graph_adjacency.hh

// graph-tool -- a general graph modification and manipulation thingy
//
// Copyright (C) 2006-2015 Tiago de Paula Peixoto <tiago@skewed.de>
//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License
// as published by the Free Software Foundation; either version 3
// of the License, or (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <http://www.gnu.org/licenses/>.

#ifndef GRAPH_ADJACENCY_HH
#define GRAPH_ADJACENCY_HH

#include <vector>
#include <deque>
#include <utility>
#include <numeric>
#include <iostream>
#include <tuple>
#include <boost/iterator.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/range/irange.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/graph/properties.hpp>
#include <boost/iterator/transform_iterator.hpp>
#include <boost/iterator/iterator_facade.hpp>

#include "transform_iterator.hh"

namespace boost
{

// ========================================================================
// Forward declarations
// ========================================================================

template <class Vertex>
class adj_list;

// forward declaration of manipulation functions
template <class Vertex>
std::pair<typename adj_list<Vertex>::vertex_iterator,
          typename adj_list<Vertex>::vertex_iterator>
vertices(const adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::edge_iterator,
          typename adj_list<Vertex>::edge_iterator>
edges(const adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::edge_descriptor, bool>
edge(Vertex s, Vertex t, const adj_list<Vertex>& g);

template <class Vertex>
size_t out_degree(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
size_t in_degree(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::out_edge_iterator,
          typename adj_list<Vertex>::out_edge_iterator>
out_edges(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::in_edge_iterator,
          typename adj_list<Vertex>::in_edge_iterator>
in_edges(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::adjacency_iterator,
          typename adj_list<Vertex>::adjacency_iterator>
adjacent_vertices(Vertex v, const adj_list<Vertex>& g);

template <class Vertex>
size_t num_vertices(const adj_list<Vertex>& g);

template <class Vertex>
size_t num_edges(const adj_list<Vertex>& g);

template <class Vertex>
Vertex add_vertex(adj_list<Vertex>& g);

template <class Vertex>
void clear_vertex(Vertex v, adj_list<Vertex>& g);

template <class Vertex>
void remove_vertex(Vertex v, adj_list<Vertex>& g);

template <class Vertex>
void remove_vertex_fast(Vertex v, adj_list<Vertex>& g);

template <class Vertex>
std::pair<typename adj_list<Vertex>::edge_descriptor, bool>
add_edge(Vertex s, Vertex t, adj_list<Vertex>& g);

template <class Vertex>
void remove_edge(Vertex s, Vertex t, adj_list<Vertex>& g);

template <class Vertex>
void remove_edge(const typename adj_list<Vertex>::edge_descriptor& e,
                 adj_list<Vertex>& g);

// ========================================================================
// adj_list<Vertex>
// ========================================================================
//
// adj_list is a very simple adjacency list implementation for bidirectional
// graphs based on std::vector, meant to be reasonably efficient both
// memory-wise and computationally. It maintains a list of in and out-edges for
// each vertex, and each edge has a built-in index (which is replicated in both
// lists). For each edge, a total of 4 integers is necessary: the source and
// target vertices, in the in_edges and out_edges lists, respectively, and the
// (same) edge index in both lists. The integer type is given by the Vertex
// template parameter. It achieves about half as much memory as
// boost::adjacency_list with an edge index property map and the same integer
// type.

// The complexity guarantees and iterator invalidation rules are the same as
// boost::adjacency_list with vector storage selectors for both vertex and edge
// lists.

