RhodeCode

  ///

  /// This class not only make a copy of a graph, but it can create

  /// references and cross references between the nodes, edges and arcs of

  /// the two graphs, and it can copy maps for using with the newly created

  /// graph.

  ///

  /// To make a copy from a graph, first an instance of GraphCopy

  /// should be created, then the data belongs to the graph should

  /// assigned to copy. In the end, the \c run() member should be

  /// called.

  ///

  /// The next code copies a graph with several data:

  ///\code

  ///  GraphCopy<OrigGraph, NewGraph> cg(orig_graph, new_graph);

  ///  // Create references for the nodes

  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);

  ///  cg.nodeRef(nr);

  ///  // Create cross references (inverse) for the edges

  ///  NewGraph::EdgeMap<OrigGraph::Edge> ecr(new_graph);

  ///  cg.edgeCrossRef(ecr);

  ///  // Copy an edge map

  ///  OrigGraph::EdgeMap<double> oemap(orig_graph);

  ///  NewGraph::EdgeMap<double> nemap(new_graph);

  ///  cg.edgeMap(oemap, nemap);

  ///  // Copy a node

  ///  OrigGraph::Node on;

  ///  NewGraph::Node nn;

  ///  cg.node(on, nn);

  ///  // Execute copying

  ///  cg.run();

  ///\endcode

  template <typename From, typename To>

  class GraphCopy {

  private:

    typedef typename From::Node Node;

    typedef typename From::NodeIt NodeIt;

    typedef typename From::Arc Arc;

    typedef typename From::ArcIt ArcIt;

    typedef typename From::Edge Edge;

    typedef typename From::EdgeIt EdgeIt;

    typedef typename To::Node TNode;

    typedef typename To::Arc TArc;

    typedef typename To::Edge TEdge;

    typedef typename From::template NodeMap<TNode> NodeRefMap;

    typedef typename From::template EdgeMap<TEdge> EdgeRefMap;

    struct ArcRefMap {

      ArcRefMap(const From& from, const To& to,

                const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)

        : _from(from), _to(to),

          _edge_ref(edge_ref), _node_ref(node_ref) {}

      typedef typename From::Arc Key;

      typedef typename To::Arc Value;

      Value operator[](const Key& key) const {

        bool forward = _from.u(key) != _from.v(key) ?

          _node_ref[_from.source(key)] ==

          _to.source(_to.direct(_edge_ref[key], true)) :

          _from.direction(key);

        return _to.direct(_edge_ref[key], forward);

      }

      const From& _from;

      const To& _to;

      const EdgeRefMap& _edge_ref;

      const NodeRefMap& _node_ref;

    };

  public:

    /// \brief Constructor of GraphCopy.

    ///

    /// Constructor of GraphCopy for copying the content of the

    /// \c from graph into the \c to graph.

    GraphCopy(const From& from, To& to)

      : _from(from), _to(to) {}

    /// \brief Destructor of GraphCopy

    ///

    /// Destructor of GraphCopy.

    ~GraphCopy() {

      for (int i = 0; i < int(_node_maps.size()); ++i) {

        delete _node_maps[i];

      }

      for (int i = 0; i < int(_arc_maps.size()); ++i) {

        delete _arc_maps[i];

      }

      for (int i = 0; i < int(_edge_maps.size()); ++i) {

        delete _edge_maps[i];

      }

    }

    /// \brief Copy the node references into the given map.

    ///

    /// This function copies the node references into the given map.

    /// The parameter should be a map, whose key type is the Node type of

    /// the source graph, while the value type is the Node type of the

    /// destination graph.

    template <typename NodeRef>

    GraphCopy& nodeRef(NodeRef& map) {

      _node_maps.push_back(new _core_bits::RefCopy<From, Node,

                           NodeRefMap, NodeRef>(map));

      return *this;

    }

    /// \brief Copy the node cross references into the given map.

