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#include <boost/graph/overloading.hpp>
21#include <boost/concept/assert.hpp>
22
23namespace boost {
24
25 //==========================================================================
26 // This is Tarjan's algorithm for strongly connected components
27 // from his paper "Depth first search and linear graph algorithms".
28 // It calculates the components in a single application of DFS.
29 // We implement the algorithm as a dfs-visitor.
30
31 namespace detail {
32
33 template <typename ComponentMap, typename RootMap, typename DiscoverTime,
34 typename Stack>
35 class tarjan_scc_visitor : public dfs_visitor<>
36 {
37 typedef typename property_traits<ComponentMap>::value_type comp_type;
38 typedef typename property_traits<DiscoverTime>::value_type time_type;
39 public:
40 tarjan_scc_visitor(ComponentMap comp_map, RootMap r, DiscoverTime d,
41 comp_type& c_, Stack& s_)
42 : c(c_), comp(comp_map), root(r), discover_time(d),
43 dfs_time(time_type()), s(s_) { }
44
45 template <typename Graph>
46 void discover_vertex(typename graph_traits<Graph>::vertex_descriptor v,
47 const Graph&) {
48 put(root, v, v);
49 put(comp, v, (std::numeric_limits<comp_type>::max)());
50 put(discover_time, v, dfs_time++);
51 s.push(v);
52 }
53 template <typename Graph>
54 void finish_vertex(typename graph_traits<Graph>::vertex_descriptor v,
55 const Graph& g) {
56 typename graph_traits<Graph>::vertex_descriptor w;
57 typename graph_traits<Graph>::out_edge_iterator ei, ei_end;
58 for (boost::tie(ei, ei_end) = out_edges(v, g); ei != ei_end; ++ei) {
59 w = target(*ei, g);
60 if (get(comp, w) == (std::numeric_limits<comp_type>::max)())
61 put(root, v, this->min_discover_time(get(root,v), get(root,w)));
62 }
63 if (get(root, v) == v) {
64 do {
65 w = s.top(); s.pop();
66 put(comp, w, c);
67 } while (w != v);
68 ++c;
69 }
70 }
71 private:
72 template <typename Vertex>
73 Vertex min_discover_time(Vertex u, Vertex v) {
74 return get(discover_time, u) < get(discover_time,v) ? u : v;
75 }
76
77 comp_type& c;
78 ComponentMap comp;
79 RootMap root;
80 DiscoverTime discover_time;
81 time_type dfs_time;
82 Stack& s;
83 };
84
85 template <class Graph, class ComponentMap, class RootMap,
86 class DiscoverTime, class P, class T, class R>
87 typename property_traits<ComponentMap>::value_type
88 strong_components_impl
89 (const Graph& g, // Input
90 ComponentMap comp, // Output
91 // Internal record keeping
92 RootMap root,
93 DiscoverTime discover_time,
94 const bgl_named_params<P, T, R>& params)
95 {
96 typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
97 BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<ComponentMap, Vertex> ));
98 BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<RootMap, Vertex> ));
99 typedef typename property_traits<RootMap>::value_type RootV;
100 BOOST_CONCEPT_ASSERT(( ConvertibleConcept<RootV, Vertex> ));
101 BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<DiscoverTime, Vertex> ));
102
103 typename property_traits<ComponentMap>::value_type total = 0;
104
105 std::stack<Vertex> s;
106 detail::tarjan_scc_visitor<ComponentMap, RootMap, DiscoverTime,
107 std::stack<Vertex> >
108 vis(comp, root, discover_time, total, s);
109 depth_first_search(g, params.visitor(vis));
110 return total;
111 }
112
113 //-------------------------------------------------------------------------
114 // The dispatch functions handle the defaults for the rank and discover
115 // time property maps.