template <class Vertex = size_t>
class adj_list
{
public:
    struct graph_tag {};
    typedef Vertex vertex_t;

    struct edge_descriptor
    {
        edge_descriptor()
            : s(std::numeric_limits<vertex_t>::max()),
              t(std::numeric_limits<vertex_t>::max()),
              idx(std::numeric_limits<vertex_t>::max()), inv(false) {};
        edge_descriptor(vertex_t s, vertex_t t, vertex_t idx, bool inv)
            : s(s), t(t), idx(idx), inv(inv) {}

        bool operator==(const edge_descriptor& other) const
        {
            return idx == other.idx;
        }
        bool operator!=(const edge_descriptor& other) const
        {
            return idx != other.idx;
        }
        bool operator<(const edge_descriptor& other) const
        {
            return idx < other.idx;
        }

        vertex_t s, t, idx;
        bool inv;
    };

    typedef std::vector<std::pair<vertex_t, vertex_t> > edge_list_t;
    typedef typename integer_range<Vertex>::iterator vertex_iterator;

    adj_list(): _n_edges(0), _last_idx(0), _keep_epos(false) {}

    struct get_vertex
    {
        get_vertex() {}
        typedef Vertex result_type;
        Vertex operator()(const std::pair<vertex_t, vertex_t>& v) const
        { return v.first; }
    };

    typedef transform_random_access_iterator<get_vertex, typename edge_list_t::const_iterator>
        adjacency_iterator;

    struct make_out_edge
    {
        make_out_edge(vertex_t src): _src(src) {}
        make_out_edge() {}
        vertex_t _src;
        typedef edge_descriptor result_type;
        edge_descriptor operator()(const std::pair<vertex_t, vertex_t>& v) const
        { return edge_descriptor(_src, v.first, v.second, false); }
    };

    struct make_in_edge
    {
        make_in_edge(vertex_t tgt): _tgt(tgt) {}
        make_in_edge() {}
        vertex_t _tgt;
        typedef edge_descriptor result_type;
        edge_descriptor operator()(const std::pair<vertex_t, vertex_t>& v) const
        { return edge_descriptor(v.first, _tgt, v.second, false); }
    };

    typedef transform_random_access_iterator<make_out_edge, typename edge_list_t::const_iterator>
        out_edge_iterator;
    typedef transform_random_access_iterator<make_in_edge, typename edge_list_t::const_iterator>
        in_edge_iterator;

    class edge_iterator:
        public boost::iterator_facade<edge_iterator,
                                      edge_descriptor,
                                      boost::forward_traversal_tag,
                                      edge_descriptor>
    {
    public:
        edge_iterator() {}
        explicit edge_iterator(const typename std::vector<edge_list_t>::const_iterator& vi_begin,
                               const typename std::vector<edge_list_t>::const_iterator& vi_end,
                               const typename std::vector<edge_list_t>::const_iterator& vi,
                               const typename edge_list_t::const_iterator& ei)
            : _vi_begin(vi_begin), _vi_end(vi_end), _vi(vi), _ei(ei)
        {
            // move position to first edge
            skip();
        }

    private:
        friend class boost::iterator_core_access;

        void skip()
        {
            //skip empty vertices
            while (_vi != _vi_end && _ei == _vi->end())
            {
                ++_vi;
                if (_vi != _vi_end)
                    _ei = _vi->begin();
            }
        }

        void increment()
        {
            ++_ei;
            skip();
        }

        bool equal(edge_iterator const& other) const
        {
            if (_vi_begin == _vi_end)
                return _vi == other._vi;
            return _vi == other._vi && _ei == other._ei;
        }

        edge_descriptor dereference() const
        {
            return edge_descriptor(vertex_t(_vi - _vi_begin),
                                   _ei->first, _ei->second, false);
        }

        typename std::vector<edge_list_t>::const_iterator _vi_begin;
        typename std::vector<edge_list_t>::const_iterator _vi_end;
        typename std::vector<edge_list_t>::const_iterator _vi;
        typename edge_list_t::const_iterator _ei;
    };

    void reindex_edges()
    {
        _free_indexes.clear();
        _last_idx = 0;
        _in_edges.clear();
        _in_edges.resize(_out_edges.size());
        for (size_t i = 0; i < _out_edges.size(); ++i)
            for (size_t j = 0; j < _out_edges[i].size(); ++j)
            {
                Vertex v = _out_edges[i][j].first;
                _out_edges[i][j].second = _last_idx;
                _in_edges[v].push_back(std::make_pair(Vertex(i),
                                                      _last_idx));
                _last_idx++;
            }

