sl@0: // Copyright (C) 2001 Vladimir Prus <ghost@cs.msu.su>
sl@0: // Copyright (C) 2001 Jeremy Siek <jsiek@cs.indiana.edu>
sl@0: // Distributed under the Boost Software License, Version 1.0. (See
sl@0: // accompanying file LICENSE_1_0.txt or copy at
sl@0: // http://www.boost.org/LICENSE_1_0.txt)
sl@0: 
sl@0: // NOTE: this final is generated by libs/graph/doc/transitive_closure.w
sl@0: 
sl@0: #ifndef BOOST_GRAPH_TRANSITIVE_CLOSURE_HPP
sl@0: #define BOOST_GRAPH_TRANSITIVE_CLOSURE_HPP
sl@0: 
sl@0: #include <vector>
sl@0: #include <algorithm> // for std::min and std::max
sl@0: #include <functional>
sl@0: #include <boost/config.hpp>
sl@0: #include <boost/bind.hpp>
sl@0: #include <boost/graph/vector_as_graph.hpp>
sl@0: #include <boost/graph/strong_components.hpp>
sl@0: #include <boost/graph/topological_sort.hpp>
sl@0: #include <boost/graph/graph_concepts.hpp>
sl@0: #include <boost/graph/named_function_params.hpp>
sl@0: 
sl@0: namespace boost
sl@0: {
sl@0: 
sl@0:   namespace detail
sl@0:   {
sl@0:     inline void
sl@0:       union_successor_sets(const std::vector < std::size_t > &s1,
sl@0:                            const std::vector < std::size_t > &s2,
sl@0:                            std::vector < std::size_t > &s3)
sl@0:     {
sl@0:       BOOST_USING_STD_MIN();
sl@0:       for (std::size_t k = 0; k < s1.size(); ++k)
sl@0:         s3[k] = min BOOST_PREVENT_MACRO_SUBSTITUTION(s1[k], s2[k]);
sl@0:     }
sl@0:   }                             // namespace detail
sl@0: 
sl@0:   namespace detail
sl@0:   {
sl@0:     template < typename Container, typename ST = std::size_t,
sl@0:       typename VT = typename Container::value_type >
sl@0:       struct subscript_t:public std::unary_function < ST, VT >
sl@0:     {
sl@0:       typedef VT& result_type;
sl@0: 
sl@0:       subscript_t(Container & c):container(&c)
sl@0:       {
sl@0:       }
sl@0:       VT & operator() (const ST & i) const
sl@0:       {
sl@0:         return (*container)[i];
sl@0:       }
sl@0:     protected:
sl@0:         Container * container;
sl@0:     };
sl@0:     template < typename Container >
sl@0:       subscript_t < Container > subscript(Container & c) {
sl@0:       return subscript_t < Container > (c);
sl@0:     }
sl@0:   }                             // namespace detail
sl@0: 
sl@0:   template < typename Graph, typename GraphTC,
sl@0:     typename G_to_TC_VertexMap,
sl@0:     typename VertexIndexMap >
sl@0:     void transitive_closure(const Graph & g, GraphTC & tc,
sl@0:                             G_to_TC_VertexMap g_to_tc_map,
sl@0:                             VertexIndexMap index_map)
sl@0:   {
sl@0:     if (num_vertices(g) == 0)
sl@0:       return;
sl@0:     typedef typename graph_traits < Graph >::vertex_descriptor vertex;
sl@0:     typedef typename graph_traits < Graph >::edge_descriptor edge;
sl@0:     typedef typename graph_traits < Graph >::vertex_iterator vertex_iterator;
sl@0:     typedef typename property_traits < VertexIndexMap >::value_type size_type;
sl@0:     typedef typename graph_traits <
sl@0:       Graph >::adjacency_iterator adjacency_iterator;
sl@0: 
sl@0:     function_requires < VertexListGraphConcept < Graph > >();
sl@0:     function_requires < AdjacencyGraphConcept < Graph > >();
sl@0:     function_requires < VertexMutableGraphConcept < GraphTC > >();
sl@0:     function_requires < EdgeMutableGraphConcept < GraphTC > >();
sl@0:     function_requires < ReadablePropertyMapConcept < VertexIndexMap,
sl@0:       vertex > >();
sl@0: 