    ///

    /// This function copies the node cross references (reverse references)

    /// into the given map. The parameter should be a map, whose key type

    /// is the Node type of the destination graph, while the value type is

    /// the Node type of the source graph.

    template <typename NodeCrossRef>

    GraphCopy& nodeCrossRef(NodeCrossRef& map) {

      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,

                           NodeRefMap, NodeCrossRef>(map));

      return *this;

    }

    /// \brief Make a copy of the given node map.

    ///

    /// This function makes a copy of the given node map for the newly

    /// created graph.

    /// The key type of the new map \c tmap should be the Node type of the

    /// destination graph, and the key type of the original map \c map

    /// should be the Node type of the source graph.

    template <typename FromMap, typename ToMap>

    GraphCopy& nodeMap(const FromMap& map, ToMap& tmap) {

      _node_maps.push_back(new _core_bits::MapCopy<From, Node,

                           NodeRefMap, FromMap, ToMap>(map, tmap));

      return *this;

    }

    /// \brief Make a copy of the given node.

    ///

    /// This function makes a copy of the given node.

    GraphCopy& node(const Node& node, TNode& tnode) {

      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,

                           NodeRefMap, TNode>(node, tnode));

      return *this;

    }

    /// \brief Copy the arc references into the given map.

    ///

    /// This function copies the arc references into the given map.

    /// The parameter should be a map, whose key type is the Arc type of

    /// the source graph, while the value type is the Arc type of the

    /// destination graph.

    template <typename ArcRef>

    GraphCopy& arcRef(ArcRef& map) {

      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,

                          ArcRefMap, ArcRef>(map));

      return *this;

    }

    /// \brief Copy the arc cross references into the given map.

    ///

    /// This function copies the arc cross references (reverse references)

    /// into the given map. The parameter should be a map, whose key type

    /// is the Arc type of the destination graph, while the value type is

    /// the Arc type of the source graph.

    template <typename ArcCrossRef>

    GraphCopy& arcCrossRef(ArcCrossRef& map) {

      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,

                          ArcRefMap, ArcCrossRef>(map));

      return *this;

    }

    /// \brief Make a copy of the given arc map.

    ///

    /// This function makes a copy of the given arc map for the newly

    /// created graph.

    /// The key type of the new map \c tmap should be the Arc type of the

    /// destination graph, and the key type of the original map \c map

    /// should be the Arc type of the source graph.

    template <typename FromMap, typename ToMap>

    GraphCopy& arcMap(const FromMap& map, ToMap& tmap) {

      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,

                          ArcRefMap, FromMap, ToMap>(map, tmap));

      return *this;

    }

    /// \brief Make a copy of the given arc.

    ///

    /// This function makes a copy of the given arc.

    GraphCopy& arc(const Arc& arc, TArc& tarc) {

      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,

                          ArcRefMap, TArc>(arc, tarc));

      return *this;

    }

    /// \brief Copy the edge references into the given map.

    ///

    /// This function copies the edge references into the given map.

    /// The parameter should be a map, whose key type is the Edge type of

    /// the source graph, while the value type is the Edge type of the

    /// destination graph.

    template <typename EdgeRef>

    GraphCopy& edgeRef(EdgeRef& map) {

      _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,

                           EdgeRefMap, EdgeRef>(map));

      return *this;

    }

    /// \brief Copy the edge cross references into the given map.

    ///

    /// This function copies the edge cross references (reverse references)

    /// into the given map. The parameter should be a map, whose key type

    /// is the Edge type of the destination graph, while the value type is

    /// the Edge type of the source graph.

    template <typename EdgeCrossRef>

    GraphCopy& edgeCrossRef(EdgeCrossRef& map) {

      _edge_maps.push_back(new _core_bits::CrossRefCopy<From,

                           Edge, EdgeRefMap, EdgeCrossRef>(map));

      return *this;

    }

    /// \brief Make a copy of the given edge map.

    ///

    /// This function makes a copy of the given edge map for the newly

    /// created graph.

