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/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2010

 * 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/config.h>

#include <lemon/bits/enable_if.h>

#include <lemon/bits/traits.h>

#include <lemon/assert.h>

// Disable the following warnings when compiling with MSVC:

// C4250: 'class1' : inherits 'class2::member' via dominance

// C4355: 'this' : used in base member initializer list

// C4503: 'function' : decorated name length exceeded, name was truncated

// C4800: 'type' : forcing value to bool 'true' or 'false' (performance warning)

// C4996: 'function': was declared deprecated

#ifdef _MSC_VER

#pragma warning( disable : 4250 4355 4503 4800 4996 )

#endif

///\file

///\brief LEMON core utilities.

///

///This header file contains core utilities for LEMON.

///It is automatically included by all graph types, therefore it usually

///do not have to be included directly.

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

  /// @{

  ///Create convenience typedefs for the digraph types and iterators

  ///This \c \#define creates convenient type definitions 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

  ///Create 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

  ///Create convenience typedefs for the graph types and iterators

  ///This \c \#define creates the same convenient type definitions 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_GRAPH_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

  ///Create 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 a graph.

  ///

  /// This function counts the items (nodes, arcs etc.) in a graph.

  /// The complexity of the function is linear 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 <em>O</em>(<em>n</em>), but for some

  /// graph structures it is specialized to run in <em>O</em>(1).

  ///

  /// \note If the graph contains a \c nodeNum() member function and a

  /// \c 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 <em>O</em>(<em>m</em>), but for some

  /// graph structures it is specialized to run in <em>O</em>(1).

  ///

  /// \note If the graph contains a \c arcNum() member function and a

  /// \c ArcNumTag 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 <em>O</em>(<em>m</em>), but for some

  /// graph structures it is specialized to run in <em>O</em>(1).

  ///

  /// \note If the graph contains a \c edgeNum() member function and a

  /// \c 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 \c g.

  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 \c g.

  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 undirected graph \c g.

  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 FromMap, typename ToMap>

    class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {

    public:

      MapCopy(const FromMap& map, ToMap& tmap)

        : _map(map), _tmap(tmap) {}

      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:

      const FromMap& _map;

      ToMap& _tmap;

    };

    template <typename Digraph, typename Item, typename RefMap, typename It>

    class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {

    public:

      ItemCopy(const Item& item, It& it) : _item(item), _it(it) {}

      virtual void copy(const Digraph&, const RefMap& refMap) {

        _it = refMap[_item];

      }

    private:

      Item _item;

      It& _it;

    };

    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(const From& from, Digraph &to,

                       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(const From& from, Digraph &to,

                       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(const From& from, Graph &to,

                       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(const From& from, Graph &to,

                       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 digraphCopy() function.

  ///

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

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

  /// the two digraphs, and it can copy maps to use with the newly created

  /// digraph.

  ///

  /// To make a copy from a digraph, first an instance of DigraphCopy

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

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

  /// called.

  ///

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

  ///\code

  ///  DigraphCopy<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 arcs

  ///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);

  ///  cg.arcCrossRef(acr);

  ///  // Copy an arc map

  ///  OrigGraph::ArcMap<double> oamap(orig_graph);

  ///  NewGraph::ArcMap<double> namap(new_graph);

  ///  cg.arcMap(oamap, namap);

  ///  // Copy a node

  ///  OrigGraph::Node on;

  ///  NewGraph::Node nn;

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

  ///  // Execute copying

  ///  cg.run();

  ///\endcode

  template <typename From, typename To>

  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 of DigraphCopy.

    ///

    /// Constructor of DigraphCopy for copying the content of the

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

    DigraphCopy(const From& from, To& to)

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

    /// \brief Destructor of DigraphCopy

    ///

    /// Destructor of 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 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 digraph, while the value type is the Node type of the

    /// destination digraph.

    template <typename NodeRef>

    DigraphCopy& 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 digraph, while the value type is

    /// the Node type of the source digraph.

    template <typename NodeCrossRef>

    DigraphCopy& 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 digraph.

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

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

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

    template <typename FromMap, typename ToMap>

    DigraphCopy& 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.

    DigraphCopy& 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 digraph, while the value type is the Arc type of the

    /// destination digraph.

    template <typename ArcRef>

    DigraphCopy& 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 digraph, while the value type is

    /// the Arc type of the source digraph.

    template <typename ArcCrossRef>

    DigraphCopy& 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 digraph.

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

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

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

    template <typename FromMap, typename ToMap>

    DigraphCopy& 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.

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

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

                          ArcRefMap, TArc>(arc, tarc));

      return *this;

    }

    /// \brief Execute copying.

    ///

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

    /// copying of the assigned data.

    void run() {

      NodeRefMap nodeRefMap(_from);

      ArcRefMap arcRefMap(_from);

      _core_bits::DigraphCopySelector<To>::

        copy(_from, _to, 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.

  ///

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

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

  /// a short example shows a basic work:

  ///\code

  /// digraphCopy(src, trg).nodeRef(nr).arcCrossRef(acr).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 acr will contain the mapping from the arcs of the \c to digraph

  /// to the arcs of the \c from digraph.

  ///

  /// \see DigraphCopy

  template <typename From, typename To>

  DigraphCopy<From, To> digraphCopy(const From& from, To& to) {

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

  }

  /// \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 graphCopy() function.

  ///

  /// 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 GR>

  class ConArcIt : public GR::Arc {

    typedef typename GR::Arc Parent;

  public:

    typedef typename GR::Arc Arc;

    typedef typename GR::Node Node;

    /// \brief Constructor.

    ///

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

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

    ConArcIt(const GR& 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 GR& 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 GR& _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<