sl@0:     typedef size_type cg_vertex;
sl@0:     std::vector < cg_vertex > component_number_vec(num_vertices(g));
sl@0:     iterator_property_map < cg_vertex *, VertexIndexMap, cg_vertex, cg_vertex& >
sl@0:       component_number(&component_number_vec[0], index_map);
sl@0: 
sl@0:     int num_scc = strong_components(g, component_number,
sl@0:                                     vertex_index_map(index_map));
sl@0: 
sl@0:     std::vector < std::vector < vertex > >components;
sl@0:     build_component_lists(g, num_scc, component_number, components);
sl@0: 
sl@0:     typedef std::vector<std::vector<cg_vertex> > CG_t;
sl@0:     CG_t CG(num_scc);
sl@0:     for (cg_vertex s = 0; s < components.size(); ++s) {
sl@0:       std::vector < cg_vertex > adj;
sl@0:       for (size_type i = 0; i < components[s].size(); ++i) {
sl@0:         vertex u = components[s][i];
sl@0:         adjacency_iterator v, v_end;
sl@0:         for (tie(v, v_end) = adjacent_vertices(u, g); v != v_end; ++v) {
sl@0:           cg_vertex t = component_number[*v];
sl@0:           if (s != t)           // Avoid loops in the condensation graph
sl@0:             adj.push_back(t);
sl@0:         }
sl@0:       }
sl@0:       std::sort(adj.begin(), adj.end());
sl@0:       typename std::vector<cg_vertex>::iterator di =
sl@0:         std::unique(adj.begin(), adj.end());
sl@0:       if (di != adj.end())
sl@0:         adj.erase(di, adj.end());
sl@0:       CG[s] = adj;
sl@0:     }
sl@0: 
sl@0:     std::vector<cg_vertex> topo_order;
sl@0:     std::vector<cg_vertex> topo_number(num_vertices(CG));
sl@0:     topological_sort(CG, std::back_inserter(topo_order),
sl@0:                      vertex_index_map(identity_property_map()));
sl@0:     std::reverse(topo_order.begin(), topo_order.end());
sl@0:     size_type n = 0;
sl@0:     for (typename std::vector<cg_vertex>::iterator iter = topo_order.begin();
sl@0:          iter != topo_order.end(); ++iter)
sl@0:       topo_number[*iter] = n++;
sl@0: 
sl@0:     for (size_type i = 0; i < num_vertices(CG); ++i)
sl@0:       std::sort(CG[i].begin(), CG[i].end(),
sl@0:                 boost::bind(std::less<cg_vertex>(),
sl@0:                             boost::bind(detail::subscript(topo_number), _1),
sl@0:                             boost::bind(detail::subscript(topo_number), _2)));
sl@0: 
sl@0:     std::vector<std::vector<cg_vertex> > chains;
sl@0:     {
sl@0:       std::vector<cg_vertex> in_a_chain(num_vertices(CG));
sl@0:       for (typename std::vector<cg_vertex>::iterator i = topo_order.begin();
sl@0:            i != topo_order.end(); ++i) {
sl@0:         cg_vertex v = *i;
sl@0:         if (!in_a_chain[v]) {
sl@0:           chains.resize(chains.size() + 1);
sl@0:           std::vector<cg_vertex>& chain = chains.back();
sl@0:           for (;;) {
sl@0:             chain.push_back(v);
sl@0:             in_a_chain[v] = true;
sl@0:             typename graph_traits<CG_t>::adjacency_iterator adj_first, adj_last;
sl@0:             tie(adj_first, adj_last) = adjacent_vertices(v, CG);
sl@0:             typename graph_traits<CG_t>::adjacency_iterator next
sl@0:               = std::find_if(adj_first, adj_last,
sl@0:                              std::not1(detail::subscript(in_a_chain)));
sl@0:             if (next != adj_last)
sl@0:               v = *next;
sl@0:             else
sl@0:               break;            // end of chain, dead-end
sl@0: 
sl@0:           }
sl@0:         }
sl@0:       }
sl@0:     }
