Chris@16: //
Chris@16: //=======================================================================
Chris@16: // Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
Chris@16: // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
Chris@16: //
Chris@16: // Distributed under the Boost Software License, Version 1.0. (See
Chris@16: // accompanying file LICENSE_1_0.txt or copy at
Chris@16: // http://www.boost.org/LICENSE_1_0.txt)
Chris@16: //=======================================================================
Chris@16: //
Chris@16: 
Chris@16: #ifndef BOOST_GRAPH_STRONG_COMPONENTS_HPP
Chris@16: #define BOOST_GRAPH_STRONG_COMPONENTS_HPP
Chris@16: 
Chris@16: #include <stack>
Chris@16: #include <boost/config.hpp>
Chris@16: #include <boost/graph/depth_first_search.hpp>
Chris@16: #include <boost/type_traits/conversion_traits.hpp>
Chris@16: #include <boost/static_assert.hpp>
Chris@16: #include <boost/graph/overloading.hpp>
Chris@16: #include <boost/concept/assert.hpp>
Chris@16: 
Chris@16: namespace boost {
Chris@16: 
Chris@16:   //==========================================================================
Chris@16:   // This is Tarjan's algorithm for strongly connected components
Chris@16:   // from his paper "Depth first search and linear graph algorithms".
Chris@16:   // It calculates the components in a single application of DFS.
Chris@16:   // We implement the algorithm as a dfs-visitor.
Chris@16: 
Chris@16:   namespace detail {
Chris@16:     
Chris@16:     template <typename ComponentMap, typename RootMap, typename DiscoverTime,
Chris@16:               typename Stack>
Chris@16:     class tarjan_scc_visitor : public dfs_visitor<> 
Chris@16:     {
Chris@16:       typedef typename property_traits<ComponentMap>::value_type comp_type;
Chris@16:       typedef typename property_traits<DiscoverTime>::value_type time_type;
Chris@16:     public:
Chris@16:       tarjan_scc_visitor(ComponentMap comp_map, RootMap r, DiscoverTime d, 
Chris@16:                          comp_type& c_, Stack& s_)
Chris@16:         : c(c_), comp(comp_map), root(r), discover_time(d),
Chris@16:           dfs_time(time_type()), s(s_) { }
Chris@16: 
Chris@16:       template <typename Graph>
Chris@16:       void discover_vertex(typename graph_traits<Graph>::vertex_descriptor v,
Chris@16:                            const Graph&) {
Chris@16:         put(root, v, v);
Chris@16:         put(comp, v, (std::numeric_limits<comp_type>::max)());
Chris@16:         put(discover_time, v, dfs_time++);
Chris@16:         s.push(v);
Chris@16:       }
Chris@16:       template <typename Graph>
Chris@16:       void finish_vertex(typename graph_traits<Graph>::vertex_descriptor v,
Chris@16:                          const Graph& g) {
Chris@16:         typename graph_traits<Graph>::vertex_descriptor w;
Chris@16:         typename graph_traits<Graph>::out_edge_iterator ei, ei_end;
Chris@16:         for (boost::tie(ei, ei_end) = out_edges(v, g); ei != ei_end; ++ei) {
Chris@16:           w = target(*ei, g);
Chris@16:           if (get(comp, w) == (std::numeric_limits<comp_type>::max)())
Chris@16:             put(root, v, this->min_discover_time(get(root,v), get(root,w)));
Chris@16:         }
Chris@16:         if (get(root, v) == v) {
Chris@16:           do {
Chris@16:             w = s.top(); s.pop();
Chris@16:             put(comp, w, c);
Chris@16:           } while (w != v);
Chris@16:           ++c;
Chris@16:         }
Chris@16:       }
Chris@16:     private:
Chris@16:       template <typename Vertex>
Chris@16:       Vertex min_discover_time(Vertex u, Vertex v) {
Chris@16:         return get(discover_time, u) < get(discover_time,v) ? u : v;
Chris@16:       }
Chris@16: 
Chris@16:       comp_type& c;
Chris@16:       ComponentMap comp;
Chris@16:       RootMap root;
Chris@16:       DiscoverTime discover_time;
Chris@16:       time_type dfs_time;
Chris@16:       Stack& s;
Chris@16:     };
Chris@16:     
Chris@16:     template <class Graph, class ComponentMap, class RootMap,
Chris@16:               class DiscoverTime, class P, class T, class R>
Chris@16:     typename property_traits<ComponentMap>::value_type
Chris@16:     strong_components_impl
Chris@16:       (const Graph& g,    // Input
Chris@16:        ComponentMap comp, // Output
Chris@16:        // Internal record keeping
Chris@16:        RootMap root, 
Chris@16:        DiscoverTime discover_time,
Chris@16:        const bgl_named_params<P, T, R>& params)
