diff -r b67149f0e675 -r a5d8c039f218 lemon/core.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/core.h	Tue Jul 15 13:15:39 2008 +0200
@@ -0,0 +1,1851 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef LEMON_CORE_H
+#define LEMON_CORE_H
+
+#include <vector>
+#include <algorithm>
+
+#include <lemon/bits/enable_if.h>
+#include <lemon/bits/traits.h>
+
+///\file
+///\brief LEMON core utilities.
+
+namespace lemon {
+
+  /// \brief Dummy type to make it easier to create invalid iterators.
+  ///
+  /// Dummy type to make it easier to create invalid iterators.
+  /// See \ref INVALID for the usage.
+  struct Invalid {
+  public:
+    bool operator==(Invalid) { return true;  }
+    bool operator!=(Invalid) { return false; }
+    bool operator< (Invalid) { return false; }
+  };
+
+  /// \brief Invalid iterators.
+  ///
+  /// \ref Invalid is a global type that converts to each iterator
+  /// in such a way that the value of the target iterator will be invalid.
+#ifdef LEMON_ONLY_TEMPLATES
+  const Invalid INVALID = Invalid();
+#else
+  extern const Invalid INVALID;
+#endif
+
+  /// \addtogroup gutils
+  /// @{
+
+  ///Creates convenience typedefs for the digraph types and iterators
+
+  ///This \c \#define creates convenience typedefs for the following types
+  ///of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
+  ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
+  ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
+  ///
+  ///\note If the graph type is a dependent type, ie. the graph type depend
+  ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
+  ///macro.
+#define DIGRAPH_TYPEDEFS(Digraph)                                       \
+  typedef Digraph::Node Node;                                           \
+  typedef Digraph::NodeIt NodeIt;                                       \
+  typedef Digraph::Arc Arc;                                             \
+  typedef Digraph::ArcIt ArcIt;                                         \
+  typedef Digraph::InArcIt InArcIt;                                     \
+  typedef Digraph::OutArcIt OutArcIt;                                   \
+  typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
+  typedef Digraph::NodeMap<int> IntNodeMap;                             \
+  typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
+  typedef Digraph::ArcMap<bool> BoolArcMap;                             \
+  typedef Digraph::ArcMap<int> IntArcMap;                               \
+  typedef Digraph::ArcMap<double> DoubleArcMap
+
+  ///Creates convenience typedefs for the digraph types and iterators
+
+  ///\see DIGRAPH_TYPEDEFS
+  ///
+  ///\note Use this macro, if the graph type is a dependent type,
+  ///ie. the graph type depend on a template parameter.
+#define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
+  typedef typename Digraph::Node Node;                                  \
+  typedef typename Digraph::NodeIt NodeIt;                              \
+  typedef typename Digraph::Arc Arc;                                    \
+  typedef typename Digraph::ArcIt ArcIt;                                \
+  typedef typename Digraph::InArcIt InArcIt;                            \
+  typedef typename Digraph::OutArcIt OutArcIt;                          \
+  typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
+  typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
+  typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
+  typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
+  typedef typename Digraph::template ArcMap<int> IntArcMap;             \
+  typedef typename Digraph::template ArcMap<double> DoubleArcMap
+
+  ///Creates convenience typedefs for the graph types and iterators
+
+  ///This \c \#define creates the same convenience typedefs as defined
+  ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
+  ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
+  ///\c DoubleEdgeMap.
+  ///
+  ///\note If the graph type is a dependent type, ie. the graph type depend
+  ///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
+  ///macro.
+#define GRAPH_TYPEDEFS(Graph)                                           \
+  DIGRAPH_TYPEDEFS(Graph);                                              \
+  typedef Graph::Edge Edge;                                             \
+  typedef Graph::EdgeIt EdgeIt;                                         \
+  typedef Graph::IncEdgeIt IncEdgeIt;                                   \
+  typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
+  typedef Graph::EdgeMap<int> IntEdgeMap;                               \
+  typedef Graph::EdgeMap<double> DoubleEdgeMap
+
+  ///Creates convenience typedefs for the graph types and iterators
+
+  ///\see GRAPH_TYPEDEFS
+  ///
+  ///\note Use this macro, if the graph type is a dependent type,
+  ///ie. the graph type depend on a template parameter.
