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

 *

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

 *

 * Copyright (C) 2003-2013

 * 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/core.h>

#include <lemon/bits/map_extender.h>

#include <lemon/bits/default_map.h>

#include <lemon/concept_check.h>

#include <lemon/concepts/maps.h>

#include <lemon/bits/stl_iterators.h>

//\ingroup graphbits

//\file

//\brief Extenders for the graph types

namespace lemon {

  // \ingroup graphbits

  //

  // \brief Extender for the digraph implementations

  template <typename Base>

  class DigraphExtender : public Base {

    typedef Base Parent;

  public:

    typedef DigraphExtender Digraph;

    // Base extensions

    typedef typename Parent::Node Node;

    typedef typename Parent::Arc Arc;

    int maxId(Node) const {

      return Parent::maxNodeId();

    }

    int maxId(Arc) const {

      return Parent::maxArcId();

    }

    static Node fromId(int id, Node) {

      return Parent::nodeFromId(id);

    }

    static Arc fromId(int id, Arc) {

      return Parent::arcFromId(id);

    }

    Node oppositeNode(const Node &node, const Arc &arc) const {

      if (node == Parent::source(arc))

        return Parent::target(arc);

      else if(node == Parent::target(arc))

        return Parent::source(arc);

      else

        return INVALID;

    }

    // Alterable extension

    typedef AlterationNotifier<DigraphExtender, Node> NodeNotifier;

    typedef AlterationNotifier<DigraphExtender, Arc> ArcNotifier;

  protected:

    mutable NodeNotifier node_notifier;

    mutable ArcNotifier arc_notifier;

  public:

    NodeNotifier& notifier(Node) const {

      return node_notifier;

    }

    ArcNotifier& notifier(Arc) const {

      return arc_notifier;

    }

    class NodeIt : public Node {

      const Digraph* _digraph;

    public:

      NodeIt() {}

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

      explicit NodeIt(const Digraph& digraph) : _digraph(&digraph) {

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

      }

      NodeIt(const Digraph& digraph, const Node& node)

        : Node(node), _digraph(&digraph) {}

      NodeIt& operator++() {

        _digraph->next(*this);

        return *this;

      }

    };

    LemonRangeWrapper1<NodeIt, Digraph> nodes() const {

      return LemonRangeWrapper1<NodeIt, Digraph>(*this);

    }

    class ArcIt : public Arc {

      const Digraph* _digraph;

    public:

      ArcIt() { }

      ArcIt(Invalid i) : Arc(i) { }

      explicit ArcIt(const Digraph& digraph) : _digraph(&digraph) {

        _digraph->first(static_cast<Arc&>(*this));

      }

      ArcIt(const Digraph& digraph, const Arc& arc) :

        Arc(arc), _digraph(&digraph) { }

      ArcIt& operator++() {

        _digraph->next(*this);

        return *this;

      }

    };

    LemonRangeWrapper1<ArcIt, Digraph> arcs() const {

      return LemonRangeWrapper1<ArcIt, Digraph>(*this);

    }

    class OutArcIt : public Arc {

      const Digraph* _digraph;

    public:

      OutArcIt() { }

      OutArcIt(Invalid i) : Arc(i) { }

      OutArcIt(const Digraph& digraph, const Node& node)

        : _digraph(&digraph) {

        _digraph->firstOut(*this, node);

      }

      OutArcIt(const Digraph& digraph, const Arc& arc)

        : Arc(arc), _digraph(&digraph) {}

      OutArcIt& operator++() {

        _digraph->nextOut(*this);

        return *this;

      }

    };

    LemonRangeWrapper2<OutArcIt, Digraph, Node> outArcs(const Node& u) const {

      return LemonRangeWrapper2<OutArcIt, Digraph, Node>(*this, u);

    }

    class InArcIt : public Arc {

      const Digraph* _digraph;

    public:

      InArcIt() { }

      InArcIt(Invalid i) : Arc(i) { }

      InArcIt(const Digraph& digraph, const Node& node)

