/* -*- 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_KRUSKAL_H

#define LEMON_KRUSKAL_H

#include <algorithm>

#include <vector>

#include <lemon/unionfind.h>

#include <lemon/graph_utils.h>

#include <lemon/maps.h>

#include <lemon/radix_sort.h>

#include <lemon/bits/utility.h>

#include <lemon/bits/traits.h>

///\ingroup spantree

///\file

///\brief Kruskal's algorithm to compute a minimum cost tree

///

///Kruskal's algorithm to compute a minimum cost tree.

///

namespace lemon {

  namespace _kruskal_bits {

    template <typename Map, typename Comp>

    struct MappedComp {

      typedef typename Map::Key Key;

      const Map& map;

      Comp comp;

      MappedComp(const Map& _map) 

        : map(_map), comp() {}

      bool operator()(const Key& left, const Key& right) {

        return comp(map[left], map[right]);

      }

    };

  }

  /// \brief Default traits class of Kruskal class.

  ///

  /// Default traits class of Kruskal class.

  /// \param _UGraph Undirected graph type.

  /// \param _CostMap Type of cost map.

  template <typename _UGraph, typename _CostMap>

  struct KruskalDefaultTraits{

    /// \brief The graph type the algorithm runs on. 

    typedef _UGraph UGraph;

    /// \brief The type of the map that stores the edge costs.

    ///

    /// The type of the map that stores the edge costs.

    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.

    typedef _CostMap CostMap;

    /// \brief The type of the cost of the edges.

    typedef typename _CostMap::Value Value;

    /// \brief The type of the map that stores whether an edge is in the

    /// spanning tree or not.

    ///

    /// The type of the map that stores whether an edge is in the

    /// spanning tree or not.

    typedef typename _UGraph::template UEdgeMap<bool> TreeMap;

    /// \brief Instantiates a TreeMap.

    ///

    /// This function instantiates a \ref TreeMap.

    ///

    /// The first parameter is the graph, to which

    /// we would like to define the \ref TreeMap

    static TreeMap *createTreeMap(const _UGraph& graph){

      return new TreeMap(graph);

    }

    template <typename Iterator>

    static void sort(Iterator begin, Iterator end, const CostMap& cost) {

      _kruskal_bits::MappedComp<CostMap, std::less<Value> > comp(cost);

      std::sort(begin, end, comp);

    }

  };

  ///\ingroup spantree

  ///

  /// \brief Kruskal's algorithm to find a minimum cost tree of a graph.

  ///

  /// This class implements Kruskal's algorithm to find a minimum cost

  /// spanning tree. The 

  ///

  /// \param _UGraph Undirected graph type.

  /// \param _CostMap Type of cost map.

  template <typename _UGraph, typename _CostMap,

            typename _Traits = KruskalDefaultTraits<_UGraph, _CostMap> >

  class Kruskal {

  public:

    typedef _Traits Traits;

    typedef typename _Traits::UGraph UGraph;

    typedef typename _Traits::CostMap CostMap;

    typedef typename _Traits::TreeMap TreeMap;

    typedef typename _Traits::Value Value;

    template <typename Comp>

    struct DefSortCompareTraits : public Traits {

      template <typename Iterator>

      static void sort(Iterator begin, Iterator end, const CostMap& cost) {

        _kruskal_bits::MappedComp<CostMap, Comp> comp(cost, Comp());

        std::sort(begin, end, comp);

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting the

    /// comparator object of the standard sort

    ///

    /// \ref named-templ-param "Named parameter" for setting the

    /// comparator object of the standard sort

    template <typename Comp>

    struct DefSortCompare

      : public Kruskal<UGraph, CostMap, DefSortCompareTraits<Comp> > {

      typedef Kruskal<UGraph, CostMap, DefSortCompareTraits<Comp> > Create;

    };    

    struct DefRadixSortTraits : public Traits {

      template <typename Iterator>

      static void sort(Iterator begin, Iterator end, const CostMap& cost) {

        radixSort(begin, end, cost);

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting the

    /// sort function to radix sort

    ///

    /// \brief \ref named-templ-param "Named parameter" for setting the

    /// sort function to radix sort. The value type of the cost map should

    /// be integral, of course. 

    struct DefRadixSort

      : public Kruskal<UGraph, CostMap, DefRadixSortTraits> {

      typedef Kruskal<UGraph, CostMap, DefRadixSortTraits> Create;

    };    

    template <class TM>

    struct DefTreeMapTraits : public Traits {

      typedef TM TreeMap;

      static TreeMap *createTreeMap(const UGraph &) {

        throw UninitializedParameter();

