/* -*- 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

///

///This file provides an Euler tour iterator and ways to check

///if a digraph is euler.

namespace lemon {

  ///Euler iterator for digraphs.

  /// \ingroup graph_properties

  ///This iterator converts to the \c Arc type of the digraph and using

  ///operator ++, it provides an Euler tour of a \e directed

  ///graph (if there exists).

  ///

  ///For example

  ///if the given digraph is Euler (i.e it has only one nontrivial component

  ///and the in-degree is equal to the out-degree for all nodes),

  ///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 is not Euler then the resulted tour will not be full or closed.

  ///\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> nedge;

    std::list<Arc> euler;

  public:

    ///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.

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

      : g(gr), nedge(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) nedge[n]=OutArcIt(g,n);

        while (nedge[start]!=INVALID) {

          euler.push_back(nedge[start]);

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

          ++nedge[start];

          start=next;

        }

      }

    }

    ///Arc Conversion

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

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

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

    ///Next arc of the tour

    DiEulerIt &operator++() {

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

      euler.pop_front();

      //This produces a warning.Strange.

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

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

      while(nedge[s]!=INVALID) {

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

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

        ++nedge[s];

        s=n;

      }

      return *this;

    }

    ///Postfix incrementation

    ///\warning This incrementation

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

    ///expect.

    Arc operator++(int)

    {

      Arc e=*this;

      ++(*this);

      return e;

    }

  };

  ///Euler iterator for graphs.

  /// \ingroup graph_properties

  ///This iterator converts to the \c Arc (or \c Edge)

  ///type of the digraph and using

  ///operator ++, it provides an Euler tour of an undirected

  ///digraph (if there exists).

  ///

  ///For example

  ///if the given digraph if Euler (i.e it has only one nontrivial 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 the iterator provides an Euler tour of an graph,

  ///it still returns Arcs in order to indicate the direction of the tour.

  ///(But Arc will convert to Edges, of course).

  ///

  ///If \c g is not Euler then the resulted tour will not be full or closed.

  ///\sa EulerIt

  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> nedge;

    typename GR::template EdgeMap<bool> visited;

    std::list<Arc> euler;

  public:

    ///Constructor

    ///\param gr An graph.

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

    ///       the tour will start from the first node.

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

      : g(gr), nedge(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) nedge[n]=OutArcIt(g,n);

        while(nedge[start]!=INVALID) {

          euler.push_back(nedge[start]);

          visited[nedge[start]]=true;

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

          ++nedge[start];

          start=next;

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

        }

      }

    }

    ///Arc Conversion

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

    ///Arc Conversion

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

    ///\e

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

    ///\e

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

    ///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(nedge[s]!=INVALID) {

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

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

        else {

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

          visited[nedge[s]]=true;

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

          ++nedge[s];

          s=n;

        }

      }

      return *this;

    }

    ///Postfix incrementation

    ///\warning This incrementation

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

    ///expect.

    Arc operator++(int)

    {

      Arc e=*this;

      ++(*this);

      return e;

    }

  };

  ///Checks if the graph is Eulerian

  /// \ingroup graph_properties

  ///Checks if the graph is Eulerian. It works for both directed and undirected

  ///graphs.

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

  ///and only if it is connected and the number of its 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 arcs is even

  ///for each node. <em>Therefore, there are digraphs which are not Eulerian,

  ///but still have an Euler tour</em>.

  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<const GR>(g));

  }

}

#endif