/* -*- 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_prop

 /// \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_prop

   ///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<class Digraph>

   class DiEulerIt

   {

     typedef typename Digraph::Node Node;

     typedef typename Digraph::NodeIt NodeIt;

     typedef typename Digraph::Arc Arc;

     typedef typename Digraph::ArcIt ArcIt;

     typedef typename Digraph::OutArcIt OutArcIt;

     typedef typename Digraph::InArcIt InArcIt;

     const Digraph &g;

     typename Digraph::template NodeMap<OutArcIt> nedge;

     std::list<Arc> euler;

   public:

     ///Constructor

     ///\param _g 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 Digraph &_g,typename Digraph::Node start=INVALID)

       : g(_g), nedge(g)

     {

       if(start==INVALID) start=NodeIt(g);

       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_prop

   ///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<class Digraph>

   class EulerIt

   {

     typedef typename Digraph::Node Node;

     typedef typename Digraph::NodeIt NodeIt;

     typedef typename Digraph::Arc Arc;

     typedef typename Digraph::Edge Edge;

     typedef typename Digraph::ArcIt ArcIt;

     typedef typename Digraph::OutArcIt OutArcIt;

     typedef typename Digraph::InArcIt InArcIt;

     const Digraph &g;

     typename Digraph::template NodeMap<OutArcIt> nedge;

     typename Digraph::template EdgeMap<bool> visited;

     std::list<Arc> euler;

   public:

     ///Constructor

     ///\param _g 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 Digraph &_g,typename Digraph::Node start=INVALID)

       : g(_g), nedge(g), visited(g,false)

     {

       if(start==INVALID) start=NodeIt(g);

       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_prop

   ///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<class Digraph>

 #ifdef DOXYGEN

   bool

 #else

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

   eulerian(const Digraph &g)

   {

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

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

     return connected(g);

   }

   template<class Digraph>

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

 #endif

   eulerian(const Digraph &g)

   {

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

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

     return connected(Undirector<const Digraph>(g));

   }

 }

 #endif