lemon-1.1: comparison lemon/graph

equal deleted inserted replaced

--1:000000000000
+:16827ada2380
+/* -*- C++ -*-
+*
+* 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_GRAPH_UTILS_H
+#define LEMON_GRAPH_UTILS_H
+#include <iterator>
+#include <vector>
+#include <map>
+#include <cmath>
+#include <algorithm>
+#include <lemon/bits/invalid.h>
+#include <lemon/bits/utility.h>
+#include <lemon/maps.h>
+#include <lemon/bits/traits.h>
+#include <lemon/bits/alteration_notifier.h>
+#include <lemon/bits/default_map.h>
+///\ingroup gutils
+///\file
+///\brief Digraph utilities.
+namespace lemon {
+/// \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
+///\note If \c G it a template parameter, it should be used in this way.
+///\code
+///  GRAPH_TYPEDEFS(typename G);
+///\endcode
+///
+///\warning There are no typedefs for the digraph maps because of the lack of
+///template typedefs in C++.
+#define GRAPH_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
+///Creates convenience typedefs for the graph types and iterators
+///This \c \#define creates the same convenience typedefs as defined by
+///\ref GRAPH_TYPEDEFS(Digraph) and three more, namely it creates
+///\c Edge, \c EdgeIt, \c IncArcIt,
+///
+///\note If \c G it a template parameter, it should be used in this way.
+///\code
+///  UGRAPH_TYPEDEFS(typename G);
+///\endcode
+///
+///\warning There are no typedefs for the digraph maps because of the lack of
+///template typedefs in C++.
+#define UGRAPH_TYPEDEFS(Digraph)				\
+GRAPH_TYPEDEFS(Digraph);				\
+typedef Digraph:: Edge   Edge;			\
+typedef Digraph:: EdgeIt EdgeIt;			\
+typedef Digraph:: IncArcIt   IncArcIt
+///\brief Creates convenience typedefs for the bipartite digraph
+///types and iterators
+///This \c \#define creates the same convenience typedefs as defined by
+///\ref UGRAPH_TYPEDEFS(Digraph) and two more, namely it creates
+///\c RedIt, \c BlueIt,
+///
+///\note If \c G it a template parameter, it should be used in this way.
+///\code
+///  BPUGRAPH_TYPEDEFS(typename G);
+///\endcode
+///
+///\warning There are no typedefs for the digraph maps because of the lack of
+///template typedefs in C++.
+#define BPUGRAPH_TYPEDEFS(Digraph)            \
+UGRAPH_TYPEDEFS(Digraph);		    \
+typedef Digraph::Red Red;             \
+typedef Digraph::Blue Blue;             \
+typedef Digraph::RedIt RedIt;	    \
+typedef Digraph::BlueIt BlueIt
+/// \brief Function to count the items in the digraph.
+///
+/// This function counts the items (nodes, arcs etc) in the digraph.
+/// The complexity of the function is O(n) because
+/// it iterates on all of the items.
+template <typename Digraph, typename Item>
+inline int countItems(const Digraph& g) {
+typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+int num = 0;
+for (ItemIt it(g); it != INVALID; ++it) {
+++num;
+}
+return num;
+}
+// Node counting:
+namespace _digraph_utils_bits {
+template <typename Digraph, typename Enable = void>
+struct CountNodesSelector {
+static int count(const Digraph &g) {
+return countItems<Digraph, typename Digraph::Node>(g);
+}
+};
+template <typename Digraph>
+struct CountNodesSelector<
+Digraph, typename
+enable_if<typename Digraph::NodeNumTag, void>::type>
+{
+static int count(const Digraph &g) {
+return g.nodeNum();
+}
+};
+}
+/// \brief Function to count the nodes in the digraph.
+///
+/// This function counts the nodes in the digraph.
+/// The complexity of the function is O(n) but for some
+/// digraph structures it is specialized to run in O(1).
+///
+/// If the digraph 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 Digraph>
+inline int countNodes(const Digraph& g) {
+return _digraph_utils_bits::CountNodesSelector<Digraph>::count(g);
+}
+namespace _digraph_utils_bits {
+template <typename Digraph, typename Enable = void>
+struct CountRedsSelector {
+static int count(const Digraph &g) {
+return countItems<Digraph, typename Digraph::Red>(g);
+}
+};
+template <typename Digraph>
+struct CountRedsSelector<
+Digraph, typename
+enable_if<typename Digraph::NodeNumTag, void>::type>
+{
+static int count(const Digraph &g) {
+return g.redNum();
+}
+};
+}
+/// \brief Function to count the reds in the digraph.
+///
+/// This function counts the reds in the digraph.
+/// The complexity of the function is O(an) but for some
+/// digraph structures it is specialized to run in O(1).
+///
+/// If the digraph contains an \e redNum() member function and a
+/// \e NodeNumTag tag then this function calls directly the member
+/// function to query the cardinality of the A-node set.
+template <typename Digraph>
+inline int countReds(const Digraph& g) {
+return _digraph_utils_bits::CountRedsSelector<Digraph>::count(g);
+}
+namespace _digraph_utils_bits {
+template <typename Digraph, typename Enable = void>
+struct CountBluesSelector {
+static int count(const Digraph &g) {
+return countItems<Digraph, typename Digraph::Blue>(g);
+}
+};
+template <typename Digraph>
+struct CountBluesSelector<
+Digraph, typename
+enable_if<typename Digraph::NodeNumTag, void>::type>
+{
+static int count(const Digraph &g) {
+return g.blueNum();
+}
+};
+}
+/// \brief Function to count the blues in the digraph.
+///
+/// This function counts the blues in the digraph.
+/// The complexity of the function is O(bn) but for some
+/// digraph structures it is specialized to run in O(1).
+///
+/// If the digraph contains a \e blueNum() member function and a
+/// \e NodeNumTag tag then this function calls directly the member
+/// function to query the cardinality of the B-node set.
+template <typename Digraph>
+inline int countBlues(const Digraph& g) {
+return _digraph_utils_bits::CountBluesSelector<Digraph>::count(g);
+}
+// Arc counting:
+namespace _digraph_utils_bits {
+template <typename Digraph, typename Enable = void>
+struct CountArcsSelector {
+static int count(const Digraph &g) {
+return countItems<Digraph, typename Digraph::Arc>(g);
+}
+};
+template <typename Digraph>
+struct CountArcsSelector<
+Digraph,
+typename enable_if<typename Digraph::ArcNumTag, void>::type>
+{
+static int count(const Digraph &g) {
+return g.arcNum();
+}
+};
+}
+/// \brief Function to count the arcs in the digraph.
+///
+/// This function counts the arcs in the digraph.
+/// The complexity of the function is O(e) but for some
+/// digraph structures it is specialized to run in O(1).
+///
+/// If the digraph contains a \e arcNum() member function and a
+/// \e ArcNumTag tag then this function calls directly the member
+/// function to query the cardinality of the arc set.
+template <typename Digraph>
+inline int countArcs(const Digraph& g) {
+return _digraph_utils_bits::CountArcsSelector<Digraph>::count(g);
+}
+// Undirected arc counting:
+namespace _digraph_utils_bits {
+template <typename Digraph, typename Enable = void>
+struct CountEdgesSelector {
+static int count(const Digraph &g) {
+return countItems<Digraph, typename Digraph::Edge>(g);
+}
+};
+template <typename Digraph>
+struct CountEdgesSelector<
+Digraph,
+typename enable_if<typename Digraph::ArcNumTag, void>::type>
+{
+static int count(const Digraph &g) {
+return g.edgeNum();
+}
+};
+}
+/// \brief Function to count the edges in the digraph.
+///
+/// This function counts the edges in the digraph.
+/// The complexity of the function is O(e) but for some
+/// digraph structures it is specialized to run in O(1).
+///
+/// If the digraph contains a \e edgeNum() member function and a
+/// \e ArcNumTag tag then this function calls directly the member
+/// function to query the cardinality of the edge set.
+template <typename Digraph>
+inline int countEdges(const Digraph& g) {
+return _digraph_utils_bits::CountEdgesSelector<Digraph>::count(g);
+}
+template <typename Digraph, typename DegIt>
+inline int countNodeDegree(const Digraph& _g, const typename Digraph::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 digraph.
+template <typename Digraph>
+inline int countOutArcs(const Digraph& _g,  const typename Digraph::Node& _n) {
+return countNodeDegree<Digraph, typename Digraph::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 digraph.
+template <typename Digraph>
+inline int countInArcs(const Digraph& _g,  const typename Digraph::Node& _n) {
+return countNodeDegree<Digraph, typename Digraph::InArcIt>(_g, _n);
+}
+/// \brief Function to count the number of the inc-arcs to node \c n.
+///
+/// This function counts the number of the inc-arcs to node \c n
+/// in the digraph.
+template <typename Digraph>
+inline int countIncArcs(const Digraph& _g,  const typename Digraph::Node& _n) {
+return countNodeDegree<Digraph, typename Digraph::IncArcIt>(_g, _n);
+}
+namespace _digraph_utils_bits {
+template <typename Digraph, typename Enable = void>
+struct FindArcSelector {
+typedef typename Digraph::Node Node;
+typedef typename Digraph::Arc Arc;
+static Arc find(const Digraph &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 Digraph>
+struct FindArcSelector<
+Digraph,
+typename enable_if<typename Digraph::FindArcTag, void>::type>
+{
+typedef typename Digraph::Node Node;
+typedef typename Digraph::Arc Arc;
+static Arc find(const Digraph &g, Node u, Node v, Arc prev) {
+return g.findArc(u, v, prev);
+}
+};
+}
+/// \brief Finds an arc between two nodes of a digraph.
+///
+/// Finds an arc from node \c u to node \c v in 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
+///
+///\sa ArcLookUp
+///\sa AllArcLookUp
+///\sa DynArcLookUp
+///\sa ConArcIt
+template <typename Digraph>
+inline typename Digraph::Arc
+findArc(const Digraph &g, typename Digraph::Node u, typename Digraph::Node v,
+typename Digraph::Arc prev = INVALID) {
+return _digraph_utils_bits::FindArcSelector<Digraph>::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<Digraph> it(g, src, trg); it != INVALID; ++it) {
+///   ...
+/// }
+///\endcode
+///
+///\sa findArc()
+///\sa ArcLookUp
+///\sa AllArcLookUp
+///\sa DynArcLookUp
+///
+/// \author Balazs Dezso
+template <typename _Digraph>
+class ConArcIt : public _Digraph::Arc {
+public:
+typedef _Digraph Digraph;
+typedef typename Digraph::Arc Parent;
+typedef typename Digraph::Arc Arc;
+typedef typename Digraph::Node Node;
+/// \brief Constructor.
+///
+/// Construct a new ConArcIt iterating on the arcs which
+/// connects the \c u and \c v node.
+ConArcIt(const Digraph& g, Node u, Node v) : digraph(g) {
+Parent::operator=(findArc(digraph, u, v));
+}
+/// \brief Constructor.
+///
+/// Construct a new ConArcIt which continues the iterating from
+/// the \c e arc.
+ConArcIt(const Digraph& g, Arc e) : Parent(e), digraph(g) {}
+/// \brief Increment operator.
+///
+/// It increments the iterator and gives back the next arc.
+ConArcIt& operator++() {
+Parent::operator=(findArc(digraph, digraph.source(*this),
+				 digraph.target(*this), *this));
+return *this;
+}
+private:
+const Digraph& digraph;
+};
+namespace _digraph_utils_bits {
+template <typename Digraph, typename Enable = void>
+struct FindEdgeSelector {
+typedef typename Digraph::Node Node;
+typedef typename Digraph::Edge Edge;
+static Edge find(const Digraph &g, Node u, Node v, Edge e) {
+bool b;
+if (u != v) {
+if (e == INVALID) {
+g.firstInc(e, b, u);
+} else {
+b = g.source(e) == u;
+g.nextInc(e, b);
+}
+while (e != INVALID && (b ? g.target(e) : g.source(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.target(e) != v)) {
+g.nextInc(e, b);
+}
+}
+return e;
+}
+};
+template <typename Digraph>
+struct FindEdgeSelector<
+Digraph,
+typename enable_if<typename Digraph::FindArcTag, void>::type>
+{
+typedef typename Digraph::Node Node;
+typedef typename Digraph::Edge Edge;
+static Edge find(const Digraph &g, Node u, Node v, Edge prev) {
+return g.findEdge(u, v, prev);
+}
+};
+}
+/// \brief Finds an edge between two nodes of a digraph.
+///
+/// Finds an edge from node \c u to node \c v in digraph \c g.
+/// If the node \c u and node \c v is equal then each loop arc
+/// will be enumerated.
+///
+/// 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 ConArcIt
+template <typename Digraph>
+inline typename Digraph::Edge
+findEdge(const Digraph &g, typename Digraph::Node u, typename Digraph::Node v,
+typename Digraph::Edge p = INVALID) {
+return _digraph_utils_bits::FindEdgeSelector<Digraph>::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<Digraph> it(g, src, trg); it != INVALID; ++it) {
+///   ...
+/// }
+///\endcode
+///
+///\sa findEdge()
+///
+/// \author Balazs Dezso
+template <typename _Digraph>
+class ConEdgeIt : public _Digraph::Edge {
+public:
+typedef _Digraph Digraph;
+typedef typename Digraph::Edge Parent;
+typedef typename Digraph::Edge Edge;
+typedef typename Digraph::Node Node;
+/// \brief Constructor.
+///
+/// Construct a new ConEdgeIt iterating on the arcs which
+/// connects the \c u and \c v node.
+ConEdgeIt(const Digraph& g, Node u, Node v) : digraph(g) {
+Parent::operator=(findEdge(digraph, u, v));
+}
+/// \brief Constructor.
+///
+/// Construct a new ConEdgeIt which continues the iterating from
+/// the \c e arc.
+ConEdgeIt(const Digraph& g, Edge e) : Parent(e), digraph(g) {}
+/// \brief Increment operator.
+///
+/// It increments the iterator and gives back the next arc.
+ConEdgeIt& operator++() {
+Parent::operator=(findEdge(digraph, digraph.source(*this),
+				      digraph.target(*this), *this));
+return *this;
+}
+private:
+const Digraph& digraph;
+};
+/// \brief Copy a map.
+///
+/// This function copies the \c from map to the \c to map. It uses the
+/// given iterator to iterate on the data structure and it uses the \c ref
+/// mapping to convert the from's keys to the to's keys.
+template <typename To, typename From,
+	    typename ItemIt, typename Ref>
+void copyMap(To& to, const From& from,
+	       ItemIt it, const Ref& ref) {
+for (; it != INVALID; ++it) {
+to[ref[it]] = from[it];
+}
+}
+/// \brief Copy the from map to the to map.
+///
+/// Copy the \c from map to the \c to map. It uses the given iterator
+/// to iterate on the data structure.
+template <typename To, typename From, typename ItemIt>
+void copyMap(To& to, const From& from, ItemIt it) {
+for (; it != INVALID; ++it) {
+to[it] = from[it];
+}
+}
+namespace _digraph_utils_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.addArc(nodeRefMap[from.source(it)],
+				       nodeRefMap[from.target(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);
+}
+};
+template <typename BpGraph, typename Enable = void>
+struct BpGraphCopySelector {
+template <typename From, typename RedRefMap,
+typename BlueRefMap, typename EdgeRefMap>
+static void copy(BpGraph &to, const From& from,
+RedRefMap& redRefMap, BlueRefMap& blueRefMap,
+EdgeRefMap& edgeRefMap) {
+for (typename From::RedIt it(from); it != INVALID; ++it) {
+redRefMap[it] = to.addRed();
+}
+for (typename From::BlueIt it(from); it != INVALID; ++it) {
+blueRefMap[it] = to.addBlue();
+}
+for (typename From::EdgeIt it(from); it != INVALID; ++it) {
+edgeRefMap[it] = to.addArc(redRefMap[from.red(it)],
+blueRefMap[from.blue(it)]);
+}
+}
+};
+template <typename BpGraph>
+struct BpGraphCopySelector<
+BpGraph,
+typename enable_if<typename BpGraph::BuildTag, void>::type>
+{
+template <typename From, typename RedRefMap,
+typename BlueRefMap, typename EdgeRefMap>
+static void copy(BpGraph &to, const From& from,
+RedRefMap& redRefMap, BlueRefMap& blueRefMap,
+EdgeRefMap& edgeRefMap) {
+to.build(from, redRefMap, blueRefMap, 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.
+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(nodeMapCopies.size()); ++i) {
+delete nodeMapCopies[i];
+}
+for (int i = 0; i < int(arcMapCopies.size()); ++i) {
+delete arcMapCopies[i];
+}
+}
+/// \brief Copies the node references into the given map.
+///
+/// Copies the node references into the given map.
+template <typename NodeRef>
+DigraphCopy& nodeRef(NodeRef& map) {
+nodeMapCopies.push_back(new _digraph_utils_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>
+DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
+nodeMapCopies.push_back(new _digraph_utils_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 to digraph's node type,
+/// and the copied map's key type is the from digraph's node
+/// type.
+template <typename ToMap, typename FromMap>
+DigraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
+nodeMapCopies.push_back(new _digraph_utils_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) {
+nodeMapCopies.push_back(new _digraph_utils_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) {
+arcMapCopies.push_back(new _digraph_utils_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) {
+arcMapCopies.push_back(new _digraph_utils_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) {
+arcMapCopies.push_back(new _digraph_utils_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) {
+arcMapCopies.push_back(new _digraph_utils_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);
+_digraph_utils_bits::DigraphCopySelector<To>::
+copy(to, from, nodeRefMap, arcRefMap);
+for (int i = 0; i < int(nodeMapCopies.size()); ++i) {
+nodeMapCopies[i]->copy(from, nodeRefMap);
+}
+for (int i = 0; i < int(arcMapCopies.size()); ++i) {
+arcMapCopies[i]->copy(from, arcRefMap);
+}
+}
+protected:
+const From& from;
+To& to;
+std::vector<_digraph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* >
+nodeMapCopies;
+std::vector<_digraph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* >
+arcMapCopies;
+};
+/// \brief Copy a digraph to another digraph.
+///
+/// Copy a digraph to another digraph.
+/// The usage of the function:
+///
+///\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 an graph.
+///
+/// Class to copy an graph to another digraph (duplicate a digraph).
+/// The simplest way of using it is through the \c copyGraph() function.
+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.direction(key) ==
+(node_ref[from.source(static_cast<const Edge&>(key))] ==
+to.source(edge_ref[static_cast<const Edge&>(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 DigraphCopy.
+///
+/// It copies the content of the \c _from digraph into the
+/// \c _to digraph.
+GraphCopy(To& _to, const From& _from)
+: from(_from), to(_to) {}
+/// \brief Destructor of the DigraphCopy
+///
+/// Destructor of the DigraphCopy
+~GraphCopy() {
+for (int i = 0; i < int(nodeMapCopies.size()); ++i) {
+delete nodeMapCopies[i];
+}
+for (int i = 0; i < int(arcMapCopies.size()); ++i) {
+delete arcMapCopies[i];
+}
+for (int i = 0; i < int(edgeMapCopies.size()); ++i) {
+delete edgeMapCopies[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) {
+nodeMapCopies.push_back(new _digraph_utils_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) {
+nodeMapCopies.push_back(new _digraph_utils_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 to digraph's node type,
+/// and the copied map's key type is the from digraph's node
+/// type.
+template <typename ToMap, typename FromMap>
+GraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
+nodeMapCopies.push_back(new _digraph_utils_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) {
+nodeMapCopies.push_back(new _digraph_utils_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) {
+arcMapCopies.push_back(new _digraph_utils_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) {
+arcMapCopies.push_back(new _digraph_utils_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>
+GraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
+arcMapCopies.push_back(new _digraph_utils_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) {
+arcMapCopies.push_back(new _digraph_utils_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) {
+edgeMapCopies.push_back(new _digraph_utils_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) {
+edgeMapCopies.push_back(new _digraph_utils_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 digraph.
+/// The new map's key type is the to digraph's edge type,
+/// and the copied map's key type is the from digraph's edge
+/// type.
+template <typename ToMap, typename FromMap>
+GraphCopy& edgeMap(ToMap& tmap, const FromMap& map) {
+edgeMapCopies.push_back(new _digraph_utils_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) {
+edgeMapCopies.push_back(new _digraph_utils_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);
+_digraph_utils_bits::GraphCopySelector<To>::
+copy(to, from, nodeRefMap, edgeRefMap);
+for (int i = 0; i < int(nodeMapCopies.size()); ++i) {
+nodeMapCopies[i]->copy(from, nodeRefMap);
+}
+for (int i = 0; i < int(edgeMapCopies.size()); ++i) {
+edgeMapCopies[i]->copy(from, edgeRefMap);
+}
+for (int i = 0; i < int(arcMapCopies.size()); ++i) {
+arcMapCopies[i]->copy(from, arcRefMap);
+}
+}
+private:
+const From& from;
+To& to;
+std::vector<_digraph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* >
+nodeMapCopies;
+std::vector<_digraph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* >
+arcMapCopies;
+std::vector<_digraph_utils_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
+edgeMapCopies;
+};
+/// \brief Copy an graph to another digraph.
+///
+/// Copy an graph to another digraph.
+/// The usage of the function:
+///
+///\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 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 GraphCopy
+template <typename To, typename From>
+GraphCopy<To, From>
+copyGraph(To& to, const From& from) {
+return GraphCopy<To, From>(to, from);
+}
+/// \brief Class to copy a bipartite digraph.
+///
+/// Class to copy a bipartite digraph to another digraph
+/// (duplicate a digraph).  The simplest way of using it is through
+/// the \c copyBpGraph() function.
+template <typename To, typename From>
+class BpGraphCopy {
+private:
+typedef typename From::Node Node;
+typedef typename From::Red Red;
+typedef typename From::Blue Blue;
+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 RedMap<TNode> RedRefMap;
+typedef typename From::template BlueMap<TNode> BlueRefMap;
+typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
+struct NodeRefMap {
+NodeRefMap(const From& _from, const RedRefMap& _red_ref,
+const BlueRefMap& _blue_ref)
+: from(_from), red_ref(_red_ref), blue_ref(_blue_ref) {}
+typedef typename From::Node Key;
+typedef typename To::Node Value;
+Value operator[](const Key& key) const {
+	return from.red(key) ? red_ref[key] : blue_ref[key];
+}
+const From& from;
+const RedRefMap& red_ref;
+const BlueRefMap& blue_ref;
+};
+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.direction(key) ==
+(node_ref[from.source(static_cast<const Edge&>(key))] ==
+to.source(edge_ref[static_cast<const Edge&>(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 DigraphCopy.