116 // dispatch with class specialization to avoid VC++ bug
117
118 template <class DiscoverTimeMap>
119 struct strong_comp_dispatch2 {
120 template <class Graph, class ComponentMap, class RootMap, class P, class T, class R>
121 inline static typename property_traits<ComponentMap>::value_type
122 apply(const Graph& g,
123 ComponentMap comp,
124 RootMap r_map,
125 const bgl_named_params<P, T, R>& params,
126 DiscoverTimeMap time_map)
127 {
128 return strong_components_impl(g, comp, r_map, time_map, params);
129 }
130 };
131
132
133 template <>
134 struct strong_comp_dispatch2<param_not_found> {
135 template <class Graph, class ComponentMap, class RootMap,
136 class P, class T, class R>
137 inline static typename property_traits<ComponentMap>::value_type
138 apply(const Graph& g,
139 ComponentMap comp,
140 RootMap r_map,
141 const bgl_named_params<P, T, R>& params,
142 param_not_found)
143 {
144 typedef typename graph_traits<Graph>::vertices_size_type size_type;
145 size_type n = num_vertices(g) > 0 ? num_vertices(g) : 1;
146 std::vector<size_type> time_vec(n);
147 return strong_components_impl
148 (g, comp, r_map,
149 make_iterator_property_map(time_vec.begin(), choose_const_pmap
150 (get_param(params, vertex_index),
151 g, vertex_index), time_vec[0]),
152 params);
153 }
154 };
155
156 template <class Graph, class ComponentMap, class RootMap,
157 class P, class T, class R, class DiscoverTimeMap>
158 inline typename property_traits<ComponentMap>::value_type
159 scc_helper2(const Graph& g,
160 ComponentMap comp,
161 RootMap r_map,
162 const bgl_named_params<P, T, R>& params,
163 DiscoverTimeMap time_map)
164 {
165 return strong_comp_dispatch2<DiscoverTimeMap>::apply(g, comp, r_map, params, time_map);
166 }
167
168 template <class RootMap>
169 struct strong_comp_dispatch1 {
170
171 template <class Graph, class ComponentMap, class P, class T, class R>
172 inline static typename property_traits<ComponentMap>::value_type
173 apply(const Graph& g,
174 ComponentMap comp,
175 const bgl_named_params<P, T, R>& params,
176 RootMap r_map)
177 {
178 return scc_helper2(g, comp, r_map, params, get_param(params, vertex_discover_time));
179 }
180 };
181 template <>
182 struct strong_comp_dispatch1<param_not_found> {
183
184 template <class Graph, class ComponentMap,
185 class P, class T, class R>
186 inline static typename property_traits<ComponentMap>::value_type
187 apply(const Graph& g,
188 ComponentMap comp,
189 const bgl_named_params<P, T, R>& params,
190 param_not_found)
191 {
192 typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
193 typename std::vector<Vertex>::size_type
194 n = num_vertices(g) > 0 ? num_vertices(g) : 1;
195 std::vector<Vertex> root_vec(n);
196 return scc_helper2
197 (g, comp,
198 make_iterator_property_map(root_vec.begin(), choose_const_pmap
199 (get_param(params, vertex_index),
200 g, vertex_index), root_vec[0]),
201 params,
202 get_param(params, vertex_discover_time));
203 }
204 };
205
206 template <class Graph, class ComponentMap, class RootMap,
207 class P, class T, class R>
208 inline typename property_traits<ComponentMap>::value_type
209 scc_helper1(const Graph& g,
210 ComponentMap comp,
211 const bgl_named_params<P, T, R>& params,
212 RootMap r_map)
213 {
214 return detail::strong_comp_dispatch1<RootMap>::apply(g, comp, params,
215 r_map);
216 }
217
218 } // namespace detail
219
220 template <class Graph, class ComponentMap,
221 class P, class T, class R>
222 inline typename property_traits<ComponentMap>::value_type
223 strong_components(const Graph& g, ComponentMap comp,
224 const bgl_named_params<P, T, R>& params
225 BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph, vertex_list_graph_tag))
226 {
227 typedef typename graph_traits<Graph>::directed_category DirCat;
228 BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));
229 return detail::scc_helper1(g, comp, params,
230 get_param(params, vertex_root_t()));
231 }
232
