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/* -*- C++ -*-

 *

 * 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_GRAPH_UTILS_H

#define LEMON_GRAPH_UTILS_H

#include <iterator>

#include <vector>

#include <map>

#include <cmath>

#include <algorithm>

#include <lemon/bits/invalid.h>

#include <lemon/bits/utility.h>

#include <lemon/maps.h>

#include <lemon/bits/traits.h>

#include <lemon/bits/alteration_notifier.h>

#include <lemon/bits/default_map.h>

///\ingroup gutils

///\file

///\brief Graph utilities.

namespace lemon {

  /// \addtogroup gutils

  /// @{

  namespace _graph_utils_bits {

    template <typename Graph>

    struct Node { typedef typename Graph::Node type; };

    template <typename Graph>

    struct NodeIt { typedef typename Graph::NodeIt type; };

    template <typename Graph>

    struct Arc { typedef typename Graph::Arc type; };

    template <typename Graph>

    struct ArcIt { typedef typename Graph::ArcIt type; };

    template <typename Graph>

    struct Edge { typedef typename Graph::Edge type; };

    template <typename Graph>

    struct EdgeIt { typedef typename Graph::EdgeIt type; };

    template <typename Graph>

    struct OutArcIt { typedef typename Graph::OutArcIt type; };

    template <typename Graph>

    struct InArcIt { typedef typename Graph::InArcIt type; };

    template <typename Graph>

    struct IncEdgeIt { typedef typename Graph::IncEdgeIt type; };

    template <typename Graph>

    struct BoolNodeMap { 

      typedef typename Graph::template NodeMap<bool> type; 

    };

    template <typename Graph>

    struct IntNodeMap { 

      typedef typename Graph::template NodeMap<int> type; 

    };

    template <typename Graph>

    struct DoubleNodeMap { 

      typedef typename Graph::template NodeMap<double> type; 

    };

    template <typename Graph>

    struct BoolArcMap { 

      typedef typename Graph::template ArcMap<bool> type; 

    };

    template <typename Graph>

    struct IntArcMap { 

      typedef typename Graph::template ArcMap<int> type; 

    };

    template <typename Graph>

    struct DoubleArcMap { 

      typedef typename Graph::template ArcMap<double> type; 

    };

    template <typename Graph>

    struct BoolEdgeMap { 

      typedef typename Graph::template EdgeMap<bool> type; 

    };

    template <typename Graph>

    struct IntEdgeMap { 

      typedef typename Graph::template EdgeMap<int> type; 

    };

    template <typename Graph>

    struct DoubleEdgeMap { 

      typedef typename Graph::template EdgeMap<double> type; 

    };

  }

  ///Creates convenience typedefs for the digraph types and iterators

  ///This \c \#define creates convenience typedefs for the following types

  ///of \c Digraph: \c Node,  \c NodeIt, \c Arc, \c ArcIt, \c InArcIt,

  ///\c OutArcIt, \c BoolNodeMap, \c IntNodeMap, \c DoubleNodeMap, 

  ///\c BoolArcMap, \c IntArcMap, \c DoubleArcMap. 

