namespace skeleton {

   /// \addtogroup paths

     /// \addtogroup skeletons

   /// @{

     /// @{

   //! \brief A structure for representing directed path in a graph.

     //! \brief A structure for representing directed path in a graph.

   //!

     //!

   //! A structure for representing directed path in a graph.

     //! A structure for representing directed path in a graph.

   //! \param Graph The graph type in which the path is.

     //! \param GR The graph type in which the path is.

   //! \param DM DebugMode, defaults to DefaultDebugMode.

     //! 

   //! 

     //! In a sense, the path can be treated as a graph, for is has \c NodeIt

   //! In a sense, the path can be treated as a graph, for is has \c NodeIt

     //! and \c EdgeIt with the same usage. These types converts to the \c Node

   //! and \c EdgeIt with the same usage. These types converts to the \c Node

     //! and \c Edge of the original graph.

   //! and \c Edge of the original graph.

     template<typename GR>

   //!

     class Path {

   //! \todo Thoroughfully check all the range and consistency tests.

   template<typename Graph, typename DM = DefaultDebugMode>

   class DirPath {

   public:

     /// Edge type of the underlying graph.

     typedef typename Graph::Edge GraphEdge; 

     /// Node type of the underlying graph.

     typedef typename Graph::Node GraphNode;

     class NodeIt;

     class EdgeIt;

   protected:

     const Graph *gr;

     typedef std::vector<GraphEdge> Container;

     Container edges;

   public:

     /// \param _G The graph in which the path is.

     ///

     DirPath(const Graph &_G) : gr(&_G) {}

     /// \brief Subpath constructor.

     ///

     /// Subpath defined by two nodes.

     /// \warning It is an error if the two edges are not in order!

     DirPath(const DirPath &P, const NodeIt &a, const NodeIt &b) {

       if( DM::range_check && (!a.valid() || !b.valid) ) {

 	// FIXME: this check should be more elaborate...

 	fault("DirPath, subpath ctor: invalid bounding nodes");

       }

       gr = P.gr;

       edges.insert(edges.end(), P.edges.begin()+a.idx, P.edges.begin()+b.idx);

     }

     /// \brief Subpath constructor.

     ///

     /// Subpath defined by two edges. Contains edges in [a,b)

     /// \warning It is an error if the two edges are not in order!

     DirPath(const DirPath &P, const EdgeIt &a, const EdgeIt &b) {

       if( DM::range_check && (!a.valid() || !b.valid) ) {

 	// FIXME: this check should be more elaborate...

 	fault("DirPath, subpath ctor: invalid bounding nodes");

       }

       gr = P.gr;

       edges.insert(edges.end(), P.edges.begin()+a.idx, P.edges.begin()+b.idx);

     }

     /// Length of the path.

     size_t length() const { return edges.size(); }

     /// Returns whether the path is empty.

     bool empty() const { return edges.empty(); }

     /// Resets the path to an empty path.

     void clear() { edges.clear(); }

     /// \brief Starting point of the path.

     ///

     /// Starting point of the path.

     /// Returns INVALID if the path is empty.

     GraphNode from() const {

       return empty() ? INVALID : gr->tail(edges[0]);

     }

     /// \brief End point of the path.

     ///

     /// End point of the path.

     /// Returns INVALID if the path is empty.

     GraphNode to() const {

       return empty() ? INVALID : gr->head(edges[length()-1]);

     }

     /// \brief Initializes node or edge iterator to point to the first

     /// node or edge.

     ///

     /// \sa nth

     template<typename It>

     It& first(It &i) const { return i=It(*this); }

     /// \brief Initializes node iterator to point to the node of a given index.

     NodeIt& nth(NodeIt &i, int n) const {

       if( DM::range_check && (n<0 || n>int(length())) )

 	fault("DirPath::nth: index out of range");

       return i=NodeIt(*this, n);

     }

     /// \brief Initializes edge iterator to point to the edge of a given index.

     EdgeIt& nth(EdgeIt &i, int n) const {

       if( DM::range_check && (n<0 || n>=int(length())) )

 	fault("DirPath::nth: index out of range");

       return i=EdgeIt(*this, n);

     }

     /// Checks validity of a node or edge iterator.

     template<typename It>

     static

     bool valid(const It &i) { return i.valid(); }

     /// Steps the given node or edge iterator.

     template<typename It>

     static

     It& next(It &e) {

       if( DM::range_check && !e.valid() )

 	fault("DirPath::next() on invalid iterator");

       return ++e;

     }

     /// \brief Returns node iterator pointing to the head node of the

     /// given edge iterator.

