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: