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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_SMART_GRAPH_H

#define LEMON_SMART_GRAPH_H

///\ingroup graphs

///\file

///\brief SmartDigraph and SmartGraph classes.

#include <vector>

#include <lemon/core.h>

#include <lemon/error.h>

#include <lemon/bits/graph_extender.h>

namespace lemon {

  class SmartDigraph;

  ///Base of SmartDigraph

  ///Base of SmartDigraph

  ///

  class SmartDigraphBase {

  protected:

    struct NodeT

    {

      int first_in, first_out;

      NodeT() {}

    };

    struct ArcT

    {

      int target, source, next_in, next_out;

      ArcT() {}

    };

    std::vector<NodeT> nodes;

    std::vector<ArcT> arcs;

  public:

    typedef SmartDigraphBase Graph;

    class Node;

    class Arc;

  public:

    SmartDigraphBase() : nodes(), arcs() { }

    SmartDigraphBase(const SmartDigraphBase &_g)

      : nodes(_g.nodes), arcs(_g.arcs) { }

    typedef True NodeNumTag;

    typedef True ArcNumTag;

    int nodeNum() const { return nodes.size(); }

    int arcNum() const { return arcs.size(); }

    int maxNodeId() const { return nodes.size()-1; }

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

    Node addNode() {

      int n = nodes.size();

      nodes.push_back(NodeT());

      nodes[n].first_in = -1;

      nodes[n].first_out = -1;

      return Node(n);

    }

    Arc addArc(Node u, Node v) {

      int n = arcs.size();

      arcs.push_back(ArcT());

      arcs[n].source = u._id;

      arcs[n].target = v._id;

      arcs[n].next_out = nodes[u._id].first_out;

      arcs[n].next_in = nodes[v._id].first_in;

      nodes[u._id].first_out = nodes[v._id].first_in = n;

      return Arc(n);

    }

    void clear() {

      arcs.clear();

      nodes.clear();

    }

    Node source(Arc a) const { return Node(arcs[a._id].source); }

    Node target(Arc a) const { return Node(arcs[a._id].target); }

    static int id(Node v) { return v._id; }

    static int id(Arc a) { return a._id; }

    static Node nodeFromId(int id) { return Node(id);}

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

    bool valid(Node n) const {

      return n._id >= 0 && n._id < static_cast<int>(nodes.size());

    }

    bool valid(Arc a) const {

      return a._id >= 0 && a._id < static_cast<int>(arcs.size());

    }

    class Node {

      friend class SmartDigraphBase;

      friend class SmartDigraph;

    protected:

      int _id;

      explicit Node(int id) : _id(id) {}

    public:

      Node() {}

      Node (Invalid) : _id(-1) {}

      bool operator==(const Node i) const {return _id == i._id;}

      bool operator!=(const Node i) const {return _id != i._id;}

      bool operator<(const Node i) const {return _id < i._id;}

    };

    class Arc {

      friend class SmartDigraphBase;

      friend class SmartDigraph;

    protected:

      int _id;

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

    public:

      Arc() { }

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

      bool operator==(const Arc i) const {return _id == i._id;}

      bool operator!=(const Arc i) const {return _id != i._id;}

      bool operator<(const Arc i) const {return _id < i._id;}

    };

    void first(Node& node) const {

      node._id = nodes.size() - 1;

    }

    static void next(Node& node) {

      --node._id;

    }

    void first(Arc& arc) const {

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

    }

    static void next(Arc& arc) {

      --arc._id;

    }

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

      arc._id = nodes[node._id].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._id].first_in;

    }

    void nextIn(Arc& arc) const {

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

    }

  };

  typedef DigraphExtender<SmartDigraphBase> ExtendedSmartDigraphBase;

  ///\ingroup graphs

  ///

  ///\brief A smart directed graph class.

  ///

  ///This is a simple and fast digraph implementation.

  ///It is also quite memory efficient, but at the price

  ///that <b> it does support only limited (only stack-like)

  ///node and arc deletions</b>.