     NodeIt head(const EdgeIt& e) const {

       if( DM::range_check && !e.valid() )

 	fault("DirPath::head() on invalid iterator");

       return NodeIt(*this, e.idx+1);

     }

     /// \brief Returns node iterator pointing to the tail node of the

     /// given edge iterator.

     NodeIt tail(const EdgeIt& e) const {

       if( DM::range_check && !e.valid() )

 	fault("DirPath::tail() on invalid iterator");

       return NodeIt(*this, e.idx);

     }

     /* Iterator classes */

     /**

      * \brief Iterator class to iterate on the edges of the paths

      * 

      * \ingroup paths

      * This class is used to iterate on the edges of the paths

      *

      * Of course it converts to Graph::Edge

      * 

      * \todo Its interface differs from the standard edge iterator.

      * Yes, it shouldn't.

      */

     class EdgeIt {

       friend class DirPath;

       int idx;

       const DirPath *p;

       /// Default constructor

       EdgeIt() {}

       /// Type of the underlying graph.

       /// Invalid constructor

       typedef typename GR Graph;

       EdgeIt(Invalid) : idx(-1), p(0) {}

       /// Edge type of the underlying graph.

       /// Constructor with starting point

       typedef typename Graph::Edge GraphEdge; 

       EdgeIt(const DirPath &_p, int _idx = 0) :

       /// Node type of the underlying graph.

 	idx(_idx), p(&_p) { validate(); }

       typedef typename Graph::Node GraphNode;

       class NodeIt;

       ///Validity check

       class EdgeIt;

       bool valid() const { return idx!=-1; }

       /// \param _G The graph in which the path is.

       ///Conversion to Graph::Edge

       ///

       operator GraphEdge () const {

       Path(const Graph &_G) {}

 	return valid() ? p->edges[idx] : INVALID;

       }

       /// Length of the path.

       size_t length() const {}

       /// Next edge

       /// Returns whether the path is empty.

       EdgeIt& operator++() { ++idx; validate(); return *this; }

       bool empty() const {}

       /// Comparison operator

       /// Resets the path to an empty path.

       bool operator==(const EdgeIt& e) const { return idx==e.idx; }

       void clear() {}

       /// Comparison operator

       bool operator!=(const EdgeIt& e) const { return idx!=e.idx; }

       /// \brief Starting point of the path.

       /// Comparison operator

       ///

       bool operator<(const EdgeIt& e) const { return idx<e.idx; }

       /// Starting point of the path.

       /// Returns INVALID if the path is empty.

     private:

       NodeIt head() const {}

       // FIXME: comparison between signed and unsigned...

       /// \brief End point of the path.

       // Jo ez igy? Vagy esetleg legyen a length() int?

       ///

       void validate() { if( size_t(idx) >= p->length() ) idx=-1; }

       /// End point of the path.

       /// Returns INVALID if the path is empty.

       NodeIt tail() const {}

       /// \brief First NodeIt/EdgeIt.

       ///

       /// Initializes node or edge iterator to point to the first

       /// node or edge.

       template<typename It>

       It& first(It &i) const { return i=It(*this); }

       /// \brief The head of an edge.

       ///

       /// Returns node iterator pointing to the head node of the

       /// given edge iterator.

       NodeIt head(const EdgeIt& e) const {}

       /// \brief The tail of an edge.

       ///

       /// Returns node iterator pointing to the tail node of the

       /// given edge iterator.

       NodeIt tail(const EdgeIt& e) const {}

       /* Iterator classes */

       /**

        * \brief Iterator class to iterate on the edges of the paths

        * 

        * \ingroup skeletons

        * This class is used to iterate on the edges of the paths

        *

        * Of course it converts to Graph::Edge

        * 

        */

       class EdgeIt {

       public:

 	/// Default constructor

 	EdgeIt() {}

 	/// Invalid constructor

 	EdgeIt(Invalid) {}

 	/// Constructor with starting point

 	EdgeIt(const Path &_p) {}

 	operator GraphEdge () const {}

 	/// Next edge

 	EdgeIt& operator++() {}

 	/// Comparison operator

 	bool operator==(const EdgeIt& e) const {}

 	/// Comparison operator

 	bool operator!=(const EdgeIt& e) const {}

 // 	/// Comparison operator

 //      /// \todo It is not clear what is the "natural" ordering.