+#define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
+  TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
+  typedef typename Graph::Edge Edge;                                    \
+  typedef typename Graph::EdgeIt EdgeIt;                                \
+  typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
+  typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
+  typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
+  typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
+
+  /// \brief Function to count the items in the graph.
+  ///
+  /// This function counts the items (nodes, arcs etc) in the graph.
+  /// The complexity of the function is O(n) because
+  /// it iterates on all of the items.
+  template <typename Graph, typename Item>
+  inline int countItems(const Graph& g) {
+    typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
+    int num = 0;
+    for (ItemIt it(g); it != INVALID; ++it) {
+      ++num;
+    }
+    return num;
+  }
+
+  // Node counting:
+
+  namespace _core_bits {
+
+    template <typename Graph, typename Enable = void>
+    struct CountNodesSelector {
+      static int count(const Graph &g) {
+        return countItems<Graph, typename Graph::Node>(g);
+      }
+    };
+
+    template <typename Graph>
+    struct CountNodesSelector<
+      Graph, typename
+      enable_if<typename Graph::NodeNumTag, void>::type>
+    {
+      static int count(const Graph &g) {
+        return g.nodeNum();
+      }
+    };
+  }
+
+  /// \brief Function to count the nodes in the graph.
+  ///
+  /// This function counts the nodes in the graph.
+  /// The complexity of the function is O(n) but for some
+  /// graph structures it is specialized to run in O(1).
+  ///
+  /// If the graph contains a \e nodeNum() member function and a
+  /// \e NodeNumTag tag then this function calls directly the member
+  /// function to query the cardinality of the node set.
+  template <typename Graph>
+  inline int countNodes(const Graph& g) {
+    return _core_bits::CountNodesSelector<Graph>::count(g);
+  }
+
+  // Arc counting:
+
+  namespace _core_bits {
+
+    template <typename Graph, typename Enable = void>
+    struct CountArcsSelector {
+      static int count(const Graph &g) {
+        return countItems<Graph, typename Graph::Arc>(g);
+      }
+    };
+
+    template <typename Graph>
+    struct CountArcsSelector<
+      Graph,
+      typename enable_if<typename Graph::ArcNumTag, void>::type>
+    {
+      static int count(const Graph &g) {
+        return g.arcNum();
+      }
+    };
+  }
+
+  /// \brief Function to count the arcs in the graph.
+  ///
+  /// This function counts the arcs in the graph.
+  /// The complexity of the function is O(e) but for some
+  /// graph structures it is specialized to run in O(1).
+  ///
+  /// If the graph contains a \e arcNum() member function and a
+  /// \e EdgeNumTag tag then this function calls directly the member
+  /// function to query the cardinality of the arc set.
+  template <typename Graph>
+  inline int countArcs(const Graph& g) {
+    return _core_bits::CountArcsSelector<Graph>::count(g);
+  }
+
+  // Edge counting:
+  namespace _core_bits {
+
+    template <typename Graph, typename Enable = void>
+    struct CountEdgesSelector {
+      static int count(const Graph &g) {
+        return countItems<Graph, typename Graph::Edge>(g);
+      }
+    };
+
+    template <typename Graph>
+    struct CountEdgesSelector<
+      Graph,
+      typename enable_if<typename Graph::EdgeNumTag, void>::type>
+    {
+      static int count(const Graph &g) {
+        return g.edgeNum();
+      }
+    };
+  }
+
+  /// \brief Function to count the edges in the graph.
+  ///
+  /// This function counts the edges in the graph.
+  /// The complexity of the function is O(m) but for some
+  /// graph structures it is specialized to run in O(1).
+  ///
+  /// If the graph contains a \e edgeNum() member function and a
+  /// \e EdgeNumTag tag then this function calls directly the member
+  /// function to query the cardinality of the edge set.
+  template <typename Graph>
+  inline int countEdges(const Graph& g) {
+    return _core_bits::CountEdgesSelector<Graph>::count(g);
+
+  }
+
+
+  template <typename Graph, typename DegIt>
+  inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
+    int num = 0;
+    for (DegIt it(_g, _n); it != INVALID; ++it) {
+      ++num;
+    }
+    return num;
+  }
+
+  /// \brief Function to count the number of the out-arcs from node \c n.
+  ///
+  /// This function counts the number of the out-arcs from node \c n
+  /// in the graph.
