williamr@2: //
williamr@2: //=======================================================================
williamr@2: // Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
williamr@2: // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
williamr@2: //
williamr@2: // Distributed under the Boost Software License, Version 1.0. (See
williamr@2: // accompanying file LICENSE_1_0.txt or copy at
williamr@2: // http://www.boost.org/LICENSE_1_0.txt)
williamr@2: //=======================================================================
williamr@2: //
williamr@2:
williamr@2: #ifndef BOOST_GRAPH_STRONG_COMPONENTS_HPP
williamr@2: #define BOOST_GRAPH_STRONG_COMPONENTS_HPP
williamr@2:
williamr@2: #include <stack>
williamr@2: #include <boost/config.hpp>
williamr@2: #include <boost/graph/depth_first_search.hpp>
williamr@2: #include <boost/type_traits/conversion_traits.hpp>
williamr@2: #include <boost/static_assert.hpp>
williamr@2:
williamr@2: namespace boost {
williamr@2:
williamr@2: //==========================================================================
williamr@2: // This is Tarjan's algorithm for strongly connected components
williamr@2: // from his paper "Depth first search and linear graph algorithms".
williamr@2: // It calculates the components in a single application of DFS.
williamr@2: // We implement the algorithm as a dfs-visitor.
williamr@2:
williamr@2: namespace detail {
williamr@2:
williamr@2: template <typename ComponentMap, typename RootMap, typename DiscoverTime,
williamr@2: typename Stack>
williamr@2: class tarjan_scc_visitor : public dfs_visitor<>
williamr@2: {
williamr@2: typedef typename property_traits<ComponentMap>::value_type comp_type;
williamr@2: typedef typename property_traits<DiscoverTime>::value_type time_type;
williamr@2: public:
williamr@2: tarjan_scc_visitor(ComponentMap comp_map, RootMap r, DiscoverTime d,
williamr@2: comp_type& c_, Stack& s_)
williamr@2: : c(c_), comp(comp_map), root(r), discover_time(d),
williamr@2: dfs_time(time_type()), s(s_) { }
williamr@2:
williamr@2: template <typename Graph>
williamr@2: void discover_vertex(typename graph_traits<Graph>::vertex_descriptor v,
williamr@2: const Graph&) {
williamr@2: put(root, v, v);
williamr@2: put(comp, v, (std::numeric_limits<comp_type>::max)());
williamr@2: put(discover_time, v, dfs_time++);
williamr@2: s.push(v);
williamr@2: }
williamr@2: template <typename Graph>
williamr@2: void finish_vertex(typename graph_traits<Graph>::vertex_descriptor v,
williamr@2: const Graph& g) {
williamr@2: typename graph_traits<Graph>::vertex_descriptor w;
williamr@2: typename graph_traits<Graph>::out_edge_iterator ei, ei_end;
williamr@2: for (tie(ei, ei_end) = out_edges(v, g); ei != ei_end; ++ei) {
williamr@2: w = target(*ei, g);
williamr@2: if (get(comp, w) == (std::numeric_limits<comp_type>::max)())
williamr@2: put(root, v, this->min_discover_time(get(root,v), get(root,w)));
williamr@2: }
williamr@2: if (get(root, v) == v) {
williamr@2: do {
williamr@2: w = s.top(); s.pop();
williamr@2: put(comp, w, c);
williamr@2: } while (w != v);
williamr@2: ++c;
williamr@2: }
williamr@2: }
williamr@2: private:
williamr@2: template <typename Vertex>
williamr@2: Vertex min_discover_time(Vertex u, Vertex v) {
williamr@2: return get(discover_time, u) < get(discover_time,v) ? u : v;
williamr@2: }
williamr@2:
williamr@2: comp_type& c;
williamr@2: ComponentMap comp;
williamr@2: RootMap root;
williamr@2: DiscoverTime discover_time;
williamr@2: time_type dfs_time;
williamr@2: Stack& s;
williamr@2: };
williamr@2:
williamr@2: template <class Graph, class ComponentMap, class RootMap,
williamr@2: class DiscoverTime, class P, class T, class R>
williamr@2: typename property_traits<ComponentMap>::value_type
williamr@2: strong_components_impl
williamr@2: (const Graph& g, // Input
williamr@2: ComponentMap comp, // Output
williamr@2: // Internal record keeping
williamr@2: RootMap root,
williamr@2: DiscoverTime discover_time,
