// Copyright (C) 2001 Vladimir Prus <ghost@cs.msu.su>
// Copyright (C) 2001 Jeremy Siek <jsiek@cs.indiana.edu>
// 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)

// NOTE: this final is generated by libs/graph/doc/transitive_closure.w

#ifndef BOOST_GRAPH_TRANSITIVE_CLOSURE_HPP
#define BOOST_GRAPH_TRANSITIVE_CLOSURE_HPP

#include <vector>
#include <algorithm> // for std::min and std::max
#include <functional>
#include <boost/config.hpp>
#include <boost/bind.hpp>
#include <boost/graph/vector_as_graph.hpp>
#include <boost/graph/strong_components.hpp>
#include <boost/graph/topological_sort.hpp>
#include <boost/graph/graph_concepts.hpp>
#include <boost/graph/named_function_params.hpp>

namespace boost
{

  namespace detail
  {
    inline void
      union_successor_sets(const std::vector < std::size_t > &s1,
                           const std::vector < std::size_t > &s2,
                           std::vector < std::size_t > &s3)
    {
      BOOST_USING_STD_MIN();
      for (std::size_t k = 0; k < s1.size(); ++k)
        s3[k] = min BOOST_PREVENT_MACRO_SUBSTITUTION(s1[k], s2[k]);
    }
  }                             // namespace detail

  namespace detail
  {
    template < typename Container, typename ST = std::size_t,
      typename VT = typename Container::value_type >
      struct subscript_t:public std::unary_function < ST, VT >
    {
      typedef VT& result_type;

      subscript_t(Container & c):container(&c)
      {
      }
      VT & operator() (const ST & i) const
      {
        return (*container)[i];
      }
    protected:
        Container * container;
    };
    template < typename Container >
      subscript_t < Container > subscript(Container & c) {
      return subscript_t < Container > (c);
    }
  }                             // namespace detail

  template < typename Graph, typename GraphTC,
    typename G_to_TC_VertexMap,
    typename VertexIndexMap >
    void transitive_closure(const Graph & g, GraphTC & tc,
                            G_to_TC_VertexMap g_to_tc_map,
                            VertexIndexMap index_map)
  {
    if (num_vertices(g) == 0)
      return;
    typedef typename graph_traits < Graph >::vertex_descriptor vertex;
    typedef typename graph_traits < Graph >::edge_descriptor edge;
    typedef typename graph_traits < Graph >::vertex_iterator vertex_iterator;
    typedef typename property_traits < VertexIndexMap >::value_type size_type;
    typedef typename graph_traits <
      Graph >::adjacency_iterator adjacency_iterator;

    function_requires < VertexListGraphConcept < Graph > >();
    function_requires < AdjacencyGraphConcept < Graph > >();
    function_requires < VertexMutableGraphConcept < GraphTC > >();
    function_requires < EdgeMutableGraphConcept < GraphTC > >();
    function_requires < ReadablePropertyMapConcept < VertexIndexMap,
      vertex > >();

    typedef size_type cg_vertex;
    std::vector < cg_vertex > component_number_vec(num_vertices(g));
    iterator_property_map < cg_vertex *, VertexIndexMap, cg_vertex, cg_vertex& >
      component_number(&component_number_vec[0], index_map);

    int num_scc = strong_components(g, component_number,
                                    vertex_index_map(index_map));

    std::vector < std::vector < vertex > >components;
    build_component_lists(g, num_scc, component_number, components);

    typedef std::vector<std::vector<cg_vertex> > CG_t;
    CG_t CG(num_scc);
    for (cg_vertex s = 0; s < components.size(); ++s) {
      std::vector < cg_vertex > adj;
      for (size_type i = 0; i < components[s].size(); ++i) {
        vertex u = components[s][i];
        adjacency_iterator v, v_end;
        for (tie(v, v_end) = adjacent_vertices(u, g); v != v_end; ++v) {
          cg_vertex t = component_number[*v];
          if (s != t)           // Avoid loops in the condensation graph
            adj.push_back(t);
        }
      }
      std::sort(adj.begin(), adj.end());
      typename std::vector<cg_vertex>::iterator di =
        std::unique(adj.begin(), adj.end());
      if (di != adj.end())
        adj.erase(di, adj.end());
      CG[s] = adj;
    }

    std::vector<cg_vertex> topo_order;
    std::vector<cg_vertex> topo_number(num_vertices(CG));
    topological_sort(CG, std::back_inserter(topo_order),
                     vertex_index_map(identity_property_map()));
    std::reverse(topo_order.begin(), topo_order.end());
    size_type n = 0;
    for (typename std::vector<cg_vertex>::iterator iter = topo_order.begin();
         iter != topo_order.end(); ++iter)
      topo_number[*iter] = n++;

    for (size_type i = 0; i < num_vertices(CG); ++i)
      std::sort(CG[i].begin(), CG[i].end(),
                boost::bind(std::less<cg_vertex>(),
                            boost::bind(detail::subscript(topo_number), _1),
                            boost::bind(detail::subscript(topo_number), _2)));

    std::vector<std::vector<cg_vertex> > chains;
    {
      std::vector<cg_vertex> in_a_chain(num_vertices(CG));
      for (typename std::vector<cg_vertex>::iterator i = topo_order.begin();
           i != topo_order.end(); ++i) {
        cg_vertex v = *i;
        if (!in_a_chain[v]) {
          chains.resize(chains.size() + 1);
          std::vector<cg_vertex>& chain = chains.back();
          for (;;) {
            chain.push_back(v);
            in_a_chain[v] = true;
            typename graph_traits<CG_t>::adjacency_iterator adj_first, adj_last;
            tie(adj_first, adj_last) = adjacent_vertices(v, CG);
            typename graph_traits<CG_t>::adjacency_iterator next
              = std::find_if(adj_first, adj_last,
                             not1(detail::subscript(in_a_chain)));
            if (next != adj_last)
              v = *next;
            else
              break;            // end of chain, dead-end

          }
        }
      }
    }
    std::vector<size_type> chain_number(num_vertices(CG));
    std::vector<size_type> pos_in_chain(num_vertices(CG));
    for (size_type i = 0; i < chains.size(); ++i)
      for (size_type j = 0; j < chains[i].size(); ++j) {
        cg_vertex v = chains[i][j];
        chain_number[v] = i;
        pos_in_chain[v] = j;
      }

    cg_vertex inf = (std::numeric_limits< cg_vertex >::max)();
    std::vector<std::vector<cg_vertex> > successors(num_vertices(CG),
                                                    std::vector<cg_vertex>
                                                    (chains.size(), inf));
    for (typename std::vector<cg_vertex>::reverse_iterator
           i = topo_order.rbegin(); i != topo_order.rend(); ++i) {
      cg_vertex u = *i;
      typename graph_traits<CG_t>::adjacency_iterator adj, adj_last;
      for (tie(adj, adj_last) = adjacent_vertices(u, CG);
           adj != adj_last; ++adj) {
        cg_vertex v = *adj;
        if (topo_number[v] < successors[u][chain_number[v]]) {
          // Succ(u) = Succ(u) U Succ(v)
          detail::union_successor_sets(successors[u], successors[v],
                                       successors[u]);
          // Succ(u) = Succ(u) U {v}
          successors[u][chain_number[v]] = topo_number[v];
        }
      }
    }

    for (size_type i = 0; i < CG.size(); ++i)
      CG[i].clear();
    for (size_type i = 0; i < CG.size(); ++i)
      for (size_type j = 0; j < chains.size(); ++j) {
        size_type topo_num = successors[i][j];
        if (topo_num < inf) {
          cg_vertex v = topo_order[topo_num];
          for (size_type k = pos_in_chain[v]; k < chains[j].size(); ++k)
            CG[i].push_back(chains[j][k]);
        }
      }


    // Add vertices to the transitive closure graph
    typedef typename graph_traits < GraphTC >::vertex_descriptor tc_vertex;
    {
      vertex_iterator i, i_end;
      for (tie(i, i_end) = vertices(g); i != i_end; ++i)
        g_to_tc_map[*i] = add_vertex(tc);
    }
    // Add edges between all the vertices in two adjacent SCCs
    typename graph_traits<CG_t>::vertex_iterator si, si_end;
    for (tie(si, si_end) = vertices(CG); si != si_end; ++si) {
      cg_vertex s = *si;
      typename graph_traits<CG_t>::adjacency_iterator i, i_end;
      for (tie(i, i_end) = adjacent_vertices(s, CG); i != i_end; ++i) {
        cg_vertex t = *i;
        for (size_type k = 0; k < components[s].size(); ++k)
          for (size_type l = 0; l < components[t].size(); ++l)
            add_edge(g_to_tc_map[components[s][k]],
                     g_to_tc_map[components[t][l]], tc);
      }
    }
    // Add edges connecting all vertices in a SCC
    for (size_type i = 0; i < components.size(); ++i)
      if (components[i].size() > 1)
        for (size_type k = 0; k < components[i].size(); ++k)
          for (size_type l = 0; l < components[i].size(); ++l) {
            vertex u = components[i][k], v = components[i][l];
            add_edge(g_to_tc_map[u], g_to_tc_map[v], tc);
          }

