/* -*- 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_EDGE_SET_H

 #define LEMON_EDGE_SET_H

 #include <lemon/core.h>

 #include <lemon/bits/edge_set_extender.h>

 /// \ingroup semi_adaptors

 /// \file

 /// \brief ArcSet and EdgeSet classes.

 ///

 /// Graphs which use another graph's node-set as own.

 namespace lemon {

   template <typename _Graph>

   class ListArcSetBase {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Node Node;

     typedef typename Graph::NodeIt NodeIt;

   protected:

     struct NodeT {

       int first_out, first_in;

       NodeT() : first_out(-1), first_in(-1) {}

     };

     typedef typename ItemSetTraits<Graph, Node>::

     template Map<NodeT>::Type NodesImplBase;

     NodesImplBase* nodes;

     struct ArcT {

       Node source, target;

       int next_out, next_in;

       int prev_out, prev_in;

       ArcT() : prev_out(-1), prev_in(-1) {}

     };

     std::vector<ArcT> arcs;

     int first_arc;

     int first_free_arc;

     const Graph* graph;

     void initalize(const Graph& _graph, NodesImplBase& _nodes) {

       graph = &_graph;

       nodes = &_nodes;

     }

   public:

     class Arc {

       friend class ListArcSetBase<Graph>;

     protected:

       Arc(int _id) : id(_id) {}

       int id;

     public:

       Arc() {}

       Arc(Invalid) : id(-1) {}

       bool operator==(const Arc& arc) const { return id == arc.id; }

       bool operator!=(const Arc& arc) const { return id != arc.id; }

       bool operator<(const Arc& arc) const { return id < arc.id; }

     };

     ListArcSetBase() : first_arc(-1), first_free_arc(-1) {}

     Arc addArc(const Node& u, const Node& v) {

       int n;

       if (first_free_arc == -1) {

         n = arcs.size();

         arcs.push_back(ArcT());

       } else {

         n = first_free_arc;

         first_free_arc = arcs[first_free_arc].next_in;

       }

       arcs[n].next_in = (*nodes)[v].first_in;

       if ((*nodes)[v].first_in != -1) {

         arcs[(*nodes)[v].first_in].prev_in = n;

       }

       (*nodes)[v].first_in = n;

       arcs[n].next_out = (*nodes)[u].first_out;

       if ((*nodes)[u].first_out != -1) {

         arcs[(*nodes)[u].first_out].prev_out = n;

       }

       (*nodes)[u].first_out = n;

       arcs[n].source = u;

       arcs[n].target = v;

       return Arc(n);

     }

     void erase(const Arc& arc) {

       int n = arc.id;

       if (arcs[n].prev_in != -1) {

         arcs[arcs[n].prev_in].next_in = arcs[n].next_in;

       } else {

         (*nodes)[arcs[n].target].first_in = arcs[n].next_in;

       }

       if (arcs[n].next_in != -1) {

         arcs[arcs[n].next_in].prev_in = arcs[n].prev_in;

       }

       if (arcs[n].prev_out != -1) {

         arcs[arcs[n].prev_out].next_out = arcs[n].next_out;

       } else {

         (*nodes)[arcs[n].source].first_out = arcs[n].next_out;

       }

       if (arcs[n].next_out != -1) {

         arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;

       }

     }

     void clear() {

       Node node;

       for (first(node); node != INVALID; next(node)) {

         (*nodes)[node].first_in = -1;

         (*nodes)[node].first_out = -1;

       }

       arcs.clear();

       first_arc = -1;

       first_free_arc = -1;

     }

     void first(Node& node) const {

       graph->first(node);

     }

     void next(Node& node) const {

       graph->next(node);

     }

     void first(Arc& arc) const {

       Node node;

       first(node);

       while (node != INVALID && (*nodes)[node].first_in == -1) {

         next(node);

       }

       arc.id = (node == INVALID) ? -1 : (*nodes)[node].first_in;

     }

     void next(Arc& arc) const {

       if (arcs[arc.id].next_in != -1) {

         arc.id = arcs[arc.id].next_in;

       } else {

         Node node = arcs[arc.id].target;

         next(node);

         while (node != INVALID && (*nodes)[node].first_in == -1) {

           next(node);

         }

         arc.id = (node == INVALID) ? -1 : (*nodes)[node].first_in;

       }

     }

     void firstOut(Arc& arc, const Node& node) const {

       arc.id = (*nodes)[node].first_out;

