/* -*- 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