#define DIGRAPH_TYPEDEFS(Digraph)					\

  typedef typename ::lemon::_graph_utils_bits::				\

  Node<Digraph>::type Node;						\

  typedef typename ::lemon::_graph_utils_bits::				\

  NodeIt<Digraph>::type	NodeIt;						\

  typedef typename ::lemon::_graph_utils_bits::				\

  Arc<Digraph>::type Arc;						\

  typedef typename ::lemon::_graph_utils_bits::				\

  ArcIt<Digraph>::type ArcIt;						\

  typedef typename ::lemon::_graph_utils_bits::				\

  OutArcIt<Digraph>::type OutArcIt;					\

  typedef typename ::lemon::_graph_utils_bits::				\

  InArcIt<Digraph>::type InArcIt;					\

  typedef typename ::lemon::_graph_utils_bits::				\

  BoolNodeMap<Digraph>::type BoolNodeMap;				\

  typedef typename ::lemon::_graph_utils_bits::				\

  IntNodeMap<Digraph>::type IntNodeMap;					\

  typedef typename ::lemon::_graph_utils_bits::				\

  DoubleNodeMap<Digraph>::type DoubleNodeMap;				\

  typedef typename ::lemon::_graph_utils_bits::				\

  BoolArcMap<Digraph>::type BoolArcMap;					\

  typedef typename ::lemon::_graph_utils_bits::				\

  IntArcMap<Digraph>::type IntArcMap;					\

  typedef typename ::lemon::_graph_utils_bits::				\

  DoubleArcMap<Digraph>::type DoubleArcMap

  ///Creates convenience typedefs for the graph types and iterators

  ///This \c \#define creates the same convenience typedefs as defined

  ///by \ref DIGRAPH_TYPEDEFS(Graph) and six more, namely it creates

  ///\c Edge, \c EdgeIt, \c IncEdgeIt, \c BoolEdgeMap, \c IntEdgeMap,

  ///\c DoubleEdgeMap.

#define GRAPH_TYPEDEFS(Graph)						\

  DIGRAPH_TYPEDEFS(Graph);						\

  typedef typename ::lemon::_graph_utils_bits::				\

  Edge<Graph>::type Edge;						\

  typedef typename ::lemon::_graph_utils_bits::				\

  EdgeIt<Graph>::type EdgeIt;						\

  typedef typename ::lemon::_graph_utils_bits::				\

  typedef typename ::lemon::_graph_utils_bits::				\

  BoolEdgeMap<Graph>::type BoolEdgeMap;					\

  typedef typename ::lemon::_graph_utils_bits::				\

  IntEdgeMap<Graph>::type IntEdgeMap;					\

  typedef typename ::lemon::_graph_utils_bits::				\

  DoubleEdgeMap<Graph>::type DoubleEdgeMap

  /// \brief Function to count the items in the graph.

  ///

  /// This function counts the items (nodes, arcs etc) in the graph.

  /// The complexity of the function is O(n) because

  /// it iterates on all of the items.

  template <typename Graph, typename Item>

  inline int countItems(const Graph& g) {

    typedef typename ItemSetTraits<Graph, Item>::ItemIt ItemIt;

    int num = 0;

    for (ItemIt it(g); it != INVALID; ++it) {

      ++num;

    }

    return num;

  }

  // Node counting:

  namespace _graph_utils_bits {

    template <typename Graph, typename Enable = void>

    struct CountNodesSelector {

      static int count(const Graph &g) {

        return countItems<Graph, typename Graph::Node>(g);

      }

    };

    template <typename Graph>

    struct CountNodesSelector<

      Graph, typename 

      enable_if<typename Graph::NodeNumTag, void>::type> 

    {

      static int count(const Graph &g) {

        return g.nodeNum();

      }

    };    

  }

  /// \brief Function to count the nodes in the graph.

  ///

  /// This function counts the nodes in the graph.

  /// The complexity of the function is O(n) but for some

  /// graph structures it is specialized to run in O(1).

  ///

  /// If the graph contains a \e nodeNum() member function and a 

  /// \e NodeNumTag tag then this function calls directly the member

  /// function to query the cardinality of the node set.

  template <typename Graph>

  inline int countNodes(const Graph& g) {

    return _graph_utils_bits::CountNodesSelector<Graph>::count(g);

  }

  // Arc counting:

  namespace _graph_utils_bits {

    template <typename Graph, typename Enable = void>

    struct CountArcsSelector {

      static int count(const Graph &g) {

        return countItems<Graph, typename Graph::Arc>(g);

      }

    };

    template <typename Graph>

    struct CountArcsSelector<

      Graph, 

      typename enable_if<typename Graph::ArcNumTag, void>::type> 

    {

      static int count(const Graph &g) {

        return g.arcNum();

      }

    };    

  }

  /// \brief Function to count the arcs in the graph.

  ///

  /// This function counts the arcs in the graph.

  /// The complexity of the function is O(e) but for some

  /// graph structures it is specialized to run in O(1).

  ///

  /// If the graph contains a \e arcNum() member function and a 

  /// \e EdgeNumTag tag then this function calls directly the member

  /// function to query the cardinality of the arc set.

  template <typename Graph>

  inline int countArcs(const Graph& g) {

    return _graph_utils_bits::CountArcsSelector<Graph>::count(g);

  }

  // Edge counting:

  namespace _graph_utils_bits {

    template <typename Graph, typename Enable = void>

    struct CountEdgesSelector {

      static int count(const Graph &g) {

        return countItems<Graph, typename Graph::Edge>(g);

      }

    };

    template <typename Graph>

    struct CountEdgesSelector<

      Graph, 

      typename enable_if<typename Graph::EdgeNumTag, void>::type> 

    {

      static int count(const Graph &g) {

        return g.edgeNum();

      }

    };    

  }

  /// \brief Function to count the edges in the graph.

  ///

  /// This function counts the edges in the graph.

  /// The complexity of the function is O(m) but for some

  /// graph structures it is specialized to run in O(1).

  ///

  /// If the graph contains a \e edgeNum() member function and a 

  /// \e EdgeNumTag tag then this function calls directly the member

  /// function to query the cardinality of the edge set.

  template <typename Graph>

  inline int countEdges(const Graph& g) {

    return _graph_utils_bits::CountEdgesSelector<Graph>::count(g);

  }

  template <typename Graph, typename DegIt>

  inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {

    int num = 0;

    for (DegIt it(_g, _n); it != INVALID; ++it) {

      ++num;

    }

    return num;

  }

  /// \brief Function to count the number of the out-arcs from node \c n.

  ///

  /// This function counts the number of the out-arcs from node \c n

  /// in the graph.  

  template <typename Graph>

  inline int countOutArcs(const Graph& _g,  const typename Graph::Node& _n) {

    return countNodeDegree<Graph, typename Graph::OutArcIt>(_g, _n);

  }

  /// \brief Function to count the number of the in-arcs to node \c n.

  ///

  /// This function counts the number of the in-arcs to node \c n

  /// in the graph.  

  template <typename Graph>

  inline int countInArcs(const Graph& _g,  const typename Graph::Node& _n) {

    return countNodeDegree<Graph, typename Graph::InArcIt>(_g, _n);

  }

  /// \brief Function to count the number of the inc-edges to node \c n.

  ///

  /// This function counts the number of the inc-edges to node \c n

  /// in the graph.  

  template <typename Graph>

  inline int countIncEdges(const Graph& _g,  const typename Graph::Node& _n) {

    return countNodeDegree<Graph, typename Graph::IncEdgeIt>(_g, _n);

  }

  namespace _graph_utils_bits {

    template <typename Graph, typename Enable = void>

    struct FindArcSelector {

      typedef typename Graph::Node Node;

      typedef typename Graph::Arc Arc;

      static Arc find(const Graph &g, Node u, Node v, Arc e) {

        if (e == INVALID) {

          g.firstOut(e, u);

        } else {

          g.nextOut(e);

        }

        while (e != INVALID && g.target(e) != v) {

          g.nextOut(e);

        }

        return e;

      }

    };

    template <typename Graph>

    struct FindArcSelector<

      Graph, 

      typename enable_if<typename Graph::FindEdgeTag, void>::type> 

    {

      typedef typename Graph::Node Node;

      typedef typename Graph::Arc Arc;

      static Arc find(const Graph &g, Node u, Node v, Arc prev) {

        return g.findArc(u, v, prev);

      }

    };    

  }

  /// \brief Finds an arc between two nodes of a graph.

  ///

  /// Finds an arc from node \c u to node \c v in graph \c g.

  ///

  /// If \c prev is \ref INVALID (this is the default value), then

  /// it finds the first arc from \c u to \c v. Otherwise it looks for

  /// the next arc from \c u to \c v after \c prev.

  /// \return The found arc or \ref INVALID if there is no such an arc.

  ///

  /// Thus you can iterate through each arc from \c u to \c v as it follows.

  ///\code

  /// for(Arc e=findArc(g,u,v);e!=INVALID;e=findArc(g,u,v,e)) {

  ///   ...

  /// }

  ///\endcode

  ///

  ///\sa ArcLookUp

  ///\sa AllArcLookUp

  ///\sa DynArcLookUp

  ///\sa ConArcIt

  template <typename Graph>

  inline typename Graph::Arc 

  findArc(const Graph &g, typename Graph::Node u, typename Graph::Node v,

           typename Graph::Arc prev = INVALID) {

    return _graph_utils_bits::FindArcSelector<Graph>::find(g, u, v, prev);

  }

  /// \brief Iterator for iterating on arcs connected the same nodes.

  ///

  /// Iterator for iterating on arcs connected the same nodes. It is 

  /// higher level interface for the findArc() function. You can

  /// use it the following way:

  ///\code

  /// for (ConArcIt<Graph> it(g, src, trg); it != INVALID; ++it) {

  ///   ...

