source: lemon-0.x/src/work/klao/path.h @ 682:1ea8162ce638

// -*- 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 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?
      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) {
      e.forw = ( G.tail(*e.it) == _first );
    }
    else {
      e.forw = ( G.tail(*e.it) == G.tail(edges[k-1]) ||
                 G.tail(*e.it) == G.head(edges[k-1]) );
    }
    return e;
  }
    
  template<typename Gr>
  typename DynamicPath<Gr>::NodeIt&
  DynamicPath<Gr>::nth(NodeIt &n, size_t k) const {
    if( k>length() ) {
      // FIXME: invalid NodeIt
      n.idx = length()+1;
      n.tail = true;
      return n;
    }
    if( k==length() ) {
      n.idx = length();
      n.tail = true;
      return n;
    }
    n = tail(nth<EdgeIt>(k));
    return n;
  }

  // Reszut konstruktorok:


  template<typename Gr>
  DynamicPath<Gr>::DynamicPath(const DynamicPath &P, const EdgeIt &a,
                               const EdgeIt &b) :
    G(P.G), edges(a.it, b.it)    // WARNING: if b.it < a.it this will blow up! 
  {
    if( G.valid(P._first) && a.it < P.edges.end() ) {
      _first = ( a.forw ? G.tail(*a.it) : G.head(*a.it) );
      if( b.it < P.edges.end() ) {
        _last = ( b.forw ? G.tail(*b.it) : G.head(*b.it) );
      }
      else {
        _last = P._last;
      }
    }
  }

  template<typename Gr>
  DynamicPath<Gr>::DynamicPath(const DynamicPath &P, const NodeIt &a,
                               const NodeIt &b) : G(P.G)
  {
    if( !P.valid(a) || !P.valid(b) )
      return;

    int ai = a.idx, bi = b.idx;
    if( bi<ai )
      std::swap(ai,bi);
    
    edges.resize(bi-ai);
    copy(P.edges.begin()+ai, P.edges.begin()+bi, edges.begin());

    _first = P.graphNode(a);
    _last = P.graphNode(b);
  }

  ///@}

} // namespace hugo

#endif // HUGO_PATH_H