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting

    /// TreeMap

    ///

    /// \ref named-templ-param "Named parameter" for setting TreeMap

    ///

    template <class TM>

    struct DefTreeMap

      : public Kruskal< UGraph, CostMap, DefTreeMapTraits<TM> > {

      typedef Kruskal< UGraph, CostMap, DefTreeMapTraits<TM> > Create;

    };    

  private:

    typedef typename UGraph::Node Node;

    typedef typename UGraph::NodeIt NodeIt;

    typedef typename UGraph::UEdge UEdge;

    typedef typename UGraph::UEdgeIt UEdgeIt;

    const UGraph& graph;

    const CostMap& cost;

    std::vector<UEdge> edges;

    typedef typename UGraph::template NodeMap<int> UfIndex;

    typedef UnionFind<UfIndex> Uf;

    UfIndex *ufi;

    Uf *uf;

    int index;

    void initStructures() {

      if (!_tree) {

        _tree = Traits::createTreeMap(graph);

        local_tree = true;

      }

      if (!uf) {

        ufi = new typename UGraph::template NodeMap<int>(graph);

        uf = new UnionFind<typename UGraph::template NodeMap<int> >(*ufi);

      }

    }

    void initUnionFind() {

      uf->clear();

      for (NodeIt it(graph); it != INVALID; ++it) {

        uf->insert(it);

      }

    }

    bool local_tree;

    TreeMap* _tree;

  public:

    /// \brief Constructor

    ///

    /// Constructor of the algorithm.

    Kruskal(const UGraph& _graph, const CostMap& _cost) 

      : graph(_graph), cost(_cost),

        ufi(0), uf(0), local_tree(false), _tree(0) {}

    /// \brief Destructor

    ///

    /// Destructor

    ~Kruskal() {

      if (local_tree) {

        delete _tree;

      }

      if (uf) {

        delete uf;

        delete ufi;

      }

    }

    /// \brief Sets the map storing the tree edges.

    ///

    /// Sets the map storing the tree edges.

    /// If you don't use this function before calling \ref run(),

    /// it will allocate one. The destuctor deallocates this

    /// automatically allocated map, of course.

    /// \return \c *this </tt>

    Kruskal& treeMap(TreeMap &m){

      if (local_tree) {

	delete _tree;

	local_tree = false;

      }

      _tree = &m;

      return *this;

    }

    /// \brief Initialize the algorithm

    ///

    /// This member function initializes the unionfind data structure

    /// and sorts the edges into ascending order

    void init() {

      initStructures();

      initUnionFind();

      for (UEdgeIt e(graph); e != INVALID; ++e) {

        edges.push_back(e);

        _tree->set(e, false);

      }      

      Traits::sort(edges.begin(), edges.end(), cost); 

      index = 0;

    }

    /// \brief Initialize the algorithm

    ///

    /// This member function initializes the unionfind data structure

    /// and sets the edge order to the given sequence. The given

    /// sequence should be a valid STL range of undirected edges.

    template <typename Iterator>

    void initPresorted(Iterator begin, Iterator end) {

      initStructures();

      initUnionFind();

      edges.clear();

      std::copy(begin, end, std::back_inserter(edges));

      index = 0;

    }

    /// \brief Initialize the algorithm

    ///

    /// This member function initializes the unionfind data structure

    /// and sets the tree to empty. It does not change the order of

    /// the edges, it uses the order of the previous running.

    void reinit() {

      initStructures();

      initUnionFind();

      for (UEdgeIt e(graph); e != INVALID; ++e) {

        _tree->set(e, false);

      }

      index = 0;

    }

    /// \brief Executes the algorithm.

    ///

    /// Executes the algorithm.

    ///

    /// \pre init() must be called before using this function.

    ///

    /// This method runs the %Kruskal algorithm.

    void start() {

      while (index < int(edges.size())) {

        if (uf->join(graph.target(edges[index]), graph.source(edges[index]))) {

          _tree->set(edges[index], true);

        }

        ++index;

      }

    }

    /// \brief Runs the prim algorithm until it find a new tree edge

    ///

    /// Runs the prim algorithm until it find a new tree edge. If it

    /// does not next tree edge in the sequence it gives back \c INVALID.

    UEdge findNextTreeEdge() {

      while (index < int(edges.size())) {

        if (uf->join(graph.target(edges[index]), graph.source(edges[index]))) {

          _tree->set(edges[index], true);

          return edges[index++];

        }        

        ++index;

      }

      return INVALID;

    }

    /// \brief Processes the next edge in the sequence

    ///

    /// Processes the next edge in the sequence.

    ///

    /// \return The prcocessed edge.

    ///

    /// \warning The sequence must not be empty!

    UEdge processNextEdge() {

      UEdge edge = edges[index++];

      processEdge(edge);

      return edge;

    }

    /// \brief Processes an arbitrary edge

    ///

    /// Processes the next edge in the sequence.