  ///It conforms to the \ref concepts::Digraph "Digraph concept" with

  ///an important extra feature that its maps are real \ref

  ///concepts::ReferenceMap "reference map"s.

  ///

  ///\sa concepts::Digraph.

  class SmartDigraph : public ExtendedSmartDigraphBase {

  public:

    typedef ExtendedSmartDigraphBase Parent;

  private:

    ///SmartDigraph is \e not copy constructible. Use DigraphCopy() instead.

    ///SmartDigraph is \e not copy constructible. Use DigraphCopy() instead.

    ///

    SmartDigraph(const SmartDigraph &) : ExtendedSmartDigraphBase() {};

    ///\brief Assignment of SmartDigraph to another one is \e not allowed.

    ///Use DigraphCopy() instead.

    ///Assignment of SmartDigraph to another one is \e not allowed.

    ///Use DigraphCopy() instead.

    void operator=(const SmartDigraph &) {}

  public:

    /// Constructor

    /// Constructor.

    ///

    SmartDigraph() {};

    ///Add a new node to the digraph.

    /// \return the new node.

    ///

    Node addNode() { return Parent::addNode(); }

    ///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 Using this it is possible to avoid the superfluous memory

    /// allocation.

    /// Using this it is possible to avoid the superfluous memory

    /// allocation: if you know that the digraph you want to build will

    /// be very large (e.g. it will contain millions of nodes and/or arcs)

    /// then it is worth reserving space for this amount before starting

    /// to build the digraph.

    /// \sa reserveArc

    void reserveNode(int n) { nodes.reserve(n); };

    /// \brief Using this it is possible to avoid the superfluous memory

    /// allocation.

    /// Using this it is possible to avoid the superfluous memory

    /// allocation: if you know that the digraph you want to build will

    /// be very large (e.g. it will contain millions of nodes and/or arcs)

    /// then it is worth reserving space for this amount before starting

    /// to build the digraph.

    /// \sa reserveNode

    void reserveArc(int m) { arcs.reserve(m); };

    /// \brief Node validity check

    ///

    /// This function gives back true if the given node is valid,

    /// ie. it is a real node of the graph.

    ///

    /// \warning A removed node (using Snapshot) could become valid again

    /// when new nodes are added to the graph.

    bool valid(Node n) const { return Parent::valid(n); }

    /// \brief Arc validity check

    ///

    /// This function gives back true if the given arc is valid,

    /// ie. it is a real arc of the graph.

    ///

    /// \warning A removed arc (using Snapshot) could become valid again

    /// when new arcs are added to the graph.

    bool valid(Arc a) const { return Parent::valid(a); }

    ///Clear the digraph.

    ///Erase all the nodes and arcs from the digraph.

    ///

    void clear() {

      Parent::clear();

    }

    ///Split a node.

    ///This function splits a node. First a new node is added to the digraph,

    ///then the source of each outgoing arc of \c n is moved to this new node.

    ///If \c connect is \c true (this is the default value), then a new arc

    ///from \c n to the newly created node is also added.

    ///\return The newly created node.

    ///

    ///\note The <tt>Arc</tt>s

    ///referencing a moved arc remain

    ///valid. However <tt>InArc</tt>'s and <tt>OutArc</tt>'s

    ///may be invalidated.

    ///\warning This functionality cannot be used together with the Snapshot

    ///feature.

    Node split(Node n, bool connect = true)

    {

      Node b = addNode();

      nodes[b._id].first_out=nodes[n._id].first_out;

      nodes[n._id].first_out=-1;

      if(connect) addArc(n,b);

      return b;

    }

  public:

    class Snapshot;

  protected:

    void restoreSnapshot(const Snapshot &s)

    {

      while(s.arc_num<arcs.size()) {

        Arc arc = arcFromId(arcs.size()-1);

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

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

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

        arcs.pop_back();

      }

      while(s.node_num<nodes.size()) {

        Node node = nodeFromId(nodes.size()-1);

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

        nodes.pop_back();

      }

    }

  public:

    ///Class to make a snapshot of the digraph and to restrore to it later.