    /// The key type of the new map \c tmap should be the Edge type of the

    /// destination graph, and the key type of the original map \c map

    /// should be the Edge type of the source graph.

    template <typename FromMap, typename ToMap>

    GraphCopy& edgeMap(const FromMap& map, ToMap& tmap) {

      _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,

                           EdgeRefMap, FromMap, ToMap>(map, tmap));

      return *this;

    }

    /// \brief Make a copy of the given edge.

    ///

    /// This function makes a copy of the given edge.

    GraphCopy& edge(const Edge& edge, TEdge& tedge) {

      _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,

                           EdgeRefMap, TEdge>(edge, tedge));

      return *this;

    }

    /// \brief Execute copying.

    ///

    /// This function executes the copying of the graph along with the

    /// copying of the assigned data.

    void run() {

      NodeRefMap nodeRefMap(_from);

      EdgeRefMap edgeRefMap(_from);

      ArcRefMap arcRefMap(_from, _to, edgeRefMap, nodeRefMap);

      _core_bits::GraphCopySelector<To>::

        copy(_from, _to, nodeRefMap, edgeRefMap);

      for (int i = 0; i < int(_node_maps.size()); ++i) {

        _node_maps[i]->copy(_from, nodeRefMap);

      }

      for (int i = 0; i < int(_edge_maps.size()); ++i) {

        _edge_maps[i]->copy(_from, edgeRefMap);

      }

      for (int i = 0; i < int(_arc_maps.size()); ++i) {

        _arc_maps[i]->copy(_from, arcRefMap);

      }

    }

  private:

    const From& _from;

    To& _to;

    std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >

      _node_maps;

    std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >

      _arc_maps;

    std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >

      _edge_maps;

  };

  /// \brief Copy a graph to another graph.

  ///

  /// This function copies a graph to another graph.

  /// The complete usage of it is detailed in the GraphCopy class,

  /// but a short example shows a basic work:

  ///\code

  /// graphCopy(src, trg).nodeRef(nr).edgeCrossRef(ecr).run();

  ///\endcode

  ///

  /// After the copy the \c nr map will contain the mapping from the

  /// nodes of the \c from graph to the nodes of the \c to graph and

  /// \c ecr will contain the mapping from the edges of the \c to graph

  /// to the edges of the \c from graph.

  ///

  /// \see GraphCopy

  template <typename From, typename To>

  GraphCopy<From, To>

  graphCopy(const From& from, To& to) {

    return GraphCopy<From, To>(from, to);

  }

  namespace _core_bits {

    template <typename Graph, typename Enable = void>

    struct FindArcSelector {

      typedef typename Graph::Node Node;

      typedef typename Graph::Arc Arc;

      static Arc find(const Graph &g, Node u, Node v, Arc e) {

        if (e == INVALID) {

          g.firstOut(e, u);

        } else {

          g.nextOut(e);

        }

        while (e != INVALID && g.target(e) != v) {

          g.nextOut(e);

        }

        return e;

      }

    };

    template <typename Graph>

    struct FindArcSelector<

      Graph,

      typename enable_if<typename Graph::FindArcTag, void>::type>

    {

      typedef typename Graph::Node Node;

      typedef typename Graph::Arc Arc;

      static Arc find(const Graph &g, Node u, Node v, Arc prev) {

        return g.findArc(u, v, prev);

      }

    };

  }

  /// \brief Find an arc between two nodes of a digraph.

  ///

  /// This function finds an arc from node \c u to node \c v in the

  /// digraph \c g.

  ///

  /// If \c prev is \ref INVALID (this is the default value), then

  /// it finds the first arc from \c u to \c v. Otherwise it looks for

  /// the next arc from \c u to \c v after \c prev.

  /// \return The found arc or \ref INVALID if there is no such an arc.

  ///

  /// Thus you can iterate through each arc from \c u to \c v as it follows.

  ///\code

  /// for(Arc e = findArc(g,u,v); e != INVALID; e = findArc(g,u,v,e)) {

  ///   ...

  /// }

  ///\endcode

  ///

  /// \note \ref ConArcIt provides iterator interface for the same

  /// functionality.