 // 	bool operator<(const EdgeIt& e) const {}

       };

       /**

        * \brief Iterator class to iterate on the nodes of the paths

        * 

        * \ingroup skeletons

        * This class is used to iterate on the nodes of the paths

        *

        * Of course it converts to Graph::Node.

        * 

        */

       class NodeIt {

       public:

 	/// Default constructor

 	NodeIt() {}

 	/// Invalid constructor

 	NodeIt(Invalid) {}

 	/// Constructor with starting point

 	NodeIt(const Path &_p) {}

 	///Conversion to Graph::Node

 	operator const GraphNode& () const {}

 	/// Next node

 	NodeIt& operator++() {}

 	/// Comparison operator

 	bool operator==(const NodeIt& e) const {}

 	/// Comparison operator

 	bool operator!=(const NodeIt& e) const {}

 // 	/// Comparison operator

 //      /// \todo It is not clear what is the "natural" ordering.

 // 	bool operator<(const NodeIt& e) const {}

       };

       friend class Builder;    

       /**

        * \brief Class to build paths

        * 

        * \ingroup skeletons

        * This class is used to fill a path with edges.

        *

        * You can push new edges to the front and to the back of the path in

        * arbitrary order then you should commit these changes to the graph.

        *

        * While the builder is active (after the first modifying

        * operation and until the call of \ref commit())

        * the underlining Path is in a

        * "transitional" state (operations on it have undefined result).

        */

       class Builder {

       public:

 	///\param _P the path you want to fill in.

 	///

 	Builder(Path &_P) : P(_P) {}

 	/// Sets the starting node of the path.

 	/// Sets the starting node of the path. Edge added to the path

 	/// afterwards have to be incident to this node.

 	/// You \em must start building an empry path with this functions.

 	/// (And you \em must \em not use it later).

 	/// \sa pushFront()

 	/// \sa pushBack()

 	void setStartNode(const GraphNode &) {}

 	///Push a new edge to the front of the path

 	///Push a new edge to the front of the path.

 	///If the path is empty, you \em must call \ref setStartNode() before

 	///the first use of \ref pushFront().

 	void pushFront(const GraphEdge& e) {}

 	///Push a new edge to the back of the path

 	///Push a new edge to the back of the path.

 	///If the path is empty, you \em must call \ref setStartNode() before

 	///the first use of \ref pushBack().

 	void pushBack(const GraphEdge& e) {}

 	///Commit the changes to the path.

 	void commit() {}

 	///Reserve (front) storage for the builder in advance.

 	///If you know an reasonable upper bound of the number of the edges

 	///to add to the front of the path,

 	///using this function you may speed up the building.

 	void reserveFront(size_t r) {}

 	///Reserve (back) storage for the builder in advance.

 	///If you know an reasonable upper bound of the number of the edges

 	///to add to the back of the path,

 	///using this function you may speed up the building.

 	void reserveBack(size_t r) {}

       };

     /**

   ///@}

      * \brief Iterator class to iterate on the nodes of the paths

      * 

      * \ingroup paths

      * This class is used to iterate on the nodes of the paths

      *

      * Of course it converts to Graph::Node

      * 

      * \todo Its interface differs from the standard node iterator.

      * Yes, it shouldn't.

      */

     class NodeIt {

       friend class DirPath;

       int idx;

       const DirPath *p;

     public:

       /// Default constructor

       NodeIt() {}

       /// Invalid constructor

       NodeIt(Invalid) : idx(-1), p(0) {}

       /// Constructor with starting point

       NodeIt(const DirPath &_p, int _idx = 0) :

 	idx(_idx), p(&_p) { validate(); }

       ///Validity check

       bool valid() const { return idx!=-1; }

       ///Conversion to Graph::Node

       operator const GraphNode& () const {

 	if(idx >= p->length())

 	  return p->to();

 	else if(idx >= 0)

 	  return p->gr->tail(p->edges[idx]);

 	else

 	  return INVALID;

       }

       /// Next node

       NodeIt& operator++() { ++idx; validate(); return *this; }

       /// Comparison operator

       bool operator==(const NodeIt& e) const { return idx==e.idx; }

       /// Comparison operator

       bool operator!=(const NodeIt& e) const { return idx!=e.idx; }

       /// Comparison operator

       bool operator<(const NodeIt& e) const { return idx<e.idx; }

     private:

       void validate() { if( size_t(idx) > p->length() ) idx=-1; }

     };

     friend class Builder;    

     /**

      * \brief Class to build paths

      * 

      * \ingroup paths

      * This class is used to fill a path with edges.

