/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2007

 * 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_BITS_GRAPH_EXTENDER_H

#define LEMON_BITS_GRAPH_EXTENDER_H

#include <lemon/bits/invalid.h>

#include <lemon/error.h>

#include <lemon/bits/map_extender.h>

#include <lemon/bits/default_map.h>

#include <lemon/concept_check.h>

#include <lemon/concepts/maps.h>

///\ingroup graphbits

///\file

///\brief Extenders for the graph types

namespace lemon {

  /// \ingroup graphbits

  ///

  /// \brief Extender for the Graphs

  template <typename Base>

  class GraphExtender : public Base {

  public:

    typedef Base Parent;

    typedef GraphExtender Graph;

    // Base extensions

    typedef typename Parent::Node Node;

    typedef typename Parent::Edge Edge;

    int maxId(Node) const {

      return Parent::maxNodeId();

    }

    int maxId(Edge) const {

      return Parent::maxEdgeId();

    }

    Node fromId(int id, Node) const {

      return Parent::nodeFromId(id);

    }

    Edge fromId(int id, Edge) const {

      return Parent::edgeFromId(id);

    }

    Node oppositeNode(const Node &n, const Edge &e) const {

      if (n == Parent::source(e))

	return Parent::target(e);

      else if(n==Parent::target(e))

	return Parent::source(e);

      else

	return INVALID;

    }

    // Alterable extension

    typedef AlterationNotifier<GraphExtender, Node> NodeNotifier;

    typedef AlterationNotifier<GraphExtender, Edge> EdgeNotifier;

  protected:

    mutable NodeNotifier node_notifier;

    mutable EdgeNotifier edge_notifier;

  public:

    NodeNotifier& notifier(Node) const {

      return node_notifier;

    }

    EdgeNotifier& notifier(Edge) const {

      return edge_notifier;

    }

    class NodeIt : public Node { 

      const Graph* graph;

    public:

      NodeIt() {}

      NodeIt(Invalid i) : Node(i) { }

      explicit NodeIt(const Graph& _graph) : graph(&_graph) {

	_graph.first(static_cast<Node&>(*this));

      }

      NodeIt(const Graph& _graph, const Node& node) 

	: Node(node), graph(&_graph) {}

      NodeIt& operator++() { 

	graph->next(*this);

	return *this; 

      }

    };

    class EdgeIt : public Edge { 

      const Graph* graph;

    public:

      EdgeIt() { }

      EdgeIt(Invalid i) : Edge(i) { }

      explicit EdgeIt(const Graph& _graph) : graph(&_graph) {

	_graph.first(static_cast<Edge&>(*this));

      }

      EdgeIt(const Graph& _graph, const Edge& e) : 

	Edge(e), graph(&_graph) { }

      EdgeIt& operator++() { 

	graph->next(*this);

	return *this; 

      }

    };

    class OutEdgeIt : public Edge { 

      const Graph* graph;

    public:

      OutEdgeIt() { }

      OutEdgeIt(Invalid i) : Edge(i) { }

      OutEdgeIt(const Graph& _graph, const Node& node) 

	: graph(&_graph) {

	_graph.firstOut(*this, node);

      }

      OutEdgeIt(const Graph& _graph, const Edge& edge) 

	: Edge(edge), graph(&_graph) {}

      OutEdgeIt& operator++() { 

	graph->nextOut(*this);

	return *this; 

      }

    };

    class InEdgeIt : public Edge { 

      const Graph* graph;

    public:

      InEdgeIt() { }

      InEdgeIt(Invalid i) : Edge(i) { }

      InEdgeIt(const Graph& _graph, const Node& node) 

	: graph(&_graph) {

	_graph.firstIn(*this, node);

      }

      InEdgeIt(const Graph& _graph, const Edge& edge) : 

	Edge(edge), graph(&_graph) {}

      InEdgeIt& operator++() { 

	graph->nextIn(*this);

	return *this; 

      }

    };

    /// \brief Base node of the iterator

    ///

    /// Returns the base node (i.e. the source in this case) of the iterator

    Node baseNode(const OutEdgeIt &e) const {

      return Parent::source(e);