  ///

  ///\sa ConArcIt

  ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp

  template <typename Graph>

  inline typename Graph::Arc

  findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,

          typename Graph::Arc prev = INVALID) {

    return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);

  }

  /// \brief Iterator for iterating on parallel arcs connecting the same nodes.

  ///

  /// Iterator for iterating on parallel arcs connecting the same nodes. It is

  /// a higher level interface for the \ref findArc() function. You can

  /// use it the following way:

  ///\code

  /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {

  ///   ...

  /// }

  ///\endcode

  ///

  ///\sa findArc()

  ///\sa ArcLookUp, AllArcLookUp, DynArcLookUp

  template <typename _Graph>

  class ConArcIt : public _Graph::Arc {

  public:

    typedef _Graph Graph;

    typedef typename Graph::Arc Parent;

    typedef typename Graph::Arc Arc;

    typedef typename Graph::Node Node;

    /// \brief Constructor.

    ///

    /// Construct a new ConArcIt iterating on the arcs that

    /// connects nodes \c u and \c v.

    ConArcIt(const Graph& g, Node u, Node v) : _graph(g) {

      Parent::operator=(findArc(_graph, u, v));

    }

    /// \brief Constructor.

    ///

    /// Construct a new ConArcIt that continues the iterating from arc \c a.

    ConArcIt(const Graph& g, Arc a) : Parent(a), _graph(g) {}

    /// \brief Increment operator.

    ///

    /// It increments the iterator and gives back the next arc.

    ConArcIt& operator++() {

      Parent::operator=(findArc(_graph, _graph.source(*this),

                                _graph.target(*this), *this));

      return *this;

    }

  private:

    const Graph& _graph;

  };

  namespace _core_bits {

    template <typename Graph, typename Enable = void>

    struct FindEdgeSelector {

      typedef typename Graph::Node Node;

      typedef typename Graph::Edge Edge;

      static Edge find(const Graph &g, Node u, Node v, Edge e) {

        bool b;

        if (u != v) {

          if (e == INVALID) {

            g.firstInc(e, b, u);

          } else {

            b = g.u(e) == u;

            g.nextInc(e, b);

          }

          while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {

            g.nextInc(e, b);

          }

        } else {

          if (e == INVALID) {

            g.firstInc(e, b, u);

          } else {

            b = true;

            g.nextInc(e, b);

          }

          while (e != INVALID && (!b || g.v(e) != v)) {

            g.nextInc(e, b);

          }

        }

        return e;

      }

    };

    template <typename Graph>

    struct FindEdgeSelector<

      Graph,

      typename enable_if<typename Graph::FindEdgeTag, void>::type>

    {

      typedef typename Graph::Node Node;

      typedef typename Graph::Edge Edge;

      static Edge find(const Graph &g, Node u, Node v, Edge prev) {

        return g.findEdge(u, v, prev);

      }

    };

  }

  /// \brief Find an edge between two nodes of a graph.

  ///

  /// This function finds an edge from node \c u to node \c v in graph \c g.

  /// If node \c u and node \c v is equal then each loop edge

  /// will be enumerated once.

  ///

  /// If \c prev is \ref INVALID (this is the default value), then

  /// it finds the first edge from \c u to \c v. Otherwise it looks for

  /// the next edge from \c u to \c v after \c prev.

  /// \return The found edge or \ref INVALID if there is no such an edge.

  ///

  /// Thus you can iterate through each edge between \c u and \c v

  /// as it follows.

  ///\code

  /// for(Edge e = findEdge(g,u,v); e != INVALID; e = findEdge(g,u,v,e)) {

  ///   ...

  /// }

  ///\endcode

  ///

  /// \note \ref ConEdgeIt provides iterator interface for the same

  /// functionality.

  ///

  ///\sa ConEdgeIt

  template <typename Graph>

  inline typename Graph::Edge

  findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,

            typename Graph::Edge p = INVALID) {

    return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);

  }

  /// \brief Iterator for iterating on parallel edges connecting the same nodes.