        : _digraph(&digraph) {

        _digraph->firstIn(*this, node);

      }

      InArcIt(const Digraph& digraph, const Arc& arc) :

        Arc(arc), _digraph(&digraph) {}

      InArcIt& operator++() {

        _digraph->nextIn(*this);

        return *this;

      }

    };

    LemonRangeWrapper2<InArcIt, Digraph, Node> inArcs(const Node& u) const {

      return LemonRangeWrapper2<InArcIt, Digraph, Node>(*this, u);

    }

    // \brief Base node of the iterator

    //

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

    Node baseNode(const OutArcIt &arc) const {

      return Parent::source(arc);

    }

    // \brief Running node of the iterator

    //

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

    // iterator

    Node runningNode(const OutArcIt &arc) const {

      return Parent::target(arc);

    }

    // \brief Base node of the iterator

    //

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

    Node baseNode(const InArcIt &arc) const {

      return Parent::target(arc);

    }

    // \brief Running node of the iterator

    //

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

    // iterator

    Node runningNode(const InArcIt &arc) const {

      return Parent::source(arc);

    }

    template <typename _Value>

    class NodeMap

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

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

    public:

      explicit NodeMap(const Digraph& digraph)

        : Parent(digraph) {}

      NodeMap(const Digraph& digraph, const _Value& value)

        : Parent(digraph, value) {}

    private:

      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 ArcMap

      : public MapExtender<DefaultMap<Digraph, Arc, _Value> > {

      typedef MapExtender<DefaultMap<Digraph, Arc, _Value> > Parent;

    public:

      explicit ArcMap(const Digraph& digraph)

        : Parent(digraph) {}

      ArcMap(const Digraph& digraph, const _Value& value)

        : Parent(digraph, value) {}

    private:

      ArcMap& operator=(const ArcMap& cmap) {

        return operator=<ArcMap>(cmap);

      }

      template <typename CMap>

      ArcMap& operator=(const CMap& cmap) {

        Parent::operator=(cmap);

        return *this;

      }

    };

    Node addNode() {

      Node node = Parent::addNode();

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

      return node;

    }

    Arc addArc(const Node& from, const Node& to) {

      Arc arc = Parent::addArc(from, to);

      notifier(Arc()).add(arc);

      return arc;

    }

    void clear() {

      notifier(Arc()).clear();

      notifier(Node()).clear();

      Parent::clear();

    }

    template <typename Digraph, typename NodeRefMap, typename ArcRefMap>

    void build(const Digraph& digraph, NodeRefMap& nodeRef, ArcRefMap& arcRef) {

      Parent::build(digraph, nodeRef, arcRef);

      notifier(Node()).build();

      notifier(Arc()).build();

    }

    void erase(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);

      }

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

      Parent::erase(node);

    }

    void erase(const Arc& arc) {

      notifier(Arc()).erase(arc);

      Parent::erase(arc);

    }

    DigraphExtender() {

      node_notifier.setContainer(*this);

      arc_notifier.setContainer(*this);

    }

    ~DigraphExtender() {

      arc_notifier.clear();

      node_notifier.clear();

    }

  };

  // \ingroup _graphbits

  //

  // \brief Extender for the Graphs

  template <typename Base>

  class GraphExtender : public Base {

    typedef Base Parent;

  public:

    typedef GraphExtender Graph;

    typedef True UndirectedTag;

    typedef typename Parent::Node Node;

    typedef typename Parent::Arc Arc;

    typedef typename Parent::Edge Edge;

    // Graph extension

    int maxId(Node) const {

      return Parent::maxNodeId();

    }

    int maxId(Arc) const {

      return Parent::maxArcId();

    }

    int maxId(Edge) const {

      return Parent::maxEdgeId();

    }

    static Node fromId(int id, Node) {

      return Parent::nodeFromId(id);

    }

    static Arc fromId(int id, Arc) {

      return Parent::arcFromId(id);

    }

    static Edge fromId(int id, Edge) {

      return Parent::edgeFromId(id);