Chris@16:     {
Chris@16:       typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
Chris@16:       BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<ComponentMap, Vertex> ));
Chris@16:       BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<RootMap, Vertex> ));
Chris@16:       typedef typename property_traits<RootMap>::value_type RootV;
Chris@16:       BOOST_CONCEPT_ASSERT(( ConvertibleConcept<RootV, Vertex> ));
Chris@16:       BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<DiscoverTime, Vertex> ));
Chris@16: 
Chris@16:       typename property_traits<ComponentMap>::value_type total = 0;
Chris@16: 
Chris@16:       std::stack<Vertex> s;
Chris@16:       detail::tarjan_scc_visitor<ComponentMap, RootMap, DiscoverTime, 
Chris@16:         std::stack<Vertex> > 
Chris@16:         vis(comp, root, discover_time, total, s);
Chris@16:       depth_first_search(g, params.visitor(vis));
Chris@16:       return total;
Chris@16:     }
Chris@16: 
Chris@16:     //-------------------------------------------------------------------------
Chris@16:     // The dispatch functions handle the defaults for the rank and discover
Chris@16:     // time property maps.
Chris@16:     // dispatch with class specialization to avoid VC++ bug
Chris@16: 
Chris@16:     template <class DiscoverTimeMap>
Chris@16:     struct strong_comp_dispatch2 {
Chris@16:       template <class Graph, class ComponentMap, class RootMap, class P, class T, class R>
Chris@16:       inline static typename property_traits<ComponentMap>::value_type
Chris@16:       apply(const Graph& g,
Chris@16:             ComponentMap comp,
Chris@16:             RootMap r_map,
Chris@16:             const bgl_named_params<P, T, R>& params,
Chris@16:             DiscoverTimeMap time_map)
Chris@16:       {
Chris@16:         return strong_components_impl(g, comp, r_map, time_map, params);
Chris@16:       }
Chris@16:     };
Chris@16: 
Chris@16: 
Chris@16:     template <>
Chris@16:     struct strong_comp_dispatch2<param_not_found> {
Chris@16:       template <class Graph, class ComponentMap, class RootMap,
Chris@16:                 class P, class T, class R>
Chris@16:       inline static typename property_traits<ComponentMap>::value_type
Chris@16:       apply(const Graph& g,
Chris@16:             ComponentMap comp,
Chris@16:             RootMap r_map,
Chris@16:             const bgl_named_params<P, T, R>& params,
Chris@16:             param_not_found)
Chris@16:       {
Chris@16:         typedef typename graph_traits<Graph>::vertices_size_type size_type;
Chris@16:         size_type       n = num_vertices(g) > 0 ? num_vertices(g) : 1;
Chris@16:         std::vector<size_type> time_vec(n);
Chris@16:         return strong_components_impl
Chris@16:           (g, comp, r_map,
Chris@16:            make_iterator_property_map(time_vec.begin(), choose_const_pmap
Chris@16:                                       (get_param(params, vertex_index),
Chris@16:                                        g, vertex_index), time_vec[0]),
Chris@16:            params);
Chris@16:       }
Chris@16:     };
Chris@16: 
Chris@16:     template <class Graph, class ComponentMap, class RootMap,
Chris@16:               class P, class T, class R, class DiscoverTimeMap>
Chris@16:     inline typename property_traits<ComponentMap>::value_type
Chris@16:     scc_helper2(const Graph& g,
Chris@16:                 ComponentMap comp,
Chris@16:                 RootMap r_map,
Chris@16:                 const bgl_named_params<P, T, R>& params,
Chris@16:                 DiscoverTimeMap time_map)
Chris@16:     {
Chris@16:       return strong_comp_dispatch2<DiscoverTimeMap>::apply(g, comp, r_map, params, time_map);
Chris@16:     }
Chris@16: 
Chris@16:     template <class RootMap>
Chris@16:     struct strong_comp_dispatch1 {
Chris@16: 
Chris@16:       template <class Graph, class ComponentMap, class P, class T, class R>
Chris@16:       inline static typename property_traits<ComponentMap>::value_type
Chris@16:       apply(const Graph& g,
Chris@16:             ComponentMap comp,
Chris@16:             const bgl_named_params<P, T, R>& params,
Chris@16:             RootMap r_map)
Chris@16:       {
Chris@16:         return scc_helper2(g, comp, r_map, params, get_param(params, vertex_discover_time));
Chris@16:       }
Chris@16:     };
Chris@16:     template <>
Chris@16:     struct strong_comp_dispatch1<param_not_found> {
Chris@16: 
