//=======================================================================

 // Copyright 2002 Indiana University.

 // Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek

 //

 // 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)

 //=======================================================================

 #ifndef BOOST_GRAPH_DAG_SHORTEST_PATHS_HPP

 #define BOOST_GRAPH_DAG_SHORTEST_PATHS_HPP

 #include <boost/graph/topological_sort.hpp>

 #include <boost/graph/dijkstra_shortest_paths.hpp>

 // single-source shortest paths for a Directed Acyclic Graph (DAG)

 namespace boost {

   // Initalize distances and call depth first search

   template <class VertexListGraph, class DijkstraVisitor, 

             class DistanceMap, class WeightMap, class ColorMap, 

             class PredecessorMap,

             class Compare, class Combine, 

             class DistInf, class DistZero>

   inline void

   dag_shortest_paths

     (const VertexListGraph& g,

      typename graph_traits<VertexListGraph>::vertex_descriptor s, 

      DistanceMap distance, WeightMap weight, ColorMap color,

      PredecessorMap pred,

      DijkstraVisitor vis, Compare compare, Combine combine, 

      DistInf inf, DistZero zero)

   {

     typedef typename graph_traits<VertexListGraph>::vertex_descriptor Vertex;

     std::vector<Vertex> rev_topo_order;

     rev_topo_order.reserve(num_vertices(g));

     // Call 'depth_first_visit', not 'topological_sort', because we don't

     // want to traverse the entire graph, only vertices reachable from 's',

     // and 'topological_sort' will traverse everything. The logic below

     // is the same as for 'topological_sort', only we call 'depth_first_visit'

     // and 'topological_sort' calls 'depth_first_search'.

     topo_sort_visitor<std::back_insert_iterator<std::vector<Vertex> > >

         topo_visitor(std::back_inserter(rev_topo_order));

     depth_first_visit(g, s, topo_visitor, color);

     typename graph_traits<VertexListGraph>::vertex_iterator ui, ui_end;

     for (tie(ui, ui_end) = vertices(g); ui != ui_end; ++ui) {

       put(distance, *ui, inf);

       put(pred, *ui, *ui);

     }

     put(distance, s, zero);

     vis.discover_vertex(s, g);

     typename std::vector<Vertex>::reverse_iterator i;

     for (i = rev_topo_order.rbegin(); i != rev_topo_order.rend(); ++i) {

       Vertex u = *i;

       vis.examine_vertex(u, g);

       typename graph_traits<VertexListGraph>::out_edge_iterator e, e_end;

       for (tie(e, e_end) = out_edges(u, g); e != e_end; ++e) {

         vis.discover_vertex(target(*e, g), g);

         bool decreased = relax(*e, g, weight, pred, distance, 

                                combine, compare);

         if (decreased)

           vis.edge_relaxed(*e, g);

         else

           vis.edge_not_relaxed(*e, g);

       }

       vis.finish_vertex(u, g);      

     }

   }

   namespace detail {

     // Defaults are the same as Dijkstra's algorithm

     // Handle Distance Compare, Combine, Inf and Zero defaults

     template <class VertexListGraph, class DijkstraVisitor, 

       class DistanceMap, class WeightMap, class ColorMap, 

       class IndexMap, class Params>

     inline void

     dag_sp_dispatch2

       (const VertexListGraph& g,

        typename graph_traits<VertexListGraph>::vertex_descriptor s, 

        DistanceMap distance, WeightMap weight, ColorMap color, IndexMap id,

        DijkstraVisitor vis, const Params& params)

     {

       typedef typename property_traits<DistanceMap>::value_type D;

       dummy_property_map p_map;

       dag_shortest_paths

         (g, s, distance, weight, color, 

          choose_param(get_param(params, vertex_predecessor), p_map),

          vis, 

          choose_param(get_param(params, distance_compare_t()), std::less<D>()),

          choose_param(get_param(params, distance_combine_t()), closed_plus<D>()),

          choose_param(get_param(params, distance_inf_t()), 

                       (std::numeric_limits<D>::max)()),

          choose_param(get_param(params, distance_zero_t()), 

                       D()));

     }

     // Handle DistanceMap and ColorMap defaults

     template <class VertexListGraph, class DijkstraVisitor, 

               class DistanceMap, class WeightMap, class ColorMap,

               class IndexMap, class Params>

     inline void

     dag_sp_dispatch1

       (const VertexListGraph& g,

        typename graph_traits<VertexListGraph>::vertex_descriptor s, 

        DistanceMap distance, WeightMap weight, ColorMap color, IndexMap id,

        DijkstraVisitor vis, const Params& params)

     {

       typedef typename property_traits<WeightMap>::value_type T;

       typename std::vector<T>::size_type n;

       n = is_default_param(distance) ? num_vertices(g) : 1;

       std::vector<T> distance_map(n);

       n = is_default_param(color) ? num_vertices(g) : 1;

       std::vector<default_color_type> color_map(n);

       dag_sp_dispatch2

         (g, s, 

          choose_param(distance, 

                       make_iterator_property_map(distance_map.begin(), id,

                                                  distance_map[0])),

          weight, 

          choose_param(color,

                       make_iterator_property_map(color_map.begin(), id, 

                                                  color_map[0])),

          id, vis, params);

     }

   } // namespace detail 

   template <class VertexListGraph, class Param, class Tag, class Rest>

   inline void

   dag_shortest_paths

     (const VertexListGraph& g,

      typename graph_traits<VertexListGraph>::vertex_descriptor s,

      const bgl_named_params<Param,Tag,Rest>& params)

   {

     // assert that the graph is directed...

     null_visitor null_vis;

     detail::dag_sp_dispatch1

       (g, s, 

        get_param(params, vertex_distance),

        choose_const_pmap(get_param(params, edge_weight), g, edge_weight),

        get_param(params, vertex_color),

        choose_const_pmap(get_param(params, vertex_index), g, vertex_index),

        choose_param(get_param(params, graph_visitor),

                     make_dijkstra_visitor(null_vis)),

        params);

   }

 } // namespace boost

 #endif // BOOST_GRAPH_DAG_SHORTEST_PATHS_HPP