    ///Class to make a snapshot of the digraph and to restrore to it later.

    ///

    ///The newly added nodes and arcs can be removed using the

    ///restore() function.

    ///\note After you restore a state, you cannot restore

    ///a later state, in other word you cannot add again the arcs deleted

    ///by restore() using another one Snapshot instance.

    ///

    ///\warning If you do not use correctly the snapshot that can cause

    ///either broken program, invalid state of the digraph, valid but

    ///not the restored digraph or no change. Because the runtime performance

    ///the validity of the snapshot is not stored.

    class Snapshot

    {

      SmartDigraph *_graph;

    protected:

      friend class SmartDigraph;

      unsigned int node_num;

      unsigned int arc_num;

    public:

      ///Default constructor.

      ///Default constructor.

      ///To actually make a snapshot you must call save().

      ///

      Snapshot() : _graph(0) {}

      ///Constructor that immediately makes a snapshot

      ///This constructor immediately makes a snapshot of the digraph.

      ///\param graph The digraph we make a snapshot of.

      Snapshot(SmartDigraph &graph) : _graph(&graph) {

        node_num=_graph->nodes.size();

        arc_num=_graph->arcs.size();

      }

      ///Make a snapshot.

      ///Make a snapshot of the digraph.

      ///

      ///This function can be called more than once. In case of a repeated

      ///call, the previous snapshot gets lost.

      ///\param graph The digraph we make the snapshot of.

      void save(SmartDigraph &graph)

      {

        _graph=&graph;

        node_num=_graph->nodes.size();

        arc_num=_graph->arcs.size();

      }

      ///Undo the changes until a snapshot.

      ///Undo the changes until a snapshot created by save().

      ///

      ///\note After you restored a state, you cannot restore

      ///a later state, in other word you cannot add again the arcs deleted

      ///by restore().

      void restore()

      {

        _graph->restoreSnapshot(*this);

      }

    };

  };

  class SmartGraphBase {

  protected:

    struct NodeT {

      int first_out;

    };

    struct ArcT {

      int target;

      int next_out;

    };

    std::vector<NodeT> nodes;

    std::vector<ArcT> arcs;

    int first_free_arc;

  public:

    typedef SmartGraphBase Digraph;

    class Node;

    class Arc;

    class Edge;

    class Node {

      friend class SmartGraphBase;

    protected:

      int _id;

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

    public:

      Node() {}

      Node (Invalid) { _id = -1; }

      bool operator==(const Node& node) const {return _id == node._id;}

      bool operator!=(const Node& node) const {return _id != node._id;}

      bool operator<(const Node& node) const {return _id < node._id;}

    };

    class Edge {

      friend class SmartGraphBase;

    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 SmartGraphBase;

    protected:

      int _id;

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

    public:

      operator Edge() const {

        return _id != -1 ? edgeFromId(_id / 2) : INVALID;

      }

      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;}

    };

    SmartGraphBase()

      : nodes(), arcs() {}

    typedef True NodeNumTag;

    typedef True EdgeNumTag;

    typedef True ArcNumTag;

    int nodeNum() const { return nodes.size(); }

    int edgeNum() const { return arcs.size() / 2; }

    int arcNum() const { return arcs.size(); }

    int maxNodeId() const { return nodes.size()-1; }

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

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

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

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

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

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

    static bool direction(Arc e) {

      return (e._id & 1) == 1;

    }

    static Arc direct(Edge e, bool d) {

      return Arc(e._id * 2 + (d ? 1 : 0));

    }

    void first(Node& node) const {

      node._id = nodes.size() - 1;

    }

    void next(Node& node) const {

      --node._id;

    }

    void first(Arc& arc) const {

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

    }

    void next(Arc& arc) const {

      --arc._id;

    }

    void first(Edge& arc) const {

      arc._id = arcs.size() / 2 - 1;

    }

    void next(Edge& arc) const {

      --arc._id;

    }

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

      arc._id = nodes[v._id].first_out;

    }

    void nextOut(Arc &arc) const {

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

    }

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

      arc._id = ((nodes[v._id].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& d, const Node& v) const {

      int de = nodes[v._id].first_out;

      if (de != -1) {

        arc._id = de / 2;

        d = ((de & 1) == 1);

      } else {

        arc._id = -1;

        d = true;

      }

    }

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

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

      if (de != -1) {

        arc._id = de / 2;

        d = ((de & 1) == 1);

      } else {

        arc._id = -1;

        d = true;

      }

    }

    static int id(Node v) { return v._id; }

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

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

    static Node nodeFromId(int id) { return Node(id);}

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

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

    bool valid(Node n) const {

      return n._id >= 0 && n._id < static_cast<int>(nodes.size());

    }

    bool valid(Arc a) const {

      return a._id >= 0 && a._id < static_cast<int>(arcs.size());

    }

    bool valid(Edge e) const {

      return e._id >= 0 && 2 * e._id < static_cast<int>(arcs.size());

    }

    Node addNode() {

      int n = nodes.size();

      nodes.push_back(NodeT());

      nodes[n].first_out = -1;

      return Node(n);

    }

    Edge addEdge(Node u, Node v) {

      int n = arcs.size();

      arcs.push_back(ArcT());

      arcs.push_back(ArcT());

      arcs[n].target = u._id;

      arcs[n | 1].target = v._id;

      arcs[n].next_out = nodes[v._id].first_out;

      nodes[v._id].first_out = n;

      arcs[n | 1].next_out = nodes[u._id].first_out;

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

      return Edge(n / 2);

    }

    void clear() {

      arcs.clear();

      nodes.clear();

    }

  };

  typedef GraphExtender<SmartGraphBase> ExtendedSmartGraphBase;

  /// \ingroup graphs

  ///

  /// \brief A smart undirected graph class.

  ///

  /// This is a simple and fast graph implementation.

  /// It is also quite memory efficient, but at the price

  /// that <b> it does support only limited (only stack-like)

  /// node and arc deletions</b>.

  /// Except from this it conforms to

  /// the \ref concepts::Graph "Graph concept".

  ///

  /// It also has an

  /// important extra feature that

  /// its maps are real \ref concepts::ReferenceMap "reference map"s.

  ///

  /// \sa concepts::Graph.

  ///

  class SmartGraph : public ExtendedSmartGraphBase {

  private:

    ///SmartGraph is \e not copy constructible. Use GraphCopy() instead.

    ///SmartGraph is \e not copy constructible. Use GraphCopy() instead.

    ///

    SmartGraph(const SmartGraph &) : ExtendedSmartGraphBase() {};

    ///\brief Assignment of SmartGraph to another one is \e not allowed.

    ///Use GraphCopy() instead.

    ///Assignment of SmartGraph to another one is \e not allowed.

    ///Use GraphCopy() instead.

    void operator=(const SmartGraph &) {}

  public:

    typedef ExtendedSmartGraphBase Parent;

    /// Constructor

    /// Constructor.

    ///

    SmartGraph() {}

    ///Add a new node to the graph.

    /// \return the new node.

    ///

    Node addNode() { return Parent::addNode(); }

    ///Add a new edge to the graph.

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

    ///and \c t.

    ///\return the new edge.

    Edge addEdge(const Node& s, const Node& t) {

      return Parent::addEdge(s, t);

    }

    /// \brief Node validity check

    ///

    /// This function gives back true if the given node is valid,

    /// ie. it is a real node of the graph.

    ///

    /// \warning A removed node (using Snapshot) could become valid again

    /// when new nodes are added to the graph.

    bool valid(Node n) const { return Parent::valid(n); }

    /// \brief Arc validity check

    ///

    /// This function gives back true if the given arc is valid,

    /// ie. it is a real arc of the graph.