        if (_keep_epos)
            rebuild_epos();
    }

    void set_keep_epos(bool keep)
    {
        if (keep)
        {
            if (!_keep_epos)
                rebuild_epos();
        }
        else
        {
            _epos.clear();
        }
        _keep_epos = keep;
    }

    bool get_keep_epos()
    {
        return _keep_epos;
    }

    size_t get_last_index() const { return _last_idx; }

    static Vertex null_vertex() { return std::numeric_limits<Vertex>::max(); }

private:
    typedef std::vector<edge_list_t> vertex_list_t;
    vertex_list_t _out_edges;
    vertex_list_t _in_edges;
    size_t _n_edges;
    size_t _last_idx;
    std::deque<size_t> _free_indexes; // indexes of deleted edges to be used up
                                      // for new edges to avoid very large
                                      // indexes, and unnecessary property map
                                      // memory use
    bool _keep_epos;
    std::vector<std::pair<int32_t, int32_t> > _epos;

    void rebuild_epos()
    {
        _epos.resize(_last_idx + 1);
        for (size_t i = 0; i < _out_edges.size(); ++i)
        {
            for (size_t j = 0; j < _out_edges[i].size(); ++j)
            {
                size_t idx = _out_edges[i][j].second;
                _epos[idx].first = j;
            }

            for (size_t j = 0; j < _in_edges[i].size(); ++j)
            {
                size_t idx = _in_edges[i][j].second;
                _epos[idx].second = j;
            }
        }
    }

    // manipulation functions
    friend std::pair<vertex_iterator, vertex_iterator>
    vertices<>(const adj_list<Vertex>& g);

    friend std::pair<edge_iterator, edge_iterator>
    edges<>(const adj_list<Vertex>& g);

    friend std::pair<edge_descriptor, bool>
    edge<>(Vertex s, Vertex t, const adj_list<Vertex>& g);

    friend size_t out_degree<>(Vertex v, const adj_list<Vertex>& g);

    friend size_t in_degree<>(Vertex v, const adj_list<Vertex>& g);

    friend std::pair<out_edge_iterator, out_edge_iterator>
    out_edges<>(Vertex v, const adj_list<Vertex>& g);

    friend std::pair<in_edge_iterator, in_edge_iterator>
    in_edges<>(Vertex v, const adj_list<Vertex>& g);

    friend std::pair<adjacency_iterator, adjacency_iterator>
    adjacent_vertices<>(Vertex v, const adj_list<Vertex>& g);

    friend size_t num_vertices<>(const adj_list<Vertex>& g);

    friend size_t num_edges<>(const adj_list<Vertex>& g);

    friend Vertex add_vertex<>(adj_list<Vertex>& g);

    friend void clear_vertex<>(Vertex v, adj_list<Vertex>& g);

    friend void remove_vertex<>(Vertex v, adj_list<Vertex>& g);

    friend void remove_vertex_fast<>(Vertex v, adj_list<Vertex>& g);

    friend std::pair<edge_descriptor, bool>
    add_edge<>(Vertex s, Vertex t, adj_list<Vertex>& g);

    friend void remove_edge<>(Vertex s, Vertex t, adj_list<Vertex>& g);

    friend void remove_edge<>(const edge_descriptor& e, adj_list<Vertex>& g);
};

//========================================================================
// Graph traits and BGL scaffolding
//========================================================================

struct adj_list_traversal_tag
    : public vertex_list_graph_tag,
      public edge_list_graph_tag,
      public adjacency_graph_tag,
      public bidirectional_graph_tag,
      public adjacency_matrix_tag {};

template <class Vertex>
struct graph_traits<adj_list<Vertex> >
{
    typedef Vertex vertex_descriptor;
    typedef typename adj_list<Vertex>::edge_descriptor edge_descriptor;
    typedef typename adj_list<Vertex>::edge_iterator edge_iterator;
    typedef typename adj_list<Vertex>::adjacency_iterator adjacency_iterator;