+///
+/// It copies the content of the \c _from digraph into the
+/// \c _to digraph.
+BpGraphCopy(To& _to, const From& _from)
+: from(_from), to(_to) {}
+/// \brief Destructor of the DigraphCopy
+///
+/// Destructor of the DigraphCopy
+~BpGraphCopy() {
+for (int i = 0; i < int(redMapCopies.size()); ++i) {
+delete redMapCopies[i];
+}
+for (int i = 0; i < int(blueMapCopies.size()); ++i) {
+delete blueMapCopies[i];
+}
+for (int i = 0; i < int(nodeMapCopies.size()); ++i) {
+delete nodeMapCopies[i];
+}
+for (int i = 0; i < int(arcMapCopies.size()); ++i) {
+delete arcMapCopies[i];
+}
+for (int i = 0; i < int(edgeMapCopies.size()); ++i) {
+delete edgeMapCopies[i];
+}
+}
+/// \brief Copies the A-node references into the given map.
+///
+/// Copies the A-node references into the given map.
+template <typename RedRef>
+BpGraphCopy& redRef(RedRef& map) {
+redMapCopies.push_back(new _digraph_utils_bits::RefCopy<From, Red,
+RedRefMap, RedRef>(map));
+return *this;
+}
+/// \brief Copies the A-node cross references into the given map.
+///
+/// Copies the A-node cross references (reverse references) into
+/// the given map.
+template <typename RedCrossRef>
+BpGraphCopy& redCrossRef(RedCrossRef& map) {
+redMapCopies.push_back(new _digraph_utils_bits::CrossRefCopy<From,
+Red, RedRefMap, RedCrossRef>(map));
+return *this;
+}
+/// \brief Make copy of the given A-node map.
+///
+/// Makes copy of the given map for the newly created digraph.
+/// The new map's key type is the to digraph's node type,
+/// and the copied map's key type is the from digraph's node
+/// type.
+template <typename ToMap, typename FromMap>
+BpGraphCopy& redMap(ToMap& tmap, const FromMap& map) {
+redMapCopies.push_back(new _digraph_utils_bits::MapCopy<From, Red,
+RedRefMap, ToMap, FromMap>(tmap, map));
+return *this;
+}
+/// \brief Copies the B-node references into the given map.
+///
+/// Copies the B-node references into the given map.
+template <typename BlueRef>
+BpGraphCopy& blueRef(BlueRef& map) {
+blueMapCopies.push_back(new _digraph_utils_bits::RefCopy<From, Blue,
+BlueRefMap, BlueRef>(map));
+return *this;
+}
+/// \brief Copies the B-node cross references into the given map.
+///
+///  Copies the B-node cross references (reverse references) into
+///  the given map.
+template <typename BlueCrossRef>
+BpGraphCopy& blueCrossRef(BlueCrossRef& map) {
+blueMapCopies.push_back(new _digraph_utils_bits::CrossRefCopy<From,
+Blue, BlueRefMap, BlueCrossRef>(map));
+return *this;
+}
+/// \brief Make copy of the given B-node map.
+///
+/// Makes copy of the given map for the newly created digraph.
+/// The new map's key type is the to digraph's node type,
+/// and the copied map's key type is the from digraph's node
+/// type.
+template <typename ToMap, typename FromMap>
+BpGraphCopy& blueMap(ToMap& tmap, const FromMap& map) {
+blueMapCopies.push_back(new _digraph_utils_bits::MapCopy<From, Blue,
+BlueRefMap, ToMap, FromMap>(tmap, map));
+return *this;
+}
+/// \brief Copies the node references into the given map.
+///
+/// Copies the node references into the given map.
+template <typename NodeRef>
+BpGraphCopy& nodeRef(NodeRef& map) {
+nodeMapCopies.push_back(new _digraph_utils_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>
+BpGraphCopy& nodeCrossRef(NodeCrossRef& map) {
+nodeMapCopies.push_back(new _digraph_utils_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 to digraph's node type,
+/// and the copied map's key type is the from digraph's node
+/// type.
+template <typename ToMap, typename FromMap>
+BpGraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
+nodeMapCopies.push_back(new _digraph_utils_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.
+BpGraphCopy& node(TNode& tnode, const Node& snode) {
+nodeMapCopies.push_back(new _digraph_utils_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>
+BpGraphCopy& arcRef(ArcRef& map) {
+arcMapCopies.push_back(new _digraph_utils_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>
+BpGraphCopy& arcCrossRef(ArcCrossRef& map) {
+arcMapCopies.push_back(new _digraph_utils_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>
+BpGraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
+arcMapCopies.push_back(new _digraph_utils_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.
+BpGraphCopy& arc(TArc& tarc, const Arc& sarc) {
+arcMapCopies.push_back(new _digraph_utils_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>
+BpGraphCopy& edgeRef(EdgeRef& map) {
+edgeMapCopies.push_back(new _digraph_utils_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>
+BpGraphCopy& edgeCrossRef(EdgeCrossRef& map) {
+edgeMapCopies.push_back(new _digraph_utils_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 digraph.
+/// The new map's key type is the to digraph's edge type,
+/// and the copied map's key type is the from digraph's edge
+/// type.
+template <typename ToMap, typename FromMap>
+BpGraphCopy& edgeMap(ToMap& tmap, const FromMap& map) {
+edgeMapCopies.push_back(new _digraph_utils_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.
+BpGraphCopy& edge(TEdge& tedge, const Edge& sedge) {
+edgeMapCopies.push_back(new _digraph_utils_bits::ItemCopy<From, Edge,
+EdgeRefMap, TEdge>(tedge, sedge));
+return *this;
+}
+/// \brief Executes the copies.
+///
+/// Executes the copies.
+void run() {
+RedRefMap redRefMap(from);
+BlueRefMap blueRefMap(from);
+NodeRefMap nodeRefMap(from, redRefMap, blueRefMap);
+EdgeRefMap edgeRefMap(from);
+ArcRefMap arcRefMap(to, from, edgeRefMap, nodeRefMap);
+_digraph_utils_bits::BpGraphCopySelector<To>::
+copy(to, from, redRefMap, blueRefMap, edgeRefMap);
+for (int i = 0; i < int(redMapCopies.size()); ++i) {
+redMapCopies[i]->copy(from, redRefMap);
+}
+for (int i = 0; i < int(blueMapCopies.size()); ++i) {
+blueMapCopies[i]->copy(from, blueRefMap);
+}
+for (int i = 0; i < int(nodeMapCopies.size()); ++i) {
+nodeMapCopies[i]->copy(from, nodeRefMap);
+}
+for (int i = 0; i < int(edgeMapCopies.size()); ++i) {
+edgeMapCopies[i]->copy(from, edgeRefMap);
+}
+for (int i = 0; i < int(arcMapCopies.size()); ++i) {
+arcMapCopies[i]->copy(from, arcRefMap);
+}
+}
+private:
+const From& from;
+To& to;
+std::vector<_digraph_utils_bits::MapCopyBase<From, Red, RedRefMap>* >
+redMapCopies;
+std::vector<_digraph_utils_bits::MapCopyBase<From, Blue, BlueRefMap>* >
+blueMapCopies;
+std::vector<_digraph_utils_bits::MapCopyBase<From, Node, NodeRefMap>* >
+nodeMapCopies;
+std::vector<_digraph_utils_bits::MapCopyBase<From, Arc, ArcRefMap>* >
+arcMapCopies;
+std::vector<_digraph_utils_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
+edgeMapCopies;
+};
+/// \brief Copy a bipartite digraph to another digraph.