williamr@2: const bgl_named_params<P, T, R>& params)
williamr@2: {
williamr@2: typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
williamr@2: function_requires< ReadWritePropertyMapConcept<ComponentMap, Vertex> >();
williamr@2: function_requires< ReadWritePropertyMapConcept<RootMap, Vertex> >();
williamr@2: typedef typename property_traits<RootMap>::value_type RootV;
williamr@2: function_requires< ConvertibleConcept<RootV, Vertex> >();
williamr@2: function_requires< ReadWritePropertyMapConcept<DiscoverTime, Vertex> >();
williamr@2:
williamr@2: typename property_traits<ComponentMap>::value_type total = 0;
williamr@2:
williamr@2: std::stack<Vertex> s;
williamr@2: detail::tarjan_scc_visitor<ComponentMap, RootMap, DiscoverTime,
williamr@2: std::stack<Vertex> >
williamr@2: vis(comp, root, discover_time, total, s);
williamr@2: depth_first_search(g, params.visitor(vis));
williamr@2: return total;
williamr@2: }
williamr@2:
williamr@2: //-------------------------------------------------------------------------
williamr@2: // The dispatch functions handle the defaults for the rank and discover
williamr@2: // time property maps.
williamr@2: // dispatch with class specialization to avoid VC++ bug
williamr@2:
williamr@2: template <class DiscoverTimeMap>
williamr@2: struct strong_comp_dispatch2 {
williamr@2: template <class Graph, class ComponentMap, class RootMap, class P, class T, class R>
williamr@2: inline static typename property_traits<ComponentMap>::value_type
williamr@2: apply(const Graph& g,
williamr@2: ComponentMap comp,
williamr@2: RootMap r_map,
williamr@2: const bgl_named_params<P, T, R>& params,
williamr@2: DiscoverTimeMap time_map)
williamr@2: {
williamr@2: return strong_components_impl(g, comp, r_map, time_map, params);
williamr@2: }
williamr@2: };
williamr@2:
williamr@2:
williamr@2: template <>
williamr@2: struct strong_comp_dispatch2<detail::error_property_not_found> {
williamr@2: template <class Graph, class ComponentMap, class RootMap,
williamr@2: class P, class T, class R>
williamr@2: inline static typename property_traits<ComponentMap>::value_type
williamr@2: apply(const Graph& g,
williamr@2: ComponentMap comp,
williamr@2: RootMap r_map,
williamr@2: const bgl_named_params<P, T, R>& params,
williamr@2: detail::error_property_not_found)
williamr@2: {
williamr@2: typedef typename graph_traits<Graph>::vertices_size_type size_type;
williamr@2: size_type n = num_vertices(g) > 0 ? num_vertices(g) : 1;
williamr@2: std::vector<size_type> time_vec(n);
williamr@2: return strong_components_impl
williamr@2: (g, comp, r_map,
williamr@2: make_iterator_property_map(time_vec.begin(), choose_const_pmap
williamr@2: (get_param(params, vertex_index),
williamr@2: g, vertex_index), time_vec[0]),
williamr@2: params);
williamr@2: }
williamr@2: };
williamr@2:
williamr@2: template <class Graph, class ComponentMap, class RootMap,
williamr@2: class P, class T, class R, class DiscoverTimeMap>
williamr@2: inline typename property_traits<ComponentMap>::value_type
williamr@2: scc_helper2(const Graph& g,
williamr@2: ComponentMap comp,
williamr@2: RootMap r_map,
williamr@2: const bgl_named_params<P, T, R>& params,
williamr@2: DiscoverTimeMap time_map)
williamr@2: {
williamr@2: return strong_comp_dispatch2<DiscoverTimeMap>::apply(g, comp, r_map, params, time_map);
williamr@2: }
williamr@2:
williamr@2: template <class RootMap>
williamr@2: struct strong_comp_dispatch1 {
williamr@2:
williamr@2: template <class Graph, class ComponentMap, class P, class T, class R>
williamr@2: inline static typename property_traits<ComponentMap>::value_type
williamr@2: apply(const Graph& g,
williamr@2: ComponentMap comp,
williamr@2: const bgl_named_params<P, T, R>& params,
williamr@2: RootMap r_map)
williamr@2: {
williamr@2: return scc_helper2(g, comp, r_map, params, get_param(params, vertex_discover_time));
williamr@2: }
williamr@2: };
williamr@2: template <>
