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// //======================================================================= // 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 #include #include #include #include #include #include #include #include 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; BOOST_CONCEPT_ASSERT((VertexListGraphConcept< Graph >)); BOOST_CONCEPT_ASSERT((EdgeListGraphConcept< Graph >)); BOOST_CONCEPT_ASSERT((OutputIteratorConcept< OutputIterator, Edge >)); BOOST_CONCEPT_ASSERT((ReadWritePropertyMapConcept< Rank, Vertex >)); BOOST_CONCEPT_ASSERT((ReadWritePropertyMapConcept< Parent, Vertex >)); BOOST_CONCEPT_ASSERT((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; BOOST_CONCEPT_ASSERT((ComparableConcept< W_value >)); BOOST_CONCEPT_ASSERT((ConvertibleConcept< P_value, Vertex >)); BOOST_CONCEPT_ASSERT((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; 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