+  template <typename Graph>
+  inline int countOutArcs(const Graph& _g,  const typename Graph::Node& _n) {
+    return countNodeDegree<Graph, typename Graph::OutArcIt>(_g, _n);
+  }
+
+  /// \brief Function to count the number of the in-arcs to node \c n.
+  ///
+  /// This function counts the number of the in-arcs to node \c n
+  /// in the graph.
+  template <typename Graph>
+  inline int countInArcs(const Graph& _g,  const typename Graph::Node& _n) {
+    return countNodeDegree<Graph, typename Graph::InArcIt>(_g, _n);
+  }
+
+  /// \brief Function to count the number of the inc-edges to node \c n.
+  ///
+  /// This function counts the number of the inc-edges to node \c n
+  /// in the graph.
+  template <typename Graph>
+  inline int countIncEdges(const Graph& _g,  const typename Graph::Node& _n) {
+    return countNodeDegree<Graph, typename Graph::IncEdgeIt>(_g, _n);
+  }
+
+  namespace _core_bits {
+
+    template <typename Digraph, typename Item, typename RefMap>
+    class MapCopyBase {
+    public:
+      virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
+
+      virtual ~MapCopyBase() {}
+    };
+
+    template <typename Digraph, typename Item, typename RefMap,
+              typename ToMap, typename FromMap>
+    class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
+    public:
+
+      MapCopy(ToMap& tmap, const FromMap& map)
+        : _tmap(tmap), _map(map) {}
+
+      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
+        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+        for (ItemIt it(digraph); it != INVALID; ++it) {
+          _tmap.set(refMap[it], _map[it]);
+        }
+      }
+
+    private:
+      ToMap& _tmap;
+      const FromMap& _map;
+    };
+
+    template <typename Digraph, typename Item, typename RefMap, typename It>
+    class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
+    public:
+
+      ItemCopy(It& it, const Item& item) : _it(it), _item(item) {}
+
+      virtual void copy(const Digraph&, const RefMap& refMap) {
+        _it = refMap[_item];
+      }
+
+    private:
+      It& _it;
+      Item _item;
+    };
+
+    template <typename Digraph, typename Item, typename RefMap, typename Ref>
+    class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
+    public:
+
+      RefCopy(Ref& map) : _map(map) {}
+
+      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
+        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+        for (ItemIt it(digraph); it != INVALID; ++it) {
+          _map.set(it, refMap[it]);
+        }
+      }
+
+    private:
+      Ref& _map;
+    };
+
+    template <typename Digraph, typename Item, typename RefMap,
+              typename CrossRef>
+    class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
+    public:
+
+      CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
+
+      virtual void copy(const Digraph& digraph, const RefMap& refMap) {
+        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+        for (ItemIt it(digraph); it != INVALID; ++it) {
+          _cmap.set(refMap[it], it);
+        }
+      }
+
+    private:
+      CrossRef& _cmap;
+    };
+
+    template <typename Digraph, typename Enable = void>
+    struct DigraphCopySelector {
+      template <typename From, typename NodeRefMap, typename ArcRefMap>
+      static void copy(Digraph &to, const From& from,
+                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
+        for (typename From::NodeIt it(from); it != INVALID; ++it) {
+          nodeRefMap[it] = to.addNode();
+        }
+        for (typename From::ArcIt it(from); it != INVALID; ++it) {
+          arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
+                                    nodeRefMap[from.target(it)]);
+        }
+      }
+    };
+
+    template <typename Digraph>
+    struct DigraphCopySelector<
+      Digraph,
+      typename enable_if<typename Digraph::BuildTag, void>::type>
+    {
+      template <typename From, typename NodeRefMap, typename ArcRefMap>
+      static void copy(Digraph &to, const From& from,
+                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
+        to.build(from, nodeRefMap, arcRefMap);
+      }
+    };
+
+    template <typename Graph, typename Enable = void>
+    struct GraphCopySelector {
+      template <typename From, typename NodeRefMap, typename EdgeRefMap>
+      static void copy(Graph &to, const From& from,
+                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
+        for (typename From::NodeIt it(from); it != INVALID; ++it) {
+          nodeRefMap[it] = to.addNode();
+        }
+        for (typename From::EdgeIt it(from); it != INVALID; ++it) {
+          edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
+                                      nodeRefMap[from.v(it)]);
+        }
+      }
+    };
+
+    template <typename Graph>
+    struct GraphCopySelector<
+      Graph,
+      typename enable_if<typename Graph::BuildTag, void>::type>
+    {
+      template <typename From, typename NodeRefMap, typename EdgeRefMap>
+      static void copy(Graph &to, const From& from,
+                       NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
+        to.build(from, nodeRefMap, edgeRefMap);
+      }
+    };
+
+  }
+
+  /// \brief Class to copy a digraph.
