Chris@16: //
Chris@16: //=======================================================================
Chris@16: // Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
Chris@16: // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
Chris@16: //
Chris@16: // Distributed under the Boost Software License, Version 1.0. (See
Chris@16: // accompanying file LICENSE_1_0.txt or copy at
Chris@16: // http://www.boost.org/LICENSE_1_0.txt)
Chris@16: //=======================================================================
Chris@16: //
Chris@16: #ifndef BOOST_GRAPH_MST_KRUSKAL_HPP
Chris@16: #define BOOST_GRAPH_MST_KRUSKAL_HPP
Chris@16: 
Chris@16: /*
Chris@16:  *Minimum Spanning Tree 
Chris@16:  *         Kruskal Algorithm
Chris@16:  *
Chris@16:  *Requirement:
Chris@16:  *      undirected graph
Chris@16:  */
Chris@16: 
Chris@16: #include <vector>
Chris@16: #include <queue>
Chris@16: #include <functional>
Chris@16: 
Chris@16: #include <boost/property_map/property_map.hpp>
Chris@16: #include <boost/graph/graph_concepts.hpp>
Chris@16: #include <boost/graph/named_function_params.hpp>
Chris@16: #include <boost/pending/disjoint_sets.hpp>
Chris@16: #include <boost/pending/indirect_cmp.hpp>
Chris@16: #include <boost/concept/assert.hpp>
Chris@16: 
Chris@16: 
Chris@16: namespace boost {
Chris@16: 
Chris@16:   // Kruskal's algorithm for Minimum Spanning Tree
Chris@16:   //
Chris@16:   // This is a greedy algorithm to calculate the Minimum Spanning Tree
Chris@16:   // for an undirected graph with weighted edges. The output will be a
Chris@16:   // set of edges.
Chris@16:   //
Chris@16: 
Chris@16:   namespace detail {
Chris@16: 
Chris@16:     template <class Graph, class OutputIterator, 
Chris@16:               class Rank, class Parent, class Weight>
Chris@16:     void
Chris@16:     kruskal_mst_impl(const Graph& G, 
Chris@16:                      OutputIterator spanning_tree_edges, 
Chris@16:                      Rank rank, Parent parent, Weight weight)
Chris@16:     {
Chris@16:       if (num_vertices(G) == 0) return; // Nothing to do in this case
Chris@16:       typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
Chris@16:       typedef typename graph_traits<Graph>::edge_descriptor Edge;
Chris@16:       BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<Graph> ));
Chris@16:       BOOST_CONCEPT_ASSERT(( EdgeListGraphConcept<Graph> ));
Chris@16:       BOOST_CONCEPT_ASSERT(( OutputIteratorConcept<OutputIterator, Edge> ));
Chris@16:       BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<Rank, Vertex> ));
Chris@16:       BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<Parent, Vertex> ));
Chris@16:       BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<Weight, Edge> ));
Chris@16:       typedef typename property_traits<Weight>::value_type W_value;
Chris@16:       typedef typename property_traits<Rank>::value_type R_value;
Chris@16:       typedef typename property_traits<Parent>::value_type P_value;
Chris@16:       BOOST_CONCEPT_ASSERT(( ComparableConcept<W_value> ));
Chris@16:       BOOST_CONCEPT_ASSERT(( ConvertibleConcept<P_value, Vertex> ));
Chris@16:       BOOST_CONCEPT_ASSERT(( IntegerConcept<R_value> ));
Chris@16: 
Chris@16:       disjoint_sets<Rank, Parent>  dset(rank, parent);
Chris@16: 
Chris@16:       typename graph_traits<Graph>::vertex_iterator ui, uiend;
Chris@16:       for (boost::tie(ui, uiend) = vertices(G); ui != uiend; ++ui)
Chris@16:         dset.make_set(*ui);
Chris@16: 
Chris@16:       typedef indirect_cmp<Weight, std::greater<W_value> > weight_greater;
Chris@16:       weight_greater wl(weight);
Chris@16:       std::priority_queue<Edge, std::vector<Edge>, weight_greater> Q(wl);