    // Find loopbacks in the original graph.
    // Need to add it to transitive closure.
    {
      vertex_iterator i, i_end;
      for (tie(i, i_end) = vertices(g); i != i_end; ++i)
        {
          adjacency_iterator ab, ae;
          for (boost::tie(ab, ae) = adjacent_vertices(*i, g); ab != ae; ++ab)
            {
              if (*ab == *i)
                if (components[component_number[*i]].size() == 1)
                  add_edge(g_to_tc_map[*i], g_to_tc_map[*i], tc);
            }
        }
    }
  }

  template <typename Graph, typename GraphTC>
  void transitive_closure(const Graph & g, GraphTC & tc)
  {
    if (num_vertices(g) == 0)
      return;
    typedef typename property_map<Graph, vertex_index_t>::const_type
      VertexIndexMap;
    VertexIndexMap index_map = get(vertex_index, g);

    typedef typename graph_traits<GraphTC>::vertex_descriptor tc_vertex;
    std::vector<tc_vertex> to_tc_vec(num_vertices(g));
    iterator_property_map < tc_vertex *, VertexIndexMap, tc_vertex, tc_vertex&>
      g_to_tc_map(&to_tc_vec[0], index_map);

    transitive_closure(g, tc, g_to_tc_map, index_map);
  }

  namespace detail
  {
    template < typename Graph, typename GraphTC, typename G_to_TC_VertexMap,
      typename VertexIndexMap>
    void transitive_closure_dispatch
      (const Graph & g, GraphTC & tc,
       G_to_TC_VertexMap g_to_tc_map, VertexIndexMap index_map)
    {
      typedef typename graph_traits < GraphTC >::vertex_descriptor tc_vertex;
      typename std::vector < tc_vertex >::size_type
        n = is_default_param(g_to_tc_map) ? num_vertices(g) : 1;
      std::vector < tc_vertex > to_tc_vec(n);

      transitive_closure
        (g, tc,
         choose_param(g_to_tc_map, make_iterator_property_map
                      (to_tc_vec.begin(), index_map, to_tc_vec[0])),
         index_map);
    }
  }                             // namespace detail

  template < typename Graph, typename GraphTC,
    typename P, typename T, typename R >
    void transitive_closure(const Graph & g, GraphTC & tc,
                            const bgl_named_params < P, T, R > &params)
  {
    if (num_vertices(g) == 0)
      return;
    detail::transitive_closure_dispatch
      (g, tc, get_param(params, orig_to_copy_t()),
       choose_const_pmap(get_param(params, vertex_index), g, vertex_index) );
  }


  template < typename G > void warshall_transitive_closure(G & g)
  {
    typedef typename graph_traits < G >::vertex_descriptor vertex;
    typedef typename graph_traits < G >::vertex_iterator vertex_iterator;

    function_requires < AdjacencyMatrixConcept < G > >();
    function_requires < EdgeMutableGraphConcept < G > >();

    // Matrix form:
    // for k
    //  for i
    //    if A[i,k]
    //      for j
    //        A[i,j] = A[i,j] | A[k,j]
    vertex_iterator ki, ke, ii, ie, ji, je;
    for (tie(ki, ke) = vertices(g); ki != ke; ++ki)
      for (tie(ii, ie) = vertices(g); ii != ie; ++ii)
        if (edge(*ii, *ki, g).second)
          for (tie(ji, je) = vertices(g); ji != je; ++ji)
            if (!edge(*ii, *ji, g).second && edge(*ki, *ji, g).second) {
              add_edge(*ii, *ji, g);
            }
  }


  template < typename G > void warren_transitive_closure(G & g)
  {
    using namespace boost;
    typedef typename graph_traits < G >::vertex_descriptor vertex;
    typedef typename graph_traits < G >::vertex_iterator vertex_iterator;

    function_requires < AdjacencyMatrixConcept < G > >();
    function_requires < EdgeMutableGraphConcept < G > >();

    // Make sure second loop will work
    if (num_vertices(g) == 0)
      return;

    // for i = 2 to n
    //    for k = 1 to i - 1
    //      if A[i,k]
    //        for j = 1 to n
    //          A[i,j] = A[i,j] | A[k,j]

    vertex_iterator ic, ie, jc, je, kc, ke;
    for (tie(ic, ie) = vertices(g), ++ic; ic != ie; ++ic)
      for (tie(kc, ke) = vertices(g); *kc != *ic; ++kc)
        if (edge(*ic, *kc, g).second)
          for (tie(jc, je) = vertices(g); jc != je; ++jc)
            if (!edge(*ic, *jc, g).second && edge(*kc, *jc, g).second) {
              add_edge(*ic, *jc, g);
            }
    //  for i = 1 to n - 1
    //    for k = i + 1 to n
    //      if A[i,k]
    //        for j = 1 to n
    //          A[i,j] = A[i,j] | A[k,j]

    for (tie(ic, ie) = vertices(g), --ie; ic != ie; ++ic)
      for (kc = ic, ke = ie, ++kc; kc != ke; ++kc)
        if (edge(*ic, *kc, g).second)
          for (tie(jc, je) = vertices(g); jc != je; ++jc)
            if (!edge(*ic, *jc, g).second && edge(*kc, *jc, g).second) {
              add_edge(*ic, *jc, g);
            }
  }


}                               // namespace boost

#endif // BOOST_GRAPH_TRANSITIVE_CLOSURE_HPP
