Chris@16: // Copyright (C) 2001 Vladimir Prus <ghost@cs.msu.su>
Chris@16: // Copyright (C) 2001 Jeremy Siek <jsiek@cs.indiana.edu>
Chris@16: // Distributed under the Boost Software License, Version 1.0. (See
Chris@16: // accompanying file LICENSE_1_0.txt or copy at
Chris@16: // http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: // NOTE: this final is generated by libs/graph/doc/transitive_closure.w
Chris@16: 
Chris@16: #ifndef BOOST_GRAPH_TRANSITIVE_CLOSURE_HPP
Chris@16: #define BOOST_GRAPH_TRANSITIVE_CLOSURE_HPP
Chris@16: 
Chris@16: #include <vector>
Chris@16: #include <algorithm> // for std::min and std::max
Chris@16: #include <functional>
Chris@16: #include <boost/config.hpp>
Chris@16: #include <boost/bind.hpp>
Chris@16: #include <boost/graph/strong_components.hpp>
Chris@16: #include <boost/graph/topological_sort.hpp>
Chris@16: #include <boost/graph/graph_concepts.hpp>
Chris@16: #include <boost/graph/named_function_params.hpp>
Chris@16: #include <boost/graph/adjacency_list.hpp>
Chris@16: #include <boost/concept/assert.hpp>
Chris@16: 
Chris@16: namespace boost
Chris@16: {
Chris@16: 
Chris@16:   namespace detail
Chris@16:   {
Chris@16:     inline void
Chris@16:       union_successor_sets(const std::vector < std::size_t > &s1,
Chris@16:                            const std::vector < std::size_t > &s2,
Chris@16:                            std::vector < std::size_t > &s3)
Chris@16:     {
Chris@16:       BOOST_USING_STD_MIN();
Chris@16:       for (std::size_t k = 0; k < s1.size(); ++k)
Chris@16:         s3[k] = min BOOST_PREVENT_MACRO_SUBSTITUTION(s1[k], s2[k]);
Chris@16:     }
Chris@16:   }                             // namespace detail
Chris@16: 
Chris@16:   namespace detail
Chris@16:   {
Chris@16:     template < typename TheContainer, typename ST = std::size_t,
Chris@16:       typename VT = typename TheContainer::value_type >
Chris@16:       struct subscript_t:public std::unary_function < ST, VT >
Chris@16:     {
Chris@16:       typedef VT& result_type;
Chris@16: 
Chris@16:       subscript_t(TheContainer & c):container(&c)
Chris@16:       {
Chris@16:       }
Chris@16:       VT & operator() (const ST & i) const
Chris@16:       {
Chris@16:         return (*container)[i];
Chris@16:       }
Chris@16:     protected:
Chris@16:         TheContainer * container;
Chris@16:     };
Chris@16:     template < typename TheContainer >
Chris@16:       subscript_t < TheContainer > subscript(TheContainer & c) {
Chris@16:       return subscript_t < TheContainer > (c);
Chris@16:     }
Chris@16:   }                             // namespace detail
Chris@16: 
Chris@16:   template < typename Graph, typename GraphTC,
Chris@16:     typename G_to_TC_VertexMap,
Chris@16:     typename VertexIndexMap >
Chris@16:     void transitive_closure(const Graph & g, GraphTC & tc,
Chris@16:                             G_to_TC_VertexMap g_to_tc_map,
Chris@16:                             VertexIndexMap index_map)
Chris@16:   {
Chris@16:     if (num_vertices(g) == 0)
Chris@16:       return;
Chris@16:     typedef typename graph_traits < Graph >::vertex_descriptor vertex;
Chris@16:     typedef typename graph_traits < Graph >::vertex_iterator vertex_iterator;
Chris@16:     typedef typename property_traits < VertexIndexMap >::value_type size_type;
Chris@16:     typedef typename graph_traits <
Chris@16:       Graph >::adjacency_iterator adjacency_iterator;
Chris@16: 
Chris@16:     BOOST_CONCEPT_ASSERT(( VertexListGraphConcept < Graph > ));
Chris@16:     BOOST_CONCEPT_ASSERT(( AdjacencyGraphConcept < Graph > ));
Chris@16:     BOOST_CONCEPT_ASSERT(( VertexMutableGraphConcept < GraphTC > ));
Chris@16:     BOOST_CONCEPT_ASSERT(( EdgeMutableGraphConcept < GraphTC > ));
Chris@16:     BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept < VertexIndexMap,
Chris@16:       vertex > ));
Chris@16: 
Chris@16:     typedef size_type cg_vertex;
