author | hgs |
Thu, 14 Oct 2010 14:15:50 +0530 | |
changeset 72 | 403e7f6ed6c5 |
parent 0 | e4d67989cc36 |
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// Copyright 2004, 2005 The Trustees of Indiana University. |
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// Distributed under the Boost Software License, Version 1.0. |
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// (See accompanying file LICENSE_1_0.txt or copy at |
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// http://www.boost.org/LICENSE_1_0.txt) |
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// Authors: Jeremiah Willcock |
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// Douglas Gregor |
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// Andrew Lumsdaine |
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#ifndef BOOST_GRAPH_ERDOS_RENYI_GENERATOR_HPP |
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#define BOOST_GRAPH_ERDOS_RENYI_GENERATOR_HPP |
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#include <cassert> |
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#include <iterator> |
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#include <utility> |
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#include <boost/shared_ptr.hpp> |
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#include <boost/random/uniform_int.hpp> |
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#include <boost/graph/graph_traits.hpp> |
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#include <boost/random/geometric_distribution.hpp> |
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#include <boost/type_traits/is_base_and_derived.hpp> |
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#include <boost/type_traits/is_same.hpp> |
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#include <cmath> |
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namespace boost { |
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template<typename RandomGenerator, typename Graph> |
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class erdos_renyi_iterator |
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{ |
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typedef typename graph_traits<Graph>::directed_category directed_category; |
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typedef typename graph_traits<Graph>::vertices_size_type vertices_size_type; |
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typedef typename graph_traits<Graph>::edges_size_type edges_size_type; |
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BOOST_STATIC_CONSTANT |
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(bool, |
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is_undirected = (is_base_and_derived<undirected_tag, |
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directed_category>::value |
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|| is_same<undirected_tag, directed_category>::value)); |
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public: |
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typedef std::input_iterator_tag iterator_category; |
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typedef std::pair<vertices_size_type, vertices_size_type> value_type; |
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typedef const value_type& reference; |
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typedef const value_type* pointer; |
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typedef void difference_type; |
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erdos_renyi_iterator() : gen(), n(0), edges(0), allow_self_loops(false) {} |
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erdos_renyi_iterator(RandomGenerator& gen, vertices_size_type n, |
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double fraction = 0.0, bool allow_self_loops = false) |
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: gen(&gen), n(n), edges(edges_size_type(fraction * n * n)), |
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allow_self_loops(allow_self_loops) |
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{ |
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if (is_undirected) edges = edges / 2; |
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next(); |
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} |
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erdos_renyi_iterator(RandomGenerator& gen, vertices_size_type n, |
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edges_size_type m, bool allow_self_loops = false) |
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: gen(&gen), n(n), edges(m), |
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allow_self_loops(allow_self_loops) |
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{ |
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next(); |
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} |
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reference operator*() const { return current; } |
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pointer operator->() const { return ¤t; } |
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erdos_renyi_iterator& operator++() |
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{ |
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--edges; |
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next(); |
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return *this; |
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} |
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erdos_renyi_iterator operator++(int) |
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{ |
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erdos_renyi_iterator temp(*this); |
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++(*this); |
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return temp; |
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} |
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bool operator==(const erdos_renyi_iterator& other) const |
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{ return edges == other.edges; } |
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bool operator!=(const erdos_renyi_iterator& other) const |
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{ return !(*this == other); } |
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private: |
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void next() |
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{ |
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uniform_int<vertices_size_type> rand_vertex(0, n-1); |
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current.first = rand_vertex(*gen); |
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do { |
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current.second = rand_vertex(*gen); |
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} while (current.first == current.second && !allow_self_loops); |
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} |
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RandomGenerator* gen; |
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vertices_size_type n; |
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edges_size_type edges; |
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bool allow_self_loops; |
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value_type current; |
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}; |
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template<typename RandomGenerator, typename Graph> |
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class sorted_erdos_renyi_iterator |
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106 |
{ |
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typedef typename graph_traits<Graph>::directed_category directed_category; |
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typedef typename graph_traits<Graph>::vertices_size_type vertices_size_type; |
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typedef typename graph_traits<Graph>::edges_size_type edges_size_type; |
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110 |
|
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BOOST_STATIC_CONSTANT |
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(bool, |
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is_undirected = (is_base_and_derived<undirected_tag, |
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directed_category>::value |
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|| is_same<undirected_tag, directed_category>::value)); |
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116 |
|
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public: |
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typedef std::input_iterator_tag iterator_category; |
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typedef std::pair<vertices_size_type, vertices_size_type> value_type; |
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typedef const value_type& reference; |
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typedef const value_type* pointer; |
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typedef void difference_type; |
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123 |
|
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sorted_erdos_renyi_iterator() |