williamr@2: struct strong_comp_dispatch1<detail::error_property_not_found> {
williamr@2:
williamr@2: template <class Graph, class ComponentMap,
williamr@2: class P, class T, class R>
williamr@2: inline static typename property_traits<ComponentMap>::value_type
williamr@2: apply(const Graph& g,
williamr@2: ComponentMap comp,
williamr@2: const bgl_named_params<P, T, R>& params,
williamr@2: detail::error_property_not_found)
williamr@2: {
williamr@2: typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
williamr@2: typename std::vector<Vertex>::size_type
williamr@2: n = num_vertices(g) > 0 ? num_vertices(g) : 1;
williamr@2: std::vector<Vertex> root_vec(n);
williamr@2: return scc_helper2
williamr@2: (g, comp,
williamr@2: make_iterator_property_map(root_vec.begin(), choose_const_pmap
williamr@2: (get_param(params, vertex_index),
williamr@2: g, vertex_index), root_vec[0]),
williamr@2: params,
williamr@2: get_param(params, vertex_discover_time));
williamr@2: }
williamr@2: };
williamr@2:
williamr@2: template <class Graph, class ComponentMap, class RootMap,
williamr@2: class P, class T, class R>
williamr@2: inline typename property_traits<ComponentMap>::value_type
williamr@2: scc_helper1(const Graph& g,
williamr@2: ComponentMap comp,
williamr@2: const bgl_named_params<P, T, R>& params,
williamr@2: RootMap r_map)
williamr@2: {
williamr@2: return detail::strong_comp_dispatch1<RootMap>::apply(g, comp, params,
williamr@2: r_map);
williamr@2: }
williamr@2:
williamr@2: } // namespace detail
williamr@2:
williamr@2: template <class Graph, class ComponentMap,
williamr@2: class P, class T, class R>
williamr@2: inline typename property_traits<ComponentMap>::value_type
williamr@2: strong_components(const Graph& g, ComponentMap comp,
williamr@2: const bgl_named_params<P, T, R>& params)
williamr@2: {
williamr@2: typedef typename graph_traits<Graph>::directed_category DirCat;
williamr@2: BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));
williamr@2: return detail::scc_helper1(g, comp, params,
williamr@2: get_param(params, vertex_root_t()));
williamr@2: }
williamr@2:
williamr@2: template <class Graph, class ComponentMap>
williamr@2: inline typename property_traits<ComponentMap>::value_type
williamr@2: strong_components(const Graph& g, ComponentMap comp)
williamr@2: {
williamr@2: typedef typename graph_traits<Graph>::directed_category DirCat;
williamr@2: BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));
williamr@2: bgl_named_params<int, int> params(0);
williamr@2: return strong_components(g, comp, params);
williamr@2: }
williamr@2:
williamr@2: template <typename Graph, typename ComponentMap, typename ComponentLists>
williamr@2: void build_component_lists
williamr@2: (const Graph& g,
williamr@2: typename graph_traits<Graph>::vertices_size_type num_scc,
williamr@2: ComponentMap component_number,
williamr@2: ComponentLists& components)
williamr@2: {
williamr@2: components.resize(num_scc);
williamr@2: typename graph_traits<Graph>::vertex_iterator vi, vi_end;
williamr@2: for (tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
williamr@2: components[component_number[*vi]].push_back(*vi);
williamr@2: }
williamr@2:
williamr@2:
williamr@2: } // namespace boost
williamr@2:
williamr@2: #include <queue>
williamr@2: #include <vector>
williamr@2: #include <boost/graph/transpose_graph.hpp>
williamr@2: #include <boost/pending/indirect_cmp.hpp>
williamr@2: #include <boost/graph/connected_components.hpp> // for components_recorder
williamr@2:
williamr@2: namespace boost {
williamr@2:
williamr@2: //==========================================================================
williamr@2: // This is the version of strongly connected components from
williamr@2: // "Intro. to Algorithms" by Cormen, Leiserson, Rivest, which was
williamr@2: // adapted from "Data Structure and Algorithms" by Aho, Hopcroft,
williamr@2: // and Ullman, who credit the algorithm to S.R. Kosaraju and M. Sharir.
