1 //

     2 //=======================================================================

     3 // Copyright 1997, 1998, 1999, 2000 University of Notre Dame.

     4 // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek

     5 //

     6 // Distributed under the Boost Software License, Version 1.0. (See

     7 // accompanying file LICENSE_1_0.txt or copy at

     8 // http://www.boost.org/LICENSE_1_0.txt)

     9 //=======================================================================

    10 //

    11 

    12 #ifndef BOOST_GRAPH_STRONG_COMPONENTS_HPP

    13 #define BOOST_GRAPH_STRONG_COMPONENTS_HPP

    14 

    15 #include <stack>

    16 #include <boost/config.hpp>

    17 #include <boost/graph/depth_first_search.hpp>

    18 #include <boost/type_traits/conversion_traits.hpp>

    19 #include <boost/static_assert.hpp>

    20 

    21 namespace boost {

    22 

    23   //==========================================================================

    24   // This is Tarjan's algorithm for strongly connected components

    25   // from his paper "Depth first search and linear graph algorithms".

    26   // It calculates the components in a single application of DFS.

    27   // We implement the algorithm as a dfs-visitor.

    28 

    29   namespace detail {

    30     

    31     template <typename ComponentMap, typename RootMap, typename DiscoverTime,

    32               typename Stack>

    33     class tarjan_scc_visitor : public dfs_visitor<> 

    34     {

    35       typedef typename property_traits<ComponentMap>::value_type comp_type;

    36       typedef typename property_traits<DiscoverTime>::value_type time_type;

    37     public:

    38       tarjan_scc_visitor(ComponentMap comp_map, RootMap r, DiscoverTime d, 

    39                          comp_type& c_, Stack& s_)

    40         : c(c_), comp(comp_map), root(r), discover_time(d),

    41           dfs_time(time_type()), s(s_) { }

    42 

    43       template <typename Graph>

    44       void discover_vertex(typename graph_traits<Graph>::vertex_descriptor v,

    45                            const Graph&) {

    46         put(root, v, v);

    47         put(comp, v, (std::numeric_limits<comp_type>::max)());

    48         put(discover_time, v, dfs_time++);

    49         s.push(v);

    50       }

    51       template <typename Graph>

    52       void finish_vertex(typename graph_traits<Graph>::vertex_descriptor v,

    53                          const Graph& g) {

    54         typename graph_traits<Graph>::vertex_descriptor w;

    55         typename graph_traits<Graph>::out_edge_iterator ei, ei_end;

    56         for (tie(ei, ei_end) = out_edges(v, g); ei != ei_end; ++ei) {

    57           w = target(*ei, g);

    58           if (get(comp, w) == (std::numeric_limits<comp_type>::max)())

    59             put(root, v, this->min_discover_time(get(root,v), get(root,w)));

    60         }

    61         if (get(root, v) == v) {

    62           do {

    63             w = s.top(); s.pop();

    64             put(comp, w, c);

    65           } while (w != v);

    66           ++c;

    67         }

    68       }

    69     private:

    70       template <typename Vertex>

    71       Vertex min_discover_time(Vertex u, Vertex v) {

    72         return get(discover_time, u) < get(discover_time,v) ? u : v;

    73       }

    74 

    75       comp_type& c;

    76       ComponentMap comp;

    77       RootMap root;

    78       DiscoverTime discover_time;

    79       time_type dfs_time;

    80       Stack& s;

    81     };

    82     

    83     template <class Graph, class ComponentMap, class RootMap,

    84               class DiscoverTime, class P, class T, class R>

    85     typename property_traits<ComponentMap>::value_type

    86     strong_components_impl

    87       (const Graph& g,    // Input

    88        ComponentMap comp, // Output

    89        // Internal record keeping

    90        RootMap root, 

    91        DiscoverTime discover_time,

    92        const bgl_named_params<P, T, R>& params)

    93     {

    94       typedef typename graph_traits<Graph>::vertex_descriptor Vertex;

    95       function_requires< ReadWritePropertyMapConcept<ComponentMap, Vertex> >();

    96       function_requires< ReadWritePropertyMapConcept<RootMap, Vertex> >();

    97       typedef typename property_traits<RootMap>::value_type RootV;

    98       function_requires< ConvertibleConcept<RootV, Vertex> >();

    99       function_requires< ReadWritePropertyMapConcept<DiscoverTime, Vertex> >();

   100 

   101       typename property_traits<ComponentMap>::value_type total = 0;

   102 

   103       std::stack<Vertex> s;

   104       detail::tarjan_scc_visitor<ComponentMap, RootMap, DiscoverTime, 

   105         std::stack<Vertex> > 

   106         vis(comp, root, discover_time, total, s);

   107       depth_first_search(g, params.visitor(vis));

   108       return total;

   109     }

   110 

   111     //-------------------------------------------------------------------------

   112     // The dispatch functions handle the defaults for the rank and discover

   113     // time property maps.