     }

     void nextOut(Arc& arc) const {

       arc.id = arcs[arc.id].next_out;

     }

     void firstIn(Arc& arc, const Node& node) const {

       arc.id = (*nodes)[node].first_in;

     }

     void nextIn(Arc& arc) const {

       arc.id = arcs[arc.id].next_in;

     }

     int id(const Node& node) const { return graph->id(node); }

     int id(const Arc& arc) const { return arc.id; }

     Node nodeFromId(int ix) const { return graph->nodeFromId(ix); }

     Arc arcFromId(int ix) const { return Arc(ix); }

     int maxNodeId() const { return graph->maxNodeId(); };

     int maxArcId() const { return arcs.size() - 1; }

     Node source(const Arc& arc) const { return arcs[arc.id].source;}

     Node target(const Arc& arc) const { return arcs[arc.id].target;}

     typedef typename ItemSetTraits<Graph, Node>::ItemNotifier NodeNotifier;

     NodeNotifier& notifier(Node) const {

       return graph->notifier(Node());

     }

     template <typename _Value>

     class NodeMap : public Graph::template NodeMap<_Value> {

     public:

       typedef typename _Graph::template NodeMap<_Value> Parent;

       explicit NodeMap(const ListArcSetBase<Graph>& arcset)

         : Parent(*arcset.graph) {}

       NodeMap(const ListArcSetBase<Graph>& arcset, const _Value& value)

         : Parent(*arcset.graph, value) {}

       NodeMap& operator=(const NodeMap& cmap) {

         return operator=<NodeMap>(cmap);

       }

       template <typename CMap>

       NodeMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

   };

   /// \ingroup semi_adaptors

   ///

   /// \brief Digraph using a node set of another digraph or graph and

   /// an own arc set.

   ///

   /// This structure can be used to establish another directed graph

   /// over a node set of an existing one. This class uses the same

   /// Node type as the underlying graph, and each valid node of the

   /// original graph is valid in this arc set, therefore the node

   /// objects of the original graph can be used directly with this

   /// class. The node handling functions (id handling, observing, and

   /// iterators) works equivalently as in the original graph.

   ///

   /// This implementation is based on doubly-linked lists, from each

   /// node the outgoing and the incoming arcs make up lists, therefore

   /// one arc can be erased in constant time. It also makes possible,

   /// that node can be removed from the underlying graph, in this case

   /// all arcs incident to the given node is erased from the arc set.

   ///

   /// \param _Graph The type of the graph which shares its node set with

   /// this class. Its interface must conform to the

   /// \ref concepts::Digraph "Digraph" or \ref concepts::Graph "Graph"

   /// concept.

   ///

   /// This class is fully conform to the \ref concepts::Digraph

   /// "Digraph" concept.

   template <typename _Graph>

   class ListArcSet : public ArcSetExtender<ListArcSetBase<_Graph> > {

   public:

     typedef ArcSetExtender<ListArcSetBase<_Graph> > Parent;

     typedef typename Parent::Node Node;

     typedef typename Parent::Arc Arc;

     typedef _Graph Graph;

     typedef typename Parent::NodesImplBase NodesImplBase;

     void eraseNode(const Node& node) {

       Arc arc;

       Parent::firstOut(arc, node);

       while (arc != INVALID ) {

         erase(arc);

         Parent::firstOut(arc, node);

       }

       Parent::firstIn(arc, node);

       while (arc != INVALID ) {

         erase(arc);

         Parent::firstIn(arc, node);

       }

     }

     void clearNodes() {

       Parent::clear();

     }

     class NodesImpl : public NodesImplBase {

     public:

       typedef NodesImplBase Parent;

       NodesImpl(const Graph& graph, ListArcSet& arcset)

         : Parent(graph), _arcset(arcset) {}

       virtual ~NodesImpl() {}

     protected:

       virtual void erase(const Node& node) {

         _arcset.eraseNode(node);

         Parent::erase(node);

       }

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

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

           _arcset.eraseNode(nodes[i]);

         }

         Parent::erase(nodes);

       }

       virtual void clear() {

         _arcset.clearNodes();

         Parent::clear();

       }

     private:

       ListArcSet& _arcset;

     };

     NodesImpl nodes;

   public:

     /// \brief Constructor of the ArcSet.

     ///

     /// Constructor of the ArcSet.

     ListArcSet(const Graph& graph) : nodes(graph, *this) {

       Parent::initalize(graph, nodes);

     }

     /// \brief Add a new arc to the digraph.

     ///

     /// Add a new arc to the digraph with source node \c s

     /// and target node \c t.

     /// \return the new arc.

     Arc addArc(const Node& s, const Node& t) {

       return Parent::addArc(s, t);

     }

     /// \brief Erase an arc from the digraph.

     ///

     /// Erase an arc \c a from the digraph.

     void erase(const Arc& a) {

       return Parent::erase(a);

     }

   };

   template <typename _Graph>

   class ListEdgeSetBase {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Node Node;

     typedef typename Graph::NodeIt NodeIt;

   protected:

     struct NodeT {

       int first_out;

       NodeT() : first_out(-1) {}

     };

     typedef typename ItemSetTraits<Graph, Node>::

     template Map<NodeT>::Type NodesImplBase;

     NodesImplBase* nodes;

     struct ArcT {

       Node target;

       int prev_out, next_out;

       ArcT() : prev_out(-1), next_out(-1) {}

     };

     std::vector<ArcT> arcs;

     int first_arc;

     int first_free_arc;

     const Graph* graph;

     void initalize(const Graph& _graph, NodesImplBase& _nodes) {

       graph = &_graph;

       nodes = &_nodes;

     }

   public:

     class Edge {

       friend class ListEdgeSetBase;

     protected:

       int id;

       explicit Edge(int _id) { id = _id;}

     public:

       Edge() {}

       Edge (Invalid) { id = -1; }

       bool operator==(const Edge& arc) const {return id == arc.id;}

       bool operator!=(const Edge& arc) const {return id != arc.id;}

       bool operator<(const Edge& arc) const {return id < arc.id;}

     };

     class Arc {

       friend class ListEdgeSetBase;

     protected:

       Arc(int _id) : id(_id) {}

       int id;

     public:

       operator Edge() const { return edgeFromId(id / 2); }

       Arc() {}

       Arc(Invalid) : id(-1) {}

       bool operator==(const Arc& arc) const { return id == arc.id; }

       bool operator!=(const Arc& arc) const { return id != arc.id; }

       bool operator<(const Arc& arc) const { return id < arc.id; }

     };

     ListEdgeSetBase() : first_arc(-1), first_free_arc(-1) {}

     Edge addEdge(const Node& u, const Node& v) {

       int n;

       if (first_free_arc == -1) {

         n = arcs.size();

         arcs.push_back(ArcT());

         arcs.push_back(ArcT());

       } else {

         n = first_free_arc;

         first_free_arc = arcs[n].next_out;

       }

       arcs[n].target = u;

       arcs[n | 1].target = v;

       arcs[n].next_out = (*nodes)[v].first_out;

       if ((*nodes)[v].first_out != -1) {

         arcs[(*nodes)[v].first_out].prev_out = n;

       }

       (*nodes)[v].first_out = n;

       arcs[n].prev_out = -1;

       if ((*nodes)[u].first_out != -1) {

         arcs[(*nodes)[u].first_out].prev_out = (n | 1);

       }

       arcs[n | 1].next_out = (*nodes)[u].first_out;

       (*nodes)[u].first_out = (n | 1);

       arcs[n | 1].prev_out = -1;

       return Edge(n / 2);

     }

     void erase(const Edge& arc) {

       int n = arc.id * 2;

       if (arcs[n].next_out != -1) {

         arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;

       }

       if (arcs[n].prev_out != -1) {

         arcs[arcs[n].prev_out].next_out = arcs[n].next_out;

       } else {

         (*nodes)[arcs[n | 1].target].first_out = arcs[n].next_out;

       }

       if (arcs[n | 1].next_out != -1) {

         arcs[arcs[n | 1].next_out].prev_out = arcs[n | 1].prev_out;

       }

       if (arcs[n | 1].prev_out != -1) {

         arcs[arcs[n | 1].prev_out].next_out = arcs[n | 1].next_out;

       } else {

         (*nodes)[arcs[n].target].first_out = arcs[n | 1].next_out;

       }

       arcs[n].next_out = first_free_arc;

       first_free_arc = n;

     }

     void clear() {

       Node node;

       for (first(node); node != INVALID; next(node)) {

         (*nodes)[node].first_out = -1;

       }

       arcs.clear();

       first_arc = -1;

       first_free_arc = -1;

     }

     void first(Node& node) const {

       graph->first(node);