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: gen(), rand_vertex(0.5), n(0), allow_self_loops(false), |
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src((std::numeric_limits<vertices_size_type>::max)()), tgt(0), prob(0) {} |
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sorted_erdos_renyi_iterator(RandomGenerator& gen, vertices_size_type n, |
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double prob = 0.0, |
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bool allow_self_loops = false) |
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: gen(), |
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// The "1.0 - prob" in the next line is to work around a Boost.Random |
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// (and TR1) bug in the specification of geometric_distribution. It |
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// should be replaced by "prob" when the issue is fixed. |
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rand_vertex(1.0 - prob), |
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n(n), allow_self_loops(allow_self_loops), src(0), tgt(0), prob(prob) |
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136 |
{ |
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this->gen.reset(new uniform_01<RandomGenerator>(gen)); |
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138 |
|
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if (prob == 0.0) {src = (std::numeric_limits<vertices_size_type>::max)(); return;} |
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next(); |
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} |
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142 |
|
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reference operator*() const { return current; } |
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pointer operator->() const { return ¤t; } |
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145 |
|
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sorted_erdos_renyi_iterator& operator++() |
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{ |
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next(); |
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return *this; |
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} |
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151 |
|
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sorted_erdos_renyi_iterator operator++(int) |
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153 |
{ |
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sorted_erdos_renyi_iterator temp(*this); |
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++(*this); |
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return temp; |
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} |
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158 |
|
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bool operator==(const sorted_erdos_renyi_iterator& other) const |
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{ return src == other.src && tgt == other.tgt; } |
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161 |
|
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bool operator!=(const sorted_erdos_renyi_iterator& other) const |
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{ return !(*this == other); } |
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164 |
|
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private: |
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void next() |
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{ |
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using std::sqrt; |
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using std::floor; |
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170 |
|
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// In order to get the edges from the generator in sorted order, one |
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// effective (but slow) procedure would be to use a |
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// bernoulli_distribution for each legal (src, tgt) pair. Because of the |
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// O(n^2) cost of that, a geometric distribution is used. The geometric |
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// distribution tells how many times the bernoulli_distribution would |
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// need to be run until it returns true. Thus, this distribution can be |
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// used to step through the edges which are actually present. Everything |
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// beyond "tgt += increment" is done to effectively convert linear |
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// indexing (the partial sums of the geometric distribution output) into |
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// graph edges. |
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assert (src != (std::numeric_limits<vertices_size_type>::max)()); |
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vertices_size_type increment = rand_vertex(*gen); |
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tgt += increment; |
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if (is_undirected) { |
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// Update src and tgt based on position of tgt |
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// Basically, we want the greatest src_increment such that (in \bbQ): |
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// src_increment * (src + allow_self_loops + src_increment - 1/2) <= tgt |
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// The result of the LHS of this, evaluated with the computed |
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// src_increment, is then subtracted from tgt |
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double src_minus_half = (src + allow_self_loops) - 0.5; |
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double disc = src_minus_half * src_minus_half + 2 * tgt; |
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double src_increment_fp = floor(sqrt(disc) - src_minus_half); |
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vertices_size_type src_increment = vertices_size_type(src_increment_fp); |
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if (src + src_increment >= n) { |
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src = n; |
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} else { |
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tgt -= (src + allow_self_loops) * src_increment + |
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src_increment * (src_increment - 1) / 2; |
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src += src_increment; |
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} |
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} else { |
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// Number of out edge positions possible from each vertex in this graph |
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vertices_size_type possible_out_edges = n - (allow_self_loops ? 0 : 1); |
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src += (std::min)(n - src, tgt / possible_out_edges); |
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tgt %= possible_out_edges; |
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} |
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// Set end of graph code so (src, tgt) will be the same as for the end |
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// sorted_erdos_renyi_iterator |
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if (src >= n) {src = (std::numeric_limits<vertices_size_type>::max)(); tgt = 0;} |
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// Copy (src, tgt) into current |
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current.first = src; |
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current.second = tgt; |
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// Adjust for (src, src) edge being forbidden |
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if (!allow_self_loops && tgt >= src) ++current.second; |
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} |
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|
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shared_ptr<uniform_01<RandomGenerator> > gen; |
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geometric_distribution<vertices_size_type> rand_vertex; |
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vertices_size_type n; |
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bool allow_self_loops; |
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vertices_size_type src, tgt; |
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value_type current; |
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double prob; |
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}; |
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|
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} // end namespace boost |
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|
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#endif // BOOST_GRAPH_ERDOS_RENYI_GENERATOR_HPP |