Chris@16:       template <class Graph, class ComponentMap, 
Chris@16:                 class P, class T, class R>
Chris@16:       inline static typename property_traits<ComponentMap>::value_type
Chris@16:       apply(const Graph& g,
Chris@16:             ComponentMap comp,
Chris@16:             const bgl_named_params<P, T, R>& params,
Chris@16:             param_not_found)
Chris@16:       {
Chris@16:         typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
Chris@16:         typename std::vector<Vertex>::size_type
Chris@16:           n = num_vertices(g) > 0 ? num_vertices(g) : 1;
Chris@16:         std::vector<Vertex> root_vec(n);
Chris@16:         return scc_helper2
Chris@16:           (g, comp, 
Chris@16:            make_iterator_property_map(root_vec.begin(), choose_const_pmap
Chris@16:                                       (get_param(params, vertex_index),
Chris@16:                                        g, vertex_index), root_vec[0]),
Chris@16:            params, 
Chris@16:            get_param(params, vertex_discover_time));
Chris@16:       }
Chris@16:     };
Chris@16: 
Chris@16:     template <class Graph, class ComponentMap, class RootMap,
Chris@16:               class P, class T, class R>
Chris@16:     inline typename property_traits<ComponentMap>::value_type
Chris@16:     scc_helper1(const Graph& g,
Chris@16:                ComponentMap comp,
Chris@16:                const bgl_named_params<P, T, R>& params,
Chris@16:                RootMap r_map)
Chris@16:     {
Chris@16:       return detail::strong_comp_dispatch1<RootMap>::apply(g, comp, params,
Chris@16:                                                            r_map);
Chris@16:     }
Chris@16: 
Chris@16:   } // namespace detail 
Chris@16: 
Chris@16:   template <class Graph, class ComponentMap, 
Chris@16:             class P, class T, class R>
Chris@16:   inline typename property_traits<ComponentMap>::value_type
Chris@16:   strong_components(const Graph& g, ComponentMap comp,
Chris@16:                     const bgl_named_params<P, T, R>& params
Chris@16:                     BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph, vertex_list_graph_tag))
Chris@16:   {
Chris@16:     typedef typename graph_traits<Graph>::directed_category DirCat;
Chris@16:     BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));
Chris@16:     return detail::scc_helper1(g, comp, params, 
Chris@16:                                get_param(params, vertex_root_t()));
Chris@16:   }
Chris@16: 
Chris@16:   template <class Graph, class ComponentMap>
Chris@16:   inline typename property_traits<ComponentMap>::value_type
Chris@16:   strong_components(const Graph& g, ComponentMap comp
Chris@16:                     BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph, vertex_list_graph_tag))
Chris@16:   {
Chris@16:     typedef typename graph_traits<Graph>::directed_category DirCat;
Chris@16:     BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));
Chris@16:     bgl_named_params<int, int> params(0);
Chris@16:     return strong_components(g, comp, params);
Chris@16:   }
Chris@16: 
Chris@16:   template <typename Graph, typename ComponentMap, typename ComponentLists>
Chris@16:   void build_component_lists
Chris@16:     (const Graph& g,
Chris@16:      typename graph_traits<Graph>::vertices_size_type num_scc,
Chris@16:      ComponentMap component_number,
Chris@16:      ComponentLists& components)
Chris@16:   {
Chris@16:     components.resize(num_scc);
Chris@16:     typename graph_traits<Graph>::vertex_iterator vi, vi_end;
Chris@16:     for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
Chris@16:       components[component_number[*vi]].push_back(*vi);
Chris@16:   }
Chris@16: 
Chris@16: 
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #include <queue>
Chris@16: #include <vector>
Chris@16: #include <boost/graph/transpose_graph.hpp>
Chris@16: #include <boost/pending/indirect_cmp.hpp>
Chris@16: #include <boost/graph/connected_components.hpp> // for components_recorder
Chris@16: 
Chris@16: namespace boost {
Chris@16: 
Chris@16:   //==========================================================================
Chris@16:   // This is the version of strongly connected components from
Chris@16:   // "Intro. to Algorithms" by Cormen, Leiserson, Rivest, which was
Chris@16:   // adapted from "Data Structure and Algorithms" by Aho, Hopcroft,
Chris@16:   // and Ullman, who credit the algorithm to S.R. Kosaraju and M. Sharir.
