// (C) Copyright 2009 Eric Bose-Wolf
//
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0 (See accompanying file
// LICENSE_1_0.txt or http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_GRAPH_TRANSITIVE_REDUCTION_HPP
#define BOOST_GRAPH_TRANSITIVE_REDUCTION_HPP

#include <vector>
#include <algorithm> //std::find
#include <boost/concept/requires.hpp>
#include <boost/concept_check.hpp>

#include <boost/graph/graph_traits.hpp>
#include <boost/graph/topological_sort.hpp>

// also I didn't got all of the concepts thin. Am I suppose to check
// for all concepts, which are needed for functions I call? (As if I
// wouldn't do that, the users would see the functions called by
// complaining about missings concepts, which would be clearly an error
// message revealing internal implementation and should therefore be avoided?)

// the pseudocode which I followed implementing this algorithmn was taken
// from the german book Algorithmische Graphentheorie by Volker Turau
// it is proposed to be of O(n + nm_red ) where n is the number
// of vertices and m_red is the number of edges in the transitive
// reduction, but I think my implementation spoiled this up at some point
// indicated below.

namespace boost {

template <
    typename Graph, typename GraphTR, typename G_to_TR_VertexMap,
    typename VertexIndexMap
>
BOOST_CONCEPT_REQUIRES(
                      ((VertexListGraphConcept< Graph >))
                      ((IncidenceGraphConcept< Graph >))
                      ((MutableGraphConcept< GraphTR >))
                      ((ReadablePropertyMapConcept< VertexIndexMap,
                          typename graph_traits<Graph>::vertex_descriptor >))
                      ((Integer< typename
                          property_traits< VertexIndexMap >::value_type >))
                      ((LvaluePropertyMapConcept< G_to_TR_VertexMap,
                          typename graph_traits<Graph>::vertex_descriptor >)),
                       (void))
transitive_reduction(const Graph& g, GraphTR& tr,
                     G_to_TR_VertexMap g_to_tr_map,
                     VertexIndexMap g_index_map )
{
    typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
    typedef typename graph_traits<Graph>::vertex_iterator VertexIterator;
    typedef typename std::vector<Vertex>::size_type size_type;

    std::vector<Vertex> topo_order;
    topological_sort(g, std::back_inserter(topo_order));

    std::vector<size_type> topo_number_storage(num_vertices(g));

    iterator_property_map<size_type*, VertexIndexMap,
    size_type, size_type&> topo_number( &topo_number_storage[0], g_index_map );

    {
        typename std::vector<Vertex>::reverse_iterator it = topo_order.rbegin();
        size_type n = 0;
        for(; it != topo_order.rend(); ++it,++n ) {
            topo_number[ *it ] = n;
        }
    }

    std::vector< std::vector< bool > > edge_in_closure(num_vertices(g),
                                            std::vector<bool>( num_vertices(g), false));
    {
        typename std::vector<Vertex>::reverse_iterator it = topo_order.rbegin();
            for( ; it != topo_order.rend(); ++it ) {
            g_to_tr_map[*it] = add_vertex(tr);
        }
    }

    typename std::vector<Vertex>::iterator
        it = topo_order.begin(),
        end = topo_order.end();
    for( ; it != end; ++it ) {
        size_type i = topo_number[ *it ];
        edge_in_closure[i][i] = true;
        std::vector<Vertex> neighbors;

        //I have to collect the successors of *it and traverse them in
        //ascending topological order. I didn't know a better way, how to
        //do that. So what I'm doint is, collection the successors of *it here
        {
            typename Graph::out_edge_iterator oi,oi_end;
            for( boost::tie(oi, oi_end) = out_edges( *it, g ); oi != oi_end; ++oi ) {
                neighbors.push_back( target( *oi, g ) );
            }
        }

        {
            //and run through all vertices in topological order
            typename std::vector<Vertex>::reverse_iterator
                rit = topo_order.rbegin();
                rend = topo_order.rend();
            for(; rit != rend; ++rit ) {
                //looking if they are successors of *it
                if( std::find( neighbors.begin(), neighbors.end(), *rit) != neighbors.end() ) {
                    size_type j = topo_number[ *rit ];
                    if( not edge_in_closure[i][j] ) {
                    for(size_type k = j; k < num_vertices(g); ++k) {
                        if( not edge_in_closure[i][k] ) {
                        //here we need edge_in_closure to be in topological order,
                        edge_in_closure[i][k] = edge_in_closure[j][k];
                        }
                    }
                    //therefore we only access edge_in_closure only through
                    //topo_number property_map
                    add_edge(g_to_tr_map[*it], g_to_tr_map[*rit], tr);
                    } //if ( not edge_in_
                } //if (find (
            } //for( typename vector<Vertex>::reverse_iterator
        } // {

    } //for( typename vector<Vertex>::iterator

} //void transitive_reduction

} // namespace boost

#endif