// Copyright 2004, 2005 The Trustees of Indiana University.

// 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)

//  Authors: Jeremiah Willcock

//           Douglas Gregor

//           Andrew Lumsdaine

#ifndef BOOST_GRAPH_ERDOS_RENYI_GENERATOR_HPP

#define BOOST_GRAPH_ERDOS_RENYI_GENERATOR_HPP

#include <cassert>

#include <iterator>

#include <utility>

#include <boost/shared_ptr.hpp>

#include <boost/random/uniform_int.hpp>

#include <boost/graph/graph_traits.hpp>

#include <boost/random/geometric_distribution.hpp>

#include <boost/type_traits/is_base_and_derived.hpp>

#include <boost/type_traits/is_same.hpp>

#include <cmath>

namespace boost {

  template<typename RandomGenerator, typename Graph>

  class erdos_renyi_iterator

  {

    typedef typename graph_traits<Graph>::directed_category directed_category;

    typedef typename graph_traits<Graph>::vertices_size_type vertices_size_type;

    typedef typename graph_traits<Graph>::edges_size_type edges_size_type;

    BOOST_STATIC_CONSTANT

      (bool,

       is_undirected = (is_base_and_derived<undirected_tag,

                                            directed_category>::value

                        || is_same<undirected_tag, directed_category>::value));

  public:

    typedef std::input_iterator_tag iterator_category;

    typedef std::pair<vertices_size_type, vertices_size_type> value_type;

    typedef const value_type& reference;

    typedef const value_type* pointer;

    typedef void difference_type;

    erdos_renyi_iterator() : gen(), n(0), edges(0), allow_self_loops(false) {}

    erdos_renyi_iterator(RandomGenerator& gen, vertices_size_type n, 

                         double fraction = 0.0, bool allow_self_loops = false)

      : gen(&gen), n(n), edges(edges_size_type(fraction * n * n)),

        allow_self_loops(allow_self_loops)

    { 

      if (is_undirected) edges = edges / 2;

      next(); 

    }

    erdos_renyi_iterator(RandomGenerator& gen, vertices_size_type n, 

                         edges_size_type m, bool allow_self_loops = false)

      : gen(&gen), n(n), edges(m),

        allow_self_loops(allow_self_loops)

    { 

      next(); 

    }

    reference operator*() const { return current; }

    pointer operator->() const { return &current; }

    erdos_renyi_iterator& operator++()

    { 

      --edges;

      next();

      return *this;

    }

    erdos_renyi_iterator operator++(int)

    {

      erdos_renyi_iterator temp(*this);

      ++(*this);

      return temp;

    }

    bool operator==(const erdos_renyi_iterator& other) const

    { return edges == other.edges; }

    bool operator!=(const erdos_renyi_iterator& other) const

    { return !(*this == other); }

  private:

    void next()

    {

      uniform_int<vertices_size_type> rand_vertex(0, n-1);

      current.first = rand_vertex(*gen);

      do {

        current.second = rand_vertex(*gen);

      } while (current.first == current.second && !allow_self_loops);

    }

    RandomGenerator* gen;

    vertices_size_type n;

    edges_size_type edges;

    bool allow_self_loops;

    value_type current;

  };

  template<typename RandomGenerator, typename Graph>

  class sorted_erdos_renyi_iterator

  {

    typedef typename graph_traits<Graph>::directed_category directed_category;

    typedef typename graph_traits<Graph>::vertices_size_type vertices_size_type;

    typedef typename graph_traits<Graph>::edges_size_type edges_size_type;

    BOOST_STATIC_CONSTANT

      (bool,

       is_undirected = (is_base_and_derived<undirected_tag,

                                            directed_category>::value

                        || is_same<undirected_tag, directed_category>::value));

  public:

    typedef std::input_iterator_tag iterator_category;

    typedef std::pair<vertices_size_type, vertices_size_type> value_type;

    typedef const value_type& reference;

    typedef const value_type* pointer;

    typedef void difference_type;

    sorted_erdos_renyi_iterator()

