for(typename GR::NodeIt n(g);n!=INVALID;++n)

      if(countIncEdges(g,n)%2) return false;

    return connected(g);

  }

  template<class GR>

  typename disable_if<UndirectedTagIndicator<GR>,bool>::type

#endif

  eulerian(const GR &g)

  {

    for(typename GR::NodeIt n(g);n!=INVALID;++n)

      if(countInArcs(g,n)!=countOutArcs(g,n)) return false;

    return connected(undirector(g));

  }

}

#endif