    }

    /// \brief Running node of the iterator

    ///

    /// Returns the running node (i.e. the target in this case) of the

    /// iterator

    Node runningNode(const OutEdgeIt &e) const {

      return Parent::target(e);

    }

    /// \brief Base node of the iterator

    ///

    /// Returns the base node (i.e. the target in this case) of the iterator

    Node baseNode(const InEdgeIt &e) const {

      return Parent::target(e);

    }

    /// \brief Running node of the iterator

    ///

    /// Returns the running node (i.e. the source in this case) of the

    /// iterator

    Node runningNode(const InEdgeIt &e) const {

      return Parent::source(e);

    }

    template <typename _Value>

    class NodeMap 

      : public MapExtender<DefaultMap<Graph, Node, _Value> > {

    public:

      typedef GraphExtender Graph;

      typedef MapExtender<DefaultMap<Graph, Node, _Value> > Parent;

      explicit NodeMap(const Graph& graph) 

	: Parent(graph) {}

      NodeMap(const Graph& graph, const _Value& value) 

	: Parent(graph, value) {}

      NodeMap& operator=(const NodeMap& cmap) {

	return operator=<NodeMap>(cmap);

      }

      template <typename CMap>

      NodeMap& operator=(const CMap& cmap) {

        Parent::operator=(cmap);

	return *this;

      }

    };

    template <typename _Value>

    class EdgeMap 

      : public MapExtender<DefaultMap<Graph, Edge, _Value> > {

    public:

      typedef GraphExtender Graph;

      typedef MapExtender<DefaultMap<Graph, Edge, _Value> > Parent;

      explicit EdgeMap(const Graph& graph) 

	: Parent(graph) {}

      EdgeMap(const Graph& graph, const _Value& value) 

	: Parent(graph, value) {}

      EdgeMap& operator=(const EdgeMap& cmap) {

	return operator=<EdgeMap>(cmap);

      }

      template <typename CMap>

      EdgeMap& operator=(const CMap& cmap) {

        Parent::operator=(cmap);

	return *this;

      }

    };

    Node addNode() {

      Node node = Parent::addNode();

      notifier(Node()).add(node);

      return node;

    }

    Edge addEdge(const Node& from, const Node& to) {

      Edge edge = Parent::addEdge(from, to);

      notifier(Edge()).add(edge);

      return edge;

    }

    void clear() {

      notifier(Edge()).clear();

      notifier(Node()).clear();

      Parent::clear();

    }

    template <typename Graph, typename NodeRefMap, typename EdgeRefMap>

    void build(const Graph& graph, NodeRefMap& nodeRef, EdgeRefMap& edgeRef) {

      Parent::build(graph, nodeRef, edgeRef);

      notifier(Node()).build();

      notifier(Edge()).build();

    }

    void erase(const Node& node) {

      Edge edge;

      Parent::firstOut(edge, node);

      while (edge != INVALID ) {

	erase(edge);

	Parent::firstOut(edge, node);

      } 

      Parent::firstIn(edge, node);

      while (edge != INVALID ) {

	erase(edge);

	Parent::firstIn(edge, node);

      }

      notifier(Node()).erase(node);

      Parent::erase(node);

    }

    void erase(const Edge& edge) {

      notifier(Edge()).erase(edge);

      Parent::erase(edge);

    }

    GraphExtender() {

      node_notifier.setContainer(*this);

      edge_notifier.setContainer(*this);

    } 

    ~GraphExtender() {

      edge_notifier.clear();

      node_notifier.clear();

    }

  };

  /// \ingroup graphbits

  ///

  /// \brief Extender for the UGraphs

  template <typename Base> 

  class UGraphExtender : public Base {

  public:

    typedef Base Parent;

    typedef UGraphExtender Graph;

    typedef typename Parent::Node Node;

    typedef typename Parent::Edge Edge;

    typedef typename Parent::UEdge UEdge;

    // UGraph extension    

    int maxId(Node) const {

      return Parent::maxNodeId();

    }

    int maxId(Edge) const {

      return Parent::maxEdgeId();

    }

    int maxId(UEdge) const {

      return Parent::maxUEdgeId();

    }

    Node fromId(int id, Node) const {

      return Parent::nodeFromId(id);

    }

    Edge fromId(int id, Edge) const {

      return Parent::edgeFromId(id);

