//

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

// 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