      *

      * You can push new edges to the front and to the back of the path in

      * arbitrary order then you should commit these changes to the graph.

      *

      * Fundamentally, for most "Paths" (classes fulfilling the

      * PathConcept) while the builder is active (after the first modifying

      * operation and until the commit()) the original Path is in a

      * "transitional" state (operations on it have undefined result). But

      * in the case of DirPath the original path remains unchanged until the

      * commit. However we don't recomend that you use this feature.

      */

     class Builder {

       DirPath &P;

       Container front, back;

     public:

       ///\param _P the path you want to fill in.

       ///

       Builder(DirPath &_P) : P(_P) {}

       /// Sets the starting node of the path.

       /// Sets the starting node of the path. Edge added to the path

       /// afterwards have to be incident to this node.

       /// It should be called iff the path is empty and before any call to

       /// \ref pushFront() or \ref pushBack()

       void setStart(const GraphNode &) {}

       ///Push a new edge to the front of the path

       ///Push a new edge to the front of the path.

       ///\sa setStart

       void pushFront(const GraphEdge& e) {

 	if( DM::consistensy_check && !empty() && P.gr->head(e)!=from() ) {

 	  fault("DirPath::Builder::pushFront: nonincident edge");

 	}

 	front.push_back(e);

       }

       ///Push a new edge to the back of the path

       ///Push a new edge to the back of the path.

       ///\sa setStart

       void pushBack(const GraphEdge& e) {

 	if( DM::consistensy_check && !empty() && P.gr->tail(e)!=to() ) {

 	  fault("DirPath::Builder::pushBack: nonincident edge");

 	}

 	back.push_back(e);

       }

       ///Commit the changes to the path.

       void commit() {

 	if( !(front.empty() && back.empty()) ) {

 	  Container tmp;

 	  tmp.reserve(front.size()+back.size()+P.length());

 	  tmp.insert(tmp.end(), front.rbegin(), front.rend());

 	  tmp.insert(tmp.end(), P.edges.begin(), P.edges.end());

 	  tmp.insert(tmp.end(), back.begin(), back.end());

 	  P.edges.swap(tmp);

 	  front.clear();

 	  back.clear();

 	}

       }

       // FIXME: Hmm, pontosan hogy is kene ezt csinalni?

       // Hogy kenyelmes egy ilyet hasznalni?

       ///Reserve storage in advance for the builder

       ///If you know an reasonable upper bound of the number of the edges

       ///to add, using this function you can speed up the building.

       void reserve(size_t r) {

 	front.reserve(r);

 	back.reserve(r);

       }

     private:

       bool empty() {

 	return front.empty() && back.empty() && P.empty();

       }

       GraphNode from() const {

 	if( ! front.empty() )

 	  return P.gr->tail(front[front.size()-1]);

 	else if( ! P.empty() )

 	  return P.gr->tail(P.edges[0]);

 	else if( ! back.empty() )

 	  return P.gr->tail(back[0]);

 	else

 	  return INVALID;

       }

       GraphNode to() const {

 	if( ! back.empty() )

 	  return P.gr->head(back[back.size()-1]);

 	else if( ! P.empty() )

 	  return P.gr->head(P.edges[P.length()-1]);

 	else if( ! front.empty() )

 	  return P.gr->head(front[0]);

 	else

 	  return INVALID;

       }

     };

   };

   /**********************************************************************/

   //! \brief A structure for representing undirected path in a graph.

   //!

   //! A structure for representing undirected path in a graph. Ie. this is

   //! a path in a \e directed graph but the edges should not be directed

   //! forward.

   //!

   //! \param Graph The graph type in which the path is.

   //! \param DM DebugMode, defaults to DefaultDebugMode.

   //! 

   //! In a sense, the path can be treated as a graph, for is has \c NodeIt

   //! and \c EdgeIt with the same usage. These types converts to the \c Node

   //! and \c Edge of the original graph.

   //!

   //! \todo Thoroughfully check all the range and consistency tests.

   template<typename Graph, typename DM = DefaultDebugMode>

   class UndirPath {

   public:

     /// Edge type of the underlying graph.

     typedef typename Graph::Edge GraphEdge;

      /// Node type of the underlying graph.

    typedef typename Graph::Node GraphNode;

     class NodeIt;

     class EdgeIt;

   protected:

     const Graph *gr;

     typedef std::vector<GraphEdge> Container;

     Container edges;

   public:

     /// \param _G The graph in which the path is.

