lemon: comparison lemon/core.h

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+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+*
+* This file is a part of LEMON, a generic C++ optimization library.
+*
+* Copyright (C) 2003-2008
+* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+* (Egervary Research Group on Combinatorial Optimization, EGRES).
+*
+* Permission to use, modify and distribute this software is granted
+* provided that this copyright notice appears in all copies. For
+* precise terms see the accompanying LICENSE file.
+*
+* This software is provided "AS IS" with no warranty of any kind,
+* express or implied, and with no claim as to its suitability for any
+* purpose.
+*
+*/
+#ifndef LEMON_CORE_H
+#define LEMON_CORE_H
+#include <vector>
+#include <algorithm>
+#include <lemon/bits/enable_if.h>
+#include <lemon/bits/traits.h>
+///\file
+///\brief LEMON core utilities.
+namespace lemon {
+/// \brief Dummy type to make it easier to create invalid iterators.
+///
+/// Dummy type to make it easier to create invalid iterators.
+/// See \ref INVALID for the usage.
+struct Invalid {
+public:
+bool operator==(Invalid) { return true;  }
+bool operator!=(Invalid) { return false; }
+bool operator< (Invalid) { return false; }
+};
+/// \brief Invalid iterators.
+///
+/// \ref Invalid is a global type that converts to each iterator
+/// in such a way that the value of the target iterator will be invalid.
+#ifdef LEMON_ONLY_TEMPLATES
+const Invalid INVALID = Invalid();
+#else
+extern const Invalid INVALID;
+#endif
+/// \addtogroup gutils
+/// @{
+///Creates convenience typedefs for the digraph types and iterators
+///This \c \#define creates convenience typedefs for the following types
+///of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,
+///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap,
+///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap.
+///
+///\note If the graph type is a dependent type, ie. the graph type depend
+///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
+///macro.
+#define DIGRAPH_TYPEDEFS(Digraph)                                       \
+typedef Digraph::Node Node;                                           \
+typedef Digraph::NodeIt NodeIt;                                       \
+typedef Digraph::Arc Arc;                                             \
+typedef Digraph::ArcIt ArcIt;                                         \
+typedef Digraph::InArcIt InArcIt;                                     \
+typedef Digraph::OutArcIt OutArcIt;                                   \
+typedef Digraph::NodeMap<bool> BoolNodeMap;                           \
+typedef Digraph::NodeMap<int> IntNodeMap;                             \
+typedef Digraph::NodeMap<double> DoubleNodeMap;                       \
+typedef Digraph::ArcMap<bool> BoolArcMap;                             \
+typedef Digraph::ArcMap<int> IntArcMap;                               \
+typedef Digraph::ArcMap<double> DoubleArcMap
+///Creates convenience typedefs for the digraph types and iterators
+///\see DIGRAPH_TYPEDEFS
+///
+///\note Use this macro, if the graph type is a dependent type,
+///ie. the graph type depend on a template parameter.
+#define TEMPLATE_DIGRAPH_TYPEDEFS(Digraph)                              \
+typedef typename Digraph::Node Node;                                  \
+typedef typename Digraph::NodeIt NodeIt;                              \
+typedef typename Digraph::Arc Arc;                                    \
+typedef typename Digraph::ArcIt ArcIt;                                \
+typedef typename Digraph::InArcIt InArcIt;                            \
+typedef typename Digraph::OutArcIt OutArcIt;                          \
+typedef typename Digraph::template NodeMap<bool> BoolNodeMap;         \
+typedef typename Digraph::template NodeMap<int> IntNodeMap;           \
+typedef typename Digraph::template NodeMap<double> DoubleNodeMap;     \
+typedef typename Digraph::template ArcMap<bool> BoolArcMap;           \
+typedef typename Digraph::template ArcMap<int> IntArcMap;             \
+typedef typename Digraph::template ArcMap<double> DoubleArcMap
+///Creates convenience typedefs for the graph types and iterators
+///This \c \#define creates the same convenience typedefs as defined
+///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates
+///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,
+///\c DoubleEdgeMap.
+///
+///\note If the graph type is a dependent type, ie. the graph type depend
+///on a template parameter, then use \c TEMPLATE_DIGRAPH_TYPEDEFS()
+///macro.
+#define GRAPH_TYPEDEFS(Graph)                                           \
+DIGRAPH_TYPEDEFS(Graph);                                              \
+typedef Graph::Edge Edge;                                             \
+typedef Graph::EdgeIt EdgeIt;                                         \
+typedef Graph::IncEdgeIt IncEdgeIt;                                   \
+typedef Graph::EdgeMap<bool> BoolEdgeMap;                             \
+typedef Graph::EdgeMap<int> IntEdgeMap;                               \
+typedef Graph::EdgeMap<double> DoubleEdgeMap
+///Creates convenience typedefs for the graph types and iterators
+///\see GRAPH_TYPEDEFS
+///
+///\note Use this macro, if the graph type is a dependent type,
+///ie. the graph type depend on a template parameter.
+#define TEMPLATE_GRAPH_TYPEDEFS(Graph)                                  \
+TEMPLATE_DIGRAPH_TYPEDEFS(Graph);                                     \
+typedef typename Graph::Edge Edge;                                    \
+typedef typename Graph::EdgeIt EdgeIt;                                \
+typedef typename Graph::IncEdgeIt IncEdgeIt;                          \
+typedef typename Graph::template EdgeMap<bool> BoolEdgeMap;           \
+typedef typename Graph::template EdgeMap<int> IntEdgeMap;             \
+typedef typename Graph::template EdgeMap<double> DoubleEdgeMap
+/// \brief Function to count the items in the graph.
+///
+/// This function counts the items (nodes, arcs etc) in the graph.
+/// The complexity of the function is O(n) because
+/// it iterates on all of the items.
+template <typename Graph, typename Item>
+inline int countItems(const Graph& g) {
+typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;
+int num = 0;
+for (ItemIt it(g); it != INVALID; ++it) {
+++num;
+}
+return num;
+}
+// Node counting:
+namespace _core_bits {
+template <typename Graph, typename Enable = void>
+struct CountNodesSelector {
+static int count(const Graph &g) {
+return countItems<Graph, typename Graph::Node>(g);
+}
+};
+template <typename Graph>
+struct CountNodesSelector<
+Graph, typename
+enable_if<typename Graph::NodeNumTag, void>::type>
+{
+static int count(const Graph &g) {
+return g.nodeNum();
+}
+};
+}
+/// \brief Function to count the nodes in the graph.
+///
+/// This function counts the nodes in the graph.
+/// The complexity of the function is O(n) but for some
+/// graph structures it is specialized to run in O(1).
+///
+/// If the graph contains a \e nodeNum() member function and a
+/// \e NodeNumTag tag then this function calls directly the member
+/// function to query the cardinality of the node set.