    }

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

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

        return Parent::v(e);

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

        return Parent::u(e);

      else

        return INVALID;

    }

    Arc oppositeArc(const Arc &arc) const {

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

    }

    using Parent::direct;

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

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

    }

    // Alterable extension

    typedef AlterationNotifier<GraphExtender, Node> NodeNotifier;

    typedef AlterationNotifier<GraphExtender, Arc> ArcNotifier;

    typedef AlterationNotifier<GraphExtender, Edge> EdgeNotifier;

  protected:

    mutable NodeNotifier node_notifier;

    mutable ArcNotifier arc_notifier;

    mutable EdgeNotifier edge_notifier;

  public:

    NodeNotifier& notifier(Node) const {

      return node_notifier;

    }

    ArcNotifier& notifier(Arc) const {

      return arc_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;

      }

    };

    LemonRangeWrapper1<NodeIt, Graph> nodes() const {

      return LemonRangeWrapper1<NodeIt, Graph>(*this);

    }

    class ArcIt : public Arc {

      const Graph* _graph;

    public:

      ArcIt() { }

      ArcIt(Invalid i) : Arc(i) { }

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

        _graph->first(static_cast<Arc&>(*this));

      }

      ArcIt(const Graph& graph, const Arc& arc) :

        Arc(arc), _graph(&graph) { }

      ArcIt& operator++() {

        _graph->next(*this);

        return *this;

      }

    };

    LemonRangeWrapper1<ArcIt, Graph> arcs() const {

      return LemonRangeWrapper1<ArcIt, Graph>(*this);

    }

    class OutArcIt : public Arc {

      const Graph* _graph;

    public:

      OutArcIt() { }

      OutArcIt(Invalid i) : Arc(i) { }

      OutArcIt(const Graph& graph, const Node& node)

        : _graph(&graph) {

        _graph->firstOut(*this, node);

      }

      OutArcIt(const Graph& graph, const Arc& arc)

        : Arc(arc), _graph(&graph) {}

      OutArcIt& operator++() {

        _graph->nextOut(*this);

        return *this;

      }

    };

    LemonRangeWrapper2<OutArcIt, Graph, Node> outArcs(const Node& u) const {

      return LemonRangeWrapper2<OutArcIt, Graph, Node>(*this, u);

    }

    class InArcIt : public Arc {

      const Graph* _graph;

    public:

      InArcIt() { }

      InArcIt(Invalid i) : Arc(i) { }

      InArcIt(const Graph& graph, const Node& node)

        : _graph(&graph) {

        _graph->firstIn(*this, node);

      }

      InArcIt(const Graph& graph, const Arc& arc) :

        Arc(arc), _graph(&graph) {}

      InArcIt& operator++() {

        _graph->nextIn(*this);

        return *this;

      }

    };

    LemonRangeWrapper2<InArcIt, Graph, Node> inArcs(const Node& u) const {

      return LemonRangeWrapper2<InArcIt, Graph, Node>(*this, u);

    }

    class EdgeIt : public Parent::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& edge) :

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

      EdgeIt& operator++() {

        _graph->next(*this);

        return *this;

      }

    };

    LemonRangeWrapper1<EdgeIt, Graph> edges() const {

      return LemonRangeWrapper1<EdgeIt, Graph>(*this);

    }

    class IncEdgeIt : public Parent::Edge {

      friend class GraphExtender;

      const Graph* _graph;

      bool _direction;

    public:

      IncEdgeIt() { }

      IncEdgeIt(Invalid i) : Edge(i), _direction(false) { }

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

        _graph->firstInc(*this, _direction, node);

      }

      IncEdgeIt(const Graph& graph, const Edge &edge, const Node &node)

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

        _direction = (_graph->source(edge) == node);

      }

      IncEdgeIt& operator++() {

        _graph->nextInc(*this, _direction);

        return *this;

      }

    };

