//=======================================================================
// Copyright 2013 University of Warsaw.
// Authors: Piotr Wygocki 
//
// 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)
//=======================================================================
//
//
//This algorithm is described in "Network Flows: Theory, Algorithms, and Applications"
// by Ahuja, Magnanti, Orlin.

#ifndef BOOST_GRAPH_CYCLE_CANCELING_HPP
#define BOOST_GRAPH_CYCLE_CANCELING_HPP 

#include <numeric>

#include <boost/property_map/property_map.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/graph_concepts.hpp>
#include <boost/pending/indirect_cmp.hpp>
#include <boost/pending/relaxed_heap.hpp>
#include <boost/graph/bellman_ford_shortest_paths.hpp>
#include <boost/graph/iteration_macros.hpp>
#include <boost/graph/detail/augment.hpp>
#include <boost/graph/find_flow_cost.hpp>

namespace boost {


namespace detail {

template <typename PredEdgeMap, typename Vertex>
class RecordEdgeMapAndCycleVertex 
    : public bellman_visitor<edge_predecessor_recorder<PredEdgeMap, on_edge_relaxed> > {
        typedef edge_predecessor_recorder<PredEdgeMap, on_edge_relaxed> PredRec;
public:
    RecordEdgeMapAndCycleVertex(PredEdgeMap pred, Vertex & v) : 
        bellman_visitor<PredRec>(PredRec(pred)), m_v(v), m_pred(pred) {}

    template <typename Graph, typename Edge>
    void edge_not_minimized(Edge e, const Graph & g) const {
        typename graph_traits<Graph>::vertices_size_type n = num_vertices(g) + 1;

        //edge e is not minimized but does not have to be on the negative weight cycle
        //to find vertex on negative wieight cycle we move n+1 times backword in the PredEdgeMap graph.
        while(n > 0) {
            e = get(m_pred, source(e, g));
            --n;
        }
        m_v = source(e, g);
    }
private:
    Vertex & m_v;
    PredEdgeMap m_pred;
};

} //detail


template <class Graph, class Pred, class Distance, class Reversed, class ResidualCapacity, class Weight>
void cycle_canceling(const Graph &g, Weight weight, Reversed rev, ResidualCapacity residual_capacity, Pred pred, Distance distance) {
    typedef filtered_graph<const Graph, is_residual_edge<ResidualCapacity> > ResGraph;
    ResGraph gres = detail::residual_graph(g, residual_capacity);
    
    typedef graph_traits<ResGraph> ResGTraits;
    typedef graph_traits<Graph> GTraits;
    typedef typename ResGTraits::edge_descriptor edge_descriptor;
    typedef typename ResGTraits::vertex_descriptor vertex_descriptor;
    
    typename GTraits::vertices_size_type N = num_vertices(g);
    
    BGL_FORALL_VERTICES_T(v, g, Graph) {
        put(pred, v, edge_descriptor());
        put(distance, v, 0);
    }

    vertex_descriptor cycleStart;
    while(!bellman_ford_shortest_paths(gres, N, 
            weight_map(weight).
            distance_map(distance).
            visitor(detail::RecordEdgeMapAndCycleVertex<Pred, vertex_descriptor>(pred, cycleStart)))) {

        detail::augment(g, cycleStart, cycleStart, pred, residual_capacity, rev);
        
        BGL_FORALL_VERTICES_T(v, g, Graph) {
            put(pred, v, edge_descriptor());
            put(distance, v, 0);
        }
    }
}


//in this namespace argument dispatching takes place
namespace detail {

template <class Graph, class P, class T, class R, class ResidualCapacity, class Weight, class Reversed, class Pred, class Distance>
void cycle_canceling_dispatch2(
        const Graph &g, 
        Weight weight,
        Reversed rev,
        ResidualCapacity residual_capacity,
        Pred pred,
        Distance dist,
        const bgl_named_params<P, T, R>& params) {
    cycle_canceling(g, weight, rev, residual_capacity, pred, dist);
}

//setting default distance map
template <class Graph, class P, class T, class R, class Pred, class ResidualCapacity, class Weight, class Reversed>
void cycle_canceling_dispatch2(
        Graph &g, 
        Weight weight,
        Reversed rev,
        ResidualCapacity residual_capacity,
        Pred pred,
        param_not_found,
        const bgl_named_params<P, T, R>& params) {
    typedef typename property_traits<Weight>::value_type D;

    std::vector<D> d_map(num_vertices(g));

    cycle_canceling(g, weight, rev, residual_capacity, pred, 
                    make_iterator_property_map(d_map.begin(), choose_const_pmap(get_param(params, vertex_index), g, vertex_index)));
}

template <class Graph, class P, class T, class R, class ResidualCapacity, class Weight, class Reversed, class Pred>
void cycle_canceling_dispatch1(
        Graph &g, 
        Weight weight, 
        Reversed rev,
        ResidualCapacity residual_capacity,
        Pred pred,
        const bgl_named_params<P, T, R>& params) {
    cycle_canceling_dispatch2(g, weight, rev,residual_capacity,  pred, 
                                get_param(params, vertex_distance), params);
}

//setting default predecessors map
template <class Graph, class P, class T, class R, class ResidualCapacity, class Weight, class Reversed>
void cycle_canceling_dispatch1(
        Graph &g, 
        Weight weight, 
        Reversed rev,
        ResidualCapacity residual_capacity,
        param_not_found,
        const bgl_named_params<P, T, R>& params) {
    typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
    std::vector<edge_descriptor> p_map(num_vertices(g));

    cycle_canceling_dispatch2(g, weight, rev, residual_capacity,
                              make_iterator_property_map(p_map.begin(), choose_const_pmap(get_param(params, vertex_index), g, vertex_index)),
                                get_param(params, vertex_distance), params); 
}

}//detail

template <class Graph, class  P, class T, class R>
void cycle_canceling(Graph &g,
        const bgl_named_params<P, T, R>& params) {
    cycle_canceling_dispatch1(g, 
           choose_const_pmap(get_param(params, edge_weight), g, edge_weight),
           choose_const_pmap(get_param(params, edge_reverse), g, edge_reverse),
           choose_pmap(get_param(params, edge_residual_capacity), 
                       g, edge_residual_capacity),
           get_param(params, vertex_predecessor), 
           params);
}

template <class Graph>
void cycle_canceling(Graph &g) {
    bgl_named_params<int, buffer_param_t> params(0);
    cycle_canceling(g, params);
}


}

#endif /* BOOST_GRAPH_CYCLE_CANCELING_HPP */