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

// Copyright 2000 University of Notre Dame.

// Authors: Jeremy G. Siek, Andrew Lumsdaine, Lie-Quan Lee

//

// 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_EDGE_CONNECTIVITY

#define BOOST_EDGE_CONNECTIVITY

// WARNING: not-yet fully tested!

#include <boost/config.hpp>

#include <vector>

#include <set>

#include <algorithm>

#include <boost/graph/edmunds_karp_max_flow.hpp>

namespace boost {

  namespace detail {

    template <class Graph>

    inline

    std::pair<typename graph_traits<Graph>::vertex_descriptor,

              typename graph_traits<Graph>::degree_size_type>

    min_degree_vertex(Graph& g)

    {

      typedef graph_traits<Graph> Traits;

      typename Traits::vertex_descriptor p;

      typedef typename Traits::degree_size_type size_type;

      size_type delta = (std::numeric_limits<size_type>::max)();

      typename Traits::vertex_iterator i, iend;

      for (tie(i, iend) = vertices(g); i != iend; ++i)

        if (degree(*i, g) < delta) {

          delta = degree(*i, g);

          p = *i;

        }

      return std::make_pair(p, delta);

    }

    template <class Graph, class OutputIterator>

    void neighbors(const Graph& g, 

                   typename graph_traits<Graph>::vertex_descriptor u,

                   OutputIterator result)

    {

      typename graph_traits<Graph>::adjacency_iterator ai, aend;

      for (tie(ai, aend) = adjacent_vertices(u, g); ai != aend; ++ai)

        *result++ = *ai;

    }

    template <class Graph, class VertexIterator, class OutputIterator>

    void neighbors(const Graph& g, 

                   VertexIterator first, VertexIterator last,

                   OutputIterator result)

    {

      for (; first != last; ++first)

        neighbors(g, *first, result);

    }

  } // namespace detail

  // O(m n)

  template <class VertexListGraph, class OutputIterator>

  typename graph_traits<VertexListGraph>::degree_size_type

  edge_connectivity(VertexListGraph& g, OutputIterator disconnecting_set)

  {

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

    // Type Definitions

    typedef graph_traits<VertexListGraph> Traits;

    typedef typename Traits::vertex_iterator vertex_iterator;

    typedef typename Traits::edge_iterator edge_iterator;

    typedef typename Traits::out_edge_iterator out_edge_iterator;

    typedef typename Traits::vertex_descriptor vertex_descriptor;

    typedef typename Traits::degree_size_type degree_size_type;

    typedef color_traits<default_color_type> Color;

    typedef adjacency_list_traits<vecS, vecS, directedS> Tr;

    typedef typename Tr::edge_descriptor Tr_edge_desc;

    typedef adjacency_list<vecS, vecS, directedS, no_property, 

      property<edge_capacity_t, degree_size_type,

        property<edge_residual_capacity_t, degree_size_type,

          property<edge_reverse_t, Tr_edge_desc> > > > 

      FlowGraph;

    typedef typename graph_traits<FlowGraph>::edge_descriptor edge_descriptor;

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

    // Variable Declarations

    vertex_descriptor u, v, p, k;

    edge_descriptor e1, e2;

    bool inserted;

    vertex_iterator vi, vi_end;

    edge_iterator ei, ei_end;

    degree_size_type delta, alpha_star, alpha_S_k;

    std::set<vertex_descriptor> S, neighbor_S;

    std::vector<vertex_descriptor> S_star, non_neighbor_S;

    std::vector<default_color_type> color(num_vertices(g));

    std::vector<edge_descriptor> pred(num_vertices(g));

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

    // Create a network flow graph out of the undirected graph

    FlowGraph flow_g(num_vertices(g));

    typename property_map<FlowGraph, edge_capacity_t>::type

      cap = get(edge_capacity, flow_g);

    typename property_map<FlowGraph, edge_residual_capacity_t>::type

      res_cap = get(edge_residual_capacity, flow_g);

    typename property_map<FlowGraph, edge_reverse_t>::type

      rev_edge = get(edge_reverse, flow_g);

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

      u = source(*ei, g), v = target(*ei, g);

      tie(e1, inserted) = add_edge(u, v, flow_g);

      cap[e1] = 1;

      tie(e2, inserted) = add_edge(v, u, flow_g);

      cap[e2] = 1; // not sure about this

      rev_edge[e1] = e2;

      rev_edge[e2] = e1;

    }

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

    // The Algorithm

    tie(p, delta) = detail::min_degree_vertex(g);

    S_star.push_back(p);

    alpha_star = delta;

    S.insert(p);

    neighbor_S.insert(p);

    detail::neighbors(g, S.begin(), S.end(), 

                      std::inserter(neighbor_S, neighbor_S.begin()));

    std::set_difference(vertices(g).first, vertices(g).second,

                        neighbor_S.begin(), neighbor_S.end(),

                        std::back_inserter(non_neighbor_S));

    while (!non_neighbor_S.empty()) { // at most n - 1 times

      k = non_neighbor_S.front();

      alpha_S_k = edmunds_karp_max_flow

        (flow_g, p, k, cap, res_cap, rev_edge, &color[0], &pred[0]);

      if (alpha_S_k < alpha_star) {

        alpha_star = alpha_S_k;

        S_star.clear();

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

          if (color[*vi] != Color::white())

            S_star.push_back(*vi);

      }

      S.insert(k);

      neighbor_S.insert(k);

      detail::neighbors(g, k, std::inserter(neighbor_S, neighbor_S.begin()));

      non_neighbor_S.clear();

      std::set_difference(vertices(g).first, vertices(g).second,

                          neighbor_S.begin(), neighbor_S.end(),

                          std::back_inserter(non_neighbor_S));

    }

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

    // Compute edges of the cut [S*, ~S*]

    std::vector<bool> in_S_star(num_vertices(g), false);

    typename std::vector<vertex_descriptor>::iterator si;

    for (si = S_star.begin(); si != S_star.end(); ++si)

      in_S_star[*si] = true;

    degree_size_type c = 0;

    for (si = S_star.begin(); si != S_star.end(); ++si) {

      out_edge_iterator ei, ei_end;

      for (tie(ei, ei_end) = out_edges(*si, g); ei != ei_end; ++ei)

        if (!in_S_star[target(*ei, g)]) {

          *disconnecting_set++ = *ei;

          ++c;

        }

    }

    return c;

  }

} // namespace boost

#endif // BOOST_EDGE_CONNECTIVITY