233 template <class Graph, class ComponentMap>
234 inline typename property_traits<ComponentMap>::value_type
235 strong_components(const Graph& g, ComponentMap comp
236 BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph, vertex_list_graph_tag))
237 {
238 typedef typename graph_traits<Graph>::directed_category DirCat;
239 BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));
240 bgl_named_params<int, int> params(0);
241 return strong_components(g, comp, params);
242 }
243
244 template <typename Graph, typename ComponentMap, typename ComponentLists>
245 void build_component_lists
246 (const Graph& g,
247 typename graph_traits<Graph>::vertices_size_type num_scc,
248 ComponentMap component_number,
249 ComponentLists& components)
250 {
251 components.resize(num_scc);
252 typename graph_traits<Graph>::vertex_iterator vi, vi_end;
253 for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
254 components[component_number[*vi]].push_back(*vi);
255 }
256
257
258} // namespace boost
259
260#include <queue>
261#include <vector>
262#include <boost/graph/transpose_graph.hpp>
263#include <boost/pending/indirect_cmp.hpp>
264#include <boost/graph/connected_components.hpp> // for components_recorder
265
266namespace boost {
267
268 //==========================================================================
269 // This is the version of strongly connected components from
270 // "Intro. to Algorithms" by Cormen, Leiserson, Rivest, which was
271 // adapted from "Data Structure and Algorithms" by Aho, Hopcroft,
272 // and Ullman, who credit the algorithm to S.R. Kosaraju and M. Sharir.
273 // The algorithm is based on computing DFS forests the graph
274 // and its transpose.
275
276 // This algorithm is slower than Tarjan's by a constant factor, uses
277 // more memory, and puts more requirements on the graph type.
278
279 template <class Graph, class DFSVisitor, class ComponentsMap,
280 class DiscoverTime, class FinishTime,
281 class ColorMap>
282 typename property_traits<ComponentsMap>::value_type
283 kosaraju_strong_components(Graph& G, ComponentsMap c,
284 FinishTime finish_time, ColorMap color)
285 {
286 BOOST_CONCEPT_ASSERT(( MutableGraphConcept<Graph> ));
287 // ...
288
289 typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
290 typedef typename property_traits<ColorMap>::value_type ColorValue;
291 typedef color_traits<ColorValue> Color;
292 typename property_traits<FinishTime>::value_type time = 0;
293 depth_first_search
294 (G, make_dfs_visitor(stamp_times(finish_time, time, on_finish_vertex())),
295 color);
296
297 Graph G_T(num_vertices(G));
298 transpose_graph(G, G_T);
299
300 typedef typename property_traits<ComponentsMap>::value_type count_type;
301
302 count_type c_count(0);
303 detail::components_recorder<ComponentsMap>
304 vis(c, c_count);
305
306 // initialize G_T
307 typename graph_traits<Graph>::vertex_iterator ui, ui_end;
308 for (boost::tie(ui, ui_end) = vertices(G_T); ui != ui_end; ++ui)
309 put(color, *ui, Color::white());
310
311 typedef typename property_traits<FinishTime>::value_type D;
312 typedef indirect_cmp< FinishTime, std::less<D> > Compare;
313
314 Compare fl(finish_time);
315 std::priority_queue<Vertex, std::vector<Vertex>, Compare > Q(fl);
316
317 typename graph_traits<Graph>::vertex_iterator i, j, iend, jend;
318 boost::tie(i, iend) = vertices(G_T);
319 boost::tie(j, jend) = vertices(G);
320 for ( ; i != iend; ++i, ++j) {
321 put(finish_time, *i, get(finish_time, *j));
322 Q.push(*i);
323 }
324
325 while ( !Q.empty() ) {
326 Vertex u = Q.top();
327 Q.pop();
328 if (get(color, u) == Color::white()) {
329 depth_first_visit(G_T, u, vis, color);
330 ++c_count;
331 }
332 }
333 return c_count;
334 }
335
336} // namespace boost
337
338#ifdef BOOST_GRAPH_USE_MPI
339# include <boost/graph/distributed/strong_components.hpp>
340#endif
341
342#endif // BOOST_GRAPH_STRONG_COMPONENTS_HPP
343

source code of boost/boost/graph/strong_components.hpp