+  ///
+  /// Class to copy a digraph to another digraph (duplicate a digraph). The
+  /// simplest way of using it is through the \c copyDigraph() function.
+  ///
+  /// This class not just make a copy of a graph, but it can create
+  /// references and cross references between the nodes and arcs of
+  /// the two graphs, it can copy maps for use with the newly created
+  /// graph and copy nodes and arcs.
+  ///
+  /// To make a copy from a graph, first an instance of DigraphCopy
+  /// 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
+  ///  DigraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
+  ///  // create a reference for the nodes
+  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
+  ///  dc.nodeRef(nr);
+  ///  // create a cross reference (inverse) for the arcs
+  ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
+  ///  dc.arcCrossRef(acr);
+  ///  // copy an arc map
+  ///  OrigGraph::ArcMap<double> oamap(orig_graph);
+  ///  NewGraph::ArcMap<double> namap(new_graph);
+  ///  dc.arcMap(namap, oamap);
+  ///  // copy a node
+  ///  OrigGraph::Node on;
+  ///  NewGraph::Node nn;
+  ///  dc.node(nn, on);
+  ///  // Executions of copy
+  ///  dc.run();
+  ///\endcode
+  template <typename To, typename From>
+  class DigraphCopy {
+  private:
+
+    typedef typename From::Node Node;
+    typedef typename From::NodeIt NodeIt;
+    typedef typename From::Arc Arc;
+    typedef typename From::ArcIt ArcIt;
+
+    typedef typename To::Node TNode;
+    typedef typename To::Arc TArc;
+
+    typedef typename From::template NodeMap<TNode> NodeRefMap;
+    typedef typename From::template ArcMap<TArc> ArcRefMap;
+
+
+  public:
+
+
+    /// \brief Constructor for the DigraphCopy.
+    ///
+    /// It copies the content of the \c _from digraph into the
+    /// \c _to digraph.
+    DigraphCopy(To& to, const From& from)
+      : _from(from), _to(to) {}
+
+    /// \brief Destructor of the DigraphCopy
+    ///
+    /// Destructor of the DigraphCopy
+    ~DigraphCopy() {
+      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];
+      }
+
+    }
+
+    /// \brief Copies the node references into the given map.
+    ///
+    /// Copies the node references into the given map. The parameter
+    /// should be a map, which 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>
+    DigraphCopy& nodeRef(NodeRef& map) {
+      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
+                           NodeRefMap, NodeRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the node cross references into the given map.
+    ///
+    ///  Copies the node cross references (reverse references) into
+    ///  the given map. The parameter should be a map, which 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>
+    DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
+      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
+                           NodeRefMap, NodeCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created digraph.
+    /// The new map's key type is the destination graph's node type,
+    /// and the copied map's key type is the source graph's node type.
+    template <typename ToMap, typename FromMap>
+    DigraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
+      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
+                           NodeRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given node.
+    ///
+    /// Make a copy of the given node.
+    DigraphCopy& node(TNode& tnode, const Node& snode) {
+      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
+                           NodeRefMap, TNode>(tnode, snode));
+      return *this;
+    }
+
+    /// \brief Copies the arc references into the given map.
+    ///
+    /// Copies the arc references into the given map.
+    template <typename ArcRef>
+    DigraphCopy& arcRef(ArcRef& map) {
+      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
+                          ArcRefMap, ArcRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the arc cross references into the given map.
+    ///
+    ///  Copies the arc cross references (reverse references) into
+    ///  the given map.
+    template <typename ArcCrossRef>
+    DigraphCopy& arcCrossRef(ArcCrossRef& map) {
+      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
+                          ArcRefMap, ArcCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created digraph.
+    /// The new map's key type is the to digraph's arc type,
+    /// and the copied map's key type is the from digraph's arc
+    /// type.
+    template <typename ToMap, typename FromMap>
+    DigraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
+      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
+                          ArcRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given arc.
+    ///
+    /// Make a copy of the given arc.