Chris@16:     std::vector < cg_vertex > component_number_vec(num_vertices(g));
Chris@16:     iterator_property_map < cg_vertex *, VertexIndexMap, cg_vertex, cg_vertex& >
Chris@16:       component_number(&component_number_vec[0], index_map);
Chris@16: 
Chris@16:     int num_scc = strong_components(g, component_number,
Chris@16:                                     vertex_index_map(index_map));
Chris@16: 
Chris@16:     std::vector < std::vector < vertex > >components;
Chris@16:     build_component_lists(g, num_scc, component_number, components);
Chris@16: 
Chris@16:     typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS> CG_t;
Chris@16:     CG_t CG(num_scc);
Chris@16:     for (cg_vertex s = 0; s < components.size(); ++s) {
Chris@16:       std::vector < cg_vertex > adj;
Chris@16:       for (size_type i = 0; i < components[s].size(); ++i) {
Chris@16:         vertex u = components[s][i];
Chris@16:         adjacency_iterator v, v_end;
Chris@16:         for (boost::tie(v, v_end) = adjacent_vertices(u, g); v != v_end; ++v) {
Chris@16:           cg_vertex t = component_number[*v];
Chris@16:           if (s != t)           // Avoid loops in the condensation graph
Chris@16:             adj.push_back(t);
Chris@16:         }
Chris@16:       }
Chris@16:       std::sort(adj.begin(), adj.end());
Chris@16:       typename std::vector<cg_vertex>::iterator di =
Chris@16:         std::unique(adj.begin(), adj.end());
Chris@16:       if (di != adj.end())
Chris@16:         adj.erase(di, adj.end());
Chris@16:       for (typename std::vector<cg_vertex>::const_iterator i = adj.begin();
Chris@16:            i != adj.end(); ++i) {
Chris@16:         add_edge(s, *i, CG);
Chris@16:       }
Chris@16:     }
Chris@16: 
Chris@16:     std::vector<cg_vertex> topo_order;
Chris@16:     std::vector<cg_vertex> topo_number(num_vertices(CG));
Chris@16:     topological_sort(CG, std::back_inserter(topo_order),
Chris@16:                      vertex_index_map(identity_property_map()));
Chris@16:     std::reverse(topo_order.begin(), topo_order.end());
Chris@16:     size_type n = 0;
Chris@16:     for (typename std::vector<cg_vertex>::iterator iter = topo_order.begin();
Chris@16:          iter != topo_order.end(); ++iter)
Chris@16:       topo_number[*iter] = n++;
Chris@16: 
Chris@16:     std::vector<std::vector<cg_vertex> > CG_vec(num_vertices(CG));
Chris@16:     for (size_type i = 0; i < num_vertices(CG); ++i) {
Chris@16:       typedef typename boost::graph_traits<CG_t>::adjacency_iterator cg_adj_iter;
Chris@16:       std::pair<cg_adj_iter, cg_adj_iter> pr = adjacent_vertices(i, CG);
Chris@16:       CG_vec[i].assign(pr.first, pr.second);
Chris@16:       std::sort(CG_vec[i].begin(), CG_vec[i].end(),
Chris@16:                 boost::bind(std::less<cg_vertex>(),
Chris@16:                             boost::bind(detail::subscript(topo_number), _1),
Chris@16:                             boost::bind(detail::subscript(topo_number), _2)));
Chris@16:     }
Chris@16: 
Chris@16:     std::vector<std::vector<cg_vertex> > chains;
Chris@16:     {
Chris@16:       std::vector<cg_vertex> in_a_chain(CG_vec.size());
Chris@16:       for (typename std::vector<cg_vertex>::iterator i = topo_order.begin();
Chris@16:            i != topo_order.end(); ++i) {
Chris@16:         cg_vertex v = *i;
Chris@16:         if (!in_a_chain[v]) {
Chris@16:           chains.resize(chains.size() + 1);
Chris@16:           std::vector<cg_vertex>& chain = chains.back();
Chris@16:           for (;;) {
Chris@16:             chain.push_back(v);
Chris@16:             in_a_chain[v] = true;
Chris@16:             typename std::vector<cg_vertex>::const_iterator next
Chris@16:               = std::find_if(CG_vec[v].begin(), CG_vec[v].end(),
Chris@16:                              std::not1(detail::subscript(in_a_chain)));
Chris@16:             if (next != CG_vec[v].end())
Chris@16:               v = *next;
Chris@16:             else