   114     // dispatch with class specialization to avoid VC++ bug

   115 

   116     template <class DiscoverTimeMap>

   117     struct strong_comp_dispatch2 {

   118       template <class Graph, class ComponentMap, class RootMap, class P, class T, class R>

   119       inline static typename property_traits<ComponentMap>::value_type

   120       apply(const Graph& g,

   121             ComponentMap comp,

   122             RootMap r_map,

   123             const bgl_named_params<P, T, R>& params,

   124             DiscoverTimeMap time_map)

   125       {

   126         return strong_components_impl(g, comp, r_map, time_map, params);

   127       }

   128     };

   129 

   130 

   131     template <>

   132     struct strong_comp_dispatch2<detail::error_property_not_found> {

   133       template <class Graph, class ComponentMap, class RootMap,

   134                 class P, class T, class R>

   135       inline static typename property_traits<ComponentMap>::value_type

   136       apply(const Graph& g,

   137             ComponentMap comp,

   138             RootMap r_map,

   139             const bgl_named_params<P, T, R>& params,

   140             detail::error_property_not_found)

   141       {

   142         typedef typename graph_traits<Graph>::vertices_size_type size_type;

   143         size_type       n = num_vertices(g) > 0 ? num_vertices(g) : 1;

   144         std::vector<size_type> time_vec(n);

   145         return strong_components_impl

   146           (g, comp, r_map,

   147            make_iterator_property_map(time_vec.begin(), choose_const_pmap

   148                                       (get_param(params, vertex_index),

   149                                        g, vertex_index), time_vec[0]),

   150            params);

   151       }

   152     };

   153 

   154     template <class Graph, class ComponentMap, class RootMap,

   155               class P, class T, class R, class DiscoverTimeMap>

   156     inline typename property_traits<ComponentMap>::value_type

   157     scc_helper2(const Graph& g,

   158                 ComponentMap comp,

   159                 RootMap r_map,

   160                 const bgl_named_params<P, T, R>& params,

   161                 DiscoverTimeMap time_map)

   162     {

   163       return strong_comp_dispatch2<DiscoverTimeMap>::apply(g, comp, r_map, params, time_map);

   164     }

   165 

   166     template <class RootMap>

   167     struct strong_comp_dispatch1 {

   168 

   169       template <class Graph, class ComponentMap, class P, class T, class R>

   170       inline static typename property_traits<ComponentMap>::value_type

   171       apply(const Graph& g,

   172             ComponentMap comp,

   173             const bgl_named_params<P, T, R>& params,

   174             RootMap r_map)

   175       {

   176         return scc_helper2(g, comp, r_map, params, get_param(params, vertex_discover_time));

   177       }

   178     };

   179     template <>

   180     struct strong_comp_dispatch1<detail::error_property_not_found> {

   181 

   182       template <class Graph, class ComponentMap, 

   183                 class P, class T, class R>

   184       inline static typename property_traits<ComponentMap>::value_type

   185       apply(const Graph& g,

   186             ComponentMap comp,

   187             const bgl_named_params<P, T, R>& params,

   188             detail::error_property_not_found)

   189       {

   190         typedef typename graph_traits<Graph>::vertex_descriptor Vertex;

   191         typename std::vector<Vertex>::size_type

   192           n = num_vertices(g) > 0 ? num_vertices(g) : 1;

   193         std::vector<Vertex> root_vec(n);

   194         return scc_helper2

   195           (g, comp, 

   196            make_iterator_property_map(root_vec.begin(), choose_const_pmap

   197                                       (get_param(params, vertex_index),

   198                                        g, vertex_index), root_vec[0]),

   199            params, 

   200            get_param(params, vertex_discover_time));

   201       }

   202     };

   203 

   204     template <class Graph, class ComponentMap, class RootMap,

   205               class P, class T, class R>

   206     inline typename property_traits<ComponentMap>::value_type

   207     scc_helper1(const Graph& g,

   208                ComponentMap comp,

   209                const bgl_named_params<P, T, R>& params,

   210                RootMap r_map)

   211     {

   212       return detail::strong_comp_dispatch1<RootMap>::apply(g, comp, params,

   213                                                            r_map);

   214     }

   215 

   216   } // namespace detail 

   217 

   218   template <class Graph, class ComponentMap, 

   219             class P, class T, class R>

   220   inline typename property_traits<ComponentMap>::value_type

   221   strong_components(const Graph& g, ComponentMap comp,

   222                     const bgl_named_params<P, T, R>& params)