     ///

     UndirPath(const Graph &_G) : gr(&_G) {}

     /// \brief Subpath constructor.

     ///

     /// Subpath defined by two nodes.

     /// \warning It is an error if the two edges are not in order!

     UndirPath(const UndirPath &P, const NodeIt &a, const NodeIt &b) {

       if( DM::range_check && (!a.valid() || !b.valid) ) {

 	// FIXME: this check should be more elaborate...

 	fault("UndirPath, subpath ctor: invalid bounding nodes");

       }

       gr = P.gr;

       edges.insert(edges.end(), P.edges.begin()+a.idx, P.edges.begin()+b.idx);

     }

     /// \brief Subpath constructor.

     ///

     /// Subpath defined by two edges. Contains edges in [a,b)

     /// \warning It is an error if the two edges are not in order!

     UndirPath(const UndirPath &P, const EdgeIt &a, const EdgeIt &b) {

       if( DM::range_check && (!a.valid() || !b.valid) ) {

 	// FIXME: this check should be more elaborate...

 	fault("UndirPath, subpath ctor: invalid bounding nodes");

       }

       gr = P.gr;

       edges.insert(edges.end(), P.edges.begin()+a.idx, P.edges.begin()+b.idx);

     }

     /// Length of the path.

     size_t length() const { return edges.size(); }

     /// Returns whether the path is empty.

     bool empty() const { return edges.empty(); }

     /// Resets the path to an empty path.

     void clear() { edges.clear(); }

     /// \brief Starting point of the path.

     ///

     /// Starting point of the path.

     /// Returns INVALID if the path is empty.

     GraphNode from() const {

       return empty() ? INVALID : gr->tail(edges[0]);

     }

     /// \brief End point of the path.

     ///

     /// End point of the path.

     /// Returns INVALID if the path is empty.

     GraphNode to() const {

       return empty() ? INVALID : gr->head(edges[length()-1]);

     }

     /// \brief Initializes node or edge iterator to point to the first

     /// node or edge.

     ///

     /// \sa nth

     template<typename It>

     It& first(It &i) const { return i=It(*this); }

     /// \brief Initializes node iterator to point to the node of a given index.

     NodeIt& nth(NodeIt &i, int n) const {

       if( DM::range_check && (n<0 || n>int(length())) )

 	fault("UndirPath::nth: index out of range");

       return i=NodeIt(*this, n);

     }

     /// \brief Initializes edge iterator to point to the edge of a given index.

     EdgeIt& nth(EdgeIt &i, int n) const {

       if( DM::range_check && (n<0 || n>=int(length())) )

 	fault("UndirPath::nth: index out of range");

       return i=EdgeIt(*this, n);

     }

     /// Checks validity of a node or edge iterator.

     template<typename It>

     static

     bool valid(const It &i) { return i.valid(); }

     /// Steps the given node or edge iterator.

     template<typename It>

     static

     It& next(It &e) {

       if( DM::range_check && !e.valid() )

 	fault("UndirPath::next() on invalid iterator");

       return ++e;

     }

     /// \brief Returns node iterator pointing to the head node of the

     /// given edge iterator.

     NodeIt head(const EdgeIt& e) const {

       if( DM::range_check && !e.valid() )

 	fault("UndirPath::head() on invalid iterator");

       return NodeIt(*this, e.idx+1);

     }

     /// \brief Returns node iterator pointing to the tail node of the

     /// given edge iterator.

     NodeIt tail(const EdgeIt& e) const {

       if( DM::range_check && !e.valid() )

 	fault("UndirPath::tail() on invalid iterator");

       return NodeIt(*this, e.idx);

     }

     /**

      * \brief Iterator class to iterate on the edges of the paths

      * 

      * \ingroup paths

      * This class is used to iterate on the edges of the paths

      *

      * Of course it converts to Graph::Edge

      * 

      * \todo Its interface differs from the standard edge iterator.

      * Yes, it shouldn't.

      */

     class EdgeIt {

       friend class UndirPath;

       int idx;

       const UndirPath *p;

     public:

       /// Default constructor

       EdgeIt() {}

       /// Invalid constructor

       EdgeIt(Invalid) : idx(-1), p(0) {}

       /// Constructor with starting point

       EdgeIt(const UndirPath &_p, int _idx = 0) :

 	idx(_idx), p(&_p) { validate(); }

       ///Validity check

       bool valid() const { return idx!=-1; }

       ///Conversion to Graph::Edge

       operator GraphEdge () const {

 	return valid() ? p->edges[idx] : INVALID;

       }

       /// Next edge

      EdgeIt& operator++() { ++idx; validate(); return *this; }

       /// Comparison operator

       bool operator==(const EdgeIt& e) const { return idx==e.idx; }

       /// Comparison operator

       bool operator!=(const EdgeIt& e) const { return idx!=e.idx; }

       /// Comparison operator

       bool operator<(const EdgeIt& e) const { return idx<e.idx; }

     private:

       // FIXME: comparison between signed and unsigned...