    }

    UEdge fromId(int id, UEdge) const {

      return Parent::uEdgeFromId(id);

    }

    Node oppositeNode(const Node &n, const UEdge &e) const {

      if( n == Parent::source(e))

	return Parent::target(e);

      else if( n == Parent::target(e))

	return Parent::source(e);

      else

	return INVALID;

    }

    Edge oppositeEdge(const Edge &e) const {

      return Parent::direct(e, !Parent::direction(e));

    }

    using Parent::direct;

    Edge direct(const UEdge &ue, const Node &s) const {

      return Parent::direct(ue, Parent::source(ue) == s);

    }

    // Alterable extension

    typedef AlterationNotifier<UGraphExtender, Node> NodeNotifier;

    typedef AlterationNotifier<UGraphExtender, Edge> EdgeNotifier;

    typedef AlterationNotifier<UGraphExtender, UEdge> UEdgeNotifier;

  protected:

    mutable NodeNotifier node_notifier;

    mutable EdgeNotifier edge_notifier;

    mutable UEdgeNotifier uedge_notifier;

  public:

    NodeNotifier& notifier(Node) const {

      return node_notifier;

    }

    EdgeNotifier& notifier(Edge) const {

      return edge_notifier;

    }

    UEdgeNotifier& notifier(UEdge) const {

      return uedge_notifier;

    }

    class NodeIt : public Node { 

      const Graph* graph;

    public:

      NodeIt() {}

      NodeIt(Invalid i) : Node(i) { }

      explicit NodeIt(const Graph& _graph) : graph(&_graph) {

	_graph.first(static_cast<Node&>(*this));

      }

      NodeIt(const Graph& _graph, const Node& node) 

	: Node(node), graph(&_graph) {}

      NodeIt& operator++() { 

	graph->next(*this);

	return *this; 

      }

    };

    class EdgeIt : public Edge { 

      const Graph* graph;

    public:

      EdgeIt() { }

      EdgeIt(Invalid i) : Edge(i) { }

      explicit EdgeIt(const Graph& _graph) : graph(&_graph) {

	_graph.first(static_cast<Edge&>(*this));

      }

      EdgeIt(const Graph& _graph, const Edge& e) : 

	Edge(e), graph(&_graph) { }

      EdgeIt& operator++() { 

	graph->next(*this);

	return *this; 

      }

    };

    class OutEdgeIt : public Edge { 

      const Graph* graph;

    public:

      OutEdgeIt() { }

      OutEdgeIt(Invalid i) : Edge(i) { }

      OutEdgeIt(const Graph& _graph, const Node& node) 

	: graph(&_graph) {

	_graph.firstOut(*this, node);

      }

      OutEdgeIt(const Graph& _graph, const Edge& edge) 

	: Edge(edge), graph(&_graph) {}

      OutEdgeIt& operator++() { 

	graph->nextOut(*this);

	return *this; 

      }

    };

    class InEdgeIt : public Edge { 

      const Graph* graph;

    public:

      InEdgeIt() { }

      InEdgeIt(Invalid i) : Edge(i) { }

      InEdgeIt(const Graph& _graph, const Node& node) 

	: graph(&_graph) {

	_graph.firstIn(*this, node);

      }

      InEdgeIt(const Graph& _graph, const Edge& edge) : 

	Edge(edge), graph(&_graph) {}

      InEdgeIt& operator++() { 

	graph->nextIn(*this);

	return *this; 

      }

    };

    class UEdgeIt : public Parent::UEdge { 

      const Graph* graph;

    public:

      UEdgeIt() { }

      UEdgeIt(Invalid i) : UEdge(i) { }

      explicit UEdgeIt(const Graph& _graph) : graph(&_graph) {

	_graph.first(static_cast<UEdge&>(*this));

      }

      UEdgeIt(const Graph& _graph, const UEdge& e) : 

	UEdge(e), graph(&_graph) { }

      UEdgeIt& operator++() { 

	graph->next(*this);

	return *this; 

      }

    };

    class IncEdgeIt : public Parent::UEdge {

      friend class UGraphExtender;

      const Graph* graph;

      bool direction;

    public:

      IncEdgeIt() { }

      IncEdgeIt(Invalid i) : UEdge(i), direction(false) { }

      IncEdgeIt(const Graph& _graph, const Node &n) : graph(&_graph) {

	_graph.firstInc(*this, direction, n);

      }

      IncEdgeIt(const Graph& _graph, const UEdge &ue, const Node &n)

	: graph(&_graph), UEdge(ue) {

	direction = (_graph.source(ue) == n);

      }

      IncEdgeIt& operator++() {

	graph->nextInc(*this, direction);

	return *this; 

      }

    };

    /// \brief Base node of the iterator

    ///

    /// Returns the base node (ie. the source in this case) of the iterator

    Node baseNode(const OutEdgeIt &e) const {

      return Parent::source(static_cast<const Edge&>(e));

    }

    /// \brief Running node of the iterator

    ///

    /// Returns the running node (ie. the target in this case) of the

    /// iterator

    Node runningNode(const OutEdgeIt &e) const {

      return Parent::target(static_cast<const Edge&>(e));

    }

    /// \brief Base node of the iterator

    ///

    /// Returns the base node (ie. the target in this case) of the iterator

    Node baseNode(const InEdgeIt &e) const {

      return Parent::target(static_cast<const Edge&>(e));

    }

    /// \brief Running node of the iterator

    ///

    /// Returns the running node (ie. the source in this case) of the

    /// iterator

    Node runningNode(const InEdgeIt &e) const {

      return Parent::source(static_cast<const Edge&>(e));

    }

    /// Base node of the iterator

    ///

    /// Returns the base node of the iterator

    Node baseNode(const IncEdgeIt &e) const {

      return e.direction ? source(e) : target(e);

    }

    /// Running node of the iterator

    ///

    /// Returns the running node of the iterator

    Node runningNode(const IncEdgeIt &e) const {

      return e.direction ? target(e) : source(e);

    }

    // Mappable extension

    template <typename _Value>

    class NodeMap 

      : public MapExtender<DefaultMap<Graph, Node, _Value> > {

    public:

      typedef UGraphExtender Graph;

      typedef MapExtender<DefaultMap<Graph, Node, _Value> > Parent;

      NodeMap(const Graph& graph) 

	: Parent(graph) {}

      NodeMap(const Graph& graph, const _Value& value) 

	: Parent(graph, value) {}

      NodeMap& operator=(const NodeMap& cmap) {

	return operator=<NodeMap>(cmap);

      }

      template <typename CMap>

      NodeMap& operator=(const CMap& cmap) {

        Parent::operator=(cmap);

	return *this;

      }

    };

    template <typename _Value>

    class EdgeMap 

      : public MapExtender<DefaultMap<Graph, Edge, _Value> > {

    public:

      typedef UGraphExtender Graph;

      typedef MapExtender<DefaultMap<Graph, Edge, _Value> > Parent;

      EdgeMap(const Graph& graph) 

	: Parent(graph) {}

      EdgeMap(const Graph& graph, const _Value& value) 

	: Parent(graph, value) {}

      EdgeMap& operator=(const EdgeMap& cmap) {

	return operator=<EdgeMap>(cmap);

      }

      template <typename CMap>

      EdgeMap& operator=(const CMap& cmap) {

        Parent::operator=(cmap);

	return *this;

      }

    };

    template <typename _Value>

    class UEdgeMap 

      : public MapExtender<DefaultMap<Graph, UEdge, _Value> > {

    public:

      typedef UGraphExtender Graph;

      typedef MapExtender<DefaultMap<Graph, UEdge, _Value> > Parent;

      UEdgeMap(const Graph& graph) 

	: Parent(graph) {}

      UEdgeMap(const Graph& graph, const _Value& value) 

	: Parent(graph, value) {}

      UEdgeMap& operator=(const UEdgeMap& cmap) {

	return operator=<UEdgeMap>(cmap);

      }

      template <typename CMap>

      UEdgeMap& operator=(const CMap& cmap) {

        Parent::operator=(cmap);

	return *this;

      }

    };

    // Alteration extension

    Node addNode() {

      Node node = Parent::addNode();

      notifier(Node()).add(node);

      return node;