+///
+/// Copy a bipartite digraph to another digraph.
+/// The usage of the function:
+///
+///\code
+/// copyBpGraph(trg, src).redRef(anr).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 BpGraphCopy
+template <typename To, typename From>
+BpGraphCopy<To, From>
+copyBpGraph(To& to, const From& from) {
+return BpGraphCopy<To, From>(to, from);
+}
+/// @}
+/// \addtogroup digraph_maps
+/// @{
+/// Provides an immutable and unique id for each item in the digraph.
+/// The IdMap class provides a unique and immutable id for each item of the
+/// same type (e.g. node) in the digraph. This id is <ul><li>\b unique:
+/// different items (nodes) get different ids <li>\b immutable: the id of an
+/// item (node) does not change (even if you delete other nodes).  </ul>
+/// Through this map you get access (i.e. can read) the inner id values of
+/// the items stored in the digraph. This map can be inverted with its member
+/// class \c InverseMap.
+///
+template <typename _Digraph, typename _Item>
+class IdMap {
+public:
+typedef _Digraph Digraph;
+typedef int Value;
+typedef _Item Item;
+typedef _Item Key;
+/// \brief Constructor.
+///
+/// Constructor of the map.
+explicit IdMap(const Digraph& _digraph) : digraph(&_digraph) {}
+/// \brief Gives back the \e id of the item.
+///
+/// Gives back the immutable and unique \e id of the item.
+int operator[](const Item& item) const { return digraph->id(item);}
+/// \brief Gives back the item by its id.
+///
+/// Gives back the item by its id.
+Item operator()(int id) { return digraph->fromId(id, Item()); }
+private:
+const Digraph* digraph;
+public:
+/// \brief The class represents the inverse of its owner (IdMap).
+///
+/// The class represents the inverse of its owner (IdMap).
+/// \see inverse()
+class InverseMap {
+public:
+/// \brief Constructor.
+///
+/// Constructor for creating an id-to-item map.
+explicit InverseMap(const Digraph& _digraph) : digraph(&_digraph) {}
+/// \brief Constructor.
+///
+/// Constructor for creating an id-to-item map.
+explicit InverseMap(const IdMap& idMap) : digraph(idMap.digraph) {}
+/// \brief Gives back the given item from its id.
+///
+/// Gives back the given item from its id.
+///
+Item operator[](int id) const { return digraph->fromId(id, Item());}
+private:
+const Digraph* digraph;
+};
+/// \brief Gives back the inverse of the map.
+///
+/// Gives back the inverse of the IdMap.
+InverseMap inverse() const { return InverseMap(*digraph);}
+};
+/// \brief General invertable digraph-map type.
+/// This type provides simple invertable digraph-maps.
+/// The InvertableMap wraps an arbitrary ReadWriteMap
+/// and if a key is set to a new value then store it
+/// in the inverse map.
+///
+/// The values of the map can be accessed
+/// with stl compatible forward iterator.
+///
+/// \param _Digraph The digraph type.
+/// \param _Item The item type of the digraph.
+/// \param _Value The value type of the map.
+///
+/// \see IterableValueMap
+template <typename _Digraph, typename _Item, typename _Value>
+class InvertableMap : protected DefaultMap<_Digraph, _Item, _Value> {
+private:
+typedef DefaultMap<_Digraph, _Item, _Value> Map;
+typedef _Digraph Digraph;
+typedef std::map<_Value, _Item> Container;
+Container invMap;
+public:
+/// The key type of InvertableMap (Node, Arc, Edge).
+typedef typename Map::Key Key;
+/// The value type of the InvertableMap.
+typedef typename Map::Value Value;
+/// \brief Constructor.
+///
+/// Construct a new InvertableMap for the digraph.
+///
+explicit InvertableMap(const Digraph& digraph) : Map(digraph) {}
+/// \brief Forward iterator for values.
+///
+/// This iterator is an stl compatible forward
+/// iterator on the values of the map. The values can
+/// be accessed in the [beginValue, endValue) range.
+///
+class ValueIterator
+: public std::iterator<std::forward_iterator_tag, Value> {
+friend class InvertableMap;
+private:
+ValueIterator(typename Container::const_iterator _it)
+: it(_it) {}
+public:
+ValueIterator() {}
+ValueIterator& operator++() { ++it; return *this; }
+ValueIterator operator++(int) {
+ValueIterator tmp(*this);
+operator++();
+return tmp;
+}
+const Value& operator*() const { return it->first; }
+const Value* operator->() const { return &(it->first); }
+bool operator==(ValueIterator jt) const { return it == jt.it; }
+bool operator!=(ValueIterator jt) const { return it != jt.it; }
+private:
+typename Container::const_iterator it;
+};
+/// \brief Returns an iterator to the first value.
+///
+/// Returns an stl compatible iterator to the
+/// first value of the map. The values of the
+/// map can be accessed in the [beginValue, endValue)
+/// range.
+ValueIterator beginValue() const {
+return ValueIterator(invMap.begin());
+}
+/// \brief Returns an iterator after the last value.
+///
+/// Returns an stl compatible iterator after the
+/// last value of the map. The values of the
+/// map can be accessed in the [beginValue, endValue)
+/// range.
+ValueIterator endValue() const {
+return ValueIterator(invMap.end());
+}
+/// \brief The setter function of the map.
+///
+/// Sets the mapped value.
+void set(const Key& key, const Value& val) {
+Value oldval = Map::operator[](key);
+typename Container::iterator it = invMap.find(oldval);
+if (it != invMap.end() && it->second == key) {
+	invMap.erase(it);
+}
+invMap.insert(make_pair(val, key));
+Map::set(key, val);
+}
+/// \brief The getter function of the map.
+///
+/// It gives back the value associated with the key.
+typename MapTraits<Map>::ConstReturnValue
+operator[](const Key& key) const {
+return Map::operator[](key);
+}
+/// \brief Gives back the item by its value.
+///
+/// Gives back the item by its value.
+Key operator()(const Value& key) const {
+typename Container::const_iterator it = invMap.find(key);
+return it != invMap.end() ? it->second : INVALID;
+}
+protected:
+/// \brief Erase the key from the map.
+///
+/// Erase the key to the map. It is called by the
+/// \c AlterationNotifier.
+virtual void erase(const Key& key) {
+Value val = Map::operator[](key);
+typename Container::iterator it = invMap.find(val);
+if (it != invMap.end() && it->second == key) {
+	invMap.erase(it);
+}
+Map::erase(key);
+}
+/// \brief Erase more keys from the map.
+///
+/// Erase more keys from the map. It is called by the
+/// \c AlterationNotifier.
+virtual void erase(const std::vector<Key>& keys) {
+for (int i = 0; i < int(keys.size()); ++i) {
+	Value val = Map::operator[](keys[i]);
+	typename Container::iterator it = invMap.find(val);
+	if (it != invMap.end() && it->second == keys[i]) {
+	  invMap.erase(it);
+	}
+}
+Map::erase(keys);
+}
+/// \brief Clear the keys from the map and inverse map.