    typedef typename adj_list<Vertex>::out_edge_iterator out_edge_iterator;
    typedef typename adj_list<Vertex>::in_edge_iterator in_edge_iterator;

    typedef typename adj_list<Vertex>::vertex_iterator vertex_iterator;

    typedef bidirectional_tag directed_category;
    typedef allow_parallel_edge_tag edge_parallel_category;
    typedef adj_list_traversal_tag traversal_category;

    typedef Vertex vertices_size_type;
    typedef Vertex edges_size_type;
    typedef size_t degree_size_type;

    static Vertex null_vertex() { return adj_list<Vertex>::null_vertex(); }
private:
    BOOST_STATIC_ASSERT((is_convertible<typename std::iterator_traits<out_edge_iterator>::iterator_category,
                                        std::random_access_iterator_tag>::value));
    BOOST_STATIC_ASSERT((is_convertible<typename std::iterator_traits<in_edge_iterator>::iterator_category,
                                        std::random_access_iterator_tag>::value));
    BOOST_STATIC_ASSERT((is_convertible<typename std::iterator_traits<adjacency_iterator>::iterator_category,
                                        std::random_access_iterator_tag>::value));
};

template <class Vertex>
struct graph_traits<const adj_list<Vertex> >
    : public graph_traits<adj_list<Vertex> >
{
};


template <class Vertex>
struct edge_property_type<adj_list<Vertex> >
{
    typedef void type;
};

template <class Vertex>
struct vertex_property_type<adj_list<Vertex> >
{
    typedef void type;
};

template <class Vertex>
struct graph_property_type<adj_list<Vertex> >
{
    typedef void type;
};

//========================================================================
// Graph access and manipulation functions
//========================================================================

template <class Vertex>
inline __attribute__((always_inline))
std::pair<typename adj_list<Vertex>::vertex_iterator,
          typename adj_list<Vertex>::vertex_iterator>
vertices(const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::vertex_iterator vi_t;
    return std::make_pair(vi_t(0), vi_t(g._out_edges.size()));
}


template <class Vertex>
inline __attribute__((always_inline))
std::pair<typename adj_list<Vertex>::edge_iterator,
          typename adj_list<Vertex>::edge_iterator>
edges(const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::edge_list_t::const_iterator ei_t;
    typedef typename adj_list<Vertex>::vertex_list_t::const_iterator vi_t;
    ei_t ei_begin = g._out_edges.empty() ? ei_t() : g._out_edges[0].begin();
    vi_t last_vi = g._out_edges.end();
    if (!g._out_edges.empty())
        --last_vi;
    ei_t ei_end = g._out_edges.empty() ? ei_t() : last_vi->end();
    typename adj_list<Vertex>::edge_iterator ebegin(g._out_edges.begin(),
                                                    g._out_edges.end(),
                                                    g._out_edges.begin(),
                                                    ei_begin);
    typename adj_list<Vertex>::edge_iterator eend(g._out_edges.begin(),
                                                  g._out_edges.end(),
                                                  last_vi,
                                                  ei_end);
    return std::make_pair(ebegin, eend);
}

template <class Vertex>
inline __attribute__((always_inline))
Vertex vertex(size_t i, const adj_list<Vertex>&)
{
    return i;
}

template <class Vertex>
inline __attribute__((always_inline))
std::pair<typename adj_list<Vertex>::edge_descriptor, bool>
edge(Vertex s, Vertex t, const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::edge_descriptor edge_descriptor;
    const auto& oes = g._out_edges[s];
    for (size_t i = 0; i < oes.size(); ++i)
        if (oes[i].first == t)
            return std::make_pair(edge_descriptor(s, t, oes[i].second,
                                                  false),
                                  true);
    Vertex v = graph_traits<adj_list<Vertex> >::null_vertex();
    return std::make_pair(edge_descriptor(v, v, v, false), false);
}

