//

 //=======================================================================

 // 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>

 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)

   {

     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)

   {

     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

 #endif // BOOST_GRAPH_STRONG_COMPONENTS_HPP