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