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