+template <typename Graph>
+inline int countNodes(const Graph& g) {
+return _core_bits::CountNodesSelector<Graph>::count(g);
+}
+// Arc counting:
+namespace _core_bits {
+template <typename Graph, typename Enable = void>
+struct CountArcsSelector {
+static int count(const Graph &g) {
+return countItems<Graph, typename Graph::Arc>(g);
+}
+};
+template <typename Graph>
+struct CountArcsSelector<
+Graph,
+typename enable_if<typename Graph::ArcNumTag, void>::type>
+{
+static int count(const Graph &g) {
+return g.arcNum();
+}
+};
+}
+/// \brief Function to count the arcs in the graph.
+///
+/// This function counts the arcs in the graph.
+/// The complexity of the function is O(e) but for some
+/// graph structures it is specialized to run in O(1).
+///
+/// If the graph contains a \e arcNum() member function and a
+/// \e EdgeNumTag tag then this function calls directly the member
+/// function to query the cardinality of the arc set.
+template <typename Graph>
+inline int countArcs(const Graph& g) {
+return _core_bits::CountArcsSelector<Graph>::count(g);
+}
+// Edge counting:
+namespace _core_bits {
+template <typename Graph, typename Enable = void>
+struct CountEdgesSelector {
+static int count(const Graph &g) {
+return countItems<Graph, typename Graph::Edge>(g);
+}
+};
+template <typename Graph>
+struct CountEdgesSelector<
+Graph,
+typename enable_if<typename Graph::EdgeNumTag, void>::type>
+{
+static int count(const Graph &g) {
+return g.edgeNum();
+}
+};
+}
+/// \brief Function to count the edges in the graph.
+///
+/// This function counts the edges in the graph.
+/// The complexity of the function is O(m) but for some
+/// graph structures it is specialized to run in O(1).
+///
+/// If the graph contains a \e edgeNum() member function and a
+/// \e EdgeNumTag tag then this function calls directly the member
+/// function to query the cardinality of the edge set.
+template <typename Graph>
+inline int countEdges(const Graph& g) {
+return _core_bits::CountEdgesSelector<Graph>::count(g);
+}
+template <typename Graph, typename DegIt>
+inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {
+int num = 0;
+for (DegIt it(_g, _n); it != INVALID; ++it) {
+++num;
+}
+return num;
+}
+/// \brief Function to count the number of the out-arcs from node \c n.
+///
+/// This function counts the number of the out-arcs from node \c n
+/// in the graph.
+template <typename Graph>
+inline int countOutArcs(const Graph& _g,  const typename Graph::Node& _n) {
+return countNodeDegree<Graph, typename Graph::OutArcIt>(_g, _n);
+}
+/// \brief Function to count the number of the in-arcs to node \c n.
+///
+/// This function counts the number of the in-arcs to node \c n
+/// in the graph.
+template <typename Graph>
+inline int countInArcs(const Graph& _g,  const typename Graph::Node& _n) {
+return countNodeDegree<Graph, typename Graph::InArcIt>(_g, _n);
+}
+/// \brief Function to count the number of the inc-edges to node \c n.
+///
+/// This function counts the number of the inc-edges to node \c n
+/// in the graph.
+template <typename Graph>
+inline int countIncEdges(const Graph& _g,  const typename Graph::Node& _n) {
+return countNodeDegree<Graph, typename Graph::IncEdgeIt>(_g, _n);
+}
+namespace _core_bits {
+template <typename Digraph, typename Item, typename RefMap>
+class MapCopyBase {
+public:
+virtual void copy(const Digraph& from, const RefMap& refMap) = 0;
+virtual ~MapCopyBase() {}
+};
+template <typename Digraph, typename Item, typename RefMap,
+typename ToMap, typename FromMap>
+class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {
+public:
+MapCopy(ToMap& tmap, const FromMap& map)
+: _tmap(tmap), _map(map) {}
+virtual void copy(const Digraph& digraph, const RefMap& refMap) {
+typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+for (ItemIt it(digraph); it != INVALID; ++it) {
+_tmap.set(refMap[it], _map[it]);
+}
+}
+private:
+ToMap& _tmap;
+const FromMap& _map;
+};
+template <typename Digraph, typename Item, typename RefMap, typename It>
+class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {
+public:
+ItemCopy(It& it, const Item& item) : _it(it), _item(item) {}
+virtual void copy(const Digraph&, const RefMap& refMap) {
+_it = refMap[_item];
+}
+private:
+It& _it;
+Item _item;
+};
+template <typename Digraph, typename Item, typename RefMap, typename Ref>
+class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {
+public:
+RefCopy(Ref& map) : _map(map) {}
+virtual void copy(const Digraph& digraph, const RefMap& refMap) {
+typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+for (ItemIt it(digraph); it != INVALID; ++it) {
+_map.set(it, refMap[it]);
+}
+}
+private:
+Ref& _map;
+};
+template <typename Digraph, typename Item, typename RefMap,
+typename CrossRef>
+class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {
+public:
+CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}
+virtual void copy(const Digraph& digraph, const RefMap& refMap) {
+typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;
+for (ItemIt it(digraph); it != INVALID; ++it) {
+_cmap.set(refMap[it], it);
+}
+}
+private:
+CrossRef& _cmap;
+};
+template <typename Digraph, typename Enable = void>
+struct DigraphCopySelector {
+template <typename From, typename NodeRefMap, typename ArcRefMap>
+static void copy(Digraph &to, const From& from,
+NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
+for (typename From::NodeIt it(from); it != INVALID; ++it) {
+nodeRefMap[it] = to.addNode();
+}
+for (typename From::ArcIt it(from); it != INVALID; ++it) {
+arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)],
+nodeRefMap[from.target(it)]);
+}
+}
+};
+template <typename Digraph>
+struct DigraphCopySelector<
+Digraph,
+typename enable_if<typename Digraph::BuildTag, void>::type>
+{
+template <typename From, typename NodeRefMap, typename ArcRefMap>
+static void copy(Digraph &to, const From& from,
+NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {
+to.build(from, nodeRefMap, arcRefMap);
+}
+};
+template <typename Graph, typename Enable = void>
+struct GraphCopySelector {
+template <typename From, typename NodeRefMap, typename EdgeRefMap>
+static void copy(Graph &to, const From& from,
+NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
+for (typename From::NodeIt it(from); it != INVALID; ++it) {
+nodeRefMap[it] = to.addNode();
+}
+for (typename From::EdgeIt it(from); it != INVALID; ++it) {
+edgeRefMap[it] = to.addEdge(nodeRefMap[from.u(it)],
+nodeRefMap[from.v(it)]);
+}
+}
+};
+template <typename Graph>
+struct GraphCopySelector<
+Graph,
+typename enable_if<typename Graph::BuildTag, void>::type>
+{
+template <typename From, typename NodeRefMap, typename EdgeRefMap>
+static void copy(Graph &to, const From& from,
+NodeRefMap& nodeRefMap, EdgeRefMap& edgeRefMap) {
+to.build(from, nodeRefMap, edgeRefMap);
+}
+};
+}
+/// \brief Class to copy a digraph.
+///
+/// Class to copy a digraph to another digraph (duplicate a digraph). The
+/// simplest way of using it is through the \c copyDigraph() function.
+///
+/// This class not just make a copy of a graph, but it can create
+/// references and cross references between the nodes and arcs of
+/// the two graphs, it can copy maps for use with the newly created
+/// graph and copy nodes and arcs.