    LemonRangeWrapper2<IncEdgeIt, Graph, Node> incEdges(const Node& u) const {

      return LemonRangeWrapper2<IncEdgeIt, Graph, Node>(*this, u);

    }

    // \brief Base node of the iterator

    //

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

    Node baseNode(const OutArcIt &arc) const {

      return Parent::source(static_cast<const Arc&>(arc));

    }

    // \brief Running node of the iterator

    //

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

    // iterator

    Node runningNode(const OutArcIt &arc) const {

      return Parent::target(static_cast<const Arc&>(arc));

    }

    // \brief Base node of the iterator

    //

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

    Node baseNode(const InArcIt &arc) const {

      return Parent::target(static_cast<const Arc&>(arc));

    }

    // \brief Running node of the iterator

    //

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

    // iterator

    Node runningNode(const InArcIt &arc) const {

      return Parent::source(static_cast<const Arc&>(arc));

    }

    // Base node of the iterator

    //

    // Returns the base node of the iterator

    Node baseNode(const IncEdgeIt &edge) const {

      return edge._direction ? this->u(edge) : this->v(edge);

    }

    // Running node of the iterator

    //

    // Returns the running node of the iterator

    Node runningNode(const IncEdgeIt &edge) const {

      return edge._direction ? this->v(edge) : this->u(edge);

    }

    // Mappable extension

    template <typename _Value>

    class NodeMap

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

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

    public:

      explicit NodeMap(const Graph& graph)

        : Parent(graph) {}

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

        : Parent(graph, value) {}

    private:

      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 ArcMap

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

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

    public:

      explicit ArcMap(const Graph& graph)

        : Parent(graph) {}

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

        : Parent(graph, value) {}

    private:

      ArcMap& operator=(const ArcMap& cmap) {

        return operator=<ArcMap>(cmap);

      }

      template <typename CMap>

      ArcMap& operator=(const CMap& cmap) {

        Parent::operator=(cmap);

        return *this;

      }

    };

    template <typename _Value>

    class EdgeMap

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

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

    public:

      explicit EdgeMap(const Graph& graph)

        : Parent(graph) {}

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

        : Parent(graph, value) {}

    private:

      EdgeMap& operator=(const EdgeMap& cmap) {

        return operator=<EdgeMap>(cmap);

      }

      template <typename CMap>

      EdgeMap& operator=(const CMap& cmap) {

        Parent::operator=(cmap);

        return *this;

      }

    };

    // Alteration extension

    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);

      std::vector<Arc> ev;

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

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

      notifier(Arc()).add(ev);

      return edge;

    }

    void clear() {

      notifier(Arc()).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();

      notifier(Arc()).build();

    }

    void erase(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);

      }

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

      Parent::erase(node);

    }

    void erase(const Edge& edge) {

      std::vector<Arc> av;

      av.push_back(Parent::direct(edge, true));

      av.push_back(Parent::direct(edge, false));

      notifier(Arc()).erase(av);

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

      Parent::erase(edge);

    }

    GraphExtender() {

      node_notifier.setContainer(*this);

      arc_notifier.setContainer(*this);

      edge_notifier.setContainer(*this);

    }

    ~GraphExtender() {

      edge_notifier.clear();

      arc_notifier.clear();

      node_notifier.clear();

    }

  };

  // \ingroup _graphbits

  //

  // \brief Extender for the BpGraphs

  template <typename Base>

  class BpGraphExtender : public Base {

    typedef Base Parent;

  public:

    typedef BpGraphExtender BpGraph;

    typedef True UndirectedTag;

    typedef typename Parent::Node Node;

    typedef typename Parent::RedNode RedNode;

    typedef typename Parent::BlueNode BlueNode;

    typedef typename Parent::Arc Arc;

    typedef typename Parent::Edge Edge;

    // BpGraph extension

    using Parent::first;

    using Parent::next;

    using Parent::id;

    int maxId(Node) const {

      return Parent::maxNodeId();

    }

    int maxId(RedNode) const {

      return Parent::maxRedId();