    ///

    /// \return True when the edge is a tree edge.

    bool processEdge(const UEdge& edge) {

      if (uf->join(graph.target(edge), graph.source(edge))) {

        _tree->set(edge, true);

        return true;

      } else {

        return false;

      }    

    }

    /// \brief Returns \c false if there are edge to be processed in

    /// sequence

    ///

    /// Returns \c false if there are nodes to be processed in the

    /// sequence

    bool emptyQueue() {

      return index == int(edges.size());

    }

    /// \brief Returns the next edge to be processed

    ///

    /// Returns the next edge to be processed

    ///

    UEdge nextEdge() const {

      return edges[index];

    }

    /// \brief Runs %Kruskal algorithm.

    ///

    /// This method runs the %Kruskal algorithm in order to compute the

    /// minimum spanning tree (or minimum spanning forest).  The

    /// method also works on graphs that has more than one components.

    /// In this case it computes the minimum spanning forest.

    void run() {

      init();

      start();

    }

    /// \brief Returns a reference to the tree edges map

    ///

    /// Returns a reference to the TreeEdgeMap of the edges of the

    /// minimum spanning tree. The value of the map is \c true only if

    /// the edge is in the minimum spanning tree.

    ///

    const TreeMap &treeMap() const { return *_tree;}

    /// \brief Returns the total cost of the tree

    ///

    /// Returns the total cost of the tree

    Value treeValue() const {

      Value value = 0;

      for (UEdgeIt it(graph); it != INVALID; ++it) {

        if ((*_tree)[it]) {

          value += cost[it];

        }

      }

      return value;

    }

    /// \brief Returns true when the given edge is tree edge

    ///

    /// Returns true when the given edge is tree edge

    bool tree(UEdge e) const {

      return (*_tree)[e];

    }

  };

  namespace _kruskal_bits {

    template <typename Graph, typename In, typename Out>

    typename In::value_type::second_type

    kruskal(const Graph& graph, const In& in, Out& out) {

      typedef typename In::value_type::second_type Value;

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

      typedef typename Graph::Node Node;

      IndexMap index(graph);

      UnionFind<IndexMap> uf(index);

      for (typename Graph::NodeIt it(graph); it != INVALID; ++it) {

        uf.insert(it);

      }

      Value tree_value = 0;

      for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {

        if (uf.join(graph.target(it->first),graph.source(it->first))) {

          out.set(it->first, true);

          tree_value += it->second;

        }

        else {

          out.set(it->first, false);

        }

      }

      return tree_value;

    }

    template <typename Sequence>

    struct PairComp {

      typedef typename Sequence::value_type Value;

      bool operator()(const Value& left, const Value& right) {

	return left.second < right.second;

      }

    };

    template <typename In, typename Enable = void>

    struct SequenceInputIndicator {

      static const bool value = false;

    };

    template <typename In>

    struct SequenceInputIndicator<In, 

      typename exists<typename In::value_type::first_type>::type> {

      static const bool value = true;

    };

    template <typename In, typename Enable = void>

    struct MapInputIndicator {

      static const bool value = false;

    };

    template <typename In>

    struct MapInputIndicator<In, 

      typename exists<typename In::Value>::type> {

      static const bool value = true;

    };

    template <typename In, typename Enable = void>

    struct SequenceOutputIndicator {

      static const bool value = false;

    };

    template <typename Out>

    struct SequenceOutputIndicator<Out, 

      typename exists<typename Out::value_type>::type> {

      static const bool value = true;

    };

    template <typename Out, typename Enable = void>

    struct MapOutputIndicator {

      static const bool value = false;

    };

    template <typename Out>

    struct MapOutputIndicator<Out, 

      typename exists<typename Out::Value>::type> {

      static const bool value = true;

    };

    template <typename In, typename InEnable = void>

    struct KruskalValueSelector {};

    template <typename In>

    struct KruskalValueSelector<In,

      typename enable_if<SequenceInputIndicator<In>, void>::type> 

    {

      typedef typename In::value_type::second_type Value;

    };    

    template <typename In>

    struct KruskalValueSelector<In,

      typename enable_if<MapInputIndicator<In>, void>::type> 

    {

      typedef typename In::Value Value;

    };    

    template <typename Graph, typename In, typename Out,

              typename InEnable = void>

    struct KruskalInputSelector {};

    template <typename Graph, typename In, typename Out,

              typename InEnable = void>

    struct KruskalOutputSelector {};

    template <typename Graph, typename In, typename Out>

    struct KruskalInputSelector<Graph, In, Out,

      typename enable_if<SequenceInputIndicator<In>, void>::type > 

    {

      typedef typename In::value_type::second_type Value;

      static Value kruskal(const Graph& graph, const In& in, Out& out) {

        return KruskalOutputSelector<Graph, In, Out>::

          kruskal(graph, in, out);