+///
+/// To make a copy from a graph, first an instance of DigraphCopy
+/// should be created, then the data belongs to the graph should
+/// assigned to copy. In the end, the \c run() member should be
+/// called.
+///
+/// The next code copies a graph with several data:
+///\code
+///  DigraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
+///  // create a reference for the nodes
+///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
+///  dc.nodeRef(nr);
+///  // create a cross reference (inverse) for the arcs
+///  NewGraph::ArcMap<OrigGraph::Arc> acr(new_graph);
+///  dc.arcCrossRef(acr);
+///  // copy an arc map
+///  OrigGraph::ArcMap<double> oamap(orig_graph);
+///  NewGraph::ArcMap<double> namap(new_graph);
+///  dc.arcMap(namap, oamap);
+///  // copy a node
+///  OrigGraph::Node on;
+///  NewGraph::Node nn;
+///  dc.node(nn, on);
+///  // Executions of copy
+///  dc.run();
+///\endcode
+template <typename To, typename From>
+class DigraphCopy {
+private:
+typedef typename From::Node Node;
+typedef typename From::NodeIt NodeIt;
+typedef typename From::Arc Arc;
+typedef typename From::ArcIt ArcIt;
+typedef typename To::Node TNode;
+typedef typename To::Arc TArc;
+typedef typename From::template NodeMap<TNode> NodeRefMap;
+typedef typename From::template ArcMap<TArc> ArcRefMap;
+public:
+/// \brief Constructor for the DigraphCopy.
+///
+/// It copies the content of the \c _from digraph into the
+/// \c _to digraph.
+DigraphCopy(To& to, const From& from)
+: _from(from), _to(to) {}
+/// \brief Destructor of the DigraphCopy
+///
+/// Destructor of the DigraphCopy
+~DigraphCopy() {
+for (int i = 0; i < int(_node_maps.size()); ++i) {
+delete _node_maps[i];
+}
+for (int i = 0; i < int(_arc_maps.size()); ++i) {
+delete _arc_maps[i];
+}
+}
+/// \brief Copies the node references into the given map.
+///
+/// Copies the node references into the given map. The parameter
+/// should be a map, which key type is the Node type of the source
+/// graph, while the value type is the Node type of the
+/// destination graph.
+template <typename NodeRef>
+DigraphCopy& nodeRef(NodeRef& map) {
+_node_maps.push_back(new _core_bits::RefCopy<From, Node,
+NodeRefMap, NodeRef>(map));
+return *this;
+}
+/// \brief Copies the node cross references into the given map.
+///
+///  Copies the node cross references (reverse references) into
+///  the given map. The parameter should be a map, which key type
+///  is the Node type of the destination graph, while the value type is
+///  the Node type of the source graph.
+template <typename NodeCrossRef>
+DigraphCopy& nodeCrossRef(NodeCrossRef& map) {
+_node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
+NodeRefMap, NodeCrossRef>(map));
+return *this;
+}
+/// \brief Make copy of the given map.
+///
+/// Makes copy of the given map for the newly created digraph.
+/// The new map's key type is the destination graph's node type,
+/// and the copied map's key type is the source graph's node type.
+template <typename ToMap, typename FromMap>
+DigraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
+_node_maps.push_back(new _core_bits::MapCopy<From, Node,
+NodeRefMap, ToMap, FromMap>(tmap, map));
+return *this;
+}
+/// \brief Make a copy of the given node.
+///
+/// Make a copy of the given node.
+DigraphCopy& node(TNode& tnode, const Node& snode) {
+_node_maps.push_back(new _core_bits::ItemCopy<From, Node,
+NodeRefMap, TNode>(tnode, snode));
+return *this;
+}
+/// \brief Copies the arc references into the given map.
+///
+/// Copies the arc references into the given map.
+template <typename ArcRef>
+DigraphCopy& arcRef(ArcRef& map) {
+_arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
+ArcRefMap, ArcRef>(map));
+return *this;
+}
+/// \brief Copies the arc cross references into the given map.
+///
+///  Copies the arc cross references (reverse references) into
+///  the given map.
+template <typename ArcCrossRef>
+DigraphCopy& arcCrossRef(ArcCrossRef& map) {
+_arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
+ArcRefMap, ArcCrossRef>(map));
+return *this;
+}
+/// \brief Make copy of the given map.
+///
+/// Makes copy of the given map for the newly created digraph.
+/// The new map's key type is the to digraph's arc type,
+/// and the copied map's key type is the from digraph's arc
+/// type.
+template <typename ToMap, typename FromMap>
+DigraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
+_arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
+ArcRefMap, ToMap, FromMap>(tmap, map));
+return *this;
+}
+/// \brief Make a copy of the given arc.
+///
+/// Make a copy of the given arc.
+DigraphCopy& arc(TArc& tarc, const Arc& sarc) {
+_arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
+ArcRefMap, TArc>(tarc, sarc));
+return *this;
+}
+/// \brief Executes the copies.
+///
+/// Executes the copies.
+void run() {
+NodeRefMap nodeRefMap(_from);
+ArcRefMap arcRefMap(_from);
+_core_bits::DigraphCopySelector<To>::
+copy(_to, _from, nodeRefMap, arcRefMap);
+for (int i = 0; i < int(_node_maps.size()); ++i) {
+_node_maps[i]->copy(_from, nodeRefMap);
+}
+for (int i = 0; i < int(_arc_maps.size()); ++i) {
+_arc_maps[i]->copy(_from, arcRefMap);
+}
+}
+protected:
+const From& _from;
+To& _to;
+std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
+_node_maps;
+std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
+_arc_maps;
+};
+/// \brief Copy a digraph to another digraph.
+///
+/// Copy a digraph to another digraph. The complete usage of the
+/// function is detailed in the DigraphCopy class, but a short
+/// example shows a basic work:
+///\code
+/// copyDigraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
+///\endcode
+///
+/// After the copy the \c nr map will contain the mapping from the
+/// nodes of the \c from digraph to the nodes of the \c to digraph and
+/// \c ecr will contain the mapping from the arcs of the \c to digraph
+/// to the arcs of the \c from digraph.
+///
+/// \see DigraphCopy
+template <typename To, typename From>
+DigraphCopy<To, From> copyDigraph(To& to, const From& from) {
+return DigraphCopy<To, From>(to, from);
+}
+/// \brief Class to copy a graph.
+///
+/// Class to copy a graph to another graph (duplicate a graph). The
+/// simplest way of using it is through the \c copyGraph() function.
+///
+/// This class not just make a copy of a graph, but it can create
+/// references and cross references between the nodes, edges and arcs of
+/// the two graphs, it can copy maps for use with the newly created
+/// graph and copy nodes, edges and arcs.
+///
+/// To make a copy from a graph, first an instance of GraphCopy
+/// should be created, then the data belongs to the graph should
+/// assigned to copy. In the end, the \c run() member should be
+/// called.