template <class Vertex>
inline __attribute__((always_inline))
size_t out_degree(Vertex v, const adj_list<Vertex>& g)
{
    return g._out_edges[v].size();
}

template <class Vertex>
inline __attribute__((always_inline))
size_t in_degree(Vertex v, const adj_list<Vertex>& g)
{
    return g._in_edges[v].size();
}

template <class Vertex>
inline __attribute__((always_inline))
size_t degree(Vertex v, const adj_list<Vertex>& g)
{
    return in_degree(v, g) + out_degree(v, g);
}

template <class Vertex>
inline __attribute__((always_inline))
std::pair<typename adj_list<Vertex>::out_edge_iterator,
          typename adj_list<Vertex>::out_edge_iterator>
out_edges(Vertex v, const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::out_edge_iterator ei_t;
    typedef typename adj_list<Vertex>::make_out_edge mk_edge;
    return std::make_pair(ei_t(g._out_edges[v].begin(), mk_edge(v)),
                          ei_t(g._out_edges[v].end(), mk_edge(v)));
}

template <class Vertex>
inline __attribute__((always_inline))
std::pair<typename adj_list<Vertex>::in_edge_iterator,
          typename adj_list<Vertex>::in_edge_iterator>
in_edges(Vertex v, const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::in_edge_iterator ei_t;
    typedef typename adj_list<Vertex>::make_in_edge mk_edge;
    return std::make_pair(ei_t(g._in_edges[v].begin(), mk_edge(v)),
                          ei_t(g._in_edges[v].end(), mk_edge(v)));
}

template <class Vertex>
inline __attribute__((always_inline))
std::pair<typename adj_list<Vertex>::adjacency_iterator,
          typename adj_list<Vertex>::adjacency_iterator>
adjacent_vertices(Vertex v, const adj_list<Vertex>& g)
{
    typedef typename adj_list<Vertex>::adjacency_iterator ai_t;
    return std::make_pair(ai_t(g._out_edges[v].begin()),
                          ai_t(g._out_edges[v].end()));
}

template <class Vertex>
inline __attribute__((always_inline))
size_t num_vertices(const adj_list<Vertex>& g)
{
    return g._out_edges.size();
}

template <class Vertex>
inline __attribute__((always_inline))
size_t num_edges(const adj_list<Vertex>& g)
{
    return g._n_edges;
}

template <class Vertex>
inline __attribute__((always_inline))
Vertex add_vertex(adj_list<Vertex>& g)
{
    size_t n = g._out_edges.size();
    g._out_edges.resize(n + 1);
    g._in_edges.resize(n + 1);
    return n;
}

template <class Vertex>
inline void clear_vertex(Vertex v, adj_list<Vertex>& g)
{
    if (!g._keep_epos)
    {
        auto& oes = g._out_edges[v];
        for (size_t i = 0; i < oes.size(); ++i)
        {
            Vertex t = oes[i].first;
            auto& ies = g._in_edges[t];
            for (size_t j = 0; j < ies.size(); ++j)
            {
                if (ies[j].first == v)
                {
                    g._free_indexes.push_back(ies[j].second);
                    ies.erase(ies.begin() + j);
                }
            }
        }
        g._n_edges -= oes.size();
        oes.clear();

        auto& ies = g._in_edges[v];
        for (size_t i = 0; i < ies.size(); ++i)
        {
            Vertex s = ies[i].first;
            auto& oes = g._out_edges[s];
            for (size_t j = 0; j < oes.size(); ++j)
            {
                if (oes[j].first == v)
                {
                    g._free_indexes.push_back(oes[j].second);
                    oes.erase(oes.begin() + j);
                }
            }
        }
        g._n_edges -= ies.size();
        ies.clear();
    }
    else
    {
        typename adj_list<Vertex>::edge_list_t& oes = g._out_edges[v];
        for (size_t i = 0; i < oes.size(); ++i)
        {
            Vertex t = oes[i].first;
            size_t idx = oes[i].second;
            auto& ies = g._in_edges[t];
            const auto& pos = g._epos[idx];