      }

    };

    template <typename Graph, typename In, typename Out>

    struct KruskalInputSelector<Graph, In, Out,

      typename enable_if<MapInputIndicator<In>, void>::type > 

    {

      typedef typename In::Value Value;

      static Value kruskal(const Graph& graph, const In& in, Out& out) {

        typedef typename In::Key MapEdge;

        typedef typename In::Value Value;

        typedef typename ItemSetTraits<Graph, MapEdge>::ItemIt MapEdgeIt;

        typedef std::vector<std::pair<MapEdge, Value> > Sequence;

        Sequence seq;

        for (MapEdgeIt it(graph); it != INVALID; ++it) {

          seq.push_back(std::make_pair(it, in[it]));

        }

        std::sort(seq.begin(), seq.end(), PairComp<Sequence>());

        return KruskalOutputSelector<Graph, Sequence, Out>::

          kruskal(graph, seq, out);

      }

    };

    template <typename Graph, typename In, typename Out>

    struct KruskalOutputSelector<Graph, In, Out,

      typename enable_if<SequenceOutputIndicator<Out>, void>::type > 

    {

      typedef typename In::value_type::second_type Value;

      static Value kruskal(const Graph& graph, const In& in, Out& out) {

        typedef StoreBoolMap<Out> Map;

        Map map(out);

        return _kruskal_bits::kruskal(graph, in, map);

      }

    };

    template <typename Graph, typename In, typename Out>

    struct KruskalOutputSelector<Graph, In, Out,

      typename enable_if<MapOutputIndicator<Out>, void>::type > 

    {

      typedef typename In::value_type::second_type Value;

      static Value kruskal(const Graph& graph, const In& in, Out& out) {

        return _kruskal_bits::kruskal(graph, in, out);

      }

    };

  }

  /// \ingroup spantree

  ///

  /// \brief Kruskal's algorithm to find a minimum cost tree of a graph.

  ///

  /// This function runs Kruskal's algorithm to find a minimum cost tree.

  /// Due to hard C++ hacking, it accepts various input and output types.

  ///

  /// \param g The graph the algorithm runs on.

  /// It can be either \ref concepts::Graph "directed" or 

  /// \ref concepts::UGraph "undirected".

  /// If the graph is directed, the algorithm consider it to be 

  /// undirected by disregarding the direction of the edges.

  ///

  /// \param in This object is used to describe the edge costs. It can be one

  /// of the following choices.

  /// - An STL compatible 'Forward Container' with

  /// <tt>std::pair<GR::UEdge,X></tt> or

  /// <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, where

  /// \c X is the type of the costs. The pairs indicates the edges

  /// along with the assigned cost. <em>They must be in a

  /// cost-ascending order.</em>

  /// - Any readable Edge map. The values of the map indicate the edge costs.

  ///

  /// \retval out Here we also have a choise.

  /// - It can be a writable \c bool edge map.  After running the

  /// algorithm this will contain the found minimum cost spanning

  /// tree: the value of an edge will be set to \c true if it belongs

  /// to the tree, otherwise it will be set to \c false. The value of

  /// each edge will be set exactly once.

  /// - It can also be an iteraror of an STL Container with

  /// <tt>GR::UEdge</tt> or <tt>GR::Edge</tt> as its

  /// <tt>value_type</tt>.  The algorithm copies the elements of the

  /// found tree into this sequence.  For example, if we know that the

  /// spanning tree of the graph \c g has say 53 edges, then we can

  /// put its edges into an STL vector \c tree with a code like this.

  ///\code

  /// std::vector<Edge> tree(53);

  /// kruskal(g,cost,tree.begin());

  ///\endcode

  /// Or if we don't know in advance the size of the tree, we can

  /// write this.  

  ///\code std::vector<Edge> tree;

  /// kruskal(g,cost,std::back_inserter(tree)); 

  ///\endcode

  ///

  /// \return The total cost of the found tree.

  ///

  /// \warning If kruskal runs on an be consistent of using the same

  /// Edge type for input and output.

  ///

#ifdef DOXYGEN

  template <class Graph, class In, class Out>

  Value kruskal(GR const& g, const In& in, Out& out)

#else 

  template <class Graph, class In, class Out>

  inline typename _kruskal_bits::KruskalValueSelector<In>::Value 

  kruskal(const Graph& graph, const In& in, Out& out) 

#endif

  {

    return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::

      kruskal(graph, in, out);

  }

  template <class Graph, class In, class Out>

  inline typename _kruskal_bits::KruskalValueSelector<In>::Value

  kruskal(const Graph& graph, const In& in, const Out& out)

  {

    return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::

      kruskal(graph, in, out);

  }  

} //namespace lemon

#endif //LEMON_KRUSKAL_H