+///
+/// The next code copies a graph with several data:
+///\code
+///  GraphCopy<NewGraph, OrigGraph> dc(new_graph, orig_graph);
+///  // create a reference for the nodes
+///  OrigGraph::NodeMap<NewGraph::Node> nr(orig_graph);
+///  dc.nodeRef(nr);
+///  // create a cross reference (inverse) for the edges
+///  NewGraph::EdgeMap<OrigGraph::Arc> ecr(new_graph);
+///  dc.edgeCrossRef(ecr);
+///  // copy an arc map
+///  OrigGraph::ArcMap<double> oamap(orig_graph);
+///  NewGraph::ArcMap<double> namap(new_graph);
+///  dc.arcMap(namap, oamap);
+///  // copy a node
+///  OrigGraph::Node on;
+///  NewGraph::Node nn;
+///  dc.node(nn, on);
+///  // Executions of copy
+///  dc.run();
+///\endcode
+template <typename To, typename From>
+class GraphCopy {
+private:
+typedef typename From::Node Node;
+typedef typename From::NodeIt NodeIt;
+typedef typename From::Arc Arc;
+typedef typename From::ArcIt ArcIt;
+typedef typename From::Edge Edge;
+typedef typename From::EdgeIt EdgeIt;
+typedef typename To::Node TNode;
+typedef typename To::Arc TArc;
+typedef typename To::Edge TEdge;
+typedef typename From::template NodeMap<TNode> NodeRefMap;
+typedef typename From::template EdgeMap<TEdge> EdgeRefMap;
+struct ArcRefMap {
+ArcRefMap(const To& to, const From& from,
+const EdgeRefMap& edge_ref, const NodeRefMap& node_ref)
+: _to(to), _from(from),
+_edge_ref(edge_ref), _node_ref(node_ref) {}
+typedef typename From::Arc Key;
+typedef typename To::Arc Value;
+Value operator[](const Key& key) const {
+bool forward = _from.u(key) != _from.v(key) ?
+_node_ref[_from.source(key)] ==
+_to.source(_to.direct(_edge_ref[key], true)) :
+_from.direction(key);
+return _to.direct(_edge_ref[key], forward);
+}
+const To& _to;
+const From& _from;
+const EdgeRefMap& _edge_ref;
+const NodeRefMap& _node_ref;
+};
+public:
+/// \brief Constructor for the GraphCopy.
+///
+/// It copies the content of the \c _from graph into the
+/// \c _to graph.
+GraphCopy(To& to, const From& from)
+: _from(from), _to(to) {}
+/// \brief Destructor of the GraphCopy
+///
+/// Destructor of the GraphCopy
+~GraphCopy() {
+for (int i = 0; i < int(_node_maps.size()); ++i) {
+delete _node_maps[i];
+}
+for (int i = 0; i < int(_arc_maps.size()); ++i) {
+delete _arc_maps[i];
+}
+for (int i = 0; i < int(_edge_maps.size()); ++i) {
+delete _edge_maps[i];
+}
+}
+/// \brief Copies the node references into the given map.
+///
+/// Copies the node references into the given map.
+template <typename NodeRef>
+GraphCopy& nodeRef(NodeRef& map) {
+_node_maps.push_back(new _core_bits::RefCopy<From, Node,
+NodeRefMap, NodeRef>(map));
+return *this;
+}
+/// \brief Copies the node cross references into the given map.
+///
+///  Copies the node cross references (reverse references) into
+///  the given map.
+template <typename NodeCrossRef>
+GraphCopy& nodeCrossRef(NodeCrossRef& map) {
+_node_maps.push_back(new _core_bits::CrossRefCopy<From, Node,
+NodeRefMap, NodeCrossRef>(map));
+return *this;
+}
+/// \brief Make copy of the given map.
+///
+/// Makes copy of the given map for the newly created graph.
+/// The new map's key type is the to graph's node type,
+/// and the copied map's key type is the from graph's node
+/// type.
+template <typename ToMap, typename FromMap>
+GraphCopy& nodeMap(ToMap& tmap, const FromMap& map) {
+_node_maps.push_back(new _core_bits::MapCopy<From, Node,
+NodeRefMap, ToMap, FromMap>(tmap, map));
+return *this;
+}
+/// \brief Make a copy of the given node.
+///
+/// Make a copy of the given node.
+GraphCopy& node(TNode& tnode, const Node& snode) {
+_node_maps.push_back(new _core_bits::ItemCopy<From, Node,
+NodeRefMap, TNode>(tnode, snode));
+return *this;
+}
+/// \brief Copies the arc references into the given map.
+///
+/// Copies the arc references into the given map.
+template <typename ArcRef>
+GraphCopy& arcRef(ArcRef& map) {
+_arc_maps.push_back(new _core_bits::RefCopy<From, Arc,
+ArcRefMap, ArcRef>(map));
+return *this;
+}
+/// \brief Copies the arc cross references into the given map.
+///
+///  Copies the arc cross references (reverse references) into
+///  the given map.
+template <typename ArcCrossRef>
+GraphCopy& arcCrossRef(ArcCrossRef& map) {
+_arc_maps.push_back(new _core_bits::CrossRefCopy<From, Arc,
+ArcRefMap, ArcCrossRef>(map));
+return *this;
+}
+/// \brief Make copy of the given map.
+///
+/// Makes copy of the given map for the newly created graph.
+/// The new map's key type is the to graph's arc type,
+/// and the copied map's key type is the from graph's arc
+/// type.
+template <typename ToMap, typename FromMap>
+GraphCopy& arcMap(ToMap& tmap, const FromMap& map) {
+_arc_maps.push_back(new _core_bits::MapCopy<From, Arc,
+ArcRefMap, ToMap, FromMap>(tmap, map));
+return *this;
+}
+/// \brief Make a copy of the given arc.
+///
+/// Make a copy of the given arc.
+GraphCopy& arc(TArc& tarc, const Arc& sarc) {
+_arc_maps.push_back(new _core_bits::ItemCopy<From, Arc,
+ArcRefMap, TArc>(tarc, sarc));
+return *this;
+}
+/// \brief Copies the edge references into the given map.
+///
+/// Copies the edge references into the given map.
+template <typename EdgeRef>
+GraphCopy& edgeRef(EdgeRef& map) {
+_edge_maps.push_back(new _core_bits::RefCopy<From, Edge,
+EdgeRefMap, EdgeRef>(map));
+return *this;
+}
+/// \brief Copies the edge cross references into the given map.
+///
+/// Copies the edge cross references (reverse
+/// references) into the given map.
+template <typename EdgeCrossRef>
+GraphCopy& edgeCrossRef(EdgeCrossRef& map) {
+_edge_maps.push_back(new _core_bits::CrossRefCopy<From,
+Edge, EdgeRefMap, EdgeCrossRef>(map));
+return *this;
+}
+/// \brief Make copy of the given map.
+///
+/// Makes copy of the given map for the newly created graph.
+/// The new map's key type is the to graph's edge type,
+/// and the copied map's key type is the from graph's edge
+/// type.
+template <typename ToMap, typename FromMap>
+GraphCopy& edgeMap(ToMap& tmap, const FromMap& map) {
+_edge_maps.push_back(new _core_bits::MapCopy<From, Edge,
+EdgeRefMap, ToMap, FromMap>(tmap, map));
+return *this;
+}
+/// \brief Make a copy of the given edge.