   223   {

   224     typedef typename graph_traits<Graph>::directed_category DirCat;

   225     BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));

   226     return detail::scc_helper1(g, comp, params, 

   227                                get_param(params, vertex_root_t()));

   228   }

   229 

   230   template <class Graph, class ComponentMap>

   231   inline typename property_traits<ComponentMap>::value_type

   232   strong_components(const Graph& g, ComponentMap comp)

   233   {

   234     typedef typename graph_traits<Graph>::directed_category DirCat;

   235     BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));

   236     bgl_named_params<int, int> params(0);

   237     return strong_components(g, comp, params);

   238   }

   239 

   240   template <typename Graph, typename ComponentMap, typename ComponentLists>

   241   void build_component_lists

   242     (const Graph& g,

   243      typename graph_traits<Graph>::vertices_size_type num_scc,

   244      ComponentMap component_number,

   245      ComponentLists& components)

   246   {

   247     components.resize(num_scc);

   248     typename graph_traits<Graph>::vertex_iterator vi, vi_end;

   249     for (tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)

   250       components[component_number[*vi]].push_back(*vi);

   251   }

   252 

   253 

   254 } // namespace boost

   255 

   256 #include <queue>

   257 #include <vector>

   258 #include <boost/graph/transpose_graph.hpp>

   259 #include <boost/pending/indirect_cmp.hpp>

   260 #include <boost/graph/connected_components.hpp> // for components_recorder

   261 

   262 namespace boost {

   263 

   264   //==========================================================================

   265   // This is the version of strongly connected components from

   266   // "Intro. to Algorithms" by Cormen, Leiserson, Rivest, which was

   267   // adapted from "Data Structure and Algorithms" by Aho, Hopcroft,

   268   // and Ullman, who credit the algorithm to S.R. Kosaraju and M. Sharir.

   269   // The algorithm is based on computing DFS forests the graph

   270   // and its transpose.

   271 

   272   // This algorithm is slower than Tarjan's by a constant factor, uses

   273   // more memory, and puts more requirements on the graph type.

   274 

   275   template <class Graph, class DFSVisitor, class ComponentsMap,

   276             class DiscoverTime, class FinishTime,

   277             class ColorMap>

   278   typename property_traits<ComponentsMap>::value_type

   279   kosaraju_strong_components(Graph& G, ComponentsMap c,

   280                              FinishTime finish_time, ColorMap color)

   281   {

   282     function_requires< MutableGraphConcept<Graph> >();

   283     // ...

   284     

   285     typedef typename graph_traits<Graph>::vertex_descriptor Vertex;

   286     typedef typename property_traits<ColorMap>::value_type ColorValue;

   287     typedef color_traits<ColorValue> Color;

   288     typename property_traits<FinishTime>::value_type time = 0;

   289     depth_first_search

   290      (G, make_dfs_visitor(stamp_times(finish_time, time, on_finish_vertex())),

   291       color);

   292 

   293     Graph G_T(num_vertices(G));

   294     transpose_graph(G, G_T);

   295 

   296     typedef typename property_traits<ComponentsMap>::value_type count_type;

   297 

   298     count_type c_count(0);

   299     detail::components_recorder<ComponentsMap>

   300       vis(c, c_count);

   301 

   302     // initialize G_T

   303     typename graph_traits<Graph>::vertex_iterator ui, ui_end;

   304     for (tie(ui, ui_end) = vertices(G_T); ui != ui_end; ++ui)

   305       put(color, *ui, Color::white());

   306 

   307     typedef typename property_traits<FinishTime>::value_type D;

   308     typedef indirect_cmp< FinishTime, std::less<D> > Compare;

   309 

   310     Compare fl(finish_time);

   311     std::priority_queue<Vertex, std::vector<Vertex>, Compare > Q(fl);

   312 

   313     typename graph_traits<Graph>::vertex_iterator i, j, iend, jend;

   314     tie(i, iend) = vertices(G_T);

   315     tie(j, jend) = vertices(G);

   316     for ( ; i != iend; ++i, ++j) {

   317       put(finish_time, *i, get(finish_time, *j));

   318        Q.push(*i);

   319     }

   320 

   321     while ( !Q.empty() ) {

   322       Vertex u = Q.top();

   323       Q.pop();

   324       if  (get(color, u) == Color::white()) {

   325         depth_first_visit(G_T, u, vis, color);

   326         ++c_count; 

   327       }

   328     }

   329     return c_count;

   330   }

   331 

   332 } // namespace boost

   333 

   334 #endif // BOOST_GRAPH_STRONG_COMPONENTS_HPP