  ///

  /// Iterator for iterating on parallel edges connecting the same nodes.

  /// It is a higher level interface for the findEdge() function. You can

  /// use it the following way:

  ///\code

  /// for (ConEdgeIt<Graph> it(g, u, v); it != INVALID; ++it) {

  ///   ...

  /// }

  ///\endcode

  ///

  ///\sa findEdge()

  template <typename _Graph>

  class ConEdgeIt : public _Graph::Edge {

  public:

    typedef _Graph Graph;

    typedef typename Graph::Edge Parent;

    typedef typename Graph::Edge Edge;

    typedef typename Graph::Node Node;

    /// \brief Constructor.

    ///

    /// Construct a new ConEdgeIt iterating on the edges that

    /// connects nodes \c u and \c v.

    }

    /// \brief Constructor.

    ///

    /// Construct a new ConEdgeIt that continues iterating from edge \c e.

    ConEdgeIt(const Graph& g, Edge e) : Parent(e), _graph(g) {}

    /// \brief Increment operator.

    ///

    /// It increments the iterator and gives back the next edge.

    ConEdgeIt& operator++() {

      return *this;

    }

  private:

    const Graph& _graph;

  };

  ///Dynamic arc look-up between given endpoints.

  ///Using this class, you can find an arc in a digraph from a given

  ///source to a given target in amortized time <em>O</em>(log<em>d</em>),

  ///where <em>d</em> is the out-degree of the source node.

  ///

  ///It is possible to find \e all parallel arcs between two nodes with

  ///the \c operator() member.

  ///

  ///This is a dynamic data structure. Consider to use \ref ArcLookUp or

  ///\ref AllArcLookUp if your digraph is not changed so frequently.

  ///

  ///This class uses a self-adjusting binary search tree, the Splay tree

  ///of Sleator and Tarjan to guarantee the logarithmic amortized

  ///time bound for arc look-ups. This class also guarantees the

  ///optimal time bound in a constant factor for any distribution of

  ///queries.

  ///

  ///\tparam G The type of the underlying digraph.

  ///

  ///\sa ArcLookUp

  ///\sa AllArcLookUp

  template<class G>

  class DynArcLookUp

    : protected ItemSetTraits<G, typename G::Arc>::ItemNotifier::ObserverBase

  {

  public:

    typedef typename ItemSetTraits<G, typename G::Arc>

    ::ItemNotifier::ObserverBase Parent;

    TEMPLATE_DIGRAPH_TYPEDEFS(G);

    typedef G Digraph;

  protected:

    class AutoNodeMap : public ItemSetTraits<G, Node>::template Map<Arc>::Type {

    public:

      typedef typename ItemSetTraits<G, Node>::template Map<Arc>::Type Parent;

      AutoNodeMap(const G& digraph) : Parent(digraph, INVALID) {}

      virtual void add(const Node& node) {

        Parent::add(node);

        Parent::set(node, INVALID);

      }

      virtual void add(const std::vector<Node>& nodes) {

        Parent::add(nodes);

        for (int i = 0; i < int(nodes.size()); ++i) {

          Parent::set(nodes[i], INVALID);

        }

      }

      virtual void build() {

        Parent::build();

        Node it;

        typename Parent::Notifier* nf = Parent::notifier();

        for (nf->first(it); it != INVALID; nf->next(it)) {

          Parent::set(it, INVALID);

        }

      }

    };

    const Digraph &_g;

    AutoNodeMap _head;

    typename Digraph::template ArcMap<Arc> _parent;

    typename Digraph::template ArcMap<Arc> _left;

    typename Digraph::template ArcMap<Arc> _right;

    class ArcLess {

      const Digraph &g;

    public:

      ArcLess(const Digraph &_g) : g(_g) {}

      bool operator()(Arc a,Arc b) const

      {

        return g.target(a)<g.target(b);

      }

    };

  public:

    ///Constructor

    ///Constructor.

    ///

    ///It builds up the search database.

