#include<lemon/topology.h>

   ///Euler iterator for undirected graphs.

   /// \ingroup topology

   ///This iterator converts to the \c Edge type of the graph and using

   ///operator ++ it provides an Euler tour of the graph (if there exists).

   ///

   ///For example

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

   ///and the degree of each node is even),

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

   ///Euler tour of \c g.

   ///\code

   ///  for(UndirEulerIt<UndirListGraph> e(g),e!=INVALID;++e) {

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

   ///  }

   ///\endcode

   ///Although the iterator provides an Euler tour of an undirected graph,

   ///in order to indicate the direction of the tour, UndirEulerIt

   ///returns directed edges (that convert to the undirected ones, of course).

   ///

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

   ///\todo Test required

   template<class Graph>

   class UndirEulerIt

   {

     typedef typename Graph::Node Node;

     typedef typename Graph::NodeIt NodeIt;

     typedef typename Graph::Edge Edge;

     typedef typename Graph::EdgeIt EdgeIt;

     typedef typename Graph::OutEdgeIt OutEdgeIt;

     typedef typename Graph::InEdgeIt InEdgeIt;

     const Graph &g;

     typename Graph::NodeMap<OutEdgeIt> nedge;

     typename Graph::UndirEdgeMap<bool> visited;

     std::list<Edge> euler;

   public:

     ///Constructor

     ///\param _g An undirected graph.

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

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

     UndirEulerIt(const Graph &_g,typename Graph::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]=OutEdgeIt(g,n);

       while(nedge[start]!=INVALID) {

 	euler.push_back(nedge[start]);

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

 	++nedge[start];

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

       }

     }

     ///Edge Conversion

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

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

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

     ///Next edge of the tour

     UndirEulerIt &operator++() {

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

       euler.pop_front();

       typename std::list<Edge>::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]);

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

 	  ++nedge[s];

 	  s=n;

 	}

       }

       return *this;

     }

     ///Postfix incrementation

     ///\warning This incrementation

     ///returns an \c Edge, not an \ref UndirEulerIt, as one may

     ///expect.

     Edge operator++(int) 

     {

       Edge e=*this;

       ++(*this);

       return e;

     }

   };

   ///\note By definition, a directed graph is called \e Euler if

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

   ///are the same for each node.

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

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

   ///for each node. <em>Therefore, there are graphs which are not Euler, but

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

   euler(const Graph &g) 

   {

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

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

     return connected(g);

   }

   template<class Graph>

   typename disable_if<typename Graph::UndirTag,bool>::type