williamr@2: //
williamr@2: //=======================================================================
williamr@2: // Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
williamr@2: // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
williamr@2: //
williamr@2: // Distributed under the Boost Software License, Version 1.0. (See
williamr@2: // accompanying file LICENSE_1_0.txt or copy at
williamr@2: // http://www.boost.org/LICENSE_1_0.txt)
williamr@2: //=======================================================================
williamr@2: //
williamr@2: #ifndef BOOST_GRAPH_MST_KRUSKAL_HPP
williamr@2: #define BOOST_GRAPH_MST_KRUSKAL_HPP
williamr@2:
williamr@2: /*
williamr@2: *Minimum Spanning Tree
williamr@2: * Kruskal Algorithm
williamr@2: *
williamr@2: *Requirement:
williamr@2: * undirected graph
williamr@2: */
williamr@2:
williamr@2: #include <vector>
williamr@2: #include <queue>
williamr@2: #include <functional>
williamr@2:
williamr@2: #include <boost/property_map.hpp>
williamr@2: #include <boost/graph/graph_concepts.hpp>
williamr@2: #include <boost/graph/named_function_params.hpp>
williamr@2: #include <boost/pending/disjoint_sets.hpp>
williamr@2: #include <boost/pending/indirect_cmp.hpp>
williamr@2:
williamr@2:
williamr@2: namespace boost {
williamr@2:
williamr@2: // Kruskal's algorithm for Minimum Spanning Tree
williamr@2: //
williamr@2: // This is a greedy algorithm to calculate the Minimum Spanning Tree
williamr@2: // for an undirected graph with weighted edges. The output will be a
williamr@2: // set of edges.
williamr@2: //
williamr@2:
williamr@2: namespace detail {
williamr@2:
williamr@2: template <class Graph, class OutputIterator,
williamr@2: class Rank, class Parent, class Weight>
williamr@2: void
williamr@2: kruskal_mst_impl(const Graph& G,
williamr@2: OutputIterator spanning_tree_edges,
williamr@2: Rank rank, Parent parent, Weight weight)
williamr@2: {
williamr@2: if (num_vertices(G) == 0) return; // Nothing to do in this case
williamr@2: typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
williamr@2: typedef typename graph_traits<Graph>::edge_descriptor Edge;
williamr@2: function_requires<VertexListGraphConcept<Graph> >();
williamr@2: function_requires<EdgeListGraphConcept<Graph> >();
williamr@2: function_requires<OutputIteratorConcept<OutputIterator, Edge> >();
williamr@2: function_requires<ReadWritePropertyMapConcept<Rank, Vertex> >();
williamr@2: function_requires<ReadWritePropertyMapConcept<Parent, Vertex> >();
williamr@2: function_requires<ReadablePropertyMapConcept<Weight, Edge> >();
williamr@2: typedef typename property_traits<Weight>::value_type W_value;
williamr@2: typedef typename property_traits<Rank>::value_type R_value;
williamr@2: typedef typename property_traits<Parent>::value_type P_value;
williamr@2: function_requires<ComparableConcept<W_value> >();
williamr@2: function_requires<ConvertibleConcept<P_value, Vertex> >();
williamr@2: function_requires<IntegerConcept<R_value> >();
williamr@2:
williamr@2: disjoint_sets<Rank, Parent> dset(rank, parent);
williamr@2:
williamr@2: typename graph_traits<Graph>::vertex_iterator ui, uiend;
williamr@2: for (boost::tie(ui, uiend) = vertices(G); ui != uiend; ++ui)
williamr@2: dset.make_set(*ui);
williamr@2:
williamr@2: typedef indirect_cmp<Weight, std::greater<W_value> > weight_greater;
williamr@2: weight_greater wl(weight);
williamr@2: std::priority_queue<Edge, std::vector<Edge>, weight_greater> Q(wl);
williamr@2: /*push all edge into Q*/
williamr@2: typename graph_traits<Graph>::edge_iterator ei, eiend;
williamr@2: for (boost::tie(ei, eiend) = edges(G); ei != eiend; ++ei)
williamr@2: Q.push(*ei);
williamr@2:
williamr@2: while (! Q.empty()) {
williamr@2: Edge e = Q.top();
williamr@2: Q.pop();
williamr@2: Vertex u = dset.find_set(source(e, G));
williamr@2: Vertex v = dset.find_set(target(e, G));
williamr@2: if ( u != v ) {
williamr@2: *spanning_tree_edges++ = e;
williamr@2: dset.link(u, v);
williamr@2: }
williamr@2: }
williamr@2: }
williamr@2:
williamr@2: } // namespace detail
williamr@2:
williamr@2: // Named Parameters Variants
williamr@2:
williamr@2: template <class Graph, class OutputIterator>
williamr@2: inline void
williamr@2: kruskal_minimum_spanning_tree(const Graph& g,
williamr@2: OutputIterator spanning_tree_edges)
williamr@2: {
williamr@2: typedef typename graph_traits<Graph>::vertices_size_type size_type;
williamr@2: typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
williamr@2: typedef typename property_map<Graph, vertex_index_t>::type index_map_t;
williamr@2: if (num_vertices(g) == 0) return; // Nothing to do in this case
williamr@2: typename graph_traits<Graph>::vertices_size_type
williamr@2: n = num_vertices(g);
williamr@2: std::vector<size_type> rank_map(n);
williamr@2: std::vector<vertex_t> pred_map(n);
williamr@2:
williamr@2: detail::kruskal_mst_impl
williamr@2: (g, spanning_tree_edges,
williamr@2: make_iterator_property_map(rank_map.begin(), get(vertex_index, g), rank_map[0]),
williamr@2: make_iterator_property_map(pred_map.begin(), get(vertex_index, g), pred_map[0]),
williamr@2: get(edge_weight, g));
williamr@2: }
williamr@2:
williamr@2: template <class Graph, class OutputIterator, class P, class T, class R>
williamr@2: inline void
williamr@2: kruskal_minimum_spanning_tree(const Graph& g,
williamr@2: OutputIterator spanning_tree_edges,
williamr@2: const bgl_named_params<P, T, R>& params)
williamr@2: {
williamr@2: typedef typename graph_traits<Graph>::vertices_size_type size_type;
williamr@2: typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
williamr@2: if (num_vertices(g) == 0) return; // Nothing to do in this case
williamr@2: typename graph_traits<Graph>::vertices_size_type n;
williamr@2: n = is_default_param(get_param(params, vertex_rank))
williamr@2: ? num_vertices(g) : 1;
williamr@2: std::vector<size_type> rank_map(n);
williamr@2: n = is_default_param(get_param(params, vertex_predecessor))
williamr@2: ? num_vertices(g) : 1;
williamr@2: std::vector<vertex_t> pred_map(n);
williamr@2:
williamr@2: detail::kruskal_mst_impl
williamr@2: (g, spanning_tree_edges,
williamr@2: choose_param
williamr@2: (get_param(params, vertex_rank),
williamr@2: make_iterator_property_map
williamr@2: (rank_map.begin(),
williamr@2: choose_pmap(get_param(params, vertex_index), g, vertex_index), rank_map[0])),
williamr@2: choose_param
williamr@2: (get_param(params, vertex_predecessor),
williamr@2: make_iterator_property_map
williamr@2: (pred_map.begin(),
williamr@2: choose_const_pmap(get_param(params, vertex_index), g, vertex_index),
williamr@2: pred_map[0])),
williamr@2: choose_const_pmap(get_param(params, edge_weight), g, edge_weight));
williamr@2: }
williamr@2:
williamr@2: } // namespace boost
williamr@2:
williamr@2:
williamr@2: #endif // BOOST_GRAPH_MST_KRUSKAL_HPP
williamr@2: