| // |
| //======================================================================= |
| // 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 <stack> |
| #include <boost/config.hpp> |
| #include <boost/graph/depth_first_search.hpp> |
| #include <boost/type_traits/conversion_traits.hpp> |
| #include <boost/static_assert.hpp> |
| #include <boost/graph/overloading.hpp> |
| |
| 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 (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); |
| } 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; |
| function_requires< ReadWritePropertyMapConcept<ComponentMap, Vertex> >(); |
| function_requires< ReadWritePropertyMapConcept<RootMap, Vertex> >(); |
| typedef typename property_traits<RootMap>::value_type RootV; |
| function_requires< ConvertibleConcept<RootV, Vertex> >(); |
| function_requires< 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<detail::error_property_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, |
| detail::error_property_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<detail::error_property_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, |
| detail::error_property_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 (tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi) |
| components[component_number[*vi]].push_back(*vi); |
| } |
| |
| |
| } // namespace boost |
| |
| #include <queue> |
| #include <vector> |
| #include <boost/graph/transpose_graph.hpp> |
| #include <boost/pending/indirect_cmp.hpp> |
| #include <boost/graph/connected_components.hpp> // 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) |
| { |
| function_requires< 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 (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; |
| tie(i, iend) = vertices(G_T); |
| 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 |
| |
| #ifdef BOOST_GRAPH_USE_MPI |
| # include <boost/graph/distributed/strong_components.hpp> |
| #endif |
| |
| #endif // BOOST_GRAPH_STRONG_COMPONENTS_HPP |