     }

     void next(Node& node) const {

       graph->next(node);

     }

     void first(Arc& arc) const {

       Node node;

       first(node);

       while (node != INVALID && (*nodes)[node].first_out == -1) {

         next(node);

       }

       arc.id = (node == INVALID) ? -1 : (*nodes)[node].first_out;

     }

     void next(Arc& arc) const {

       if (arcs[arc.id].next_out != -1) {

         arc.id = arcs[arc.id].next_out;

       } else {

         Node node = arcs[arc.id ^ 1].target;

         next(node);

         while(node != INVALID && (*nodes)[node].first_out == -1) {

           next(node);

         }

         arc.id = (node == INVALID) ? -1 : (*nodes)[node].first_out;

       }

     }

     void first(Edge& edge) const {

       Node node;

       first(node);

       while (node != INVALID) {

         edge.id = (*nodes)[node].first_out;

         while ((edge.id & 1) != 1) {

           edge.id = arcs[edge.id].next_out;

         }

         if (edge.id != -1) {

           edge.id /= 2;

           return;

         }

         next(node);

       }

       edge.id = -1;

     }

     void next(Edge& edge) const {

       Node node = arcs[edge.id * 2].target;

       edge.id = arcs[(edge.id * 2) | 1].next_out;

       while ((edge.id & 1) != 1) {

         edge.id = arcs[edge.id].next_out;

       }

       if (edge.id != -1) {

         edge.id /= 2;

         return;

       }

       next(node);

       while (node != INVALID) {

         edge.id = (*nodes)[node].first_out;

         while ((edge.id & 1) != 1) {

           edge.id = arcs[edge.id].next_out;

         }

         if (edge.id != -1) {

           edge.id /= 2;

           return;

         }

         next(node);

       }

       edge.id = -1;

     }

     void firstOut(Arc& arc, const Node& node) const {

       arc.id = (*nodes)[node].first_out;

     }

     void nextOut(Arc& arc) const {

       arc.id = arcs[arc.id].next_out;

     }

     void firstIn(Arc& arc, const Node& node) const {

       arc.id = (((*nodes)[node].first_out) ^ 1);

       if (arc.id == -2) arc.id = -1;

     }

     void nextIn(Arc& arc) const {

       arc.id = ((arcs[arc.id ^ 1].next_out) ^ 1);

       if (arc.id == -2) arc.id = -1;

     }

     void firstInc(Edge &arc, bool& dir, const Node& node) const {

       int de = (*nodes)[node].first_out;

       if (de != -1 ) {

         arc.id = de / 2;

         dir = ((de & 1) == 1);

       } else {

         arc.id = -1;

         dir = true;

       }

     }

     void nextInc(Edge &arc, bool& dir) const {

       int de = (arcs[(arc.id * 2) | (dir ? 1 : 0)].next_out);

       if (de != -1 ) {

         arc.id = de / 2;

         dir = ((de & 1) == 1);

       } else {

         arc.id = -1;

         dir = true;

       }

     }

     static bool direction(Arc arc) {

       return (arc.id & 1) == 1;

     }

     static Arc direct(Edge edge, bool dir) {

       return Arc(edge.id * 2 + (dir ? 1 : 0));

     }

     int id(const Node& node) const { return graph->id(node); }

     static int id(Arc e) { return e.id; }

     static int id(Edge e) { return e.id; }

     Node nodeFromId(int id) const { return graph->nodeFromId(id); }

     static Arc arcFromId(int id) { return Arc(id);}

     static Edge edgeFromId(int id) { return Edge(id);}

     int maxNodeId() const { return graph->maxNodeId(); };

     int maxEdgeId() const { return arcs.size() / 2 - 1; }

     int maxArcId() const { return arcs.size()-1; }

     Node source(Arc e) const { return arcs[e.id ^ 1].target; }

     Node target(Arc e) const { return arcs[e.id].target; }

     Node u(Edge e) const { return arcs[2 * e.id].target; }

     Node v(Edge e) const { return arcs[2 * e.id + 1].target; }

     typedef typename ItemSetTraits<Graph, Node>::ItemNotifier NodeNotifier;

     NodeNotifier& notifier(Node) const {

       return graph->notifier(Node());

     }

     template <typename _Value>

     class NodeMap : public Graph::template NodeMap<_Value> {

     public:

       typedef typename _Graph::template NodeMap<_Value> Parent;

       explicit NodeMap(const ListEdgeSetBase<Graph>& arcset)

         : Parent(*arcset.graph) {}

       NodeMap(const ListEdgeSetBase<Graph>& arcset, const _Value& value)

         : Parent(*arcset.graph, value) {}

       NodeMap& operator=(const NodeMap& cmap) {

         return operator=<NodeMap>(cmap);

       }

       template <typename CMap>

       NodeMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

   };

   /// \ingroup semi_adaptors

   ///

   /// \brief Graph using a node set of another digraph or graph and an

   /// own edge set.

