// | |
//======================================================================= | |
// 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> | |
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; | |
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 | |
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) | |
{ | |
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 (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 |