    }

    UEdge addEdge(const Node& from, const Node& to) {

      UEdge uedge = Parent::addEdge(from, to);

      notifier(UEdge()).add(uedge);

      std::vector<Edge> ev;

      ev.push_back(Parent::direct(uedge, true));

      ev.push_back(Parent::direct(uedge, false));      

      notifier(Edge()).add(ev);

      return uedge;

    }

    void clear() {

      notifier(Edge()).clear();

      notifier(UEdge()).clear();

      notifier(Node()).clear();

      Parent::clear();

    }

    template <typename Graph, typename NodeRefMap, typename UEdgeRefMap>

    void build(const Graph& graph, NodeRefMap& nodeRef, 

               UEdgeRefMap& uEdgeRef) {

      Parent::build(graph, nodeRef, uEdgeRef);

      notifier(Node()).build();

      notifier(UEdge()).build();

      notifier(Edge()).build();

    }

    void erase(const Node& node) {

      Edge edge;

      Parent::firstOut(edge, node);

      while (edge != INVALID ) {

	erase(edge);

	Parent::firstOut(edge, node);

      } 

      Parent::firstIn(edge, node);

      while (edge != INVALID ) {

	erase(edge);

	Parent::firstIn(edge, node);

      }

      notifier(Node()).erase(node);

      Parent::erase(node);

    }

    void erase(const UEdge& uedge) {

      std::vector<Edge> ev;

      ev.push_back(Parent::direct(uedge, true));

      ev.push_back(Parent::direct(uedge, false));      

      notifier(Edge()).erase(ev);

      notifier(UEdge()).erase(uedge);

      Parent::erase(uedge);

    }

    UGraphExtender() {

      node_notifier.setContainer(*this); 

      edge_notifier.setContainer(*this);

      uedge_notifier.setContainer(*this);

    } 

    ~UGraphExtender() {

      uedge_notifier.clear();

      edge_notifier.clear();

      node_notifier.clear(); 

    } 

  };

  /// \ingroup graphbits

  ///

  /// \brief Extender for the BpUGraphs

  template <typename Base>

  class BpUGraphExtender : public Base {

  public:

    typedef Base Parent;

    typedef BpUGraphExtender Graph;

    typedef typename Parent::Node Node;

    typedef typename Parent::ANode ANode;

    typedef typename Parent::BNode BNode;

    typedef typename Parent::Edge Edge;

    typedef typename Parent::UEdge UEdge;

    Node oppositeNode(const Node& node, const UEdge& edge) const {

      return Parent::aNode(edge) == node ? 

	Parent::bNode(edge) : Parent::aNode(edge);

    }

    using Parent::direct;

    Edge direct(const UEdge& edge, const Node& node) const {

      return Parent::direct(edge, node == Parent::source(edge));

    }

    Edge oppositeEdge(const Edge& edge) const {

      return direct(edge, !Parent::direction(edge));

    }

    int maxId(Node) const {

      return Parent::maxNodeId();

    }

    int maxId(BNode) const {

      return Parent::maxBNodeId();

    }

    int maxId(ANode) const {

      return Parent::maxANodeId();

    }

    int maxId(Edge) const {

      return Parent::maxEdgeId();

    }

    int maxId(UEdge) const {

      return Parent::maxUEdgeId();

    }

    Node fromId(int id, Node) const {

      return Parent::nodeFromId(id);

    }

    ANode fromId(int id, ANode) const {

      return Parent::nodeFromANodeId(id);

    }

    BNode fromId(int id, BNode) const {

      return Parent::nodeFromBNodeId(id);

    }

    Edge fromId(int id, Edge) const {

      return Parent::edgeFromId(id);

    }

    UEdge fromId(int id, UEdge) const {

      return Parent::uEdgeFromId(id);

    }  

    typedef AlterationNotifier<BpUGraphExtender, ANode> ANodeNotifier;

    typedef AlterationNotifier<BpUGraphExtender, BNode> BNodeNotifier;

    typedef AlterationNotifier<BpUGraphExtender, Node> NodeNotifier;

    typedef AlterationNotifier<BpUGraphExtender, Edge> EdgeNotifier;

    typedef AlterationNotifier<BpUGraphExtender, UEdge> UEdgeNotifier;

  protected:

    mutable ANodeNotifier anode_notifier;

    mutable BNodeNotifier bnode_notifier;

    mutable NodeNotifier node_notifier;

    mutable EdgeNotifier edge_notifier;

    mutable UEdgeNotifier uedge_notifier;

  public:

