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

// 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)

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

/*

  This file implements the function

  template <class VertexAndEdgeListGraph, class DistanceMatrix,

            class P, class T, class R>

  bool

  johnson_all_pairs_shortest_paths

    (VertexAndEdgeListGraph& g, 

     DistanceMatrix& D,

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

 */

#ifndef BOOST_GRAPH_JOHNSON_HPP

#define BOOST_GRAPH_JOHNSON_HPP

#include <boost/graph/graph_traits.hpp>

#include <boost/property_map.hpp>

#include <boost/graph/bellman_ford_shortest_paths.hpp>

#include <boost/graph/dijkstra_shortest_paths.hpp>

#include <boost/graph/adjacency_list.hpp>

#include <boost/pending/ct_if.hpp>

#include <boost/type_traits/same_traits.hpp>

namespace boost {

  template <class VertexAndEdgeListGraph, class DistanceMatrix,

            class VertexID, class Weight, typename BinaryPredicate, 

            typename BinaryFunction, typename Infinity, class DistanceZero>

  bool

  johnson_all_pairs_shortest_paths(VertexAndEdgeListGraph& g1, 

               DistanceMatrix& D,

               VertexID id1, Weight w1, const BinaryPredicate& compare, 

               const BinaryFunction& combine, const Infinity& inf,

               DistanceZero zero)

  {

    typedef graph_traits<VertexAndEdgeListGraph> Traits1;

    typedef typename property_traits<Weight>::value_type DT;

    function_requires< BasicMatrixConcept<DistanceMatrix,

      typename Traits1::vertices_size_type, DT> >();

    typedef typename Traits1::directed_category DirCat;

    bool is_undirected = is_same<DirCat, undirected_tag>::value;

    typedef adjacency_list<vecS, vecS, directedS, 

      property< vertex_distance_t, DT>,

      property< edge_weight_t, DT, 

      property< edge_weight2_t, DT > > > Graph2;

    typedef graph_traits<Graph2> Traits2;

    Graph2 g2(num_vertices(g1) + 1);

    typename property_map<Graph2, edge_weight_t>::type 

      w = get(edge_weight, g2);

    typename property_map<Graph2, edge_weight2_t>::type 

      w_hat = get(edge_weight2, g2);

    typename property_map<Graph2, vertex_distance_t>::type 

      d = get(vertex_distance, g2);

    typedef typename property_map<Graph2, vertex_index_t>::type VertexID2;

    VertexID2 id2 = get(vertex_index, g2);

    // Construct g2 where V[g2] = V[g1] U {s}

    //   and  E[g2] = E[g1] U {(s,v)| v in V[g1]}

    std::vector<typename Traits1::vertex_descriptor> 

      verts1(num_vertices(g1) + 1);

    typename Traits2::vertex_descriptor s = *vertices(g2).first;

    {

      typename Traits1::vertex_iterator v, v_end;

      int i = 1;

      for (tie(v, v_end) = vertices(g1); v != v_end; ++v, ++i) {

        typename Traits2::edge_descriptor e; bool z;

        tie(e, z) = add_edge(s, get(id1, *v) + 1, g2);

        put(w, e, zero);

        verts1[i] = *v;

      }

      typename Traits1::edge_iterator e, e_end;

      for (tie(e, e_end) = edges(g1); e != e_end; ++e) {

        typename Traits2::edge_descriptor e2; bool z;

        tie(e2, z) = add_edge(get(id1, source(*e, g1)) + 1, 

                              get(id1, target(*e, g1)) + 1, g2);

        put(w, e2, get(w1, *e));

        if (is_undirected) {

          tie(e2, z) = add_edge(get(id1, target(*e, g1)) + 1, 

                                get(id1, source(*e, g1)) + 1, g2);

          put(w, e2, get(w1, *e));

        }

      }

    }

    typename Traits2::vertex_iterator v, v_end, u, u_end;

    typename Traits2::edge_iterator e, e_end;

    std::vector<DT> h_vec(num_vertices(g2));

    typedef typename std::vector<DT>::iterator iter_t;

    iterator_property_map<iter_t,VertexID2,DT,DT&> h(h_vec.begin(), id2);

    for (tie(v, v_end) = vertices(g2); v != v_end; ++v)

      d[*v] = inf;

    put(d, s, zero);

    // Using the non-named parameter versions of bellman_ford and

    // dijkstra for portability reasons.

    dummy_property_map pred; bellman_visitor<> bvis;

    if (bellman_ford_shortest_paths

        (g2, num_vertices(g2), w, pred, d, combine, compare, bvis)) {

      for (tie(v, v_end) = vertices(g2); v != v_end; ++v)

        put(h, *v, get(d, *v));

      // Reweight the edges to remove negatives

      for (tie(e, e_end) = edges(g2); e != e_end; ++e) {

        typename Traits2::vertex_descriptor a = source(*e, g2),

          b = target(*e, g2);

        put(w_hat, *e, get(w, *e) + get(h, a) - get(h, b));

      }

      for (tie(u, u_end) = vertices(g2); u != u_end; ++u) {

        dijkstra_visitor<> dvis;

        dijkstra_shortest_paths

          (g2, *u, pred, d, w_hat, id2, compare, combine, inf, zero,dvis);

        for (tie(v, v_end) = vertices(g2); v != v_end; ++v) {

          if (*u != s && *v != s) {

            typename Traits1::vertex_descriptor u1, v1;

            u1 = verts1[id2[*u]]; v1 = verts1[id2[*v]];

            D[id2[*u]-1][id2[*v]-1] = get(d, *v) + get(h, *v) - get(h, *u);

          }

        }

      }

      return true;

    } else

      return false;

  }

  template <class VertexAndEdgeListGraph, class DistanceMatrix,

            class VertexID, class Weight, class DistanceZero>

  bool

  johnson_all_pairs_shortest_paths(VertexAndEdgeListGraph& g1, 

               DistanceMatrix& D,

               VertexID id1, Weight w1, DistanceZero zero)

  {

    typedef typename property_traits<Weight>::value_type WT;

    return johnson_all_pairs_shortest_paths(g1, D, id1, w1, 

                                            std::less<WT>(),

                                            closed_plus<WT>(),

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

                                            zero);

  }

  namespace detail {

    template <class VertexAndEdgeListGraph, class DistanceMatrix,

              class P, class T, class R, class Weight, 

              class VertexID>

    bool

    johnson_dispatch(VertexAndEdgeListGraph& g, 

                     DistanceMatrix& D,

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

                     Weight w, VertexID id)

    {

      typedef typename property_traits<Weight>::value_type WT;

      return johnson_all_pairs_shortest_paths

        (g, D, id, w,

        choose_param(get_param(params, distance_compare_t()), 

          std::less<WT>()),

        choose_param(get_param(params, distance_combine_t()), 

          closed_plus<WT>()),

        choose_param(get_param(params, distance_inf_t()), 

          std::numeric_limits<WT>::max BOOST_PREVENT_MACRO_SUBSTITUTION()),

         choose_param(get_param(params, distance_zero_t()), WT()) );

    }

  } // namespace detail

  template <class VertexAndEdgeListGraph, class DistanceMatrix,

            class P, class T, class R>

  bool

  johnson_all_pairs_shortest_paths

    (VertexAndEdgeListGraph& g, 

     DistanceMatrix& D,

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

  {

    return detail::johnson_dispatch

      (g, D, params,

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

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

       );

  }

  template <class VertexAndEdgeListGraph, class DistanceMatrix>

  bool

  johnson_all_pairs_shortest_paths

    (VertexAndEdgeListGraph& g, DistanceMatrix& D)

  {

    bgl_named_params<int,int> params(1);

    return detail::johnson_dispatch

      (g, D, params, get(edge_weight, g), get(vertex_index, g));

  }

} // namespace boost

#endif // BOOST_GRAPH_JOHNSON_HPP