+    DigraphCopy& arc(TArc& tarc, const Arc& sarc) {
+      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
+                          ArcRefMap, TArc>(tarc, sarc));
+      return *this;
+    }
+
+    /// \brief Executes the copies.
+    ///
+    /// Executes the copies.
+    void run() {
+      NodeRefMap nodeRefMap(_from);
+      ArcRefMap arcRefMap(_from);
+      _core_bits::DigraphCopySelector<To>::
+        copy(_to, _from, nodeRefMap, arcRefMap);
+      for (int i = 0; i < int(_node_maps.size()); ++i) {
+        _node_maps[i]->copy(_from, nodeRefMap);
+      }
+      for (int i = 0; i < int(_arc_maps.size()); ++i) {
+        _arc_maps[i]->copy(_from, arcRefMap);
+      }
+    }
+
+  protected:
+
+
+    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;
+
+  };
+
+  /// \brief Copy a digraph to another digraph.
+  ///
+  /// Copy a digraph to another digraph. The complete usage of the
+  /// function is detailed in the DigraphCopy class, but a short
+  /// example shows a basic work:
+  ///\code
+  /// copyDigraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
+  ///\endcode
+  ///
+  /// After the copy the \c nr map will contain the mapping from the
+  /// nodes of the \c from digraph to the nodes of the \c to digraph and
+  /// \c ecr will contain the mapping from the arcs of the \c to digraph
+  /// to the arcs of the \c from digraph.
+  ///
+  /// \see DigraphCopy
+  template <typename To, typename From>
+  DigraphCopy<To, From> copyDigraph(To& to, const From& from) {
+    return DigraphCopy<To, From>(to, from);
+  }
+
+  /// \brief Class to copy a graph.
+  ///
+  /// Class to copy a graph to another graph (duplicate a graph). The
+  /// simplest way of using it is through the \c copyGraph() function.
+  ///
+  /// This class not just make a copy of a graph, but it can create
+  /// references and cross references between the nodes, edges and arcs of
+  /// the two graphs, it can copy maps for use with the newly created
+  /// graph and copy nodes, edges and arcs.
+  ///
+  /// 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<NewGraph, OrigGraph> dc(new_graph, orig_graph);
+  ///  // create a reference for the nodes
+  ///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
+  ///  dc.nodeRef(nr);
+  ///  // create a cross reference (inverse) for the edges
+  ///  NewGraph::EdgeMap<OrigGraph::Arc> ecr(new_graph);
+  ///  dc.edgeCrossRef(ecr);
+  ///  // copy an arc map
+  ///  OrigGraph::ArcMap<double> oamap(orig_graph);
+  ///  NewGraph::ArcMap<double> namap(new_graph);
+  ///  dc.arcMap(namap, oamap);
+  ///  // copy a node
+  ///  OrigGraph::Node on;
+  ///  NewGraph::Node nn;
+  ///  dc.node(nn, on);
+  ///  // Executions of copy
+  ///  dc.run();
+  ///\endcode
+  template <typename To, typename From>
+  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 To& to, const From& from,
+                const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
+        : _to(to), _from(from),
+          _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 To& _to;
+      const From& _from;
+      const EdgeRefMap& _edge_ref;
+      const NodeRefMap& _node_ref;
+    };
+
+
+  public:
+
+
+    /// \brief Constructor for the GraphCopy.
+    ///
+    /// It copies the content of the \c _from graph into the
+    /// \c _to graph.
+    GraphCopy(To& to, const From& from)
+      : _from(from), _to(to) {}
+
+    /// \brief Destructor of the GraphCopy
+    ///
+    /// Destructor of the 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 Copies the node references into the given map.
+    ///
+    /// Copies the node references into the given map.
+    template <typename NodeRef>
+    GraphCopy& nodeRef(NodeRef& map) {
+      _node_maps.push_back(new _core_bits::RefCopy<From, Node,
+                           NodeRefMap, NodeRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the node cross references into the given map.
+    ///
+    ///  Copies the node cross references (reverse references) into
+    ///  the given map.
+    template <typename NodeCrossRef>
+    GraphCopy& nodeCrossRef(NodeCrossRef& map) {
+      _node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
+                           NodeRefMap, NodeCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created graph.
+    /// The new map's key type is the to graph's node type,
+    /// and the copied map's key type is the from graph's node
+    /// type.
+    template <typename ToMap, typename FromMap>
+    GraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
+      _node_maps.push_back(new _core_bits::MapCopy<From, Node,
+                           NodeRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given node.
+    ///
+    /// Make a copy of the given node.
+    GraphCopy& node(TNode& tnode, const Node& snode) {
+      _node_maps.push_back(new _core_bits::ItemCopy<From, Node,
+                           NodeRefMap, TNode>(tnode, snode));
+      return *this;
+    }
+
+    /// \brief Copies the arc references into the given map.
+    ///
+    /// Copies the arc references into the given map.
+    template <typename ArcRef>
+    GraphCopy& arcRef(ArcRef& map) {
+      _arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
+                          ArcRefMap, ArcRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the arc cross references into the given map.
+    ///
+    ///  Copies the arc cross references (reverse references) into
+    ///  the given map.
+    template <typename ArcCrossRef>
+    GraphCopy& arcCrossRef(ArcCrossRef& map) {
+      _arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
+                          ArcRefMap, ArcCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created graph.
+    /// The new map's key type is the to graph's arc type,
+    /// and the copied map's key type is the from graph's arc
+    /// type.
+    template <typename ToMap, typename FromMap>
+    GraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
+      _arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
+                          ArcRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given arc.
+    ///
+    /// Make a copy of the given arc.
+    GraphCopy& arc(TArc& tarc, const Arc& sarc) {
+      _arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
+                          ArcRefMap, TArc>(tarc, sarc));
+      return *this;
+    }
+
+    /// \brief Copies the edge references into the given map.
+    ///
+    /// Copies the edge references into the given map.
+    template <typename EdgeRef>
+    GraphCopy& edgeRef(EdgeRef& map) {
+      _edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
+                           EdgeRefMap, EdgeRef>(map));
+      return *this;
+    }
+
+    /// \brief Copies the edge cross references into the given map.
+    ///
+    /// Copies the edge cross references (reverse
+    /// references) into the given map.
+    template <typename EdgeCrossRef>
+    GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
+      _edge_maps.push_back(new _core_bits::CrossRefCopy<From,
+                           Edge, EdgeRefMap, EdgeCrossRef>(map));
+      return *this;
+    }
+
+    /// \brief Make copy of the given map.
+    ///
+    /// Makes copy of the given map for the newly created graph.
+    /// The new map's key type is the to graph's edge type,
+    /// and the copied map's key type is the from graph's edge
+    /// type.
+    template <typename ToMap, typename FromMap>
+    GraphCopy& edgeMap(ToMap& tmap, const FromMap& map) {
+      _edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
+                           EdgeRefMap, ToMap, FromMap>(tmap, map));
+      return *this;
+    }
+
+    /// \brief Make a copy of the given edge.
+    ///
+    /// Make a copy of the given edge.
+    GraphCopy& edge(TEdge& tedge, const Edge& sedge) {
+      _edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
+                           EdgeRefMap, TEdge>(tedge, sedge));
+      return *this;
+    }
+
+    /// \brief Executes the copies.
+    ///
+    /// Executes the copies.
+    void run() {
+      NodeRefMap nodeRefMap(_from);
+      EdgeRefMap edgeRefMap(_from);
+      ArcRefMap arcRefMap(_to, _from, edgeRefMap, nodeRefMap);
+      _core_bits::GraphCopySelector<To>::
+        copy(_to, _from, 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.
+  ///
+  /// Copy a graph to another graph. The complete usage of the
+  /// function is detailed in the GraphCopy class, but a short
+  /// example shows a basic work:
+  ///\code
+  /// copyGraph(trg, src).nodeRef(nr).arcCrossRef(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 arcs of the \c to graph
+  /// to the arcs of the \c from graph.
+  ///
+  /// \see GraphCopy
+  template <typename To, typename From>
+  GraphCopy<To, From>
+  copyGraph(To& to, const From& from) {
+    return GraphCopy<To, From>(to, from);
+  }
+
+  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::FindEdgeTag, 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 Finds an arc between two nodes of a graph.
+  ///
+  /// Finds an arc from node \c u to node \c v in graph \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
+  ///
+  ///\sa ArcLookUp
+  ///\sa AllArcLookUp
+  ///\sa DynArcLookUp
+  ///\sa ConArcIt
+  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 arcs connected the same nodes.
+  ///
+  /// Iterator for iterating on arcs connected the same nodes. It is
+  /// higher level interface for the 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
+  ///\sa AllArcLookUp
+  ///\sa 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 which
+    /// connects the \c u and \c v node.
+    ConArcIt(const Graph& g, Node u, Node v) : _graph(g) {
+      Parent::operator=(findArc(_graph, u, v));
+    }
+
+    /// \brief Constructor.
+    ///
+    /// Construct a new ConArcIt which continues the iterating from
+    /// the \c e arc.
+    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 Finds an edge between two nodes of a graph.
+  ///
+  /// Finds an edge from node \c u to node \c v in graph \c g.
+  /// If the 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 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(Edge e = findEdge(g,u,v); e != INVALID;
+  ///     e = findEdge(g,u,v,e)) {
+  ///   ...
+  /// }
+  ///\endcode
+  ///
+  ///\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 edges connected the same nodes.
+  ///
+  /// Iterator for iterating on edges connected the same nodes. It is
+  /// higher level interface for the findEdge() function. You can
+  /// use it the following way:
+  ///\code
+  /// for (ConEdgeIt<Graph> it(g, src, trg); 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 which
+    /// connects the \c u and \c v node.
+    ConEdgeIt(const Graph& g, Node u, Node v) : _graph(g) {
+      Parent::operator=(findEdge(_graph, u, v));
+    }
+
+    /// \brief Constructor.
+    ///
+    /// Construct a new ConEdgeIt which continues the iterating from
+    /// the \c e edge.
+    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++() {
+      Parent::operator=(findEdge(_graph, _graph.u(*this),
+                                 _graph.v(*this), *this));
+      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(log 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 findFirst() and \c findNext() members.
+  ///
+  ///See the \ref ArcLookUp and \ref AllArcLookUp classes if your
+  ///digraph is not changed so frequently.
+  ///
+  ///This class uses a self-adjusting binary search tree, Sleator's
+  ///and Tarjan's Splay tree for guarantee the logarithmic amortized
+  ///time bound for arc lookups. 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);
+
+          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 e(_g,n);e!=INVALID;++e) v.push_back(e);
+        if(v.size()) {
+          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 in time <em>O(</em>log<em>d)</em>, where
+    /// <em>d</em> is the number of outgoing arcs of \c s.
+    ///\param s The source node
+    ///\param t The target node
+    ///\return An arc from \c s to \c t if there exists,
+    ///\ref INVALID otherwise.
+    Arc operator()(Node s, Node t) const
+    {
+      Arc a = _head[s];
+      while (true) {
+        if (_g.target(a) == t) {
+          const_cast<DynArcLookUp&>(*this).splay(a);
+          return a;
+        } else if (t < _g.target(a)) {
+          if (_left[a] == INVALID) {
+            const_cast<DynArcLookUp&>(*this).splay(a);
+            return INVALID;
+          } else {
+            a = _left[a];
+          }
+        } else  {
+          if (_right[a] == INVALID) {
+            const_cast<DynArcLookUp&>(*this).splay(a);
+            return INVALID;
+          } else {
+            a = _right[a];
+          }
+        }
+      }
+    }
+
+    ///Find the first arc between two nodes.
+
+    ///Find the first arc between two nodes in time
+    /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
+    /// outgoing arcs of \c s.
+    ///\param s The source node
+    ///\param t The target node
+    ///\return An arc from \c s to \c t if there exists, \ref INVALID
+    /// otherwise.
+    Arc findFirst(Node s, Node t) const
+    {
+      Arc a = _head[s];
+      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];
+          }
+        }
+      }
+    }
+
+    ///Find the next arc between two nodes.
+
+    ///Find the next arc between two nodes in time
+    /// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
+    /// outgoing arcs of \c s.
+    ///\param s The source node
+    ///\param t The target node
+    ///\return An arc from \c s to \c t if there exists, \ref INVALID
+    /// otherwise.
+
+    ///\note If \c e is not the result of the previous \c findFirst()
+    ///operation then the amorized time bound can not be guaranteed.
+#ifdef DOXYGEN
+    Arc findNext(Node s, Node t, Arc a) const
+#else
+    Arc findNext(Node, Node t, Arc a) const
+#endif
+    {
+      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(log 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 refresh() (or at least
+  ///refresh(Node)) this data structure
+  ///whenever the digraph changes. This is a time consuming (superlinearly
+  ///proportional (<em>O(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 data structure at a node.
+
+    ///Build up the search database of node \c n.