+///
+/// Clear the keys from the map and inverse map. It is called by the
+/// \c AlterationNotifier.
+virtual void clear() {
+invMap.clear();
+Map::clear();
+}
+public:
+/// \brief The inverse map type.
+///
+/// The inverse of this map. The subscript operator of the map
+/// gives back always the item what was last assigned to the value.
+class InverseMap {
+public:
+/// \brief Constructor of the InverseMap.
+///
+/// Constructor of the InverseMap.
+explicit InverseMap(const InvertableMap& _inverted)
+: inverted(_inverted) {}
+/// The value type of the InverseMap.
+typedef typename InvertableMap::Key Value;
+/// The key type of the InverseMap.
+typedef typename InvertableMap::Value Key;
+/// \brief Subscript operator.
+///
+/// Subscript operator. It gives back always the item
+/// what was last assigned to the value.
+Value operator[](const Key& key) const {
+	return inverted(key);
+}
+private:
+const InvertableMap& inverted;
+};
+/// \brief It gives back the just readable inverse map.
+///
+/// It gives back the just readable inverse map.
+InverseMap inverse() const {
+return InverseMap(*this);
+}
+};
+/// \brief Provides a mutable, continuous and unique descriptor for each
+/// item in the digraph.
+///
+/// The DescriptorMap class provides a unique and continuous (but mutable)
+/// descriptor (id) for each item of the same type (e.g. node) in the
+/// digraph. This id is <ul><li>\b unique: different items (nodes) get
+/// different ids <li>\b continuous: the range of the ids is the set of
+/// integers between 0 and \c n-1, where \c n is the number of the items of
+/// this type (e.g. nodes) (so the id of a node can change if you delete an
+/// other node, i.e. this id is mutable).  </ul> This map can be inverted
+/// with its member class \c InverseMap.
+///
+/// \param _Digraph The digraph class the \c DescriptorMap belongs to.
+/// \param _Item The Item is the Key of the Map. It may be Node, Arc or
+/// Edge.
+template <typename _Digraph, typename _Item>
+class DescriptorMap : protected DefaultMap<_Digraph, _Item, int> {
+typedef _Item Item;
+typedef DefaultMap<_Digraph, _Item, int> Map;
+public:
+/// The digraph class of DescriptorMap.
+typedef _Digraph Digraph;
+/// The key type of DescriptorMap (Node, Arc, Edge).
+typedef typename Map::Key Key;
+/// The value type of DescriptorMap.
+typedef typename Map::Value Value;
+/// \brief Constructor.
+///
+/// Constructor for descriptor map.
+explicit DescriptorMap(const Digraph& _digraph) : Map(_digraph) {
+Item it;
+const typename Map::Notifier* nf = Map::notifier();
+for (nf->first(it); it != INVALID; nf->next(it)) {
+	Map::set(it, invMap.size());
+	invMap.push_back(it);
+}
+}
+protected:
+/// \brief Add a new key to the map.
+///
+/// Add a new key to the map. It is called by the
+/// \c AlterationNotifier.
+virtual void add(const Item& item) {
+Map::add(item);
+Map::set(item, invMap.size());
+invMap.push_back(item);
+}
+/// \brief Add more new keys to the map.
+///
+/// Add more new keys to the map. It is called by the
+/// \c AlterationNotifier.
+virtual void add(const std::vector<Item>& items) {
+Map::add(items);
+for (int i = 0; i < int(items.size()); ++i) {
+	Map::set(items[i], invMap.size());
+	invMap.push_back(items[i]);
+}
+}
+/// \brief Erase the key from the map.
+///
+/// Erase the key from the map. It is called by the
+/// \c AlterationNotifier.
+virtual void erase(const Item& item) {
+Map::set(invMap.back(), Map::operator[](item));
+invMap[Map::operator[](item)] = invMap.back();
+invMap.pop_back();
+Map::erase(item);
+}
+/// \brief Erase more keys from the map.
+///
+/// Erase more keys from the map. It is called by the
+/// \c AlterationNotifier.
+virtual void erase(const std::vector<Item>& items) {
+for (int i = 0; i < int(items.size()); ++i) {
+	Map::set(invMap.back(), Map::operator[](items[i]));
+	invMap[Map::operator[](items[i])] = invMap.back();
+	invMap.pop_back();
+}
+Map::erase(items);
+}
+/// \brief Build the unique map.
+///
+/// Build the unique map. It is called by the
+/// \c AlterationNotifier.
+virtual void build() {
+Map::build();
+Item it;
+const typename Map::Notifier* nf = Map::notifier();
+for (nf->first(it); it != INVALID; nf->next(it)) {
+	Map::set(it, invMap.size());
+	invMap.push_back(it);
+}
+}
+/// \brief Clear the keys from the map.
+///
+/// Clear the keys from the map. It is called by the
+/// \c AlterationNotifier.
+virtual void clear() {
+invMap.clear();
+Map::clear();
+}
+public:
+/// \brief Returns the maximal value plus one.
+///
+/// Returns the maximal value plus one in the map.
+unsigned int size() const {
+return invMap.size();
+}
+/// \brief Swaps the position of the two items in the map.
+///
+/// Swaps the position of the two items in the map.
+void swap(const Item& p, const Item& q) {
+int pi = Map::operator[](p);
+int qi = Map::operator[](q);
+Map::set(p, qi);
+invMap[qi] = p;
+Map::set(q, pi);
+invMap[pi] = q;
+}
+/// \brief Gives back the \e descriptor of the item.
+///
+/// Gives back the mutable and unique \e descriptor of the map.
+int operator[](const Item& item) const {
+return Map::operator[](item);
+}
+/// \brief Gives back the item by its descriptor.
+///
+/// Gives back th item by its descriptor.
+Item operator()(int id) const {
+return invMap[id];
+}
+private:
+typedef std::vector<Item> Container;
+Container invMap;
+public:
+/// \brief The inverse map type of DescriptorMap.
+///
+/// The inverse map type of DescriptorMap.
+class InverseMap {
+public:
+/// \brief Constructor of the InverseMap.
+///
+/// Constructor of the InverseMap.
+explicit InverseMap(const DescriptorMap& _inverted)
+	: inverted(_inverted) {}
+/// The value type of the InverseMap.
+typedef typename DescriptorMap::Key Value;
+/// The key type of the InverseMap.
+typedef typename DescriptorMap::Value Key;
+/// \brief Subscript operator.
+///
+/// Subscript operator. It gives back the item
+/// that the descriptor belongs to currently.
+Value operator[](const Key& key) const {
+	return inverted(key);
+}
+/// \brief Size of the map.
+///
+/// Returns the size of the map.
+unsigned int size() const {
+	return inverted.size();
+}
+private:
+const DescriptorMap& inverted;
+};
+/// \brief Gives back the inverse of the map.
+///
+/// Gives back the inverse of the map.
+const InverseMap inverse() const {
+return InverseMap(*this);
+}
+};
+/// \brief Returns the source of the given arc.
+///
+/// The SourceMap gives back the source Node of the given arc.
+/// \see TargetMap
+/// \author Balazs Dezso
+template <typename Digraph>
+class SourceMap {
+public:
+typedef typename Digraph::Node Value;
+typedef typename Digraph::Arc Key;
+/// \brief Constructor
+///
+/// Constructor
+/// \param _digraph The digraph that the map belongs to.
+explicit SourceMap(const Digraph& _digraph) : digraph(_digraph) {}
+/// \brief The subscript operator.
+///
+/// The subscript operator.