Chris@16:               break;            // end of chain, dead-end
Chris@16: 
Chris@16:           }
Chris@16:         }
Chris@16:       }
Chris@16:     }
Chris@16:     std::vector<size_type> chain_number(CG_vec.size());
Chris@16:     std::vector<size_type> pos_in_chain(CG_vec.size());
Chris@16:     for (size_type i = 0; i < chains.size(); ++i)
Chris@16:       for (size_type j = 0; j < chains[i].size(); ++j) {
Chris@16:         cg_vertex v = chains[i][j];
Chris@16:         chain_number[v] = i;
Chris@16:         pos_in_chain[v] = j;
Chris@16:       }
Chris@16: 
Chris@16:     cg_vertex inf = (std::numeric_limits< cg_vertex >::max)();
Chris@16:     std::vector<std::vector<cg_vertex> > successors(CG_vec.size(),
Chris@16:                                                     std::vector<cg_vertex>
Chris@16:                                                     (chains.size(), inf));
Chris@16:     for (typename std::vector<cg_vertex>::reverse_iterator
Chris@16:            i = topo_order.rbegin(); i != topo_order.rend(); ++i) {
Chris@16:       cg_vertex u = *i;
Chris@16:       typename std::vector<cg_vertex>::const_iterator adj, adj_last;
Chris@16:       for (adj = CG_vec[u].begin(), adj_last = CG_vec[u].end();
Chris@16:            adj != adj_last; ++adj) {
Chris@16:         cg_vertex v = *adj;
Chris@16:         if (topo_number[v] < successors[u][chain_number[v]]) {
Chris@16:           // Succ(u) = Succ(u) U Succ(v)
Chris@16:           detail::union_successor_sets(successors[u], successors[v],
Chris@16:                                        successors[u]);
Chris@16:           // Succ(u) = Succ(u) U {v}
Chris@16:           successors[u][chain_number[v]] = topo_number[v];
Chris@16:         }
Chris@16:       }
Chris@16:     }
Chris@16: 
Chris@16:     for (size_type i = 0; i < CG_vec.size(); ++i)
Chris@16:       CG_vec[i].clear();
Chris@16:     for (size_type i = 0; i < CG_vec.size(); ++i)
Chris@16:       for (size_type j = 0; j < chains.size(); ++j) {
Chris@16:         size_type topo_num = successors[i][j];
Chris@16:         if (topo_num < inf) {
Chris@16:           cg_vertex v = topo_order[topo_num];
Chris@16:           for (size_type k = pos_in_chain[v]; k < chains[j].size(); ++k)
Chris@16:             CG_vec[i].push_back(chains[j][k]);
Chris@16:         }
Chris@16:       }
Chris@16: 
Chris@16: 
Chris@16:     // Add vertices to the transitive closure graph
Chris@16:     {
Chris@16:       vertex_iterator i, i_end;
Chris@16:       for (boost::tie(i, i_end) = vertices(g); i != i_end; ++i)
Chris@16:         g_to_tc_map[*i] = add_vertex(tc);
Chris@16:     }
Chris@16:     // Add edges between all the vertices in two adjacent SCCs
Chris@16:     typename std::vector<std::vector<cg_vertex> >::const_iterator si, si_end;
Chris@16:     for (si = CG_vec.begin(), si_end = CG_vec.end(); si != si_end; ++si) {
Chris@16:       cg_vertex s = si - CG_vec.begin();
Chris@16:       typename std::vector<cg_vertex>::const_iterator i, i_end;
Chris@16:       for (i = CG_vec[s].begin(), i_end = CG_vec[s].end(); i != i_end; ++i) {
Chris@16:         cg_vertex t = *i;
Chris@16:         for (size_type k = 0; k < components[s].size(); ++k)
Chris@16:           for (size_type l = 0; l < components[t].size(); ++l)
Chris@16:             add_edge(g_to_tc_map[components[s][k]],
Chris@16:                      g_to_tc_map[components[t][l]], tc);
Chris@16:       }
Chris@16:     }
Chris@16:     // Add edges connecting all vertices in a SCC
Chris@16:     for (size_type i = 0; i < components.size(); ++i)
Chris@16:       if (components[i].size() > 1)
Chris@16:         for (size_type k = 0; k < components[i].size(); ++k)
Chris@16:           for (size_type l = 0; l < components[i].size(); ++l) {
Chris@16:             vertex u = components[i][k], v = components[i][l];
Chris@16:             add_edge(g_to_tc_map[u], g_to_tc_map[v], tc);
Chris@16:           }
Chris@16: 
Chris@16:     // Find loopbacks in the original graph.