    DynArcLookUp(const Digraph &g)

      : _g(g),_head(g),_parent(g),_left(g),_right(g)

    {

      Parent::attach(_g.notifier(typename Digraph::Arc()));

      refresh();

    }

  protected:

    virtual void add(const Arc& arc) {

      insert(arc);

    }

    virtual void add(const std::vector<Arc>& arcs) {

      for (int i = 0; i < int(arcs.size()); ++i) {

        insert(arcs[i]);

      }

    }

    virtual void erase(const Arc& arc) {

      remove(arc);

    }

    virtual void erase(const std::vector<Arc>& arcs) {

      for (int i = 0; i < int(arcs.size()); ++i) {

        remove(arcs[i]);

      }

    }

    virtual void build() {

      refresh();

    }

    virtual void clear() {

      for(NodeIt n(_g);n!=INVALID;++n) {

        _head.set(n, INVALID);

      }

    }

    void insert(Arc arc) {

      Node s = _g.source(arc);

      Node t = _g.target(arc);

      _left.set(arc, INVALID);

      _right.set(arc, INVALID);

      Arc e = _head[s];

      if (e == INVALID) {

        _head.set(s, arc);

        _parent.set(arc, INVALID);

        return;

      }

      while (true) {

        if (t < _g.target(e)) {

          if (_left[e] == INVALID) {

            _left.set(e, arc);

            _parent.set(arc, e);

            splay(arc);

            return;

          } else {

            e = _left[e];

          }

        } else {

          if (_right[e] == INVALID) {

            _right.set(e, arc);

            _parent.set(arc, e);

            splay(arc);

            return;

          } else {

            e = _right[e];

          }

        }

      }

    }

    void remove(Arc arc) {

      if (_left[arc] == INVALID) {

        if (_right[arc] != INVALID) {

          _parent.set(_right[arc], _parent[arc]);

        }

        if (_parent[arc] != INVALID) {

          if (_left[_parent[arc]] == arc) {

            _left.set(_parent[arc], _right[arc]);

          } else {

            _right.set(_parent[arc], _right[arc]);

          }

        } else {

          _head.set(_g.source(arc), _right[arc]);

        }

      } else if (_right[arc] == INVALID) {

        _parent.set(_left[arc], _parent[arc]);

        if (_parent[arc] != INVALID) {

          if (_left[_parent[arc]] == arc) {

            _left.set(_parent[arc], _left[arc]);

          } else {

            _right.set(_parent[arc], _left[arc]);

          }

        } else {

          _head.set(_g.source(arc), _left[arc]);

        }

      } else {

        Arc e = _left[arc];

        if (_right[e] != INVALID) {

          e = _right[e];

          while (_right[e] != INVALID) {

            e = _right[e];

          }

          Arc s = _parent[e];

          _right.set(_parent[e], _left[e]);

          if (_left[e] != INVALID) {

            _parent.set(_left[e], _parent[e]);

          }

          _left.set(e, _left[arc]);

          _parent.set(_left[arc], e);

          _right.set(e, _right[arc]);

          _parent.set(_right[arc], e);

          _parent.set(e, _parent[arc]);

          if (_parent[arc] != INVALID) {

            if (_left[_parent[arc]] == arc) {

              _left.set(_parent[arc], e);

            } else {

              _right.set(_parent[arc], e);

            }

          }

          splay(s);

        } else {

          _right.set(e, _right[arc]);

          _parent.set(_right[arc], e);

          _parent.set(e, _parent[arc]);

          if (_parent[arc] != INVALID) {

            if (_left[_parent[arc]] == arc) {

              _left.set(_parent[arc], e);

            } else {

              _right.set(_parent[arc], e);

            }

          } else {

            _head.set(_g.source(arc), e);

          }

        }

      }

    }

    Arc refreshRec(std::vector<Arc> &v,int a,int b)

    {

      int m=(a+b)/2;

      Arc me=v[m];

      if (a < m) {

        Arc left = refreshRec(v,a,m-1);

        _left.set(me, left);