Chris@16:       /*push all edge into Q*/
Chris@16:       typename graph_traits<Graph>::edge_iterator ei, eiend;
Chris@16:       for (boost::tie(ei, eiend) = edges(G); ei != eiend; ++ei) 
Chris@16:         Q.push(*ei);
Chris@16: 
Chris@16:       while (! Q.empty()) {
Chris@16:         Edge e = Q.top();
Chris@16:         Q.pop();
Chris@16:         Vertex u = dset.find_set(source(e, G));
Chris@16:         Vertex v = dset.find_set(target(e, G));
Chris@16:         if ( u != v ) {
Chris@16:           *spanning_tree_edges++ = e;
Chris@16:           dset.link(u, v);
Chris@16:         }
Chris@16:       }
Chris@16:     }
Chris@16: 
Chris@16:   } // namespace detail 
Chris@16: 
Chris@16:   // Named Parameters Variants
Chris@16: 
Chris@16:   template <class Graph, class OutputIterator>
Chris@16:   inline void 
Chris@16:   kruskal_minimum_spanning_tree(const Graph& g,
Chris@16:                                 OutputIterator spanning_tree_edges)
Chris@16:   {
Chris@16:     typedef typename graph_traits<Graph>::vertices_size_type size_type;
Chris@16:     typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
Chris@16:     if (num_vertices(g) == 0) return; // Nothing to do in this case
Chris@16:     typename graph_traits<Graph>::vertices_size_type
Chris@16:       n = num_vertices(g);
Chris@16:     std::vector<size_type> rank_map(n);
Chris@16:     std::vector<vertex_t> pred_map(n);
Chris@16: 
Chris@16:     detail::kruskal_mst_impl
Chris@16:       (g, spanning_tree_edges, 
Chris@16:        make_iterator_property_map(rank_map.begin(), get(vertex_index, g), rank_map[0]),
Chris@16:        make_iterator_property_map(pred_map.begin(), get(vertex_index, g), pred_map[0]),
Chris@16:        get(edge_weight, g));
Chris@16:   }
Chris@16: 
Chris@16:   template <class Graph, class OutputIterator, class P, class T, class R>
Chris@16:   inline void
Chris@16:   kruskal_minimum_spanning_tree(const Graph& g,
Chris@16:                                 OutputIterator spanning_tree_edges, 
Chris@16:                                 const bgl_named_params<P, T, R>& params)
Chris@16:   {
Chris@16:     typedef typename graph_traits<Graph>::vertices_size_type size_type;
Chris@16:     typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
Chris@16:     if (num_vertices(g) == 0) return; // Nothing to do in this case
Chris@16:     typename graph_traits<Graph>::vertices_size_type n;
Chris@16:     n = is_default_param(get_param(params, vertex_rank))
Chris@16:                                    ? num_vertices(g) : 1;
Chris@16:     std::vector<size_type> rank_map(n);
Chris@16:     n = is_default_param(get_param(params, vertex_predecessor))
Chris@16:                                    ? num_vertices(g) : 1;
Chris@16:     std::vector<vertex_t> pred_map(n);
Chris@16:     
Chris@16:     detail::kruskal_mst_impl
Chris@16:       (g, spanning_tree_edges, 
Chris@16:        choose_param
Chris@16:        (get_param(params, vertex_rank), 
Chris@16:         make_iterator_property_map
Chris@16:         (rank_map.begin(), 
Chris@16:          choose_pmap(get_param(params, vertex_index), g, vertex_index), rank_map[0])),
Chris@16:        choose_param
Chris@16:        (get_param(params, vertex_predecessor), 
Chris@16:         make_iterator_property_map
Chris@16:         (pred_map.begin(), 
Chris@16:          choose_const_pmap(get_param(params, vertex_index), g, vertex_index), 
Chris@16:          pred_map[0])),
Chris@16:        choose_const_pmap(get_param(params, edge_weight), g, edge_weight));
Chris@16:   }
Chris@16:     
Chris@16: } // namespace boost
Chris@16: 
Chris@16: 
Chris@16: #endif // BOOST_GRAPH_MST_KRUSKAL_HPP
Chris@16: