//

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

// Copyright 1997, 1998, 1999, 2000 University of Notre Dame.

// 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_STRONG_COMPONENTS_HPP

#define BOOST_GRAPH_STRONG_COMPONENTS_HPP

#include <stack>

#include <boost/config.hpp>

#include <boost/graph/depth_first_search.hpp>

#include <boost/type_traits/conversion_traits.hpp>

#include <boost/static_assert.hpp>

namespace boost {

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

  // This is Tarjan's algorithm for strongly connected components

  // from his paper "Depth first search and linear graph algorithms".

  // It calculates the components in a single application of DFS.

  // We implement the algorithm as a dfs-visitor.

  namespace detail {

    template <typename ComponentMap, typename RootMap, typename DiscoverTime,

              typename Stack>

    class tarjan_scc_visitor : public dfs_visitor<> 

    {

      typedef typename property_traits<ComponentMap>::value_type comp_type;

      typedef typename property_traits<DiscoverTime>::value_type time_type;

    public:

      tarjan_scc_visitor(ComponentMap comp_map, RootMap r, DiscoverTime d, 

                         comp_type& c_, Stack& s_)

        : c(c_), comp(comp_map), root(r), discover_time(d),

          dfs_time(time_type()), s(s_) { }

      template <typename Graph>

      void discover_vertex(typename graph_traits<Graph>::vertex_descriptor v,

                           const Graph&) {

        put(root, v, v);

        put(comp, v, (std::numeric_limits<comp_type>::max)());

        put(discover_time, v, dfs_time++);

        s.push(v);

      }

      template <typename Graph>

      void finish_vertex(typename graph_traits<Graph>::vertex_descriptor v,

                         const Graph& g) {

        typename graph_traits<Graph>::vertex_descriptor w;

        typename graph_traits<Graph>::out_edge_iterator ei, ei_end;

        for (tie(ei, ei_end) = out_edges(v, g); ei != ei_end; ++ei) {

          w = target(*ei, g);

          if (get(comp, w) == (std::numeric_limits<comp_type>::max)())

            put(root, v, this->min_discover_time(get(root,v), get(root,w)));

        }

        if (get(root, v) == v) {

          do {

            w = s.top(); s.pop();

            put(comp, w, c);

          } while (w != v);

          ++c;

        }

      }

    private:

      template <typename Vertex>

      Vertex min_discover_time(Vertex u, Vertex v) {

        return get(discover_time, u) < get(discover_time,v) ? u : v;

      }

      comp_type& c;

      ComponentMap comp;

      RootMap root;

      DiscoverTime discover_time;

      time_type dfs_time;

      Stack& s;

    };

    template <class Graph, class ComponentMap, class RootMap,

              class DiscoverTime, class P, class T, class R>

    typename property_traits<ComponentMap>::value_type

    strong_components_impl

      (const Graph& g,    // Input

       ComponentMap comp, // Output

       // Internal record keeping

       RootMap root, 

       DiscoverTime discover_time,

       const bgl_named_params<P, T, R>& params)

    {

      typedef typename graph_traits<Graph>::vertex_descriptor Vertex;

      function_requires< ReadWritePropertyMapConcept<ComponentMap, Vertex> >();

      function_requires< ReadWritePropertyMapConcept<RootMap, Vertex> >();

      typedef typename property_traits<RootMap>::value_type RootV;

      function_requires< ConvertibleConcept<RootV, Vertex> >();

      function_requires< ReadWritePropertyMapConcept<DiscoverTime, Vertex> >();

      typename property_traits<ComponentMap>::value_type total = 0;

      std::stack<Vertex> s;

      detail::tarjan_scc_visitor<ComponentMap, RootMap, DiscoverTime, 

        std::stack<Vertex> > 

        vis(comp, root, discover_time, total, s);

      depth_first_search(g, params.visitor(vis));

      return total;

    }

    //-------------------------------------------------------------------------

    // The dispatch functions handle the defaults for the rank and discover

    // time property maps.

    // dispatch with class specialization to avoid VC++ bug

    template <class DiscoverTimeMap>

    struct strong_comp_dispatch2 {

      template <class Graph, class ComponentMap, class RootMap, class P, class T, class R>

      inline static typename property_traits<ComponentMap>::value_type

      apply(const Graph& g,

            ComponentMap comp,

            RootMap r_map,

            const bgl_named_params<P, T, R>& params,

            DiscoverTimeMap time_map)

      {

        return strong_components_impl(g, comp, r_map, time_map, params);

      }

    };

    template <>

    struct strong_comp_dispatch2<detail::error_property_not_found> {

      template <class Graph, class ComponentMap, class RootMap,

                class P, class T, class R>

      inline static typename property_traits<ComponentMap>::value_type

      apply(const Graph& g,

            ComponentMap comp,

            RootMap r_map,

            const bgl_named_params<P, T, R>& params,

            detail::error_property_not_found)

      {

        typedef typename graph_traits<Graph>::vertices_size_type size_type;

        size_type       n = num_vertices(g) > 0 ? num_vertices(g) : 1;

        std::vector<size_type> time_vec(n);

        return strong_components_impl

          (g, comp, r_map,

           make_iterator_property_map(time_vec.begin(), choose_const_pmap

                                      (get_param(params, vertex_index),

                                       g, vertex_index), time_vec[0]),

           params);

      }

    };

    template <class Graph, class ComponentMap, class RootMap,

              class P, class T, class R, class DiscoverTimeMap>

    inline typename property_traits<ComponentMap>::value_type

    scc_helper2(const Graph& g,

                ComponentMap comp,

                RootMap r_map,

                const bgl_named_params<P, T, R>& params,

                DiscoverTimeMap time_map)

    {

      return strong_comp_dispatch2<DiscoverTimeMap>::apply(g, comp, r_map, params, time_map);