            g._epos[ies.back().second].second = pos.second;
            ies[pos.second] = ies.back();
            ies.pop_back();
            g._free_indexes.push_back(idx);
        }
        g._n_edges -= oes.size();
        oes.clear();

        typename adj_list<Vertex>::edge_list_t& ies = g._in_edges[v];
        for (size_t i = 0; i < ies.size(); ++i)
        {
            Vertex s = ies[i].first;
            size_t idx = ies[i].second;
            auto& oes = g._out_edges[s];
            const auto& pos = g._epos[idx];

            g._epos[oes.back().second].first = pos.first;
            oes[pos.first] = oes.back();
            oes.pop_back();
            g._free_indexes.push_back(idx);
        }
        g._n_edges -= ies.size();
        ies.clear();
    }
}

// O(V + E)
template <class Vertex>
inline void remove_vertex(Vertex v, adj_list<Vertex>& g)
{
    clear_vertex(v, g);
    g._out_edges.erase(g._out_edges.begin() + v);
    g._in_edges.erase(g._in_edges.begin() + v);

    int i, N = g._out_edges.size();
    #pragma omp parallel for default(shared) private(i) \
        schedule(runtime) if (N > 100)
    for (i = 0; i < N; ++i)
    {
        auto& oes = g._out_edges[i];
        for (size_t j = 0; j < oes.size(); ++j)
        {
            auto& oe = oes[j];
            if (oe.first > v)
                oe.first--;
        }

        auto& ies = g._in_edges[i];
        for (size_t j = 0; j < ies.size(); ++j)
        {
            auto& ie = ies[j];
            if (ie.first > v)
                ie.first--;
        }
    }
}

// O(k + k_last)
template <class Vertex>
inline void remove_vertex_fast(Vertex v, adj_list<Vertex>& g)
{
    clear_vertex(v, g);
    Vertex back = g._out_edges.size() - 1;

    if (v < back)
    {
        g._out_edges[v].swap(g._out_edges[back]);
        g._in_edges[v].swap(g._in_edges[back]);

        for (size_t i = 0; i < g._out_edges[v].size(); ++i)
        {
            auto& eu = g._out_edges[v][i];
            Vertex u = eu.first;
            if (u == back)
            {
                eu.first = v;
            }
            else
            {
                auto& ies = g._in_edges[u];
                for (size_t j = 0; j < ies.size(); ++j)
                {
                    auto& e = ies[j];
                    if (e.first == back)
                        e.first = v;
                }
            }
        }

        for (size_t i = 0; i < g._in_edges[v].size(); ++i)
        {
            auto& eu = g._in_edges[v][i];
            Vertex u = eu.first;
            if (u == back)
            {
                eu.first = v;
            }
            else
            {
                auto& oes = g._out_edges[u];
                for (size_t j = 0; j < oes.size(); ++j)
                {
                    auto& e = oes[j];
                    if (e.first == back)
                        e.first = v;
                }
            }
        }
    }

    g._out_edges.pop_back();
    g._in_edges.pop_back();
}

template <class Vertex>
inline typename std::pair<typename adj_list<Vertex>::edge_descriptor, bool>
add_edge(Vertex s, Vertex t, adj_list<Vertex>& g)
{
    Vertex idx;
    if (g._free_indexes.empty())
    {
        idx = g._last_idx++;
    }
    else
    {
        idx = g._free_indexes.front();
        g._free_indexes.pop_front();
    }

    g._out_edges[s].push_back(std::make_pair(t, idx));
    g._in_edges[t].push_back(std::make_pair(s, idx));
    g._n_edges++;

    if (g._keep_epos)
    {
        if (idx >= g._epos.size())
            g._epos.resize(idx + 1);
        g._epos[idx].first = g._out_edges[s].size() - 1;
        g._epos[idx].second = g._in_edges[t].size() - 1;
    }

    typedef typename adj_list<Vertex>::edge_descriptor edge_descriptor;
    return std::make_pair(edge_descriptor(s, t, idx, false), true);
}