    NodeNotifier& notifier(Node) const {

      return node_notifier;

    }

    ANodeNotifier& notifier(ANode) const {

      return anode_notifier;

    }

    BNodeNotifier& notifier(BNode) const {

      return bnode_notifier;

    }

    EdgeNotifier& notifier(Edge) const {

      return edge_notifier;

    }

    UEdgeNotifier& notifier(UEdge) const {

      return uedge_notifier;

    }

    class NodeIt : public Node { 

      const Graph* graph;

    public:

      NodeIt() { }

      NodeIt(Invalid i) : Node(INVALID) { }

      explicit NodeIt(const Graph& _graph) : graph(&_graph) {

	graph->first(static_cast<Node&>(*this));

      }

      NodeIt(const Graph& _graph, const Node& node) 

	: Node(node), graph(&_graph) { }

      NodeIt& operator++() { 

	graph->next(*this);

	return *this; 

      }

    };

    class ANodeIt : public Node { 

      friend class BpUGraphExtender;

      const Graph* graph;

    public:

      ANodeIt() { }

      ANodeIt(Invalid i) : Node(INVALID) { }

      explicit ANodeIt(const Graph& _graph) : graph(&_graph) {

	graph->firstANode(static_cast<Node&>(*this));

      }

      ANodeIt(const Graph& _graph, const Node& node) 

	: Node(node), graph(&_graph) {}

      ANodeIt& operator++() { 

	graph->nextANode(*this);

	return *this; 

      }

    };

    class BNodeIt : public Node { 

      friend class BpUGraphExtender;

      const Graph* graph;

    public:

      BNodeIt() { }

      BNodeIt(Invalid i) : Node(INVALID) { }

      explicit BNodeIt(const Graph& _graph) : graph(&_graph) {

	graph->firstBNode(static_cast<Node&>(*this));

      }

      BNodeIt(const Graph& _graph, const Node& node) 

	: Node(node), graph(&_graph) {}

      BNodeIt& operator++() { 

	graph->nextBNode(*this);

	return *this; 

      }

    };

    class EdgeIt : public Edge { 

      friend class BpUGraphExtender;

      const Graph* graph;

    public:

      EdgeIt() { }

      EdgeIt(Invalid i) : Edge(INVALID) { }

      explicit EdgeIt(const Graph& _graph) : graph(&_graph) {

	graph->first(static_cast<Edge&>(*this));

      }

      EdgeIt(const Graph& _graph, const Edge& edge) 

	: Edge(edge), graph(&_graph) { }

      EdgeIt& operator++() { 

	graph->next(*this);

	return *this; 

      }

    };

    class UEdgeIt : public UEdge { 

      friend class BpUGraphExtender;

      const Graph* graph;

    public:

      UEdgeIt() { }

      UEdgeIt(Invalid i) : UEdge(INVALID) { }

      explicit UEdgeIt(const Graph& _graph) : graph(&_graph) {

	graph->first(static_cast<UEdge&>(*this));

      }

      UEdgeIt(const Graph& _graph, const UEdge& edge) 

	: UEdge(edge), graph(&_graph) { }

      UEdgeIt& operator++() { 

	graph->next(*this);

	return *this; 

      }

    };

    class OutEdgeIt : public Edge { 

      friend class BpUGraphExtender;

      const Graph* graph;

    public:

      OutEdgeIt() { }

      OutEdgeIt(Invalid i) : Edge(i) { }

      OutEdgeIt(const Graph& _graph, const Node& node) 

	: graph(&_graph) {

	graph->firstOut(*this, node);

      }

      OutEdgeIt(const Graph& _graph, const Edge& edge) 

	: Edge(edge), graph(&_graph) {}

      OutEdgeIt& operator++() { 

	graph->nextOut(*this);

	return *this; 

      }

    };

    class InEdgeIt : public Edge { 

      friend class BpUGraphExtender;

      const Graph* graph;

    public:

      InEdgeIt() { }

      InEdgeIt(Invalid i) : Edge(i) { }

      InEdgeIt(const Graph& _graph, const Node& node) 

	: graph(&_graph) {

	graph->firstIn(*this, node);