    }

    int maxId(BlueNode) const {

      return Parent::maxBlueId();

    }

    int maxId(Arc) const {

      return Parent::maxArcId();

    }

    int maxId(Edge) const {

      return Parent::maxEdgeId();

    }

    static Node fromId(int id, Node) {

      return Parent::nodeFromId(id);

    }

    static Arc fromId(int id, Arc) {

      return Parent::arcFromId(id);

    }

    static Edge fromId(int id, Edge) {

      return Parent::edgeFromId(id);

    }

    Node u(Edge e) const { return this->redNode(e); }

    Node v(Edge e) const { return this->blueNode(e); }

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

      if( n == u(e))

        return v(e);

      else if( n == v(e))

        return u(e);

      else

        return INVALID;

    }

    Arc oppositeArc(const Arc &arc) const {

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

    }

    using Parent::direct;

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

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

    }

    RedNode asRedNode(const Node& node) const {

      if (node == INVALID || Parent::blue(node)) {

        return INVALID;

      } else {

        return Parent::asRedNodeUnsafe(node);

      }

    }

    BlueNode asBlueNode(const Node& node) const {

      if (node == INVALID || Parent::red(node)) {

        return INVALID;

      } else {

        return Parent::asBlueNodeUnsafe(node);

      }

    }

    // Alterable extension

    typedef AlterationNotifier<BpGraphExtender, Node> NodeNotifier;

    typedef AlterationNotifier<BpGraphExtender, RedNode> RedNodeNotifier;

    typedef AlterationNotifier<BpGraphExtender, BlueNode> BlueNodeNotifier;

    typedef AlterationNotifier<BpGraphExtender, Arc> ArcNotifier;

    typedef AlterationNotifier<BpGraphExtender, Edge> EdgeNotifier;

  protected:

    mutable NodeNotifier node_notifier;

    mutable RedNodeNotifier red_node_notifier;

    mutable BlueNodeNotifier blue_node_notifier;

    mutable ArcNotifier arc_notifier;

    mutable EdgeNotifier edge_notifier;

  public:

    NodeNotifier& notifier(Node) const {

      return node_notifier;

    }

    RedNodeNotifier& notifier(RedNode) const {

      return red_node_notifier;

    }

    BlueNodeNotifier& notifier(BlueNode) const {

      return blue_node_notifier;

    }

    ArcNotifier& notifier(Arc) const {

      return arc_notifier;

    }

    EdgeNotifier& notifier(Edge) const {

      return edge_notifier;

    }

    class NodeIt : public Node {

      const BpGraph* _graph;

    public:

      NodeIt() {}

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

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

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

      }

      NodeIt(const BpGraph& graph, const Node& node)

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

      NodeIt& operator++() {

        _graph->next(*this);

        return *this;

      }

    };

    LemonRangeWrapper1<NodeIt, BpGraph> nodes() const {

      return LemonRangeWrapper1<NodeIt, BpGraph>(*this);

    }

    class RedNodeIt : public RedNode {

      const BpGraph* _graph;

    public:

      RedNodeIt() {}

      RedNodeIt(Invalid i) : RedNode(i) { }

      explicit RedNodeIt(const BpGraph& graph) : _graph(&graph) {

        _graph->first(static_cast<RedNode&>(*this));

      }

      RedNodeIt(const BpGraph& graph, const RedNode& node)

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

      RedNodeIt& operator++() {

        _graph->next(static_cast<RedNode&>(*this));

        return *this;

      }

    };

    LemonRangeWrapper1<RedNodeIt, BpGraph> redNodes() const {

      return LemonRangeWrapper1<RedNodeIt, BpGraph>(*this);

    }

    class BlueNodeIt : public BlueNode {

      const BpGraph* _graph;

    public:

      BlueNodeIt() {}

      BlueNodeIt(Invalid i) : BlueNode(i) { }

      explicit BlueNodeIt(const BpGraph& graph) : _graph(&graph) {

        _graph->first(static_cast<BlueNode&>(*this));

      }