Chris@16:     // Need to add it to transitive closure.
Chris@16:     {
Chris@16:       vertex_iterator i, i_end;
Chris@16:       for (boost::tie(i, i_end) = vertices(g); i != i_end; ++i)
Chris@16:         {
Chris@16:           adjacency_iterator ab, ae;
Chris@16:           for (boost::tie(ab, ae) = adjacent_vertices(*i, g); ab != ae; ++ab)
Chris@16:             {
Chris@16:               if (*ab == *i)
Chris@16:                 if (components[component_number[*i]].size() == 1)
Chris@16:                   add_edge(g_to_tc_map[*i], g_to_tc_map[*i], tc);
Chris@16:             }
Chris@16:         }
Chris@16:     }
Chris@16:   }
Chris@16: 
Chris@16:   template <typename Graph, typename GraphTC>
Chris@16:   void transitive_closure(const Graph & g, GraphTC & tc)
Chris@16:   {
Chris@16:     if (num_vertices(g) == 0)
Chris@16:       return;
Chris@16:     typedef typename property_map<Graph, vertex_index_t>::const_type
Chris@16:       VertexIndexMap;
Chris@16:     VertexIndexMap index_map = get(vertex_index, g);
Chris@16: 
Chris@16:     typedef typename graph_traits<GraphTC>::vertex_descriptor tc_vertex;
Chris@16:     std::vector<tc_vertex> to_tc_vec(num_vertices(g));
Chris@16:     iterator_property_map < tc_vertex *, VertexIndexMap, tc_vertex, tc_vertex&>
Chris@16:       g_to_tc_map(&to_tc_vec[0], index_map);
Chris@16: 
Chris@16:     transitive_closure(g, tc, g_to_tc_map, index_map);
Chris@16:   }
Chris@16: 
Chris@16:   namespace detail
Chris@16:   {
Chris@16:     template < typename Graph, typename GraphTC, typename G_to_TC_VertexMap,
Chris@16:       typename VertexIndexMap>
Chris@16:     void transitive_closure_dispatch
Chris@16:       (const Graph & g, GraphTC & tc,
Chris@16:        G_to_TC_VertexMap g_to_tc_map, VertexIndexMap index_map)
Chris@16:     {
Chris@16:       typedef typename graph_traits < GraphTC >::vertex_descriptor tc_vertex;
Chris@16:       typename std::vector < tc_vertex >::size_type
Chris@16:         n = is_default_param(g_to_tc_map) ? num_vertices(g) : 1;
Chris@16:       std::vector < tc_vertex > to_tc_vec(n);
Chris@16: 
Chris@16:       transitive_closure
Chris@16:         (g, tc,
Chris@16:          choose_param(g_to_tc_map, make_iterator_property_map
Chris@16:                       (to_tc_vec.begin(), index_map, to_tc_vec[0])),
Chris@16:          index_map);
Chris@16:     }
Chris@16:   }                             // namespace detail
Chris@16: 
Chris@16:   template < typename Graph, typename GraphTC,
Chris@16:     typename P, typename T, typename R >
Chris@16:     void transitive_closure(const Graph & g, GraphTC & tc,
Chris@16:                             const bgl_named_params < P, T, R > &params)
Chris@16:   {
Chris@16:     if (num_vertices(g) == 0)
Chris@16:       return;
Chris@16:     detail::transitive_closure_dispatch
Chris@16:       (g, tc, get_param(params, orig_to_copy_t()),
Chris@16:        choose_const_pmap(get_param(params, vertex_index), g, vertex_index) );
Chris@16:   }
Chris@16: 
Chris@16: 
