text: //
  //=======================================================================
  // 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>
  #include <boost/concept/assert.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 (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);
            } 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 <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)
    {
      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
  
  #ifdef BOOST_GRAPH_USE_MPI
  #  include <boost/graph/distributed/strong_components.hpp>
  #endif
  
  #endif // BOOST_GRAPH_STRONG_COMPONENTS_HPP
  