+///
+/// Make a copy of the given edge.
+GraphCopy& edge(TEdge& tedge, const Edge& sedge) {
+_edge_maps.push_back(new _core_bits::ItemCopy<From, Edge,
+EdgeRefMap, TEdge>(tedge, sedge));
+return *this;
+}
+/// \brief Executes the copies.
+///
+/// Executes the copies.
+void run() {
+NodeRefMap nodeRefMap(_from);
+EdgeRefMap edgeRefMap(_from);
+ArcRefMap arcRefMap(_to, _from, edgeRefMap, nodeRefMap);
+_core_bits::GraphCopySelector<To>::
+copy(_to, _from, nodeRefMap, edgeRefMap);
+for (int i = 0; i < int(_node_maps.size()); ++i) {
+_node_maps[i]->copy(_from, nodeRefMap);
+}
+for (int i = 0; i < int(_edge_maps.size()); ++i) {
+_edge_maps[i]->copy(_from, edgeRefMap);
+}
+for (int i = 0; i < int(_arc_maps.size()); ++i) {
+_arc_maps[i]->copy(_from, arcRefMap);
+}
+}
+private:
+const From& _from;
+To& _to;
+std::vector<_core_bits::MapCopyBase<From, Node, NodeRefMap>* >
+_node_maps;
+std::vector<_core_bits::MapCopyBase<From, Arc, ArcRefMap>* >
+_arc_maps;
+std::vector<_core_bits::MapCopyBase<From, Edge, EdgeRefMap>* >
+_edge_maps;
+};
+/// \brief Copy a graph to another graph.
+///
+/// Copy a graph to another graph. The complete usage of the
+/// function is detailed in the GraphCopy class, but a short
+/// example shows a basic work:
+///\code
+/// copyGraph(trg, src).nodeRef(nr).arcCrossRef(ecr).run();
+///\endcode
+///
+/// After the copy the \c nr map will contain the mapping from the
+/// nodes of the \c from graph to the nodes of the \c to graph and
+/// \c ecr will contain the mapping from the arcs of the \c to graph
+/// to the arcs of the \c from graph.
+///
+/// \see GraphCopy
+template <typename To, typename From>
+GraphCopy<To, From>
+copyGraph(To& to, const From& from) {
+return GraphCopy<To, From>(to, from);
+}
+namespace _core_bits {
+template <typename Graph, typename Enable = void>
+struct FindArcSelector {
+typedef typename Graph::Node Node;
+typedef typename Graph::Arc Arc;
+static Arc find(const Graph &g, Node u, Node v, Arc e) {
+if (e == INVALID) {
+g.firstOut(e, u);
+} else {
+g.nextOut(e);
+}
+while (e != INVALID && g.target(e) != v) {
+g.nextOut(e);
+}
+return e;
+}
+};
+template <typename Graph>
+struct FindArcSelector<
+Graph,
+typename enable_if<typename Graph::FindEdgeTag, void>::type>
+{
+typedef typename Graph::Node Node;
+typedef typename Graph::Arc Arc;
+static Arc find(const Graph &g, Node u, Node v, Arc prev) {
+return g.findArc(u, v, prev);
+}
+};
+}
+/// \brief Finds an arc between two nodes of a graph.
+///
+/// Finds an arc from node \c u to node \c v in graph \c g.
+///
+/// If \c prev is \ref INVALID (this is the default value), then
+/// it finds the first arc from \c u to \c v. Otherwise it looks for
+/// the next arc from \c u to \c v after \c prev.
+/// \return The found arc or \ref INVALID if there is no such an arc.
+///
+/// Thus you can iterate through each arc from \c u to \c v as it follows.
+///\code
+/// for(Arc e=findArc(g,u,v);e!=INVALID;e=findArc(g,u,v,e)) {
+///   ...
+/// }
+///\endcode
+///
+///\sa ArcLookUp
+///\sa AllArcLookUp
+///\sa DynArcLookUp
+///\sa ConArcIt
+template <typename Graph>
+inline typename Graph::Arc
+findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,
+typename Graph::Arc prev = INVALID) {
+return _core_bits::FindArcSelector<Graph>::find(g, u, v, prev);
+}
+/// \brief Iterator for iterating on arcs connected the same nodes.
+///
+/// Iterator for iterating on arcs connected the same nodes. It is
+/// higher level interface for the findArc() function. You can
+/// use it the following way:
+///\code
+/// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {
+///   ...
+/// }
+///\endcode
+///
+///\sa findArc()
+///\sa ArcLookUp
+///\sa AllArcLookUp
+///\sa DynArcLookUp
+template <typename _Graph>
+class ConArcIt : public _Graph::Arc {
+public:
+typedef _Graph Graph;
+typedef typename Graph::Arc Parent;
+typedef typename Graph::Arc Arc;
+typedef typename Graph::Node Node;
+/// \brief Constructor.
+///
+/// Construct a new ConArcIt iterating on the arcs which
+/// connects the \c u and \c v node.
+ConArcIt(const Graph& g, Node u, Node v) : _graph(g) {
+Parent::operator=(findArc(_graph, u, v));
+}
+/// \brief Constructor.
+///
+/// Construct a new ConArcIt which continues the iterating from
+/// the \c e arc.
+ConArcIt(const Graph& g, Arc a) : Parent(a), _graph(g) {}
+/// \brief Increment operator.
+///
+/// It increments the iterator and gives back the next arc.
+ConArcIt& operator++() {
+Parent::operator=(findArc(_graph, _graph.source(*this),
+_graph.target(*this), *this));
+return *this;
+}
+private:
+const Graph& _graph;
+};
+namespace _core_bits {
+template <typename Graph, typename Enable = void>
+struct FindEdgeSelector {
+typedef typename Graph::Node Node;
+typedef typename Graph::Edge Edge;
+static Edge find(const Graph &g, Node u, Node v, Edge e) {
+bool b;
+if (u != v) {
+if (e == INVALID) {
+g.firstInc(e, b, u);
+} else {
+b = g.u(e) == u;
+g.nextInc(e, b);
+}
+while (e != INVALID && (b ? g.v(e) : g.u(e)) != v) {
+g.nextInc(e, b);
+}
+} else {
+if (e == INVALID) {
+g.firstInc(e, b, u);
+} else {
+b = true;
+g.nextInc(e, b);
+}
+while (e != INVALID && (!b || g.v(e) != v)) {
+g.nextInc(e, b);
+}
+}
+return e;
+}
+};
+template <typename Graph>
+struct FindEdgeSelector<
+Graph,
+typename enable_if<typename Graph::FindEdgeTag, void>::type>
+{
+typedef typename Graph::Node Node;
+typedef typename Graph::Edge Edge;
+static Edge find(const Graph &g, Node u, Node v, Edge prev) {
+return g.findEdge(u, v, prev);
+}
+};
+}
+/// \brief Finds an edge between two nodes of a graph.
+///
+/// Finds an edge from node \c u to node \c v in graph \c g.
+/// If the node \c u and node \c v is equal then each loop edge
+/// will be enumerated once.
+///
+/// If \c prev is \ref INVALID (this is the default value), then
+/// it finds the first arc from \c u to \c v. Otherwise it looks for
+/// the next arc from \c u to \c v after \c prev.