       // Jo ez igy? Vagy esetleg legyen a length() int?

       void validate() { if( size_t(idx) >= p->length() ) idx=-1; }

     };

     /**

      * \brief Iterator class to iterate on the nodes of the paths

      * 

      * \ingroup paths

      * This class is used to iterate on the nodes of the paths

      *

      * Of course it converts to Graph::Node

      * 

      * \todo Its interface differs from the standard node iterator.

      * Yes, it shouldn't.

      */

     class NodeIt {

       friend class UndirPath;

       int idx;

       const UndirPath *p;

     public:

       /// Default constructor

       NodeIt() {}

       /// Invalid constructor

       NodeIt(Invalid) : idx(-1), p(0) {}

       /// Constructor with starting point

       NodeIt(const UndirPath &_p, int _idx = 0) :

 	idx(_idx), p(&_p) { validate(); }

       ///Validity check

       bool valid() const { return idx!=-1; }

       ///Conversion to Graph::Node

       operator const GraphNode& () const {

 	if(idx >= p->length())

 	  return p->to();

 	else if(idx >= 0)

 	  return p->gr->tail(p->edges[idx]);

 	else

 	  return INVALID;

       }

       /// Next node

       NodeIt& operator++() { ++idx; validate(); return *this; }

       /// Comparison operator

       bool operator==(const NodeIt& e) const { return idx==e.idx; }

       /// Comparison operator

       bool operator!=(const NodeIt& e) const { return idx!=e.idx; }

        /// Comparison operator

      bool operator<(const NodeIt& e) const { return idx<e.idx; }

     private:

       void validate() { if( size_t(idx) > p->length() ) idx=-1; }

     };

     friend class Builder;    

     /**

      * \brief Class to build paths

      * 

      * \ingroup paths

      * This class is used to fill a path with edges.

      *

      * You can push new edges to the front and to the back of the path in

      * arbitrary order then you should commit these changes to the graph.

      *

      * Fundamentally, for most "Paths" (classes fulfilling the

      * PathConcept) while the builder is active (after the first modifying

      * operation and until the commit()) the original Path is in a

      * "transitional" state (operations ot it have undefined result). But

      * in the case of UndirPath the original path is unchanged until the

      * commit. However we don't recomend that you use this feature.

      */

     class Builder {

       UndirPath &P;

       Container front, back;

     public:

       ///\param _P the path you want to fill in.

       ///

       Builder(UndirPath &_P) : P(_P) {}

       /// Sets the starting node of the path.

       /// Sets the starting node of the path. Edge added to the path

       /// afterwards have to be incident to this node.

       /// It should be called iff the path is empty and before any call to

       /// \ref pushFront() or \ref pushBack()

       void setStart(const GraphNode &) {}

       ///Push a new edge to the front of the path

       ///Push a new edge to the front of the path.

       ///\sa setStart

       void pushFront(const GraphEdge& e) {

 	if( DM::consistensy_check && !empty() && P.gr->head(e)!=from() ) {

 	  fault("UndirPath::Builder::pushFront: nonincident edge");

 	}

 	front.push_back(e);

       }

       ///Push a new edge to the back of the path

       ///Push a new edge to the back of the path.

       ///\sa setStart

       void pushBack(const GraphEdge& e) {

 	if( DM::consistensy_check && !empty() && P.gr->tail(e)!=to() ) {

 	  fault("UndirPath::Builder::pushBack: nonincident edge");

 	}

 	back.push_back(e);

       }

       ///Commit the changes to the path.

       void commit() {

 	if( !(front.empty() && back.empty()) ) {

 	  Container tmp;

 	  tmp.reserve(front.size()+back.size()+P.length());

 	  tmp.insert(tmp.end(), front.rbegin(), front.rend());

 	  tmp.insert(tmp.end(), P.edges.begin(), P.edges.end());

 	  tmp.insert(tmp.end(), back.begin(), back.end());

 	  P.edges.swap(tmp);

 	  front.clear();

 	  back.clear();

 	}

       }

       // FIXME: Hmm, pontosan hogy is kene ezt csinalni?

