// -*- c++ -*- //

///\ingroup datas

///\file

///\brief Classes for representing paths in graphs.

#ifndef HUGO_PATH_H

#define HUGO_PATH_H

#include <deque>

#include <vector>

#include <algorithm>

#include <hugo/invalid.h>

#include <hugo/error.h>

#include <debug.h>

namespace hugo {

  /// \addtogroup datas

  /// @{

  //! \brief 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 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 DirPath {

  public:

    typedef typename Graph::Edge GraphEdge;

    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 ***/

    class EdgeIt {

      friend class DirPath;

      int idx;

      const DirPath *p;

    public:

      EdgeIt() {}

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

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

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

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

      operator GraphEdge () const {

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

      }

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

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

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

      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; }

    };

    class NodeIt {

      friend class DirPath;

      int idx;

      const DirPath *p;

    public:

      NodeIt() {}

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

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

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

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

      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;

      }

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

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

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

      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 datas

     * 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 DirPath the original path is 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?

      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:

    typedef typename Graph::Edge GraphEdge;

    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);

    }

    /*** Iterator classes ***/

    class EdgeIt {

      friend class UndirPath;

      int idx;

      const UndirPath *p;

    public:

      EdgeIt() {}

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

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

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

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

      operator GraphEdge () const {

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

      }

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

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

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

      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; }

    };

    class NodeIt {

      friend class UndirPath;

      int idx;

      const UndirPath *p;

    public:

      NodeIt() {}

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

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

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

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

      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;

      }

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

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

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

      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 datas

     * 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?

      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 {

	_first = _last = n;

	return true;

      }

    }

  }

  template<typename Gr>

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

    if( G.valid(_last) ) {

      return _last == n;

    }

    else {

      if( length() > 0) {

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

	  _last = n;

	  return true;

	}

	else return false;

      }

      else {

	_first = _last = n;

	return true;

      }

    }

  }

  template<typename Gr>

  typename DynamicPath<Gr>::NodeIt

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

    NodeIt n;

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

      // FIXME: invalid-> invalid

      n.idx = length() + 1;

      n.tail = true;

      return n;

    }

    n.idx = e.it-edges.begin();

    n.tail = e.forw;

    return n;

  }

  template<typename Gr>

  typename DynamicPath<Gr>::NodeIt

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

    if( e.it == edges.end()-1 ) {

      return _last;

    }

    EdgeIt next_edge = e;

    next(next_edge);

    return tail(next_edge);

  }

  template<typename Gr>

  typename DynamicPath<Gr>::GraphEdge

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

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

      return *e.it;

    }

    else {

      return INVALID;

    }

  }

  template<typename Gr>

  typename DynamicPath<Gr>::GraphNode

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

    if( n.idx < length() ) {

      return n.tail ? G.tail(edges[n.idx]) : G.head(edges[n.idx]);

    }

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

      return _last;

    }

    else {

      return INVALID;

    }

  }

  template<typename Gr>

  typename DynamicPath<Gr>::EdgeIt&

  DynamicPath<Gr>::nth(EdgeIt &e, size_t k) const {

    if( k>=length() ) {

      // FIXME: invalid EdgeIt

      e.it = edges.end();

      e.forw = true;

      return e;

    }

    e.it = edges.begin()+k;

    if(k==0) {