        _parent.set(left, me);

      } else {

        _left.set(me, INVALID);

      }

      if (m < b) {

        Arc right = refreshRec(v,m+1,b);

        _right.set(me, right);

        _parent.set(right, me);

      } else {

        _right.set(me, INVALID);

      }

      return me;

    }

    void refresh() {

      for(NodeIt n(_g);n!=INVALID;++n) {

        std::vector<Arc> v;

        for(OutArcIt a(_g,n);a!=INVALID;++a) v.push_back(a);

        if (!v.empty()) {

          std::sort(v.begin(),v.end(),ArcLess(_g));

          Arc head = refreshRec(v,0,v.size()-1);

          _head.set(n, head);

          _parent.set(head, INVALID);

        }

        else _head.set(n, INVALID);

      }

    }

    void zig(Arc v) {

      Arc w = _parent[v];

      _parent.set(v, _parent[w]);

      _parent.set(w, v);

      _left.set(w, _right[v]);

      _right.set(v, w);

      if (_parent[v] != INVALID) {

        if (_right[_parent[v]] == w) {

          _right.set(_parent[v], v);

        } else {

          _left.set(_parent[v], v);

        }

      }

      if (_left[w] != INVALID){

        _parent.set(_left[w], w);

      }

    }

    void zag(Arc v) {

      Arc w = _parent[v];

      _parent.set(v, _parent[w]);

      _parent.set(w, v);

      _right.set(w, _left[v]);

      _left.set(v, w);

      if (_parent[v] != INVALID){

        if (_left[_parent[v]] == w) {

          _left.set(_parent[v], v);

        } else {

          _right.set(_parent[v], v);

        }

      }

      if (_right[w] != INVALID){

        _parent.set(_right[w], w);

      }

    }

    void splay(Arc v) {

      while (_parent[v] != INVALID) {

        if (v == _left[_parent[v]]) {

          if (_parent[_parent[v]] == INVALID) {

            zig(v);

          } else {

            if (_parent[v] == _left[_parent[_parent[v]]]) {

              zig(_parent[v]);

              zig(v);

            } else {

              zig(v);

              zag(v);

            }

          }

        } else {

          if (_parent[_parent[v]] == INVALID) {

            zag(v);

          } else {

            if (_parent[v] == _left[_parent[_parent[v]]]) {

              zag(v);

              zig(v);

            } else {

              zag(_parent[v]);

              zag(v);

            }

          }

        }

      }

      _head[_g.source(v)] = v;

    }

  public:

    ///Find an arc between two nodes.

    ///Find an arc between two nodes.

    ///\param s The source node.

    ///\param t The target node.

    ///\param p The previous arc between \c s and \c t. It it is INVALID or

    ///not given, the operator finds the first appropriate arc.

    ///\return An arc from \c s to \c t after \c p or

    ///\ref INVALID if there is no more.

    ///

    ///For example, you can count the number of arcs from \c u to \c v in the

    ///following way.

    ///\code

    ///DynArcLookUp<ListDigraph> ae(g);

    ///...

    ///int n = 0;

    ///for(Arc a = ae(u,v); a != INVALID; a = ae(u,v,a)) n++;

    ///\endcode

    ///

    ///Finding the arcs take at most <em>O</em>(log<em>d</em>)

    ///amortized time, specifically, the time complexity of the lookups

    ///is equal to the optimal search tree implementation for the

    ///current query distribution in a constant factor.

    ///

    ///\note This is a dynamic data structure, therefore the data

    ///structure is updated after each graph alteration. Thus although

    ///this data structure is theoretically faster than \ref ArcLookUp

    ///and \ref AllArcLookUp, it often provides worse performance than

    ///them.