       // Hogy kenyelmes egy ilyet hasznalni?

       ///Reserve storage in advance for the builder

       ///If you know an reasonable upper bound of the number of the edges

       ///to add, using this function you can speed up the building.

        void reserve(size_t r) {

 	front.reserve(r);

 	back.reserve(r);

       }

     private:

       bool empty() {

 	return front.empty() && back.empty() && P.empty();

       }

       GraphNode from() const {

 	if( ! front.empty() )

 	  return P.gr->tail(front[front.size()-1]);

 	else if( ! P.empty() )

 	  return P.gr->tail(P.edges[0]);

 	else if( ! back.empty() )

 	  return P.gr->tail(back[0]);

 	else

 	  return INVALID;

       }

       GraphNode to() const {

 	if( ! back.empty() )

 	  return P.gr->head(back[back.size()-1]);

 	else if( ! P.empty() )

 	  return P.gr->head(P.edges[P.length()-1]);

 	else if( ! front.empty() )

 	  return P.gr->head(front[0]);

 	else

 	  return INVALID;

       }

     };

   };

   /**********************************************************************/

   /* Ennek az allocatorosdinak sokkal jobban utana kene nezni a hasznalata

      elott. Eleg bonyinak nez ki, ahogyan azokat az STL-ben hasznaljak. */

   template<typename Graph>

   class DynamicPath {

   public:

     typedef typename Graph::Edge GraphEdge;

     typedef typename Graph::Node GraphNode;

     class NodeIt;

     class EdgeIt;

   protected:

     Graph& G;

     // FIXME: ehelyett eleg lenne tarolni ket boolt: a ket szelso el

     // iranyitasat:

     GraphNode _first, _last;

     typedef std::deque<GraphEdge> Container;

     Container edges;

   public:

     DynamicPath(Graph &_G) : G(_G), _first(INVALID), _last(INVALID) {}

     /// Subpath defined by two nodes.

     /// Nodes may be in reversed order, then

     /// we contstruct the reversed path.

     DynamicPath(const DynamicPath &P, const NodeIt &a, const NodeIt &b);

     /// Subpath defined by two edges. Contains edges in [a,b)

     /// It is an error if the two edges are not in order!

     DynamicPath(const DynamicPath &P, const EdgeIt &a, const EdgeIt &b);

     size_t length() const { return edges.size(); }

     GraphNode from() const { return _first; }

     GraphNode to() const { return _last; }

     NodeIt& first(NodeIt &n) const { return nth(n, 0); }

     EdgeIt& first(EdgeIt &e) const { return nth(e, 0); }

     template<typename It>

     It first() const { 

       It e;

       first(e);

       return e; 

     }

     NodeIt& nth(NodeIt &, size_t) const;

     EdgeIt& nth(EdgeIt &, size_t) const;

     template<typename It>

     It nth(size_t n) const { 

       It e;

       nth(e, n);

       return e; 

     }

     bool valid(const NodeIt &n) const { return n.idx <= length(); }

     bool valid(const EdgeIt &e) const { return e.it < edges.end(); }

     bool isForward(const EdgeIt &e) const { return e.forw; }

     /// index of a node on the path. Returns length+2 for the invalid NodeIt

     int index(const NodeIt &n) const { return n.idx; }

     /// index of an edge on the path. Returns length+1 for the invalid EdgeIt

     int index(const EdgeIt &e) const { return e.it - edges.begin(); }

     EdgeIt& next(EdgeIt &e) const;

     NodeIt& next(NodeIt &n) const;

     template <typename It>

     It getNext(It it) const {

       It tmp(it); return next(tmp);

     }

     // A path is constructed using the following four functions.

     // They return false if the requested operation is inconsistent

     // with the path constructed so far.

     // If your path has only one edge you MUST set either "from" or "to"!

     // So you probably SHOULD call it in any case to be safe (and check the

     // returned value to check if your path is consistent with your idea).

     bool pushFront(const GraphEdge &e);

     bool pushBack(const GraphEdge &e);

     bool setFrom(const GraphNode &n);

     bool setTo(const GraphNode &n);

     // WARNING: these two functions return the head/tail of an edge with

     // respect to the direction of the path!

     // So G.head(P.graphEdge(e)) == P.graphNode(P.head(e)) holds only if 

     // P.forward(e) is true (or the edge is a loop)!

     NodeIt head(const EdgeIt& e) const;

     NodeIt tail(const EdgeIt& e) const;

     // FIXME: ezeknek valami jobb nev kellene!!!