Chris@16:   template < typename G > void warshall_transitive_closure(G & g)
Chris@16:   {
Chris@16:     typedef typename graph_traits < G >::vertex_iterator vertex_iterator;
Chris@16: 
Chris@16:     BOOST_CONCEPT_ASSERT(( AdjacencyMatrixConcept < G > ));
Chris@16:     BOOST_CONCEPT_ASSERT(( EdgeMutableGraphConcept < G > ));
Chris@16: 
Chris@16:     // Matrix form:
Chris@16:     // for k
Chris@16:     //  for i
Chris@16:     //    if A[i,k]
Chris@16:     //      for j
Chris@16:     //        A[i,j] = A[i,j] | A[k,j]
Chris@16:     vertex_iterator ki, ke, ii, ie, ji, je;
Chris@16:     for (boost::tie(ki, ke) = vertices(g); ki != ke; ++ki)
Chris@16:       for (boost::tie(ii, ie) = vertices(g); ii != ie; ++ii)
Chris@16:         if (edge(*ii, *ki, g).second)
Chris@16:           for (boost::tie(ji, je) = vertices(g); ji != je; ++ji)
Chris@16:             if (!edge(*ii, *ji, g).second && edge(*ki, *ji, g).second) {
Chris@16:               add_edge(*ii, *ji, g);
Chris@16:             }
Chris@16:   }
Chris@16: 
Chris@16: 
Chris@16:   template < typename G > void warren_transitive_closure(G & g)
Chris@16:   {
Chris@16:     using namespace boost;
Chris@16:     typedef typename graph_traits < G >::vertex_iterator vertex_iterator;
Chris@16: 
Chris@16:     BOOST_CONCEPT_ASSERT(( AdjacencyMatrixConcept < G > ));
Chris@16:     BOOST_CONCEPT_ASSERT(( EdgeMutableGraphConcept < G > ));
Chris@16: 
Chris@16:     // Make sure second loop will work
Chris@16:     if (num_vertices(g) == 0)
Chris@16:       return;
Chris@16: 
Chris@16:     // for i = 2 to n
Chris@16:     //    for k = 1 to i - 1
Chris@16:     //      if A[i,k]
Chris@16:     //        for j = 1 to n
Chris@16:     //          A[i,j] = A[i,j] | A[k,j]
Chris@16: 
Chris@16:     vertex_iterator ic, ie, jc, je, kc, ke;
Chris@16:     for (boost::tie(ic, ie) = vertices(g), ++ic; ic != ie; ++ic)
Chris@16:       for (boost::tie(kc, ke) = vertices(g); *kc != *ic; ++kc)
Chris@16:         if (edge(*ic, *kc, g).second)
Chris@16:           for (boost::tie(jc, je) = vertices(g); jc != je; ++jc)
Chris@16:             if (!edge(*ic, *jc, g).second && edge(*kc, *jc, g).second) {
Chris@16:               add_edge(*ic, *jc, g);
Chris@16:             }
Chris@16:     //  for i = 1 to n - 1
Chris@16:     //    for k = i + 1 to n
Chris@16:     //      if A[i,k]
Chris@16:     //        for j = 1 to n
Chris@16:     //          A[i,j] = A[i,j] | A[k,j]
Chris@16: 
Chris@16:     for (boost::tie(ic, ie) = vertices(g), --ie; ic != ie; ++ic)
Chris@16:       for (kc = ic, ke = ie, ++kc; kc != ke; ++kc)
Chris@16:         if (edge(*ic, *kc, g).second)
Chris@16:           for (boost::tie(jc, je) = vertices(g); jc != je; ++jc)
Chris@16:             if (!edge(*ic, *jc, g).second && edge(*kc, *jc, g).second) {
Chris@16:               add_edge(*ic, *jc, g);
Chris@16:             }
Chris@16:   }
Chris@16: 
Chris@16: 
Chris@16: }                               // namespace boost
Chris@16: 
Chris@16: #endif // BOOST_GRAPH_TRANSITIVE_CLOSURE_HPP