    Arc operator()(Node s, Node t, Arc p = INVALID) const  {

      if (p == INVALID) {

        Arc a = _head[s];

        if (a == INVALID) return INVALID;

        Arc r = INVALID;

        while (true) {

          if (_g.target(a) < t) {

            if (_right[a] == INVALID) {

              const_cast<DynArcLookUp&>(*this).splay(a);

              return r;

            } else {

              a = _right[a];

            }

          } else {

            if (_g.target(a) == t) {

              r = a;

            }

            if (_left[a] == INVALID) {

              const_cast<DynArcLookUp&>(*this).splay(a);

              return r;

            } else {

              a = _left[a];

            }

          }

        }

      } else {

        Arc a = p;

        if (_right[a] != INVALID) {

          a = _right[a];

          while (_left[a] != INVALID) {

            a = _left[a];

          }

          const_cast<DynArcLookUp&>(*this).splay(a);

        } else {

          while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {

            a = _parent[a];

          }

          if (_parent[a] == INVALID) {

            return INVALID;

          } else {

            a = _parent[a];

            const_cast<DynArcLookUp&>(*this).splay(a);

          }

        }

        if (_g.target(a) == t) return a;

        else return INVALID;

      }

    }

  };

  ///Fast arc look-up between given endpoints.

  ///Using this class, you can find an arc in a digraph from a given

  ///source to a given target in time <em>O</em>(log<em>d</em>),

  ///where <em>d</em> is the out-degree of the source node.

  ///

  ///It is not possible to find \e all parallel arcs between two nodes.

  ///Use \ref AllArcLookUp for this purpose.

  ///

  ///\warning This class is static, so you should call refresh() (or at

  ///least refresh(Node)) to refresh this data structure whenever the

  ///digraph changes. This is a time consuming (superlinearly proportional

  ///(<em>O</em>(<em>m</em> log<em>m</em>)) to the number of arcs).

  ///

  ///\tparam G The type of the underlying digraph.

  ///

  ///\sa DynArcLookUp

  ///\sa AllArcLookUp

  template<class G>

  class ArcLookUp

  {

  public:

    TEMPLATE_DIGRAPH_TYPEDEFS(G);

    typedef G Digraph;

  protected:

    const Digraph &_g;

    typename Digraph::template NodeMap<Arc> _head;

    typename Digraph::template ArcMap<Arc> _left;

    typename Digraph::template ArcMap<Arc> _right;

    class ArcLess {

      const Digraph &g;

    public:

      ArcLess(const Digraph &_g) : g(_g) {}

      bool operator()(Arc a,Arc b) const

      {

        return g.target(a)<g.target(b);

      }

    };

  public:

    ///Constructor

    ///Constructor.

    ///

    ///It builds up the search database, which remains valid until the digraph

    ///changes.

    ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}

  private:

    Arc refreshRec(std::vector<Arc> &v,int a,int b)

    {

      int m=(a+b)/2;

      Arc me=v[m];

      _left[me] = a<m?refreshRec(v,a,m-1):INVALID;

      _right[me] = m<b?refreshRec(v,m+1,b):INVALID;

      return me;

    }

  public:

    ///Refresh the search data structure at a node.

    ///Build up the search database of node \c n.

    ///

    ///It runs in time <em>O</em>(<em>d</em> log<em>d</em>), where <em>d</em>

    ///is the number of the outgoing arcs of \c n.

    void refresh(Node n)

    {

      std::vector<Arc> v;

      for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);

      if(v.size()) {

        std::sort(v.begin(),v.end(),ArcLess(_g));

        _head[n]=refreshRec(v,0,v.size()-1);

      }

      else _head[n]=INVALID;

    }

    ///Refresh the full data structure.

    ///Build up the full search database. In fact, it simply calls

    ///\ref refresh(Node) "refresh(n)" for each node \c n.

    ///

    ///It runs in time <em>O</em>(<em>m</em> log<em>D</em>), where <em>m</em> is

    ///the number of the arcs in the digraph and <em>D</em> is the maximum

    ///out-degree of the digraph.

    void refresh()

    {

      for(NodeIt n(_g);n!=INVALID;++n) refresh(n);

    }

    ///Find an arc between two nodes.

    ///Find an arc between two nodes in time <em>O</em>(log<em>d</em>),