+/// \param arc The arc
+/// \return The source of the arc
+Value operator[](const Key& arc) const {
+return digraph.source(arc);
+}
+private:
+const Digraph& digraph;
+};
+/// \brief Returns a \ref SourceMap class.
+///
+/// This function just returns an \ref SourceMap class.
+/// \relates SourceMap
+template <typename Digraph>
+inline SourceMap<Digraph> sourceMap(const Digraph& digraph) {
+return SourceMap<Digraph>(digraph);
+}
+/// \brief Returns the target of the given arc.
+///
+/// The TargetMap gives back the target Node of the given arc.
+/// \see SourceMap
+/// \author Balazs Dezso
+template <typename Digraph>
+class TargetMap {
+public:
+typedef typename Digraph::Node Value;
+typedef typename Digraph::Arc Key;
+/// \brief Constructor
+///
+/// Constructor
+/// \param _digraph The digraph that the map belongs to.
+explicit TargetMap(const Digraph& _digraph) : digraph(_digraph) {}
+/// \brief The subscript operator.
+///
+/// The subscript operator.
+/// \param e The arc
+/// \return The target of the arc
+Value operator[](const Key& e) const {
+return digraph.target(e);
+}
+private:
+const Digraph& digraph;
+};
+/// \brief Returns a \ref TargetMap class.
+///
+/// This function just returns a \ref TargetMap class.
+/// \relates TargetMap
+template <typename Digraph>
+inline TargetMap<Digraph> targetMap(const Digraph& digraph) {
+return TargetMap<Digraph>(digraph);
+}
+/// \brief Returns the "forward" directed arc view of an edge.
+///
+/// Returns the "forward" directed arc view of an edge.
+/// \see BackwardMap
+/// \author Balazs Dezso
+template <typename Digraph>
+class ForwardMap {
+public:
+typedef typename Digraph::Arc Value;
+typedef typename Digraph::Edge Key;
+/// \brief Constructor
+///
+/// Constructor
+/// \param _digraph The digraph that the map belongs to.
+explicit ForwardMap(const Digraph& _digraph) : digraph(_digraph) {}
+/// \brief The subscript operator.
+///
+/// The subscript operator.
+/// \param key An edge
+/// \return The "forward" directed arc view of edge
+Value operator[](const Key& key) const {
+return digraph.direct(key, true);
+}
+private:
+const Digraph& digraph;
+};
+/// \brief Returns a \ref ForwardMap class.
+///
+/// This function just returns an \ref ForwardMap class.
+/// \relates ForwardMap
+template <typename Digraph>
+inline ForwardMap<Digraph> forwardMap(const Digraph& digraph) {
+return ForwardMap<Digraph>(digraph);
+}
+/// \brief Returns the "backward" directed arc view of an edge.
+///
+/// Returns the "backward" directed arc view of an edge.
+/// \see ForwardMap
+/// \author Balazs Dezso
+template <typename Digraph>
+class BackwardMap {
+public:
+typedef typename Digraph::Arc Value;
+typedef typename Digraph::Edge Key;
+/// \brief Constructor
+///
+/// Constructor
+/// \param _digraph The digraph that the map belongs to.
+explicit BackwardMap(const Digraph& _digraph) : digraph(_digraph) {}
+/// \brief The subscript operator.
+///
+/// The subscript operator.
+/// \param key An edge
+/// \return The "backward" directed arc view of edge
+Value operator[](const Key& key) const {
+return digraph.direct(key, false);
+}
+private:
+const Digraph& digraph;
+};
+/// \brief Returns a \ref BackwardMap class
+/// This function just returns a \ref BackwardMap class.
+/// \relates BackwardMap
+template <typename Digraph>
+inline BackwardMap<Digraph> backwardMap(const Digraph& digraph) {
+return BackwardMap<Digraph>(digraph);
+}
+/// \brief Potential difference map
+///
+/// If there is an potential map on the nodes then we
+/// can get an arc map as we get the substraction of the
+/// values of the target and source.
+template <typename Digraph, typename NodeMap>
+class PotentialDifferenceMap {
+public:
+typedef typename Digraph::Arc Key;
+typedef typename NodeMap::Value Value;
+/// \brief Constructor
+///
+/// Contructor of the map
+explicit PotentialDifferenceMap(const Digraph& _digraph,
+const NodeMap& _potential)
+: digraph(_digraph), potential(_potential) {}
+/// \brief Const subscription operator
+///
+/// Const subscription operator
+Value operator[](const Key& arc) const {
+return potential[digraph.target(arc)] - potential[digraph.source(arc)];
+}
+private:
+const Digraph& digraph;
+const NodeMap& potential;
+};
+/// \brief Returns a PotentialDifferenceMap.
+///
+/// This function just returns a PotentialDifferenceMap.
+/// \relates PotentialDifferenceMap
+template <typename Digraph, typename NodeMap>
+PotentialDifferenceMap<Digraph, NodeMap>
+potentialDifferenceMap(const Digraph& digraph, const NodeMap& potential) {
+return PotentialDifferenceMap<Digraph, NodeMap>(digraph, potential);
+}
+/// \brief Map of the node in-degrees.
+///
+/// This map returns the in-degree of a node. Once it is constructed,
+/// the degrees are stored in a standard NodeMap, so each query is done
+/// in constant time. On the other hand, the values are updated automatically
+/// whenever the digraph changes.
+///
+/// \warning Besides addNode() and addArc(), a digraph structure may provide
+/// alternative ways to modify the digraph. The correct behavior of InDegMap
+/// is not guarantied if these additional features are used. For example
+/// the functions \ref ListDigraph::changeSource() "changeSource()",
+/// \ref ListDigraph::changeTarget() "changeTarget()" and
+/// \ref ListDigraph::reverseArc() "reverseArc()"
+/// of \ref ListDigraph will \e not update the degree values correctly.
+///
+/// \sa OutDegMap
+template <typename _Digraph>
+class InDegMap
+: protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
+::ItemNotifier::ObserverBase {
+public:
+typedef _Digraph Digraph;
+typedef int Value;
+typedef typename Digraph::Node Key;
+typedef typename ItemSetTraits<_Digraph, typename _Digraph::Arc>
+::ItemNotifier::ObserverBase Parent;
+private:
+class AutoNodeMap : public DefaultMap<_Digraph, Key, int> {
+public:
+typedef DefaultMap<_Digraph, Key, int> Parent;
+typedef typename Parent::Digraph Digraph;
+AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
+virtual void add(const Key& key) {
+	Parent::add(key);
+	Parent::set(key, 0);
+}
+virtual void add(const std::vector<Key>& keys) {
+	Parent::add(keys);
+	for (int i = 0; i < int(keys.size()); ++i) {
+	  Parent::set(keys[i], 0);
+	}
+}
+virtual void build() {
+	Parent::build();
+	Key it;
+	typename Parent::Notifier* nf = Parent::notifier();
+	for (nf->first(it); it != INVALID; nf->next(it)) {
+	  Parent::set(it, 0);
+	}
+}
+};
+public:
+/// \brief Constructor.
+///
+/// Constructor for creating in-degree map.
+explicit InDegMap(const Digraph& _digraph) : digraph(_digraph), deg(_digraph) {
+Parent::attach(digraph.notifier(typename _Digraph::Arc()));
+for(typename _Digraph::NodeIt it(digraph); it != INVALID; ++it) {
+	deg[it] = countInArcs(digraph, it);
+}
+}
+/// Gives back the in-degree of a Node.
