/* -*- 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 spanning tree

///

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

///

namespace lemon {

  namespace _kruskal_bits {

    // Kruskal for directed graphs.

    template <typename Digraph, typename In, typename Out>

    typename disable_if<lemon::UndirectedTagIndicator<Digraph>,

		       typename In::value_type::second_type >::type

    kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) {

      typedef typename In::value_type::second_type Value;

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

      typedef typename Digraph::Node Node;

      IndexMap index(digraph);

      UnionFind<IndexMap> uf(index);

      for (typename Digraph::NodeIt it(digraph); 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(digraph.target(it->first),digraph.source(it->first))) {

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

          tree_value += it->second;

        }

        else {

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

        }

      }

      return tree_value;

    }

    // Kruskal for undirected graphs.

    template <typename Graph, typename In, typename Out>

    typename enable_if<lemon::UndirectedTagIndicator<Graph>,

		       typename In::value_type::second_type >::type

    kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) {

      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.u(it->first),graph.v(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 MapArc;

        typedef typename In::Value Value;

        typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt;

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

        Sequence seq;

        for (MapArcIt 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 T>

    struct RemoveConst {

      typedef T type;

    };

    template <typename T>

    struct RemoveConst<const T> {

      typedef T type;

    };

    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 LoggerBoolMap<typename RemoveConst<Out>::type> 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 algorithm to find a minimum cost spanning tree of

  /// a graph.

  ///

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

  /// spanning tree.

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

  ///

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

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

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

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

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

  ///

  /// \param in This object is used to describe the arc/edge costs. 

  /// It can be one of the following choices.

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

  /// <tt>std::pair<GR::Arc,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 arcs/edges

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

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

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

  /// arc/edge costs.

  ///

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

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

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

  /// tree: the value of an arc/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 arc/edge will be set exactly once.

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

  /// <tt>GR::Arc</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 arcs, then we can

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

  ///\code

  /// std::vector<Arc> 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<Arc> tree;

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

  ///\endcode

  ///

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

  ///

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

  /// Arc 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