+    ///
+    ///It runs in time <em>O(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(m</em>log<em>D)</em>, where <em>m</em> is
+    ///the number of the arcs of \c n 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>, where
+    /// <em>d</em> is the number of outgoing arcs of \c s.
+    ///\param s The source node
+    ///\param t The target node
+    ///\return An arc from \c s to \c t if there exists,
+    ///\ref INVALID otherwise.
+    ///
+    ///\warning If you change the digraph, refresh() must be called before using
+    ///this operator. If you change the outgoing arcs of
+    ///a single node \c n, then
+    ///\ref refresh(Node) "refresh(n)" is enough.
+    ///
+    Arc operator()(Node s, Node t) const
+    {
+      Arc e;
+      for(e=_head[s];
+          e!=INVALID&&_g.target(e)!=t;
+          e = t < _g.target(e)?_left[e]:_right[e]) ;
+      return e;
+    }
+
+  };
+
+  ///Fast look up of all arcs between given endpoints.
+
+  ///This class is the same as \ref ArcLookUp, with the addition
+  ///that it makes it possible to find all arcs between given endpoints.
+  ///
+  ///\warning This class is static, so you should refresh() (or at least
+  ///refresh(Node)) this data structure
+  ///whenever the digraph changes. This is a time consuming (superlinearly
+  ///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
+  ///
+  ///\tparam G The type of the underlying digraph.
+  ///
+  ///\sa DynArcLookUp
+  ///\sa ArcLookUp
+  template<class G>
+  class AllArcLookUp : public ArcLookUp<G>
+  {
+    using ArcLookUp<G>::_g;
+    using ArcLookUp<G>::_right;
+    using ArcLookUp<G>::_left;
+    using ArcLookUp<G>::_head;
+
+    TEMPLATE_DIGRAPH_TYPEDEFS(G);
+    typedef G Digraph;
+
+    typename Digraph::template ArcMap<Arc> _next;
+
+    Arc refreshNext(Arc head,Arc next=INVALID)
+    {
+      if(head==INVALID) return next;
+      else {
+        next=refreshNext(_right[head],next);
+//         _next[head]=next;
+        _next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
+          ? next : INVALID;
+        return refreshNext(_left[head],head);
+      }
+    }
+
+    void refreshNext()
+    {
+      for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
+    }
+
+  public:
+    ///Constructor
+
+    ///Constructor.
+    ///
+    ///It builds up the search database, which remains valid until the digraph
+    ///changes.
+    AllArcLookUp(const Digraph &g) : ArcLookUp<G>(g), _next(g) {refreshNext();}
+
+    ///Refresh the data structure at a node.
+
+    ///Build up the search database of node \c n.
+    ///
+    ///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
+    ///the number of the outgoing arcs of \c n.
+
+    void refresh(Node n)
+    {
+      ArcLookUp<G>::refresh(n);
+      refreshNext(_head[n]);
+    }
+
+    ///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(m</em>log<em>D)</em>, where <em>m</em> is
+    ///the number of the arcs of \c n and <em>D</em> is the maximum
+    ///out-degree of the digraph.
+
+    void refresh()
+    {
+      for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
+    }
+
+    ///Find an arc between two nodes.
+
+    ///Find an arc between two nodes.
+    ///\param s The source node
+    ///\param t The target node
+    ///\param prev 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 prev 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
+    ///AllArcLookUp<ListDigraph> ae(g);
+    ///...
+    ///int n=0;
+    ///for(Arc e=ae(u,v);e!=INVALID;e=ae(u,v,e)) n++;
+    ///\endcode
+    ///
+    ///Finding the first arc take <em>O(</em>log<em>d)</em> time, where
+    /// <em>d</em> is the number of outgoing arcs of \c s. Then, the
+    ///consecutive arcs are found in constant time.
+    ///
+    ///\warning If you change the digraph, refresh() must be called before using
+    ///this operator. If you change the outgoing arcs of
+    ///a single node \c n, then
+    ///\ref refresh(Node) "refresh(n)" is enough.
+    ///
+#ifdef DOXYGEN
+    Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
+#else
+    using ArcLookUp<G>::operator() ;
+    Arc operator()(Node s, Node t, Arc prev) const
+    {
+      return prev==INVALID?(*this)(s,t):_next[prev];
+    }
+#endif
+
+  };
+
+  /// @}
+
+} //namespace lemon
+
+#endif