  /// }

  ///\endcode

  /// 

  ///\sa findArc()

  ///\sa ArcLookUp

  ///\sa AllArcLookUp

  ///\sa DynArcLookUp

  ///

  /// \author Balazs Dezso 

  template <typename _Graph>

  class ConArcIt : public _Graph::Arc {

  public:

    typedef _Graph Graph;

    typedef typename Graph::Arc Parent;

    typedef typename Graph::Arc Arc;

    typedef typename Graph::Node Node;

    /// \brief Constructor.

    ///

    /// Construct a new ConArcIt iterating on the arcs which

    /// connects the \c u and \c v node.

    ConArcIt(const Graph& g, Node u, Node v) : _graph(g) {

      Parent::operator=(findArc(_graph, u, v));

    }

    /// \brief Constructor.

    ///

    /// Construct a new ConArcIt which continues the iterating from 

    /// the \c e arc.

    ConArcIt(const Graph& g, Arc a) : Parent(a), _graph(g) {}

    /// \brief Increment operator.

    ///

    /// It increments the iterator and gives back the next arc.

    ConArcIt& operator++() {

      Parent::operator=(findArc(_graph, _graph.source(*this), 

				_graph.target(*this), *this));

      return *this;

    }

  private:

    const Graph& _graph;

  };

  namespace _graph_utils_bits {

    template <typename Graph, typename Enable = void>

    struct FindEdgeSelector {

      typedef typename Graph::Node Node;

      typedef typename Graph::Edge Edge;

      static Edge find(const Graph &g, Node u, Node v, Edge e) {

        bool b;

        if (u != v) {

          if (e == INVALID) {

            g.firstInc(e, b, u);

          } else {

            b = g.source(e) == u;

            g.nextInc(e, b);

          }

          while (e != INVALID && (b ? g.target(e) : g.source(e)) != v) {

            g.nextInc(e, b);

          }

        } else {

          if (e == INVALID) {

            g.firstInc(e, b, u);

          } else {

            b = true;

            g.nextInc(e, b);

          }

          while (e != INVALID && (!b || g.target(e) != v)) {

            g.nextInc(e, b);

          }

        }

        return e;

      }

    };

    template <typename Graph>

    struct FindEdgeSelector<

      Graph, 

      typename enable_if<typename Graph::FindEdgeTag, void>::type> 

    {

      typedef typename Graph::Node Node;

      typedef typename Graph::Edge Edge;

      static Edge find(const Graph &g, Node u, Node v, Edge prev) {

        return g.findEdge(u, v, prev);

      }

    };    

  }

  /// \brief Finds an edge between two nodes of a graph.

  ///

  /// Finds an edge from node \c u to node \c v in graph \c g.

  /// If the node \c u and node \c v is equal then each loop edge

  /// will be enumerated once.

  ///

  /// If \c prev is \ref INVALID (this is the default value), then

  /// it finds the first arc from \c u to \c v. Otherwise it looks for

  /// the next arc from \c u to \c v after \c prev.

  /// \return The found arc or \ref INVALID if there is no such an arc.

  ///

  /// Thus you can iterate through each arc from \c u to \c v as it follows.

  ///\code

  /// for(Edge e = findEdge(g,u,v); e != INVALID; 

  ///     e = findEdge(g,u,v,e)) {

  ///   ...

  /// }

  ///\endcode

  ///

  ///\sa ConArcIt

  template <typename Graph>

  inline typename Graph::Edge 

  findEdge(const Graph &g, typename Graph::Node u, typename Graph::Node v,

            typename Graph::Edge p = INVALID) {

    return _graph_utils_bits::FindEdgeSelector<Graph>::find(g, u, v, p);

  }

  /// \brief Iterator for iterating on edges connected the same nodes.

  ///

  /// Iterator for iterating on edges connected the same nodes. It is 

  /// higher level interface for the findEdge() function. You can

  /// use it the following way:

  ///\code

  /// for (ConEdgeIt<Graph> it(g, src, trg); it != INVALID; ++it) {

  ///   ...

  /// }

  ///\endcode

  ///

  ///\sa findEdge()

  ///

  /// \author Balazs Dezso 

  template <typename _Graph>

  class ConEdgeIt : public _Graph::Edge {

  public:

    typedef _Graph Graph;

    typedef typename Graph::Edge Parent;

    typedef typename Graph::Edge Edge;

    typedef typename Graph::Node Node;

    /// \brief Constructor.

    ///

    /// Construct a new ConEdgeIt iterating on the edges which

    /// connects the \c u and \c v node.

    ConEdgeIt(const Graph& g, Node u, Node v) : _graph(g) {

      Parent::operator=(findEdge(_graph, u, v));

    }

    /// \brief Constructor.

    ///

    /// Construct a new ConEdgeIt which continues the iterating from 

    /// the \c e edge.

    ConEdgeIt(const Graph& g, Edge e) : Parent(e), _graph(g) {}

    /// \brief Increment operator.

    ///

    /// It increments the iterator and gives back the next edge.

    ConEdgeIt& operator++() {

      Parent::operator=(findEdge(_graph, _graph.source(*this), 

				 _graph.target(*this), *this));

      return *this;

    }

  private:

    const Graph& _graph;

  };

  namespace _graph_utils_bits {

    template <typename Digraph, typename Item, typename RefMap>

    class MapCopyBase {

    public:

      virtual void copy(const Digraph& from, const RefMap& refMap) = 0;

      virtual ~MapCopyBase() {}

    };

    template <typename Digraph, typename Item, typename RefMap, 

              typename ToMap, typename FromMap>

    class MapCopy : public MapCopyBase<Digraph, Item, RefMap> {

    public:

      MapCopy(ToMap& tmap, const FromMap& map) 

        : _tmap(tmap), _map(map) {}

      virtual void copy(const Digraph& digraph, const RefMap& refMap) {

        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;

        for (ItemIt it(digraph); it != INVALID; ++it) {

          _tmap.set(refMap[it], _map[it]);

        }

      }

    private:

      ToMap& _tmap;

      const FromMap& _map;

    };

    template <typename Digraph, typename Item, typename RefMap, typename It>

    class ItemCopy : public MapCopyBase<Digraph, Item, RefMap> {

    public:

      ItemCopy(It& it, const Item& item) : _it(it), _item(item) {}

      virtual void copy(const Digraph&, const RefMap& refMap) {

        _it = refMap[_item];

      }

    private:

      It& _it;

      Item _item;

    };

    template <typename Digraph, typename Item, typename RefMap, typename Ref>

    class RefCopy : public MapCopyBase<Digraph, Item, RefMap> {

    public:

      RefCopy(Ref& map) : _map(map) {}

      virtual void copy(const Digraph& digraph, const RefMap& refMap) {

        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;

        for (ItemIt it(digraph); it != INVALID; ++it) {

          _map.set(it, refMap[it]);

        }

      }

    private:

      Ref& _map;

    };

    template <typename Digraph, typename Item, typename RefMap, 

              typename CrossRef>

    class CrossRefCopy : public MapCopyBase<Digraph, Item, RefMap> {

    public:

      CrossRefCopy(CrossRef& cmap) : _cmap(cmap) {}

      virtual void copy(const Digraph& digraph, const RefMap& refMap) {

        typedef typename ItemSetTraits<Digraph, Item>::ItemIt ItemIt;

        for (ItemIt it(digraph); it != INVALID; ++it) {

          _cmap.set(refMap[it], it);

        }

      }

    private:

      CrossRef& _cmap;

    };

    template <typename Digraph, typename Enable = void>

    struct DigraphCopySelector {

      template <typename From, typename NodeRefMap, typename ArcRefMap>

      static void copy(Digraph &to, const From& from,

                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {

        for (typename From::NodeIt it(from); it != INVALID; ++it) {

          nodeRefMap[it] = to.addNode();

        }

        for (typename From::ArcIt it(from); it != INVALID; ++it) {

          arcRefMap[it] = to.addArc(nodeRefMap[from.source(it)], 

                                          nodeRefMap[from.target(it)]);

        }

      }

    };

    template <typename Digraph>

    struct DigraphCopySelector<

      Digraph, 

      typename enable_if<typename Digraph::BuildTag, void>::type> 

    {

      template <typename From, typename NodeRefMap, typename ArcRefMap>

      static void copy(Digraph &to, const From& from,

                       NodeRefMap& nodeRefMap, ArcRefMap& arcRefMap) {

        to.build(from, nodeRefMap, arcRefMap);

      }

    };

    template <typename Graph, typename Enable = void>