+/// \return The found arc or \ref INVALID if there is no such an arc.
+///
+/// Thus you can iterate through each arc from \c u to \c v as it follows.
+///\code
+/// for(Edge e = findEdge(g,u,v); e != INVALID;
+///     e = findEdge(g,u,v,e)) {
+///   ...
+/// }
+///\endcode
+///
+///\sa ConEdgeIt
+template <typename Graph>
+inline typename Graph::Edge
+findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,
+typename Graph::Edge p = INVALID) {
+return _core_bits::FindEdgeSelector<Graph>::find(g, u, v, p);
+}
+/// \brief Iterator for iterating on edges connected the same nodes.
+///
+/// Iterator for iterating on edges connected the same nodes. It is
+/// higher level interface for the findEdge() function. You can
+/// use it the following way:
+///\code
+/// for (ConEdgeIt<Graph> it(g, src, trg); it != INVALID; ++it) {
+///   ...
+/// }
+///\endcode
+///
+///\sa findEdge()
+template <typename _Graph>
+class ConEdgeIt : public _Graph::Edge {
+public:
+typedef _Graph Graph;
+typedef typename Graph::Edge Parent;
+typedef typename Graph::Edge Edge;
+typedef typename Graph::Node Node;
+/// \brief Constructor.
+///
+/// Construct a new ConEdgeIt iterating on the edges which
+/// connects the \c u and \c v node.
+ConEdgeIt(const Graph& g, Node u, Node v) : _graph(g) {
+Parent::operator=(findEdge(_graph, u, v));
+}
+/// \brief Constructor.
+///
+/// Construct a new ConEdgeIt which continues the iterating from
+/// the \c e edge.
+ConEdgeIt(const Graph& g, Edge e) : Parent(e), _graph(g) {}
+/// \brief Increment operator.
+///
+/// It increments the iterator and gives back the next edge.
+ConEdgeIt& operator++() {
+Parent::operator=(findEdge(_graph, _graph.u(*this),
+_graph.v(*this), *this));
+return *this;
+}
+private:
+const Graph& _graph;
+};
+///Dynamic arc look up between given endpoints.
+///Using this class, you can find an arc in a digraph from a given
+///source to a given target in amortized time <em>O(log d)</em>,
+///where <em>d</em> is the out-degree of the source node.
+///
+///It is possible to find \e all parallel arcs between two nodes with
+///the \c findFirst() and \c findNext() members.
+///
+///See the \ref ArcLookUp and \ref AllArcLookUp classes if your
+///digraph is not changed so frequently.
+///
+///This class uses a self-adjusting binary search tree, Sleator's
+///and Tarjan's Splay tree for guarantee the logarithmic amortized
+///time bound for arc lookups. This class also guarantees the
+///optimal time bound in a constant factor for any distribution of
+///queries.
+///
+///\tparam G The type of the underlying digraph.
+///
+///\sa ArcLookUp
+///\sa AllArcLookUp
+template<class G>
+class DynArcLookUp
+: protected ItemSetTraits<G, typename G::Arc>::ItemNotifier::ObserverBase
+{
+public:
+typedef typename ItemSetTraits<G, typename G::Arc>
+::ItemNotifier::ObserverBase Parent;
+TEMPLATE_DIGRAPH_TYPEDEFS(G);
+typedef G Digraph;
+protected:
+class AutoNodeMap : public ItemSetTraits<G, Node>::template Map<Arc>::Type {
+public:
+typedef typename ItemSetTraits<G, Node>::template Map<Arc>::Type Parent;
+AutoNodeMap(const G& digraph) : Parent(digraph, INVALID) {}
+virtual void add(const Node& node) {
+Parent::add(node);
+Parent::set(node, INVALID);
+}
+virtual void add(const std::vector<Node>& nodes) {
+Parent::add(nodes);
+for (int i = 0; i < int(nodes.size()); ++i) {
+Parent::set(nodes[i], INVALID);
+}
+}
+virtual void build() {
+Parent::build();
+Node it;
+typename Parent::Notifier* nf = Parent::notifier();
+for (nf->first(it); it != INVALID; nf->next(it)) {
+Parent::set(it, INVALID);
+}
+}
+};
+const Digraph &_g;
+AutoNodeMap _head;
+typename Digraph::template ArcMap<Arc> _parent;
+typename Digraph::template ArcMap<Arc> _left;
+typename Digraph::template ArcMap<Arc> _right;
+class ArcLess {
+const Digraph &g;
+public:
+ArcLess(const Digraph &_g) : g(_g) {}
+bool operator()(Arc a,Arc b) const
+{
+return g.target(a)<g.target(b);
+}
+};
+public:
+///Constructor
+///Constructor.
+///
+///It builds up the search database.
+DynArcLookUp(const Digraph &g)
+: _g(g),_head(g),_parent(g),_left(g),_right(g)
+{
+Parent::attach(_g.notifier(typename Digraph::Arc()));
+refresh();
+}
+protected:
+virtual void add(const Arc& arc) {
+insert(arc);
+}
+virtual void add(const std::vector<Arc>& arcs) {
+for (int i = 0; i < int(arcs.size()); ++i) {
+insert(arcs[i]);
+}
+}
+virtual void erase(const Arc& arc) {
+remove(arc);
+}
+virtual void erase(const std::vector<Arc>& arcs) {
+for (int i = 0; i < int(arcs.size()); ++i) {
+remove(arcs[i]);
+}
+}
+virtual void build() {
+refresh();
+}
+virtual void clear() {
+for(NodeIt n(_g);n!=INVALID;++n) {
+_head.set(n, INVALID);
+}
+}
+void insert(Arc arc) {
+Node s = _g.source(arc);
+Node t = _g.target(arc);
+_left.set(arc, INVALID);
+_right.set(arc, INVALID);
+Arc e = _head[s];
+if (e == INVALID) {
+_head.set(s, arc);
+_parent.set(arc, INVALID);
+return;
+}
+while (true) {
+if (t < _g.target(e)) {
+if (_left[e] == INVALID) {
+_left.set(e, arc);
+_parent.set(arc, e);
+splay(arc);
+return;
+} else {
+e = _left[e];
+}
+} else {
+if (_right[e] == INVALID) {
+_right.set(e, arc);
+_parent.set(arc, e);
+splay(arc);
+return;
+} else {
+e = _right[e];
+}
+}
+}
+}
+void remove(Arc arc) {
+if (_left[arc] == INVALID) {
+if (_right[arc] != INVALID) {
+_parent.set(_right[arc], _parent[arc]);
+}
+if (_parent[arc] != INVALID) {
+if (_left[_parent[arc]] == arc) {
+_left.set(_parent[arc], _right[arc]);
+} else {
+_right.set(_parent[arc], _right[arc]);
+}
+} else {
+_head.set(_g.source(arc), _right[arc]);
+}
+} else if (_right[arc] == INVALID) {
+_parent.set(_left[arc], _parent[arc]);
+if (_parent[arc] != INVALID) {
+if (_left[_parent[arc]] == arc) {
+_left.set(_parent[arc], _left[arc]);
+} else {
+_right.set(_parent[arc], _left[arc]);
+}
+} else {
+_head.set(_g.source(arc), _left[arc]);
+}
+} else {
+Arc e = _left[arc];
+if (_right[e] != INVALID) {
+e = _right[e];
+while (_right[e] != INVALID) {
+e = _right[e];
+}
+Arc s = _parent[e];
+_right.set(_parent[e], _left[e]);
+if (_left[e] != INVALID) {
+_parent.set(_left[e], _parent[e]);
+}
+_left.set(e, _left[arc]);
+_parent.set(_left[arc], e);
+_right.set(e, _right[arc]);
+_parent.set(_right[arc], e);
+_parent.set(e, _parent[arc]);
+if (_parent[arc] != INVALID) {
+if (_left[_parent[arc]] == arc) {
+_left.set(_parent[arc], e);
+} else {
+_right.set(_parent[arc], e);
+}
+}
+splay(s);
+} else {
+_right.set(e, _right[arc]);
+_parent.set(_right[arc], e);
+if (_parent[arc] != INVALID) {
+if (_left[_parent[arc]] == arc) {
+_left.set(_parent[arc], e);
+} else {
+_right.set(_parent[arc], e);
+}
+} else {
+_head.set(_g.source(arc), e);
+}
+}
+}
+}
+Arc refreshRec(std::vector<Arc> &v,int a,int b)
+{
+int m=(a+b)/2;
+Arc me=v[m];
+if (a < m) {
+Arc left = refreshRec(v,a,m-1);
+_left.set(me, left);
+_parent.set(left, me);
+} else {
+_left.set(me, INVALID);
+}
+if (m < b) {
+Arc right = refreshRec(v,m+1,b);
+_right.set(me, right);
+_parent.set(right, me);
+} else {
+_right.set(me, INVALID);
+}
+return me;
+}
+void refresh() {
+for(NodeIt n(_g);n!=INVALID;++n) {
+std::vector<Arc> v;
+for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
+if(v.size()) {
+std::sort(v.begin(),v.end(),ArcLess(_g));
+Arc head = refreshRec(v,0,v.size()-1);
+_head.set(n, head);
+_parent.set(head, INVALID);
+}
+else _head.set(n, INVALID);
+}
+}
+void zig(Arc v) {
+Arc w = _parent[v];
+_parent.set(v, _parent[w]);
+_parent.set(w, v);
+_left.set(w, _right[v]);
+_right.set(v, w);
+if (_parent[v] != INVALID) {
+if (_right[_parent[v]] == w) {
+_right.set(_parent[v], v);
+} else {
+_left.set(_parent[v], v);
+}
+}
+if (_left[w] != INVALID){
+_parent.set(_left[w], w);
+}
+}
+void zag(Arc v) {
+Arc w = _parent[v];
+_parent.set(v, _parent[w]);
+_parent.set(w, v);
+_right.set(w, _left[v]);
+_left.set(v, w);
+if (_parent[v] != INVALID){
+if (_left[_parent[v]] == w) {
+_left.set(_parent[v], v);
+} else {
+_right.set(_parent[v], v);
+}
+}
+if (_right[w] != INVALID){
+_parent.set(_right[w], w);
+}
+}
+void splay(Arc v) {
+while (_parent[v] != INVALID) {
+if (v == _left[_parent[v]]) {
+if (_parent[_parent[v]] == INVALID) {
+zig(v);
+} else {
+if (_parent[v] == _left[_parent[_parent[v]]]) {
+zig(_parent[v]);
+zig(v);
+} else {
+zig(v);
+zag(v);
+}
+}
+} else {
+if (_parent[_parent[v]] == INVALID) {
+zag(v);
+} else {
+if (_parent[v] == _left[_parent[_parent[v]]]) {
+zag(v);
+zig(v);
+} else {
+zag(_parent[v]);
+zag(v);
+}
+}
+}
+}
+_head[_g.source(v)] = v;
+}
+public:
+///Find an arc between two nodes.
+///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
+/// <em>d</em> is the number of outgoing arcs of \c s.
+///\param s The source node
+///\param t The target node
+///\return An arc from \c s to \c t if there exists,
+///\ref INVALID otherwise.
+Arc operator()(Node s, Node t) const
+{
+Arc a = _head[s];
+while (true) {
+if (_g.target(a) == t) {
+const_cast<DynArcLookUp&>(*this).splay(a);
+return a;
+} else if (t < _g.target(a)) {
+if (_left[a] == INVALID) {
+const_cast<DynArcLookUp&>(*this).splay(a);
+return INVALID;
+} else {
+a = _left[a];
+}
+} else  {
+if (_right[a] == INVALID) {
+const_cast<DynArcLookUp&>(*this).splay(a);
+return INVALID;
+} else {
+a = _right[a];
+}
+}
+}
+}
+///Find the first arc between two nodes.
+///Find the first arc between two nodes in time
+/// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
+/// outgoing arcs of \c s.
+///\param s The source node
+///\param t The target node
+///\return An arc from \c s to \c t if there exists, \ref INVALID
+/// otherwise.
+Arc findFirst(Node s, Node t) const
+{
+Arc a = _head[s];
+Arc r = INVALID;
+while (true) {
+if (_g.target(a) < t) {
+if (_right[a] == INVALID) {
+const_cast<DynArcLookUp&>(*this).splay(a);
+return r;
+} else {
+a = _right[a];
+}
+} else {
+if (_g.target(a) == t) {
+r = a;
+}
+if (_left[a] == INVALID) {
+const_cast<DynArcLookUp&>(*this).splay(a);
+return r;
+} else {
+a = _left[a];
+}
+}
+}
+}
+///Find the next arc between two nodes.
+///Find the next arc between two nodes in time
+/// <em>O(</em>log<em>d)</em>, where <em>d</em> is the number of
+/// outgoing arcs of \c s.
+///\param s The source node
+///\param t The target node
+///\return An arc from \c s to \c t if there exists, \ref INVALID
+/// otherwise.
+///\note If \c e is not the result of the previous \c findFirst()
+///operation then the amorized time bound can not be guaranteed.
+#ifdef DOXYGEN
+Arc findNext(Node s, Node t, Arc a) const
+#else
+Arc findNext(Node, Node t, Arc a) const
+#endif
+{
+if (_right[a] != INVALID) {
+a = _right[a];
+while (_left[a] != INVALID) {
+a = _left[a];
+}
+const_cast<DynArcLookUp&>(*this).splay(a);
+} else {
+while (_parent[a] != INVALID && _right[_parent[a]] ==  a) {
+a = _parent[a];
+}
+if (_parent[a] == INVALID) {
+return INVALID;
+} else {
+a = _parent[a];
+const_cast<DynArcLookUp&>(*this).splay(a);
+}
+}
+if (_g.target(a) == t) return a;
+else return INVALID;
+}
+};
+///Fast arc look up between given endpoints.
+///Using this class, you can find an arc in a digraph from a given
+///source to a given target in time <em>O(log d)</em>,
+///where <em>d</em> is the out-degree of the source node.
+///
+///It is not possible to find \e all parallel arcs between two nodes.