    }

    template <class RootMap>

    struct strong_comp_dispatch1 {

      template <class Graph, class ComponentMap, class P, class T, class R>

      inline static typename property_traits<ComponentMap>::value_type

      apply(const Graph& g,

            ComponentMap comp,

            const bgl_named_params<P, T, R>& params,

            RootMap r_map)

      {

        return scc_helper2(g, comp, r_map, params, get_param(params, vertex_discover_time));

      }

    };

    template <>

    struct strong_comp_dispatch1<detail::error_property_not_found> {

      template <class Graph, class ComponentMap, 

                class P, class T, class R>

      inline static typename property_traits<ComponentMap>::value_type

      apply(const Graph& g,

            ComponentMap comp,

            const bgl_named_params<P, T, R>& params,

            detail::error_property_not_found)

      {

        typedef typename graph_traits<Graph>::vertex_descriptor Vertex;

        typename std::vector<Vertex>::size_type

          n = num_vertices(g) > 0 ? num_vertices(g) : 1;

        std::vector<Vertex> root_vec(n);

        return scc_helper2

          (g, comp, 

           make_iterator_property_map(root_vec.begin(), choose_const_pmap

                                      (get_param(params, vertex_index),

                                       g, vertex_index), root_vec[0]),

           params, 

           get_param(params, vertex_discover_time));

      }

    };

    template <class Graph, class ComponentMap, class RootMap,

              class P, class T, class R>

    inline typename property_traits<ComponentMap>::value_type

    scc_helper1(const Graph& g,

               ComponentMap comp,

               const bgl_named_params<P, T, R>& params,

               RootMap r_map)

    {

      return detail::strong_comp_dispatch1<RootMap>::apply(g, comp, params,

                                                           r_map);

    }

  } // namespace detail 

  template <class Graph, class ComponentMap, 

            class P, class T, class R>

  inline typename property_traits<ComponentMap>::value_type

  strong_components(const Graph& g, ComponentMap comp,

                    const bgl_named_params<P, T, R>& params)

  {

    typedef typename graph_traits<Graph>::directed_category DirCat;

    BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));

    return detail::scc_helper1(g, comp, params, 

                               get_param(params, vertex_root_t()));

  }

  template <class Graph, class ComponentMap>

  inline typename property_traits<ComponentMap>::value_type

  strong_components(const Graph& g, ComponentMap comp)

  {

    typedef typename graph_traits<Graph>::directed_category DirCat;

    BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));

    bgl_named_params<int, int> params(0);

    return strong_components(g, comp, params);

  }

  template <typename Graph, typename ComponentMap, typename ComponentLists>

  void build_component_lists

    (const Graph& g,

     typename graph_traits<Graph>::vertices_size_type num_scc,

     ComponentMap component_number,

     ComponentLists& components)

  {

    components.resize(num_scc);

    typename graph_traits<Graph>::vertex_iterator vi, vi_end;

    for (tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)

      components[component_number[*vi]].push_back(*vi);

  }

} // namespace boost

#include <queue>

#include <vector>

#include <boost/graph/transpose_graph.hpp>

#include <boost/pending/indirect_cmp.hpp>

#include <boost/graph/connected_components.hpp> // for components_recorder

namespace boost {

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

  // This is the version of strongly connected components from

  // "Intro. to Algorithms" by Cormen, Leiserson, Rivest, which was

  // adapted from "Data Structure and Algorithms" by Aho, Hopcroft,

  // and Ullman, who credit the algorithm to S.R. Kosaraju and M. Sharir.

  // The algorithm is based on computing DFS forests the graph

  // and its transpose.

  // This algorithm is slower than Tarjan's by a constant factor, uses

  // more memory, and puts more requirements on the graph type.

  template <class Graph, class DFSVisitor, class ComponentsMap,

            class DiscoverTime, class FinishTime,

            class ColorMap>

  typename property_traits<ComponentsMap>::value_type

  kosaraju_strong_components(Graph& G, ComponentsMap c,

                             FinishTime finish_time, ColorMap color)

  {

    function_requires< MutableGraphConcept<Graph> >();

    // ...

    typedef typename graph_traits<Graph>::vertex_descriptor Vertex;

    typedef typename property_traits<ColorMap>::value_type ColorValue;

    typedef color_traits<ColorValue> Color;

    typename property_traits<FinishTime>::value_type time = 0;

    depth_first_search

     (G, make_dfs_visitor(stamp_times(finish_time, time, on_finish_vertex())),

      color);

    Graph G_T(num_vertices(G));

    transpose_graph(G, G_T);

    typedef typename property_traits<ComponentsMap>::value_type count_type;

    count_type c_count(0);

    detail::components_recorder<ComponentsMap>

      vis(c, c_count);

    // initialize G_T

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

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

      put(color, *ui, Color::white());

    typedef typename property_traits<FinishTime>::value_type D;

    typedef indirect_cmp< FinishTime, std::less<D> > Compare;

    Compare fl(finish_time);

    std::priority_queue<Vertex, std::vector<Vertex>, Compare > Q(fl);

    typename graph_traits<Graph>::vertex_iterator i, j, iend, jend;

    tie(i, iend) = vertices(G_T);

    tie(j, jend) = vertices(G);

    for ( ; i != iend; ++i, ++j) {

      put(finish_time, *i, get(finish_time, *j));

       Q.push(*i);

    }

    while ( !Q.empty() ) {

      Vertex u = Q.top();

      Q.pop();

      if  (get(color, u) == Color::white()) {

        depth_first_visit(G_T, u, vis, color);

        ++c_count; 

      }

    }

    return c_count;

  }

} // namespace boost

#endif // BOOST_GRAPH_STRONG_COMPONENTS_HPP