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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_STRONG_COMPONENTS_HPP #define BOOST_GRAPH_STRONG_COMPONENTS_HPP #include #include #include #include #include #include #include #include namespace boost { //========================================================================== // This is Tarjan's algorithm for strongly connected components // from his paper "Depth first search and linear graph algorithms". // It calculates the components in a single application of DFS. // We implement the algorithm as a dfs-visitor. namespace detail { template < typename ComponentMap, typename RootMap, typename DiscoverTime, typename Stack > class tarjan_scc_visitor : public dfs_visitor<> { typedef typename property_traits< ComponentMap >::value_type comp_type; typedef typename property_traits< DiscoverTime >::value_type time_type; public: tarjan_scc_visitor(ComponentMap comp_map, RootMap r, DiscoverTime d, comp_type& c_, Stack& s_) : c(c_) , comp(comp_map) , root(r) , discover_time(d) , dfs_time(time_type()) , s(s_) { } template < typename Graph > void discover_vertex( typename graph_traits< Graph >::vertex_descriptor v, const Graph&) { put(root, v, v); put(comp, v, (std::numeric_limits< comp_type >::max)()); put(discover_time, v, dfs_time++); s.push(v); } template < typename Graph > void finish_vertex( typename graph_traits< Graph >::vertex_descriptor v, const Graph& g) { typename graph_traits< Graph >::vertex_descriptor w; typename graph_traits< Graph >::out_edge_iterator ei, ei_end; for (boost::tie(ei, ei_end) = out_edges(v, g); ei != ei_end; ++ei) { w = target(*ei, g); if (get(comp, w) == (std::numeric_limits< comp_type >::max)()) put(root, v, this->min_discover_time(get(root, v), get(root, w))); } if (get(root, v) == v) { do { w = s.top(); s.pop(); put(comp, w, c); put(root, w, v); } while (w != v); ++c; } } private: template < typename Vertex > Vertex min_discover_time(Vertex u, Vertex v) { return get(discover_time, u) < get(discover_time, v) ? u : v; } comp_type& c; ComponentMap comp; RootMap root; DiscoverTime discover_time; time_type dfs_time; Stack& s; }; template < class Graph, class ComponentMap, class RootMap, class DiscoverTime, class P, class T, class R > typename property_traits< ComponentMap >::value_type strong_components_impl( const Graph& g, // Input ComponentMap comp, // Output // Internal record keeping RootMap root, DiscoverTime discover_time, const bgl_named_params< P, T, R >& params) { typedef typename graph_traits< Graph >::vertex_descriptor Vertex; BOOST_CONCEPT_ASSERT( (ReadWritePropertyMapConcept< ComponentMap, Vertex >)); BOOST_CONCEPT_ASSERT((ReadWritePropertyMapConcept< RootMap, Vertex >)); typedef typename property_traits< RootMap >::value_type RootV; BOOST_CONCEPT_ASSERT((ConvertibleConcept< RootV, Vertex >)); BOOST_CONCEPT_ASSERT( (ReadWritePropertyMapConcept< DiscoverTime, Vertex >)); typename property_traits< ComponentMap >::value_type total = 0; std::stack< Vertex > s; detail::tarjan_scc_visitor< ComponentMap, RootMap, DiscoverTime, std::stack< Vertex > > vis(comp, root, discover_time, total, s); depth_first_search(g, params.visitor(vis)); return total; } //------------------------------------------------------------------------- // The dispatch functions handle the defaults for the rank and discover // time property maps. // dispatch with class specialization to avoid VC++ bug template < class DiscoverTimeMap > struct strong_comp_dispatch2 { template < class Graph, class ComponentMap, class RootMap, class P, class T, class R > inline static typename property_traits< ComponentMap >::value_type apply(const Graph& g, ComponentMap comp, RootMap r_map, const bgl_named_params< P, T, R >& params, DiscoverTimeMap time_map) { return strong_components_impl(g, comp, r_map, time_map, params); } }; template <> struct strong_comp_dispatch2< param_not_found > { template < class Graph, class ComponentMap, class RootMap, class P, class T, class R > inline static typename property_traits< ComponentMap >::value_type apply(const Graph& g, ComponentMap comp, RootMap r_map, const bgl_named_params< P, T, R >& params, param_not_found) { typedef typename graph_traits< Graph >::vertices_size_type size_type; size_type n = num_vertices(g) > 0 ? num_vertices(g) : 1; std::vector< size_type > time_vec(n); return strong_components_impl(g, comp, r_map, make_iterator_property_map(time_vec.begin(), choose_const_pmap( get_param(params, vertex_index), g, vertex_index), time_vec[0]), params); } }; template < class Graph, class ComponentMap, class RootMap, class P, class T, class R, class DiscoverTimeMap > inline typename property_traits< ComponentMap >::value_type scc_helper2( const Graph& g, ComponentMap comp, RootMap r_map, const bgl_named_params< P, T, R >& params, DiscoverTimeMap time_map) { return strong_comp_dispatch2< DiscoverTimeMap >::apply( g, comp, r_map, params, time_map); } template < class RootMap > struct strong_comp_dispatch1 { template < class Graph, class ComponentMap, class P, class T, class R > inline static typename property_traits< ComponentMap >::value_type apply(const Graph& g, ComponentMap comp, const bgl_named_params< P, T, R >& params, RootMap r_map) { return scc_helper2(g, comp, r_map, params, get_param(params, vertex_discover_time)); } }; template <> struct strong_comp_dispatch1< param_not_found > { template < class Graph, class ComponentMap, class P, class T, class R > inline static typename property_traits< ComponentMap >::value_type apply(const Graph& g, ComponentMap comp, const bgl_named_params< P, T, R >& params, param_not_found) { typedef typename graph_traits< Graph >::vertex_descriptor Vertex; typename std::vector< Vertex >::size_type n = num_vertices(g) > 0 ? num_vertices(g) : 1; std::vector< Vertex > root_vec(n); return scc_helper2(g, comp, make_iterator_property_map(root_vec.begin(), choose_const_pmap( get_param(params, vertex_index), g, vertex_index), root_vec[0]), params, get_param(params, vertex_discover_time)); } }; template < class Graph, class ComponentMap, class RootMap, class P, class T, class R > inline typename property_traits< ComponentMap >::value_type scc_helper1( const Graph& g, ComponentMap comp, const bgl_named_params< P, T, R >& params, RootMap r_map) { return detail::strong_comp_dispatch1< RootMap >::apply( g, comp, params, r_map); } } // namespace detail template < class Graph, class ComponentMap, class P, class T, class R > inline typename property_traits< ComponentMap >::value_type strong_components( const Graph& g, ComponentMap comp, const bgl_named_params< P, T, R >& params BOOST_GRAPH_ENABLE_IF_MODELS_PARM( Graph, vertex_list_graph_tag)) { typedef typename graph_traits< Graph >::directed_category DirCat; BOOST_STATIC_ASSERT( (is_convertible< DirCat*, directed_tag* >::value == true)); return detail::scc_helper1( g, comp, params, get_param(params, vertex_root_t())); } template < class Graph, class ComponentMap > inline typename property_traits< ComponentMap >::value_type strong_components( const Graph& g, ComponentMap comp BOOST_GRAPH_ENABLE_IF_MODELS_PARM( Graph, vertex_list_graph_tag)) { typedef typename graph_traits< Graph >::directed_category DirCat; BOOST_STATIC_ASSERT( (is_convertible< DirCat*, directed_tag* >::value == true)); bgl_named_params< int, int > params(0); return strong_components(g, comp, params); } template < typename Graph, typename ComponentMap, typename ComponentLists > void build_component_lists(const Graph& g, typename graph_traits< Graph >::vertices_size_type num_scc, ComponentMap component_number, ComponentLists& components) { components.resize(num_scc); typename graph_traits< Graph >::vertex_iterator vi, vi_end; for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi) components[component_number[*vi]].push_back(*vi); } } // namespace boost #include #include #include #include #include // for components_recorder namespace boost { //========================================================================== // This is the version of strongly connected components from // "Intro. to Algorithms" by Cormen, Leiserson, Rivest, which was // adapted from "Data Structure and Algorithms" by Aho, Hopcroft, // and Ullman, who credit the algorithm to S.R. Kosaraju and M. Sharir. // The algorithm is based on computing DFS forests the graph // and its transpose. // This algorithm is slower than Tarjan's by a constant factor, uses // more memory, and puts more requirements on the graph type. template < class Graph, class DFSVisitor, class ComponentsMap, class DiscoverTime, class FinishTime, class ColorMap > typename property_traits< ComponentsMap >::value_type kosaraju_strong_components( Graph& G, ComponentsMap c, FinishTime finish_time, ColorMap color) { BOOST_CONCEPT_ASSERT((MutableGraphConcept< Graph >)); // ... typedef typename graph_traits< Graph >::vertex_descriptor Vertex; typedef typename property_traits< ColorMap >::value_type ColorValue; typedef color_traits< ColorValue > Color; typename property_traits< FinishTime >::value_type time = 0; depth_first_search(G, make_dfs_visitor(stamp_times(finish_time, time, on_finish_vertex())), color); Graph G_T(num_vertices(G)); transpose_graph(G, G_T); typedef typename property_traits< ComponentsMap >::value_type count_type; count_type c_count(0); detail::components_recorder< ComponentsMap > vis(c, c_count); // initialize G_T typename graph_traits< Graph >::vertex_iterator ui, ui_end; for (boost::tie(ui, ui_end) = vertices(G_T); ui != ui_end; ++ui) put(color, *ui, Color::white()); typedef typename property_traits< FinishTime >::value_type D; typedef indirect_cmp< FinishTime, std::less< D > > Compare; Compare fl(finish_time); std::priority_queue< Vertex, std::vector< Vertex >, Compare > Q(fl); typename graph_traits< Graph >::vertex_iterator i, j, iend, jend; boost::tie(i, iend) = vertices(G_T); boost::tie(j, jend) = vertices(G); for (; i != iend; ++i, ++j) { put(finish_time, *i, get(finish_time, *j)); Q.push(*i); } while (!Q.empty()) { Vertex u = Q.top(); Q.pop(); if (get(color, u) == Color::white()) { depth_first_visit(G_T, u, vis, color); ++c_count; } } return c_count; } } // namespace boost #include BOOST_GRAPH_MPI_INCLUDE() #endif // BOOST_GRAPH_STRONG_COMPONENTS_HPP