sl@0:     std::vector<size_type> chain_number(num_vertices(CG));
sl@0:     std::vector<size_type> pos_in_chain(num_vertices(CG));
sl@0:     for (size_type i = 0; i < chains.size(); ++i)
sl@0:       for (size_type j = 0; j < chains[i].size(); ++j) {
sl@0:         cg_vertex v = chains[i][j];
sl@0:         chain_number[v] = i;
sl@0:         pos_in_chain[v] = j;
sl@0:       }
sl@0: 
sl@0:     cg_vertex inf = (std::numeric_limits< cg_vertex >::max)();
sl@0:     std::vector<std::vector<cg_vertex> > successors(num_vertices(CG),
sl@0:                                                     std::vector<cg_vertex>
sl@0:                                                     (chains.size(), inf));
sl@0:     for (typename std::vector<cg_vertex>::reverse_iterator
sl@0:            i = topo_order.rbegin(); i != topo_order.rend(); ++i) {
sl@0:       cg_vertex u = *i;
sl@0:       typename graph_traits<CG_t>::adjacency_iterator adj, adj_last;
sl@0:       for (tie(adj, adj_last) = adjacent_vertices(u, CG);
sl@0:            adj != adj_last; ++adj) {
sl@0:         cg_vertex v = *adj;
sl@0:         if (topo_number[v] < successors[u][chain_number[v]]) {
sl@0:           // Succ(u) = Succ(u) U Succ(v)
sl@0:           detail::union_successor_sets(successors[u], successors[v],
sl@0:                                        successors[u]);
sl@0:           // Succ(u) = Succ(u) U {v}
sl@0:           successors[u][chain_number[v]] = topo_number[v];
sl@0:         }
sl@0:       }
sl@0:     }
sl@0: 
sl@0:     for (size_type i = 0; i < CG.size(); ++i)
sl@0:       CG[i].clear();
sl@0:     for (size_type i = 0; i < CG.size(); ++i)
sl@0:       for (size_type j = 0; j < chains.size(); ++j) {
sl@0:         size_type topo_num = successors[i][j];
sl@0:         if (topo_num < inf) {
sl@0:           cg_vertex v = topo_order[topo_num];
sl@0:           for (size_type k = pos_in_chain[v]; k < chains[j].size(); ++k)
sl@0:             CG[i].push_back(chains[j][k]);
sl@0:         }
sl@0:       }
sl@0: 
sl@0: 
sl@0:     // Add vertices to the transitive closure graph
sl@0:     typedef typename graph_traits < GraphTC >::vertex_descriptor tc_vertex;
sl@0:     {
sl@0:       vertex_iterator i, i_end;
sl@0:       for (tie(i, i_end) = vertices(g); i != i_end; ++i)
sl@0:         g_to_tc_map[*i] = add_vertex(tc);
sl@0:     }
sl@0:     // Add edges between all the vertices in two adjacent SCCs
sl@0:     typename graph_traits<CG_t>::vertex_iterator si, si_end;
sl@0:     for (tie(si, si_end) = vertices(CG); si != si_end; ++si) {
sl@0:       cg_vertex s = *si;
sl@0:       typename graph_traits<CG_t>::adjacency_iterator i, i_end;
sl@0:       for (tie(i, i_end) = adjacent_vertices(s, CG); i != i_end; ++i) {
sl@0:         cg_vertex t = *i;
sl@0:         for (size_type k = 0; k < components[s].size(); ++k)
sl@0:           for (size_type l = 0; l < components[t].size(); ++l)
sl@0:             add_edge(g_to_tc_map[components[s][k]],
sl@0:                      g_to_tc_map[components[t][l]], tc);
sl@0:       }
sl@0:     }
sl@0:     // Add edges connecting all vertices in a SCC
sl@0:     for (size_type i = 0; i < components.size(); ++i)
sl@0:       if (components[i].size() > 1)
sl@0:         for (size_type k = 0; k < components[i].size(); ++k)
sl@0:           for (size_type l = 0; l < components[i].size(); ++l) {
sl@0:             vertex u = components[i][k], v = components[i][l];
sl@0:             add_edge(g_to_tc_map[u], g_to_tc_map[v], tc);
sl@0:           }
sl@0: 
sl@0:     // Find loopbacks in the original graph.