     GraphEdge graphEdge(const EdgeIt& e) const;

     GraphNode graphNode(const NodeIt& n) const;

     /*** Iterator classes ***/

     class EdgeIt {

       friend class DynamicPath;

       typename Container::const_iterator it;

       bool forw;

     public:

       // FIXME: jarna neki ilyen is...

       // EdgeIt(Invalid);

       bool forward() const { return forw; }

       bool operator==(const EdgeIt& e) const { return it==e.it; }

       bool operator!=(const EdgeIt& e) const { return it!=e.it; }

       bool operator<(const EdgeIt& e) const { return it<e.it; }

     };

     class NodeIt {

       friend class DynamicPath;

       size_t idx;

       bool tail;  // Is this node the tail of the edge with same idx?

     public:

       // FIXME: jarna neki ilyen is...

       // NodeIt(Invalid);

       bool operator==(const NodeIt& n) const { return idx==n.idx; }

       bool operator!=(const NodeIt& n) const { return idx!=n.idx; }

       bool operator<(const NodeIt& n) const { return idx<n.idx; }

     };

   private:

     bool edgeIncident(const GraphEdge &e, const GraphNode &a,

 		      GraphNode &b);

     bool connectTwoEdges(const GraphEdge &e, const GraphEdge &f);

   };

   template<typename Gr>

   typename DynamicPath<Gr>::EdgeIt&

   DynamicPath<Gr>::next(DynamicPath::EdgeIt &e) const {

     if( e.it == edges.end() ) 

       return e;

     GraphNode common_node = ( e.forw ? G.head(*e.it) : G.tail(*e.it) );

     ++e.it;

     // Invalid edgeit is always forward :)

     if( e.it == edges.end() ) {

       e.forw = true;

       return e;

     }

     e.forw = ( G.tail(*e.it) == common_node );

     return e;

   }

   template<typename Gr>

   typename DynamicPath<Gr>::NodeIt& DynamicPath<Gr>::next(NodeIt &n) const {

     if( n.idx >= length() ) {

       // FIXME: invalid

       n.idx = length()+1;

       return n;

     }

     GraphNode next_node = ( n.tail ? G.head(edges[n.idx]) :

 			      G.tail(edges[n.idx]) );

     ++n.idx;

     if( n.idx < length() ) {

       n.tail = ( next_node == G.tail(edges[n.idx]) );

     }

     else {

       n.tail = true;

     }

     return n;

   }

   template<typename Gr>

   bool DynamicPath<Gr>::edgeIncident(const GraphEdge &e, const GraphNode &a,

 			  GraphNode &b) {

     if( G.tail(e) == a ) {

       b=G.head(e);

       return true;

     }

     if( G.head(e) == a ) {

       b=G.tail(e);

       return true;

     }

     return false;

   }

   template<typename Gr>

   bool DynamicPath<Gr>::connectTwoEdges(const GraphEdge &e,

 			     const GraphEdge &f) {

     if( edgeIncident(f, G.tail(e), _last) ) {

       _first = G.head(e);

       return true;

     }

     if( edgeIncident(f, G.head(e), _last) ) {

       _first = G.tail(e);

       return true;

     }

     return false;

   }

   template<typename Gr>

   bool DynamicPath<Gr>::pushFront(const GraphEdge &e) {

     if( G.valid(_first) ) {

 	if( edgeIncident(e, _first, _first) ) {

 	  edges.push_front(e);

 	  return true;

 	}

 	else

 	  return false;

     }

     else if( length() < 1 || connectTwoEdges(e, edges[0]) ) {

       edges.push_front(e);

       return true;

     }

     else

       return false;

   }

   template<typename Gr>

   bool DynamicPath<Gr>::pushBack(const GraphEdge &e) {

     if( G.valid(_last) ) {

 	if( edgeIncident(e, _last, _last) ) {

 	  edges.push_back(e);

 	  return true;

 	}

 	else

 	  return false;

     }

     else if( length() < 1 || connectTwoEdges(edges[0], e) ) {

       edges.push_back(e);

       return true;

     }

     else

       return false;

   }

   template<typename Gr>

   bool DynamicPath<Gr>::setFrom(const GraphNode &n) {

     if( G.valid(_first) ) {

       return _first == n;

     }

     else {

       if( length() > 0) {

 	if( edgeIncident(edges[0], n, _last) ) {

 	  _first = n;

 	  return true;

 	}

 	else return false;

       }

       else {