//

 //=======================================================================

 // Copyright 1997, 1998, 1999, 2000 University of Notre Dame.

 // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek

 //

 // Distributed under the Boost Software License, Version 1.0. (See

 // accompanying file LICENSE_1_0.txt or copy at

 // http://www.boost.org/LICENSE_1_0.txt)

 //=======================================================================

 //

 #ifndef BOOST_GRAPH_MST_KRUSKAL_HPP

 #define BOOST_GRAPH_MST_KRUSKAL_HPP

 /*

  *Minimum Spanning Tree 

  *         Kruskal Algorithm

  *

  *Requirement:

  *      undirected graph

  */

 #include <vector>

 #include <queue>

 #include <functional>

 #include <boost/property_map.hpp>

 #include <boost/graph/graph_concepts.hpp>

 #include <boost/graph/named_function_params.hpp>

 #include <boost/pending/disjoint_sets.hpp>

 #include <boost/pending/indirect_cmp.hpp>

 namespace boost {

   // Kruskal's algorithm for Minimum Spanning Tree

   //

   // This is a greedy algorithm to calculate the Minimum Spanning Tree

   // for an undirected graph with weighted edges. The output will be a

   // set of edges.

   //

   namespace detail {

     template <class Graph, class OutputIterator, 

               class Rank, class Parent, class Weight>

     void

     kruskal_mst_impl(const Graph& G, 

                      OutputIterator spanning_tree_edges, 

                      Rank rank, Parent parent, Weight weight)

     {

       if (num_vertices(G) == 0) return; // Nothing to do in this case

       typedef typename graph_traits<Graph>::vertex_descriptor Vertex;

       typedef typename graph_traits<Graph>::edge_descriptor Edge;

       function_requires<VertexListGraphConcept<Graph> >();

       function_requires<EdgeListGraphConcept<Graph> >();

       function_requires<OutputIteratorConcept<OutputIterator, Edge> >();

       function_requires<ReadWritePropertyMapConcept<Rank, Vertex> >();

       function_requires<ReadWritePropertyMapConcept<Parent, Vertex> >();

       function_requires<ReadablePropertyMapConcept<Weight, Edge> >();

       typedef typename property_traits<Weight>::value_type W_value;

       typedef typename property_traits<Rank>::value_type R_value;

       typedef typename property_traits<Parent>::value_type P_value;

       function_requires<ComparableConcept<W_value> >();

       function_requires<ConvertibleConcept<P_value, Vertex> >();

       function_requires<IntegerConcept<R_value> >();

       disjoint_sets<Rank, Parent>  dset(rank, parent);

       typename graph_traits<Graph>::vertex_iterator ui, uiend;

       for (boost::tie(ui, uiend) = vertices(G); ui != uiend; ++ui)

         dset.make_set(*ui);

       typedef indirect_cmp<Weight, std::greater<W_value> > weight_greater;

       weight_greater wl(weight);

       std::priority_queue<Edge, std::vector<Edge>, weight_greater> Q(wl);

       /*push all edge into Q*/

       typename graph_traits<Graph>::edge_iterator ei, eiend;

       for (boost::tie(ei, eiend) = edges(G); ei != eiend; ++ei) 

         Q.push(*ei);

       while (! Q.empty()) {

         Edge e = Q.top();

         Q.pop();

         Vertex u = dset.find_set(source(e, G));

         Vertex v = dset.find_set(target(e, G));

         if ( u != v ) {

           *spanning_tree_edges++ = e;

           dset.link(u, v);

         }

       }

     }

   } // namespace detail 

   // Named Parameters Variants

   template <class Graph, class OutputIterator>

   inline void 

   kruskal_minimum_spanning_tree(const Graph& g,

                                 OutputIterator spanning_tree_edges)

   {

     typedef typename graph_traits<Graph>::vertices_size_type size_type;

     typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;

     typedef typename property_map<Graph, vertex_index_t>::type index_map_t;

     if (num_vertices(g) == 0) return; // Nothing to do in this case

     typename graph_traits<Graph>::vertices_size_type

       n = num_vertices(g);

     std::vector<size_type> rank_map(n);

     std::vector<vertex_t> pred_map(n);

     detail::kruskal_mst_impl

       (g, spanning_tree_edges, 

        make_iterator_property_map(rank_map.begin(), get(vertex_index, g), rank_map[0]),

        make_iterator_property_map(pred_map.begin(), get(vertex_index, g), pred_map[0]),

        get(edge_weight, g));

   }

   template <class Graph, class OutputIterator, class P, class T, class R>

   inline void

   kruskal_minimum_spanning_tree(const Graph& g,

                                 OutputIterator spanning_tree_edges, 

                                 const bgl_named_params<P, T, R>& params)

   {

     typedef typename graph_traits<Graph>::vertices_size_type size_type;

     typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;

     if (num_vertices(g) == 0) return; // Nothing to do in this case

     typename graph_traits<Graph>::vertices_size_type n;

     n = is_default_param(get_param(params, vertex_rank))

                                    ? num_vertices(g) : 1;

     std::vector<size_type> rank_map(n);

     n = is_default_param(get_param(params, vertex_predecessor))

                                    ? num_vertices(g) : 1;

     std::vector<vertex_t> pred_map(n);

     detail::kruskal_mst_impl

       (g, spanning_tree_edges, 

        choose_param

        (get_param(params, vertex_rank), 

         make_iterator_property_map

         (rank_map.begin(), 

          choose_pmap(get_param(params, vertex_index), g, vertex_index), rank_map[0])),

        choose_param

        (get_param(params, vertex_predecessor), 

         make_iterator_property_map

         (pred_map.begin(), 

          choose_const_pmap(get_param(params, vertex_index), g, vertex_index), 

          pred_map[0])),

        choose_const_pmap(get_param(params, edge_weight), g, edge_weight));

   }

 } // namespace boost

 #endif // BOOST_GRAPH_MST_KRUSKAL_HPP