      : gen(), rand_vertex(0.5), n(0), allow_self_loops(false),

    src((std::numeric_limits<vertices_size_type>::max)()), tgt(0), prob(0) {}

    sorted_erdos_renyi_iterator(RandomGenerator& gen, vertices_size_type n, 

                    double prob = 0.0, 

                                bool allow_self_loops = false)

      : gen(),

        // The "1.0 - prob" in the next line is to work around a Boost.Random

        // (and TR1) bug in the specification of geometric_distribution.  It

        // should be replaced by "prob" when the issue is fixed.

        rand_vertex(1.0 - prob),

    n(n), allow_self_loops(allow_self_loops), src(0), tgt(0), prob(prob)

    { 

      this->gen.reset(new uniform_01<RandomGenerator>(gen));

      if (prob == 0.0) {src = (std::numeric_limits<vertices_size_type>::max)(); return;}

      next(); 

    }

    reference operator*() const { return current; }

    pointer operator->() const { return &current; }

    sorted_erdos_renyi_iterator& operator++()

    { 

      next();

      return *this;

    }

    sorted_erdos_renyi_iterator operator++(int)

    {

      sorted_erdos_renyi_iterator temp(*this);

      ++(*this);

      return temp;

    }

    bool operator==(const sorted_erdos_renyi_iterator& other) const

    { return src == other.src && tgt == other.tgt; }

    bool operator!=(const sorted_erdos_renyi_iterator& other) const

    { return !(*this == other); }

  private:

    void next()

    {

      using std::sqrt;

      using std::floor;

      // In order to get the edges from the generator in sorted order, one

      // effective (but slow) procedure would be to use a

      // bernoulli_distribution for each legal (src, tgt) pair.  Because of the

      // O(n^2) cost of that, a geometric distribution is used.  The geometric

      // distribution tells how many times the bernoulli_distribution would

      // need to be run until it returns true.  Thus, this distribution can be

      // used to step through the edges which are actually present.  Everything

      // beyond "tgt += increment" is done to effectively convert linear

      // indexing (the partial sums of the geometric distribution output) into

      // graph edges.

      assert (src != (std::numeric_limits<vertices_size_type>::max)());

      vertices_size_type increment = rand_vertex(*gen);

      tgt += increment;

      if (is_undirected) {

    // Update src and tgt based on position of tgt

    // Basically, we want the greatest src_increment such that (in \bbQ):

    // src_increment * (src + allow_self_loops + src_increment - 1/2) <= tgt

    // The result of the LHS of this, evaluated with the computed

    // src_increment, is then subtracted from tgt

    double src_minus_half = (src + allow_self_loops) - 0.5;

    double disc = src_minus_half * src_minus_half + 2 * tgt;

    double src_increment_fp = floor(sqrt(disc) - src_minus_half);

    vertices_size_type src_increment = vertices_size_type(src_increment_fp);

    if (src + src_increment >= n) {

      src = n;

    } else {

      tgt -= (src + allow_self_loops) * src_increment + 

         src_increment * (src_increment - 1) / 2;

      src += src_increment;

    }

      } else {

    // Number of out edge positions possible from each vertex in this graph

    vertices_size_type possible_out_edges = n - (allow_self_loops ? 0 : 1);

    src += (std::min)(n - src, tgt / possible_out_edges);

    tgt %= possible_out_edges;

      }

      // Set end of graph code so (src, tgt) will be the same as for the end

      // sorted_erdos_renyi_iterator

      if (src >= n) {src = (std::numeric_limits<vertices_size_type>::max)(); tgt = 0;}

      // Copy (src, tgt) into current

      current.first = src;

      current.second = tgt;

      // Adjust for (src, src) edge being forbidden

      if (!allow_self_loops && tgt >= src) ++current.second;

    }

    shared_ptr<uniform_01<RandomGenerator> > gen;

    geometric_distribution<vertices_size_type> rand_vertex;

    vertices_size_type n;

    bool allow_self_loops;

    vertices_size_type src, tgt;

    value_type current;

    double prob;

  };

} // end namespace boost

#endif // BOOST_GRAPH_ERDOS_RENYI_GENERATOR_HPP