   ///

   /// This structure can be used to establish another graph over a

   /// node set of an existing one. This class uses the same Node type

   /// as the underlying graph, and each valid node of the original

   /// graph is valid in this arc set, therefore the node objects of

   /// the original graph can be used directly with this class. The

   /// node handling functions (id handling, observing, and iterators)

   /// works equivalently as in the original graph.

   ///

   /// This implementation is based on doubly-linked lists, from each

   /// node the incident edges make up lists, therefore one edge can be

   /// erased in constant time. It also makes possible, that node can

   /// be removed from the underlying graph, in this case all edges

   /// incident to the given node is erased from the arc set.

   ///

   /// \param _Graph The type of the graph which shares its node set

   /// with this class. Its interface must conform to the

   /// \ref concepts::Digraph "Digraph" or \ref concepts::Graph "Graph"

   /// concept.

   ///

   /// This class is fully conform to the \ref concepts::Graph "Graph"

   /// concept.

   template <typename _Graph>

   class ListEdgeSet : public EdgeSetExtender<ListEdgeSetBase<_Graph> > {

   public:

     typedef EdgeSetExtender<ListEdgeSetBase<_Graph> > Parent;

     typedef typename Parent::Node Node;

     typedef typename Parent::Arc Arc;

     typedef typename Parent::Edge Edge;

     typedef _Graph Graph;

     typedef typename Parent::NodesImplBase NodesImplBase;

     void eraseNode(const Node& node) {

       Arc arc;

       Parent::firstOut(arc, node);

       while (arc != INVALID ) {

         erase(arc);

         Parent::firstOut(arc, node);

       }

     }

     void clearNodes() {

       Parent::clear();

     }

     class NodesImpl : public NodesImplBase {

     public:

       typedef NodesImplBase Parent;

       NodesImpl(const Graph& graph, ListEdgeSet& arcset)

         : Parent(graph), _arcset(arcset) {}

       virtual ~NodesImpl() {}

     protected:

       virtual void erase(const Node& node) {

         _arcset.eraseNode(node);

         Parent::erase(node);

       }

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

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

           _arcset.eraseNode(nodes[i]);

         }

         Parent::erase(nodes);

       }

       virtual void clear() {

         _arcset.clearNodes();

         Parent::clear();

       }

     private:

       ListEdgeSet& _arcset;

     };

     NodesImpl nodes;

   public:

     /// \brief Constructor of the EdgeSet.

     ///

     /// Constructor of the EdgeSet.

     ListEdgeSet(const Graph& graph) : nodes(graph, *this) {

       Parent::initalize(graph, nodes);

     }

     /// \brief Add a new edge to the graph.

     ///

     /// Add a new edge to the graph with node \c u

     /// and node \c v endpoints.

     /// \return the new edge.

     Edge addEdge(const Node& u, const Node& v) {

       return Parent::addEdge(u, v);

     }

     /// \brief Erase an edge from the graph.

     ///

     /// Erase the edge \c e from the graph.

     void erase(const Edge& e) {

       return Parent::erase(e);

     }

   };

   template <typename _Graph>

   class SmartArcSetBase {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Node Node;

     typedef typename Graph::NodeIt NodeIt;

   protected:

     struct NodeT {

       int first_out, first_in;

       NodeT() : first_out(-1), first_in(-1) {}

     };

     typedef typename ItemSetTraits<Graph, Node>::

     template Map<NodeT>::Type NodesImplBase;

     NodesImplBase* nodes;

     struct ArcT {

       Node source, target;

       int next_out, next_in;

       ArcT() {}

     };

     std::vector<ArcT> arcs;

     const Graph* graph;

     void initalize(const Graph& _graph, NodesImplBase& _nodes) {

       graph = &_graph;

       nodes = &_nodes;

     }

   public:

     class Arc {

       friend class SmartArcSetBase<Graph>;

     protected:

       Arc(int _id) : id(_id) {}

       int id;

     public:

       Arc() {}

       Arc(Invalid) : id(-1) {}

       bool operator==(const Arc& arc) const { return id == arc.id; }

       bool operator!=(const Arc& arc) const { return id != arc.id; }

       bool operator<(const Arc& arc) const { return id < arc.id; }

     };

     SmartArcSetBase() {}

     Arc addArc(const Node& u, const Node& v) {

       int n = arcs.size();

       arcs.push_back(ArcT());

       arcs[n].next_in = (*nodes)[v].first_in;

       (*nodes)[v].first_in = n;

       arcs[n].next_out = (*nodes)[u].first_out;

       (*nodes)[u].first_out = n;

       arcs[n].source = u;

       arcs[n].target = v;

       return Arc(n);

     }

     void clear() {

       Node node;

       for (first(node); node != INVALID; next(node)) {

         (*nodes)[node].first_in = -1;

         (*nodes)[node].first_out = -1;

       }

       arcs.clear();

     }

     void first(Node& node) const {

       graph->first(node);

     }

     void next(Node& node) const {

       graph->next(node);

     }

     void first(Arc& arc) const {

       arc.id = arcs.size() - 1;

     }

     void next(Arc& arc) const {

       --arc.id;

     }

     void firstOut(Arc& arc, const Node& node) const {

       arc.id = (*nodes)[node].first_out;

     }

     void nextOut(Arc& arc) const {

       arc.id = arcs[arc.id].next_out;

     }

     void firstIn(Arc& arc, const Node& node) const {

       arc.id = (*nodes)[node].first_in;

     }

     void nextIn(Arc& arc) const {

       arc.id = arcs[arc.id].next_in;

     }

     int id(const Node& node) const { return graph->id(node); }

     int id(const Arc& arc) const { return arc.id; }

     Node nodeFromId(int ix) const { return graph->nodeFromId(ix); }

     Arc arcFromId(int ix) const { return Arc(ix); }

     int maxNodeId() const { return graph->maxNodeId(); };

     int maxArcId() const { return arcs.size() - 1; }

     Node source(const Arc& arc) const { return arcs[arc.id].source;}

     Node target(const Arc& arc) const { return arcs[arc.id].target;}

     typedef typename ItemSetTraits<Graph, Node>::ItemNotifier NodeNotifier;

     NodeNotifier& notifier(Node) const {

       return graph->notifier(Node());

     }

     template <typename _Value>

     class NodeMap : public Graph::template NodeMap<_Value> {

     public:

       typedef typename _Graph::template NodeMap<_Value> Parent;

       explicit NodeMap(const SmartArcSetBase<Graph>& arcset)

         : Parent(*arcset.graph) { }

       NodeMap(const SmartArcSetBase<Graph>& arcset, const _Value& value)

         : Parent(*arcset.graph, value) { }

       NodeMap& operator=(const NodeMap& cmap) {

         return operator=<NodeMap>(cmap);

       }

       template <typename CMap>

       NodeMap& operator=(const CMap& cmap) {

         Parent::operator=(cmap);

         return *this;

       }

     };

   };

   /// \ingroup semi_adaptors

   ///

   /// \brief Digraph using a node set of another digraph or graph and

   /// an own arc set.

   ///

   /// This structure can be used to establish another directed graph

   /// over a node set of an existing one. This class uses the same

   /// Node type as the underlying graph, and each valid node of the

   /// original graph is valid in this arc set, therefore the node

   /// objects of the original graph can be used directly with this

   /// class. The node handling functions (id handling, observing, and

   /// iterators) works equivalently as in the original graph.

   ///

   /// \param _Graph The type of the graph which shares its node set with

   /// this class. Its interface must conform to the

   /// \ref concepts::Digraph "Digraph" or \ref concepts::Graph "Graph"

   /// concept.

   ///

   /// This implementation is slightly faster than the \c ListArcSet,

   /// because it uses continuous storage for arcs and it uses just

   /// single-linked lists for enumerate outgoing and incoming

   /// arcs. Therefore the arcs cannot be erased from the arc sets.

   ///

   /// \warning If a node is erased from the underlying graph and this

   /// node is the source or target of one arc in the arc set, then

   /// the arc set is invalidated, and it cannot be used anymore. The

   /// validity can be checked with the \c valid() member function.

   ///

   /// This class is fully conform to the \ref concepts::Digraph

   /// "Digraph" concept.

   template <typename _Graph>

   class SmartArcSet : public ArcSetExtender<SmartArcSetBase<_Graph> > {

   public:

     typedef ArcSetExtender<SmartArcSetBase<_Graph> > Parent;

     typedef typename Parent::Node Node;

     typedef typename Parent::Arc Arc;

     typedef _Graph Graph;

   protected:

     typedef typename Parent::NodesImplBase NodesImplBase;

     void eraseNode(const Node& node) {

       if (typename Parent::InArcIt(*this, node) == INVALID &&

           typename Parent::OutArcIt(*this, node) == INVALID) {

         return;

       }

       throw typename NodesImplBase::Notifier::ImmediateDetach();

     }

     void clearNodes() {

       Parent::clear();

     }

     class NodesImpl : public NodesImplBase {

     public:

       typedef NodesImplBase Parent;

       NodesImpl(const Graph& graph, SmartArcSet& arcset)

         : Parent(graph), _arcset(arcset) {}

       virtual ~NodesImpl() {}

       bool attached() const {

         return Parent::attached();

       }

     protected:

       virtual void erase(const Node& node) {

         try {

           _arcset.eraseNode(node);

           Parent::erase(node);

         } catch (const typename NodesImplBase::Notifier::ImmediateDetach&) {

           Parent::clear();

           throw;

         }

       }

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

         try {

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

             _arcset.eraseNode(nodes[i]);

           }

           Parent::erase(nodes);

         } catch (const typename NodesImplBase::Notifier::ImmediateDetach&) {

           Parent::clear();

           throw;

         }

       }

       virtual void clear() {

         _arcset.clearNodes();

         Parent::clear();

       }

     private:

       SmartArcSet& _arcset;

     };

     NodesImpl nodes;

   public:

     /// \brief Constructor of the ArcSet.

     ///

     /// Constructor of the ArcSet.

     SmartArcSet(const Graph& graph) : nodes(graph, *this) {

       Parent::initalize(graph, nodes);

     }

     /// \brief Add a new arc to the digraph.

     ///

     /// Add a new arc to the digraph with source node \c s

     /// and target node \c t.

     /// \return the new arc.

     Arc addArc(const Node& s, const Node& t) {

       return Parent::addArc(s, t);

     }

     /// \brief Validity check

     ///

     /// This functions gives back false if the ArcSet is

     /// invalidated. It occurs when a node in the underlying graph is

     /// erased and it is not isolated in the ArcSet.

     bool valid() const {

       return nodes.attached();

     }

   };

   template <typename _Graph>

   class SmartEdgeSetBase {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Node Node;

     typedef typename Graph::NodeIt NodeIt;

   protected:

     struct NodeT {

       int first_out;

       NodeT() : first_out(-1) {}

     };

     typedef typename ItemSetTraits<Graph, Node>::

     template Map<NodeT>::Type NodesImplBase;

     NodesImplBase* nodes;

     struct ArcT {

       Node target;

       int next_out;

       ArcT() {}

     };

     std::vector<ArcT> arcs;

     const Graph* graph;

     void initalize(const Graph& _graph, NodesImplBase& _nodes) {

       graph = &_graph;

       nodes = &_nodes;

     }

   public:

     class Edge {

       friend class SmartEdgeSetBase;

     protected:

       int id;

       explicit Edge(int _id) { id = _id;}

     public:

       Edge() {}

       Edge (Invalid) { id = -1; }

       bool operator==(const Edge& arc) const {return id == arc.id;}

       bool operator!=(const Edge& arc) const {return id != arc.id;}

       bool operator<(const Edge& arc) const {return id < arc.id;}

     };

     class Arc {

       friend class SmartEdgeSetBase;

     protected:

       Arc(int _id) : id(_id) {}

       int id;

     public:

       operator Edge() const { return edgeFromId(id / 2); }

       Arc() {}

       Arc(Invalid) : id(-1) {}

       bool operator==(const Arc& arc) const { return id == arc.id; }

       bool operator!=(const Arc& arc) const { return id != arc.id; }

       bool operator<(const Arc& arc) const { return id < arc.id; }

     };

     SmartEdgeSetBase() {}

     Edge addEdge(const Node& u, const Node& v) {

       int n = arcs.size();

       arcs.push_back(ArcT());

       arcs.push_back(ArcT());

       arcs[n].target = u;

       arcs[n | 1].target = v;