Chris@16:   // The algorithm is based on computing DFS forests the graph
Chris@16:   // and its transpose.
Chris@16: 
Chris@16:   // This algorithm is slower than Tarjan's by a constant factor, uses
Chris@16:   // more memory, and puts more requirements on the graph type.
Chris@16: 
Chris@16:   template <class Graph, class DFSVisitor, class ComponentsMap,
Chris@16:             class DiscoverTime, class FinishTime,
Chris@16:             class ColorMap>
Chris@16:   typename property_traits<ComponentsMap>::value_type
Chris@16:   kosaraju_strong_components(Graph& G, ComponentsMap c,
Chris@16:                              FinishTime finish_time, ColorMap color)
Chris@16:   {
Chris@16:     BOOST_CONCEPT_ASSERT(( MutableGraphConcept<Graph> ));
Chris@16:     // ...
Chris@16:     
Chris@16:     typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
Chris@16:     typedef typename property_traits<ColorMap>::value_type ColorValue;
Chris@16:     typedef color_traits<ColorValue> Color;
Chris@16:     typename property_traits<FinishTime>::value_type time = 0;
Chris@16:     depth_first_search
Chris@16:      (G, make_dfs_visitor(stamp_times(finish_time, time, on_finish_vertex())),
Chris@16:       color);
Chris@16: 
Chris@16:     Graph G_T(num_vertices(G));
Chris@16:     transpose_graph(G, G_T);
Chris@16: 
Chris@16:     typedef typename property_traits<ComponentsMap>::value_type count_type;
Chris@16: 
Chris@16:     count_type c_count(0);
Chris@16:     detail::components_recorder<ComponentsMap>
Chris@16:       vis(c, c_count);
Chris@16: 
Chris@16:     // initialize G_T
Chris@16:     typename graph_traits<Graph>::vertex_iterator ui, ui_end;
Chris@16:     for (boost::tie(ui, ui_end) = vertices(G_T); ui != ui_end; ++ui)
Chris@16:       put(color, *ui, Color::white());
Chris@16: 
Chris@16:     typedef typename property_traits<FinishTime>::value_type D;
Chris@16:     typedef indirect_cmp< FinishTime, std::less<D> > Compare;
Chris@16: 
Chris@16:     Compare fl(finish_time);
Chris@16:     std::priority_queue<Vertex, std::vector<Vertex>, Compare > Q(fl);
Chris@16: 
Chris@16:     typename graph_traits<Graph>::vertex_iterator i, j, iend, jend;
Chris@16:     boost::tie(i, iend) = vertices(G_T);
Chris@16:     boost::tie(j, jend) = vertices(G);
Chris@16:     for ( ; i != iend; ++i, ++j) {
Chris@16:       put(finish_time, *i, get(finish_time, *j));
Chris@16:        Q.push(*i);
Chris@16:     }
Chris@16: 
Chris@16:     while ( !Q.empty() ) {
Chris@16:       Vertex u = Q.top();
Chris@16:       Q.pop();
Chris@16:       if  (get(color, u) == Color::white()) {
Chris@16:         depth_first_visit(G_T, u, vis, color);
Chris@16:         ++c_count; 
Chris@16:       }
Chris@16:     }
Chris@16:     return c_count;
Chris@16:   }
Chris@16: 
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #ifdef BOOST_GRAPH_USE_MPI
Chris@16: #  include <boost/graph/distributed/strong_components.hpp>
Chris@16: #endif
Chris@16: 
Chris@16: #endif // BOOST_GRAPH_STRONG_COMPONENTS_HPP