sl@0:     // Need to add it to transitive closure.
sl@0:     {
sl@0:       vertex_iterator i, i_end;
sl@0:       for (tie(i, i_end) = vertices(g); i != i_end; ++i)
sl@0:         {
sl@0:           adjacency_iterator ab, ae;
sl@0:           for (boost::tie(ab, ae) = adjacent_vertices(*i, g); ab != ae; ++ab)
sl@0:             {
sl@0:               if (*ab == *i)
sl@0:                 if (components[component_number[*i]].size() == 1)
sl@0:                   add_edge(g_to_tc_map[*i], g_to_tc_map[*i], tc);
sl@0:             }
sl@0:         }
sl@0:     }
sl@0:   }
sl@0: 
sl@0:   template <typename Graph, typename GraphTC>
sl@0:   void transitive_closure(const Graph & g, GraphTC & tc)
sl@0:   {
sl@0:     if (num_vertices(g) == 0)
sl@0:       return;
sl@0:     typedef typename property_map<Graph, vertex_index_t>::const_type
sl@0:       VertexIndexMap;
sl@0:     VertexIndexMap index_map = get(vertex_index, g);
sl@0: 
sl@0:     typedef typename graph_traits<GraphTC>::vertex_descriptor tc_vertex;
sl@0:     std::vector<tc_vertex> to_tc_vec(num_vertices(g));
sl@0:     iterator_property_map < tc_vertex *, VertexIndexMap, tc_vertex, tc_vertex&>
sl@0:       g_to_tc_map(&to_tc_vec[0], index_map);
sl@0: 
sl@0:     transitive_closure(g, tc, g_to_tc_map, index_map);
sl@0:   }
sl@0: 
sl@0:   namespace detail
sl@0:   {
sl@0:     template < typename Graph, typename GraphTC, typename G_to_TC_VertexMap,
sl@0:       typename VertexIndexMap>
sl@0:     void transitive_closure_dispatch
sl@0:       (const Graph & g, GraphTC & tc,
sl@0:        G_to_TC_VertexMap g_to_tc_map, VertexIndexMap index_map)
sl@0:     {
sl@0:       typedef typename graph_traits < GraphTC >::vertex_descriptor tc_vertex;
sl@0:       typename std::vector < tc_vertex >::size_type
sl@0:         n = is_default_param(g_to_tc_map) ? num_vertices(g) : 1;
sl@0:       std::vector < tc_vertex > to_tc_vec(n);
sl@0: 
sl@0:       transitive_closure
sl@0:         (g, tc,
sl@0:          choose_param(g_to_tc_map, make_iterator_property_map
sl@0:                       (to_tc_vec.begin(), index_map, to_tc_vec[0])),
sl@0:          index_map);
sl@0:     }
sl@0:   }                             // namespace detail
sl@0: 
sl@0:   template < typename Graph, typename GraphTC,
sl@0:     typename P, typename T, typename R >
sl@0:     void transitive_closure(const Graph & g, GraphTC & tc,
sl@0:                             const bgl_named_params < P, T, R > &params)
sl@0:   {
sl@0:     if (num_vertices(g) == 0)
sl@0:       return;
sl@0:     detail::transitive_closure_dispatch
sl@0:       (g, tc, get_param(params, orig_to_copy_t()),
sl@0:        choose_const_pmap(get_param(params, vertex_index), g, vertex_index) );
sl@0:   }
sl@0: 
sl@0: 
sl@0:   template < typename G > void warshall_transitive_closure(G & g)
sl@0:   {
sl@0:     typedef typename graph_traits < G >::vertex_descriptor vertex;
sl@0:     typedef typename graph_traits < G >::vertex_iterator vertex_iterator;
sl@0: 
sl@0:     function_requires < AdjacencyMatrixConcept < G > >();
sl@0:     function_requires < EdgeMutableGraphConcept < G > >();
sl@0: 
sl@0:     // Matrix form:
sl@0:     // for k
sl@0:     //  for i
sl@0:     //    if A[i,k]
sl@0:     //      for j
sl@0:     //        A[i,j] = A[i,j] | A[k,j]
sl@0:     vertex_iterator ki, ke, ii, ie, ji, je;
sl@0:     for (tie(ki, ke) = vertices(g); ki != ke; ++ki)
sl@0:       for (tie(ii, ie) = vertices(g); ii != ie; ++ii)
sl@0:         if (edge(*ii, *ki, g).second)
sl@0:           for (tie(ji, je) = vertices(g); ji != je; ++ji)
sl@0:             if (!edge(*ii, *ji, g).second && edge(*ki, *ji, g).second) {
sl@0:               add_edge(*ii, *ji, g);
sl@0:             }
sl@0:   }
sl@0: 
sl@0: 
sl@0:   template < typename G > void warren_transitive_closure(G & g)
sl@0:   {
sl@0:     using namespace boost;
sl@0:     typedef typename graph_traits < G >::vertex_descriptor vertex;
sl@0:     typedef typename graph_traits < G >::vertex_iterator vertex_iterator;
sl@0: 
sl@0:     function_requires < AdjacencyMatrixConcept < G > >();
sl@0:     function_requires < EdgeMutableGraphConcept < G > >();
sl@0: 
sl@0:     // Make sure second loop will work
sl@0:     if (num_vertices(g) == 0)
sl@0:       return;
sl@0: 
sl@0:     // for i = 2 to n
sl@0:     //    for k = 1 to i - 1
sl@0:     //      if A[i,k]
sl@0:     //        for j = 1 to n
sl@0:     //          A[i,j] = A[i,j] | A[k,j]
sl@0: 
sl@0:     vertex_iterator ic, ie, jc, je, kc, ke;
sl@0:     for (tie(ic, ie) = vertices(g), ++ic; ic != ie; ++ic)
sl@0:       for (tie(kc, ke) = vertices(g); *kc != *ic; ++kc)
sl@0:         if (edge(*ic, *kc, g).second)
sl@0:           for (tie(jc, je) = vertices(g); jc != je; ++jc)
sl@0:             if (!edge(*ic, *jc, g).second && edge(*kc, *jc, g).second) {
sl@0:               add_edge(*ic, *jc, g);
sl@0:             }
sl@0:     //  for i = 1 to n - 1
sl@0:     //    for k = i + 1 to n
sl@0:     //      if A[i,k]
sl@0:     //        for j = 1 to n
sl@0:     //          A[i,j] = A[i,j] | A[k,j]
sl@0: 
sl@0:     for (tie(ic, ie) = vertices(g), --ie; ic != ie; ++ic)
sl@0:       for (kc = ic, ke = ie, ++kc; kc != ke; ++kc)
sl@0:         if (edge(*ic, *kc, g).second)
sl@0:           for (tie(jc, je) = vertices(g); jc != je; ++jc)
sl@0:             if (!edge(*ic, *jc, g).second && edge(*kc, *jc, g).second) {
sl@0:               add_edge(*ic, *jc, g);
sl@0:             }
sl@0:   }
sl@0: 
sl@0: 
sl@0: }                               // namespace boost
sl@0: 
sl@0: #endif // BOOST_GRAPH_TRANSITIVE_CLOSURE_HPP