williamr@2: // The algorithm is based on computing DFS forests the graph
williamr@2: // and its transpose.
williamr@2:
williamr@2: // This algorithm is slower than Tarjan's by a constant factor, uses
williamr@2: // more memory, and puts more requirements on the graph type.
williamr@2:
williamr@2: template <class Graph, class DFSVisitor, class ComponentsMap,
williamr@2: class DiscoverTime, class FinishTime,
williamr@2: class ColorMap>
williamr@2: typename property_traits<ComponentsMap>::value_type
williamr@2: kosaraju_strong_components(Graph& G, ComponentsMap c,
williamr@2: FinishTime finish_time, ColorMap color)
williamr@2: {
williamr@2: function_requires< MutableGraphConcept<Graph> >();
williamr@2: // ...
williamr@2:
williamr@2: typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
williamr@2: typedef typename property_traits<ColorMap>::value_type ColorValue;
williamr@2: typedef color_traits<ColorValue> Color;
williamr@2: typename property_traits<FinishTime>::value_type time = 0;
williamr@2: depth_first_search
williamr@2: (G, make_dfs_visitor(stamp_times(finish_time, time, on_finish_vertex())),
williamr@2: color);
williamr@2:
williamr@2: Graph G_T(num_vertices(G));
williamr@2: transpose_graph(G, G_T);
williamr@2:
williamr@2: typedef typename property_traits<ComponentsMap>::value_type count_type;
williamr@2:
williamr@2: count_type c_count(0);
williamr@2: detail::components_recorder<ComponentsMap>
williamr@2: vis(c, c_count);
williamr@2:
williamr@2: // initialize G_T
williamr@2: typename graph_traits<Graph>::vertex_iterator ui, ui_end;
williamr@2: for (tie(ui, ui_end) = vertices(G_T); ui != ui_end; ++ui)
williamr@2: put(color, *ui, Color::white());
williamr@2:
williamr@2: typedef typename property_traits<FinishTime>::value_type D;
williamr@2: typedef indirect_cmp< FinishTime, std::less<D> > Compare;
williamr@2:
williamr@2: Compare fl(finish_time);
williamr@2: std::priority_queue<Vertex, std::vector<Vertex>, Compare > Q(fl);
williamr@2:
williamr@2: typename graph_traits<Graph>::vertex_iterator i, j, iend, jend;
williamr@2: tie(i, iend) = vertices(G_T);
williamr@2: tie(j, jend) = vertices(G);
williamr@2: for ( ; i != iend; ++i, ++j) {
williamr@2: put(finish_time, *i, get(finish_time, *j));
williamr@2: Q.push(*i);
williamr@2: }
williamr@2:
williamr@2: while ( !Q.empty() ) {
williamr@2: Vertex u = Q.top();
williamr@2: Q.pop();
williamr@2: if (get(color, u) == Color::white()) {
williamr@2: depth_first_visit(G_T, u, vis, color);
williamr@2: ++c_count;
williamr@2: }
williamr@2: }
williamr@2: return c_count;
williamr@2: }
williamr@2:
williamr@2: } // namespace boost
williamr@2:
williamr@2: #endif // BOOST_GRAPH_STRONG_COMPONENTS_HPP