template <class Vertex>
inline void remove_edge(Vertex s, Vertex t,
                        adj_list<Vertex>& g)
{
    if (!g._keep_epos)
    {
        auto& oes = g._out_edges[s];
        for (size_t i = 0; i < oes.size(); ++i)
        {
            if (t == oes[i].first)
            {
                g._free_indexes.push_back(oes[i].second);
                oes.erase(oes.begin() + i);
                g._n_edges--;
            }
        }

        auto& ies = g._in_edges[t];
        for (size_t i = 0; i < ies.size(); ++i)
        {
            if (s == ies[i].first)
                ies.erase(ies.begin() + i);
        }
    }
    else
    {
        remove_edge(edge(s, t, g).first, g);
    }
}

template <class Vertex>
inline void remove_edge(const typename adj_list<Vertex>::edge_descriptor& e,
                        adj_list<Vertex>& g)
{
    auto& s = e.s;
    auto& t = e.t;
    auto& idx = e.idx;
    auto& oes = g._out_edges[s];
    auto& ies = g._in_edges[t];

    bool found = false;
    if (!g._keep_epos) // O(k_s + k_t)
    {
        for (size_t i = 0; i < oes.size(); ++i)
        {
            if (t == oes[i].first && idx == oes[i].second)
            {
                oes.erase(oes.begin() + i);
                found = true;
                break;
            }
        }

        for (size_t i = 0; i < ies.size(); ++i)
        {
            if (s == ies[i].first && idx == ies[i].second)
            {
                ies.erase(ies.begin() + i);
                found = true;
                break;
            }
        }
    }
    else // O(1)
    {
        if (idx < g._epos.size())
        {
            const auto& pos = g._epos[idx];

            g._epos[oes.back().second].first = pos.first;
            oes[pos.first] = oes.back();
            oes.pop_back();

            g._epos[ies.back().second].second = pos.second;
            ies[pos.second] = ies.back();
            ies.pop_back();

            found = true;
        }
    }

    if (found)
    {
        g._free_indexes.push_back(idx);
        g._n_edges--;
    }
}


template <class Vertex>
inline __attribute__((always_inline))
Vertex source(const typename adj_list<Vertex>::edge_descriptor& e,
              const adj_list<Vertex>&)
{
    return e.s;
}

template <class Vertex>
inline __attribute__((always_inline))
Vertex target(const typename adj_list<Vertex>::edge_descriptor& e,
              const adj_list<Vertex>&)
{
    return e.t;
}

//========================================================================
// Vertex and edge index property maps
//========================================================================

template <class Vertex>
struct property_map<adj_list<Vertex>, vertex_index_t>
{
    typedef identity_property_map type;
    typedef type const_type;
};

template <class Vertex>
struct property_map<const adj_list<Vertex>, vertex_index_t>
{
    typedef identity_property_map type;
    typedef type const_type;
};

template <class Vertex>
inline identity_property_map
get(vertex_index_t, adj_list<Vertex>&)
{
    return identity_property_map();
}

template <class Vertex>
inline identity_property_map
get(vertex_index_t, const adj_list<Vertex>&)
{
    return identity_property_map();
}

template<class Vertex>
class adj_edge_index_property_map:
    public put_get_helper<Vertex, adj_edge_index_property_map<Vertex> >
{
public:
    typedef typename adj_list<Vertex>::edge_descriptor key_type;
    typedef Vertex reference;
    typedef Vertex value_type;
    typedef boost::readable_property_map_tag category;

    reference operator[](const key_type& k) const {return k.idx;}
};

template <class Vertex>
struct property_map<adj_list<Vertex>, edge_index_t>
{
    typedef adj_edge_index_property_map<Vertex> type;
    typedef type const_type;

};

template <class Vertex>
inline adj_edge_index_property_map<Vertex>
get(edge_index_t, const adj_list<Vertex>&)
{
    return adj_edge_index_property_map<Vertex>();
}

} // namespace boost

#endif //GRAPH_ADJACENCY_HH