+int operator[](const Key& key) const {
+return deg[key];
+}
+protected:
+typedef typename Digraph::Arc Arc;
+virtual void add(const Arc& arc) {
+++deg[digraph.target(arc)];
+}
+virtual void add(const std::vector<Arc>& arcs) {
+for (int i = 0; i < int(arcs.size()); ++i) {
+++deg[digraph.target(arcs[i])];
+}
+}
+virtual void erase(const Arc& arc) {
+--deg[digraph.target(arc)];
+}
+virtual void erase(const std::vector<Arc>& arcs) {
+for (int i = 0; i < int(arcs.size()); ++i) {
+--deg[digraph.target(arcs[i])];
+}
+}
+virtual void build() {
+for(typename _Digraph::NodeIt it(digraph); it != INVALID; ++it) {
+	deg[it] = countInArcs(digraph, it);
+}
+}
+virtual void clear() {
+for(typename _Digraph::NodeIt it(digraph); it != INVALID; ++it) {
+	deg[it] = 0;
+}
+}
+private:
+const _Digraph& digraph;
+AutoNodeMap deg;
+};
+/// \brief Map of the node out-degrees.
+///
+/// This map returns the out-degree of a node. Once it is constructed,
+/// the degrees are stored in a standard NodeMap, so each query is done
+/// in constant time. On the other hand, the values are updated automatically
+/// whenever the digraph changes.
+///
+/// \warning Besides addNode() and addArc(), a digraph structure may provide
+/// alternative ways to modify the digraph. The correct behavior of OutDegMap
+/// is not guarantied if these additional features are used. For example
+/// the functions \ref ListDigraph::changeSource() "changeSource()",
+/// \ref ListDigraph::changeTarget() "changeTarget()" and
+/// \ref ListDigraph::reverseArc() "reverseArc()"
+/// of \ref ListDigraph will \e not update the degree values correctly.
+///
+/// \sa InDegMap
+template <typename _Digraph>
+class OutDegMap
+: protected ItemSetTraits<_Digraph, typename _Digraph::Arc>
+::ItemNotifier::ObserverBase {
+public:
+typedef typename ItemSetTraits<_Digraph, typename _Digraph::Arc>
+::ItemNotifier::ObserverBase Parent;
+typedef _Digraph Digraph;
+typedef int Value;
+typedef typename Digraph::Node Key;
+private:
+class AutoNodeMap : public DefaultMap<_Digraph, Key, int> {
+public:
+typedef DefaultMap<_Digraph, Key, int> Parent;
+typedef typename Parent::Digraph Digraph;
+AutoNodeMap(const Digraph& digraph) : Parent(digraph, 0) {}
+virtual void add(const Key& key) {
+	Parent::add(key);
+	Parent::set(key, 0);
+}
+virtual void add(const std::vector<Key>& keys) {
+	Parent::add(keys);
+	for (int i = 0; i < int(keys.size()); ++i) {
+	  Parent::set(keys[i], 0);
+	}
+}
+virtual void build() {
+	Parent::build();
+	Key it;
+	typename Parent::Notifier* nf = Parent::notifier();
+	for (nf->first(it); it != INVALID; nf->next(it)) {
+	  Parent::set(it, 0);
+	}
+}
+};
+public:
+/// \brief Constructor.
+///
+/// Constructor for creating out-degree map.
+explicit OutDegMap(const Digraph& _digraph) : digraph(_digraph), deg(_digraph) {
+Parent::attach(digraph.notifier(typename _Digraph::Arc()));
+for(typename _Digraph::NodeIt it(digraph); it != INVALID; ++it) {
+	deg[it] = countOutArcs(digraph, it);
+}
+}
+/// Gives back the out-degree of a Node.
+int operator[](const Key& key) const {
+return deg[key];
+}
+protected:
+typedef typename Digraph::Arc Arc;
+virtual void add(const Arc& arc) {
+++deg[digraph.source(arc)];
+}
+virtual void add(const std::vector<Arc>& arcs) {
+for (int i = 0; i < int(arcs.size()); ++i) {
+++deg[digraph.source(arcs[i])];
+}
+}
+virtual void erase(const Arc& arc) {
+--deg[digraph.source(arc)];
+}
+virtual void erase(const std::vector<Arc>& arcs) {
+for (int i = 0; i < int(arcs.size()); ++i) {
+--deg[digraph.source(arcs[i])];
+}
+}
+virtual void build() {
+for(typename _Digraph::NodeIt it(digraph); it != INVALID; ++it) {
+	deg[it] = countOutArcs(digraph, it);
+}
+}
+virtual void clear() {
+for(typename _Digraph::NodeIt it(digraph); it != INVALID; ++it) {
+	deg[it] = 0;
+}
+}
+private:
+const _Digraph& digraph;
+AutoNodeMap deg;
+};
+///Dynamic arc look up between given endpoints.
+///\ingroup gutils
+///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 do 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.
+///
+///\param 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;
+GRAPH_TYPEDEFS(typename G);
+typedef G Digraph;
+protected:
+class AutoNodeMap : public DefaultMap<G, Node, Arc> {
+public:
+typedef DefaultMap<G, Node, Arc> 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 e = _head[s];
+while (true) {
+	if (_g.target(e) == t) {
+	  const_cast<DynArcLookUp&>(*this).splay(e);
+	  return e;
+	} else if (t < _g.target(e)) {
+	  if (_left[e] == INVALID) {
+	    const_cast<DynArcLookUp&>(*this).splay(e);
+	    return INVALID;
+	  } else {
+	    e = _left[e];
+	  }
+	} else  {
+	  if (_right[e] == INVALID) {
+	    const_cast<DynArcLookUp&>(*this).splay(e);
+	    return INVALID;
+	  } else {
+	    e = _right[e];
+	  }
+	}
+}
+}
+///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 e = _head[s];
+Arc r = INVALID;
+while (true) {
+	if (_g.target(e) < t) {
+	  if (_right[e] == INVALID) {
+	    const_cast<DynArcLookUp&>(*this).splay(e);
+	    return r;
+	  } else {
+	    e = _right[e];
+	  }
+	} else {
+	  if (_g.target(e) == t) {
+	    r = e;
+	  }
+	  if (_left[e] == INVALID) {
+	    const_cast<DynArcLookUp&>(*this).splay(e);
+	    return r;
+	  } else {
+	    e = _left[e];
+	  }
+	}
+}
+}
+///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 e) const
+#else
+Arc findNext(Node, Node t, Arc e) const
+#endif
+{
+if (_right[e] != INVALID) {
+	e = _right[e];
+	while (_left[e] != INVALID) {
+	  e = _left[e];
+	}
+	const_cast<DynArcLookUp&>(*this).splay(e);
+} else {
+	while (_parent[e] != INVALID && _right[_parent[e]] ==  e) {
+	  e = _parent[e];
+	}
+	if (_parent[e] == INVALID) {
+	  return INVALID;
+	} else {
+	  e = _parent[e];
+	  const_cast<DynArcLookUp&>(*this).splay(e);
+	}
+}
+if (_g.target(e) == t) return e;
+else return INVALID;
+}
+};
+///Fast arc look up between given endpoints.
+///\ingroup gutils
+///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).
+///
+///\param G The type of the underlying digraph.
+///
+///\sa DynArcLookUp
+///\sa AllArcLookUp
+template<class G>
+class ArcLookUp
+{
+public:
+GRAPH_TYPEDEFS(typename 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.
+///\ingroup gutils
+///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).
+///
+///\param 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;
+GRAPH_TYPEDEFS(typename 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
+};
+/// @}
+} //END OF NAMESPACE LEMON
+#endif

changeset 121	91c0fed3181e
child 139	701c529ba737