+///Use \ref AllArcLookUp for this purpose.
+///
+///\warning This class is static, so you should refresh() (or at least
+///refresh(Node)) this data structure
+///whenever the digraph changes. This is a time consuming (superlinearly
+///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
+///
+///\tparam G The type of the underlying digraph.
+///
+///\sa DynArcLookUp
+///\sa AllArcLookUp
+template<class G>
+class ArcLookUp
+{
+public:
+TEMPLATE_DIGRAPH_TYPEDEFS(G);
+typedef G Digraph;
+protected:
+const Digraph &_g;
+typename Digraph::template NodeMap<Arc> _head;
+typename Digraph::template ArcMap<Arc> _left;
+typename Digraph::template ArcMap<Arc> _right;
+class ArcLess {
+const Digraph &g;
+public:
+ArcLess(const Digraph &_g) : g(_g) {}
+bool operator()(Arc a,Arc b) const
+{
+return g.target(a)<g.target(b);
+}
+};
+public:
+///Constructor
+///Constructor.
+///
+///It builds up the search database, which remains valid until the digraph
+///changes.
+ArcLookUp(const Digraph &g) :_g(g),_head(g),_left(g),_right(g) {refresh();}
+private:
+Arc refreshRec(std::vector<Arc> &v,int a,int b)
+{
+int m=(a+b)/2;
+Arc me=v[m];
+_left[me] = a<m?refreshRec(v,a,m-1):INVALID;
+_right[me] = m<b?refreshRec(v,m+1,b):INVALID;
+return me;
+}
+public:
+///Refresh the data structure at a node.
+///Build up the search database of node \c n.
+///
+///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
+///the number of the outgoing arcs of \c n.
+void refresh(Node n)
+{
+std::vector<Arc> v;
+for(OutArcIt e(_g,n);e!=INVALID;++e) v.push_back(e);
+if(v.size()) {
+std::sort(v.begin(),v.end(),ArcLess(_g));
+_head[n]=refreshRec(v,0,v.size()-1);
+}
+else _head[n]=INVALID;
+}
+///Refresh the full data structure.
+///Build up the full search database. In fact, it simply calls
+///\ref refresh(Node) "refresh(n)" for each node \c n.
+///
+///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
+///the number of the arcs of \c n and <em>D</em> is the maximum
+///out-degree of the digraph.
+void refresh()
+{
+for(NodeIt n(_g);n!=INVALID;++n) refresh(n);
+}
+///Find an arc between two nodes.
+///Find an arc between two nodes in time <em>O(</em>log<em>d)</em>, where
+/// <em>d</em> is the number of outgoing arcs of \c s.
+///\param s The source node
+///\param t The target node
+///\return An arc from \c s to \c t if there exists,
+///\ref INVALID otherwise.
+///
+///\warning If you change the digraph, refresh() must be called before using
+///this operator. If you change the outgoing arcs of
+///a single node \c n, then
+///\ref refresh(Node) "refresh(n)" is enough.
+///
+Arc operator()(Node s, Node t) const
+{
+Arc e;
+for(e=_head[s];
+e!=INVALID&&_g.target(e)!=t;
+e = t < _g.target(e)?_left[e]:_right[e]) ;
+return e;
+}
+};
+///Fast look up of all arcs between given endpoints.
+///This class is the same as \ref ArcLookUp, with the addition
+///that it makes it possible to find all arcs between given endpoints.
+///
+///\warning This class is static, so you should refresh() (or at least
+///refresh(Node)) this data structure
+///whenever the digraph changes. This is a time consuming (superlinearly
+///proportional (<em>O(m</em>log<em>m)</em>) to the number of arcs).
+///
+///\tparam G The type of the underlying digraph.
+///
+///\sa DynArcLookUp
+///\sa ArcLookUp
+template<class G>
+class AllArcLookUp : public ArcLookUp<G>
+{
+using ArcLookUp<G>::_g;
+using ArcLookUp<G>::_right;
+using ArcLookUp<G>::_left;
+using ArcLookUp<G>::_head;
+TEMPLATE_DIGRAPH_TYPEDEFS(G);
+typedef G Digraph;
+typename Digraph::template ArcMap<Arc> _next;
+Arc refreshNext(Arc head,Arc next=INVALID)
+{
+if(head==INVALID) return next;
+else {
+next=refreshNext(_right[head],next);
+//         _next[head]=next;
+_next[head]=( next!=INVALID && _g.target(next)==_g.target(head))
+? next : INVALID;
+return refreshNext(_left[head],head);
+}
+}
+void refreshNext()
+{
+for(NodeIt n(_g);n!=INVALID;++n) refreshNext(_head[n]);
+}
+public:
+///Constructor
+///Constructor.
+///
+///It builds up the search database, which remains valid until the digraph
+///changes.
+AllArcLookUp(const Digraph &g) : ArcLookUp<G>(g), _next(g) {refreshNext();}
+///Refresh the data structure at a node.
+///Build up the search database of node \c n.
+///
+///It runs in time <em>O(d</em>log<em>d)</em>, where <em>d</em> is
+///the number of the outgoing arcs of \c n.
+void refresh(Node n)
+{
+ArcLookUp<G>::refresh(n);
+refreshNext(_head[n]);
+}
+///Refresh the full data structure.
+///Build up the full search database. In fact, it simply calls
+///\ref refresh(Node) "refresh(n)" for each node \c n.
+///
+///It runs in time <em>O(m</em>log<em>D)</em>, where <em>m</em> is
+///the number of the arcs of \c n and <em>D</em> is the maximum
+///out-degree of the digraph.
+void refresh()
+{
+for(NodeIt n(_g);n!=INVALID;++n) refresh(_head[n]);
+}
+///Find an arc between two nodes.
+///Find an arc between two nodes.
+///\param s The source node
+///\param t The target node
+///\param prev The previous arc between \c s and \c t. It it is INVALID or
+///not given, the operator finds the first appropriate arc.
+///\return An arc from \c s to \c t after \c prev or
+///\ref INVALID if there is no more.
+///
+///For example, you can count the number of arcs from \c u to \c v in the
+///following way.
+///\code
+///AllArcLookUp<ListDigraph> ae(g);
+///...
+///int n=0;
+///for(Arc e=ae(u,v);e!=INVALID;e=ae(u,v,e)) n++;
+///\endcode
+///
+///Finding the first arc take <em>O(</em>log<em>d)</em> time, where
+/// <em>d</em> is the number of outgoing arcs of \c s. Then, the
+///consecutive arcs are found in constant time.
+///
+///\warning If you change the digraph, refresh() must be called before using
+///this operator. If you change the outgoing arcs of
+///a single node \c n, then
+///\ref refresh(Node) "refresh(n)" is enough.
+///
+#ifdef DOXYGEN
+Arc operator()(Node s, Node t, Arc prev=INVALID) const {}
+#else
+using ArcLookUp<G>::operator() ;
+Arc operator()(Node s, Node t, Arc prev) const
+{
+return prev==INVALID?(*this)(s,t):_next[prev];
+}
+#endif
+};
+/// @}
+} //namespace lemon
+#endif

changeset 320	34e185734b42
child 229	aebc0161f6e5