//
//=======================================================================
// 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>
#include <boost/graph/overloading.hpp>
#include <boost/graph/detail/mpi_include.hpp>
#include <boost/concept/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 (boost::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);
                    put(root, w, v);
                } 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;
        BOOST_CONCEPT_ASSERT(
            (ReadWritePropertyMapConcept< ComponentMap, Vertex >));
        BOOST_CONCEPT_ASSERT((ReadWritePropertyMapConcept< RootMap, Vertex >));
        typedef typename property_traits< RootMap >::value_type RootV;
        BOOST_CONCEPT_ASSERT((ConvertibleConcept< RootV, Vertex >));
        BOOST_CONCEPT_ASSERT(
            (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< param_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, param_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< param_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, param_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 BOOST_GRAPH_ENABLE_IF_MODELS_PARM(
        Graph, vertex_list_graph_tag))
{
    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 BOOST_GRAPH_ENABLE_IF_MODELS_PARM(
        Graph, vertex_list_graph_tag))
{
    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 (boost::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)
{
    BOOST_CONCEPT_ASSERT((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 (boost::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;
    boost::tie(i, iend) = vertices(G_T);
    boost::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

#include BOOST_GRAPH_MPI_INCLUDE(< boost / graph / distributed / strong_components.hpp >)

#endif // BOOST_GRAPH_STRONG_COMPONENTS_HPP