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<a href="pricing_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2021 Google LLC</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div><div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div><div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div><div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> </div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#ifndef OR_TOOLS_GLOP_PRICING_H_</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#define OR_TOOLS_GLOP_PRICING_H_</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include "absl/random/bit_gen_ref.h"</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#include "absl/random/random.h"</span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include "<a class="code" href="lp__types_8h.html">ortools/lp_data/lp_types.h</a>"</span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include "<a class="code" href="bitset_8h.html">ortools/util/bitset.h</a>"</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include "<a class="code" href="stats_8h.html">ortools/util/stats.h</a>"</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> </div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="keyword">namespace </span>glop {</div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> </div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">// Maintains a set of elements in [0, n), each with an associated value and</span></div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// allows to query the element of maximum value efficiently.</span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">//</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">// This is optimized for use in the pricing step of the simplex algorithm.</span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">// Basically at each simplex iterations, you want to:</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">//</span></div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// 1/ Get the candidate with the maximum value. The number of candidates</span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// can be close to n, or really small. You also want some randomization if</span></div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// several elements have an equivalent (maximum) value.</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">//</span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// 2/ Update the set of candidate and their values, where the number of update</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// is usually a lot smaller than n. Note that in some corner cases, there are</span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// two "updates" phases, so a position can be updated twice.</span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">//</span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// The idea is to be faster than O(num_candidates) per GetMaximum(), most of the</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// time. All updates should be in O(1) with as little overhead as possible. The</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// algorithm here dynamically maintain the top-k (for k=32) with best effort and</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// use it instead of doing a O(num_candidates) scan when possible.</span></div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">//</span></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// Note that when O(num_updates) << n, this can have a huge effect. A basic O(1)</span></div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// per update, O(num_candidates) per maximum query was taking around 60% of the</span></div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// total time on graph40-80-1rand.pb.gz ! with the top-32 algo coded here, it is</span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// around 3%, and the number of "fast" GetMaximum() that hit the top-k heap on</span></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// the first 120s of that problem was 250757 / 255659. Note that n was 282624 in</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// this case, which is not even the biggest size we can tackle.</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">//</span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// Note(user): This could be moved to util/ as a general class if someone wants</span></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// to reuse it, it is however tunned for use in Glop pricing step and might</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// becomes even more specific in the future.</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div><div class="line"><a name="l00056"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html"> 56</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html">DynamicMaximum</a> {</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="comment">// To simplify the APIs, we take a random number generator at construction.</span></div><div class="line"><a name="l00059"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a2b42bfa1c96806cf7504a5e8890fd56f"> 59</a></span>  <span class="keyword">explicit</span> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a2b42bfa1c96806cf7504a5e8890fd56f">DynamicMaximum</a>(absl::BitGenRef random) : random_(random) {}</div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span> </div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="comment">// Prepares the class to hold up to n candidates with indices in [0, n).</span></div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="comment">// Initially no indices is a candidate.</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a783736d86811c9bc5a68dd8ff1890192">ClearAndResize</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> n);</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> </div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="comment">// Returns the index with the maximum value or Index(-1) if the set is empty</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="comment">// and there is no possible candidate. If there are more than one candidate</span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="comment">// with the same maximum value, this will return a random one (not always</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="comment">// uniformly if there is a large number of ties).</span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#ae9e909718fc3aa8d0c968ef9a35f495b">GetMaximum</a>();</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span> </div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">// Removes the given index from the set of candidates.</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a06262520df93f238136b5f3fa7dd41ab">Remove</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> position);</div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span> </div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="comment">// Adds an element to the set of candidate and sets its value. If the element</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="comment">// is already present, this updates its value. The value must be finite.</span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a0288e565c7950baedeafd9d866f27f79">AddOrUpdate</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> position, <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span> </div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="comment">// Optimized version of AddOrUpdate() for the dense case. If one knows that</span></div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">// there will be O(n) updates, it is possible to call StartDenseUpdates() and</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="comment">// then use DenseAddOrUpdate() instead of AddOrUpdate() which is slighlty</span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="comment">// faster.</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="comment">//</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">// Note that calling AddOrUpdate() will still works fine, but will cause an</span></div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="comment">// extra test per call.</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a18ec8750a372cc4b685f043056912566">StartDenseUpdates</a>();</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a342bfaf1266d12b6202742bb5262f5d1">DenseAddOrUpdate</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> position, <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> </div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="comment">// Returns the current size n that was used in the last ClearAndResize().</span></div><div class="line"><a name="l00089"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#aa71d36872f416feaa853788a7a7a7ef8"> 89</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#aa71d36872f416feaa853788a7a7a7ef8">Clear</a>() { <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a783736d86811c9bc5a68dd8ff1890192">ClearAndResize</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a>(0)); }</div><div class="line"><a name="l00090"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a647917658f096ec35e9a14eaf4e1a7e3"> 90</a></span>  <a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a647917658f096ec35e9a14eaf4e1a7e3">Size</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> values_.<a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">size</a>(); }</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span> </div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="comment">// Returns some stats about this class if they are enabled.</span></div><div class="line"><a name="l00093"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#af9bc435481ae9e6e60d66a65d5394a7f"> 93</a></span>  std::string <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#af9bc435481ae9e6e60d66a65d5394a7f">StatString</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> stats_.StatString(); }</div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span> </div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="comment">// Adds an elements to the set of top elements.</span></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordtype">void</span> UpdateTopK(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> position, <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span> </div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="comment">// Returns a random element from the set {best} U {equivalent_choices_}.</span></div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="comment">// If equivalent_choices_ is empty, this just returns best.</span></div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> RandomizeIfManyChoices(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> best);</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> </div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="comment">// For tie-breaking.</span></div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  absl::BitGenRef random_;</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  std::vector<Index> equivalent_choices_;</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span> </div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="comment">// Set of candidates and their value.</span></div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">// Note that if is_candidate_[index] is false, values_[index] can be anything.</span></div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <a class="code" href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">StrictITIVector<Index, Fractional></a> values_;</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <a class="code" href="classoperations__research_1_1_bitset64.html">Bitset64<Index></a> is_candidate_;</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span> </div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="comment">// We maintain the top-k current candidates for a fixed k. Note that not all</span></div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="comment">// entries in tops_ are necessary up to date since we don't remove elements.</span></div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="comment">// There can even be duplicate elements inside if Update() add an element</span></div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="comment">// already inside. This is fine, since tops_ will be recomputed as soon as we</span></div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="comment">// can't get the true maximum from there.</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="comment">//</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="comment">// The invariant is that:</span></div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="comment">// - All elements > threshold_ are in tops_.</span></div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">// - All elements not in tops have a value <= threshold_.</span></div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="comment">// - elements == threshold_ can be in or out.</span></div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="comment">//</span></div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="comment">// In particular, the threshold only increase until the heap becomes empty and</span></div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="comment">// is recomputed from scratch by GetMaximum().</span></div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keyword">struct </span>HeapElement {</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  HeapElement() {}</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  HeapElement(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> i, <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> v) : <a class="code" href="pack_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>(i), <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>(v) {}</div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span> </div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> <a class="code" href="pack_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>;</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>;</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span> </div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="comment">// We want a min-heap: tops_.top() actually represents the k-th value, not</span></div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="comment">// the max.</span></div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> operator<(<span class="keyword">const</span> HeapElement& other)<span class="keyword"> const </span>{</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">return</span> <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> > other.value;</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  }</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  };</div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> threshold_;</div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  std::vector<HeapElement> tops_;</div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span> </div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="comment">// Statistics about the class.</span></div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keyword">struct </span>QueryStats : <span class="keyword">public</span> StatsGroup {</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  QueryStats()</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  : <a class="code" href="classoperations__research_1_1_stats_group.html#ad3718c845372a46a063163204783b7ca">StatsGroup</a>(<span class="stringliteral">"PricingStats"</span>),</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  get_maximum(<span class="stringliteral">"get_maximum"</span>, this),</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  heap_size_on_hit(<span class="stringliteral">"heap_size_on_hit"</span>, this),</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  random_choices(<span class="stringliteral">"random_choices"</span>, this) {}</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  TimeDistribution get_maximum;</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  IntegerDistribution heap_size_on_hit;</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  IntegerDistribution random_choices;</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  };</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  QueryStats stats_;</div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span> };</div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span> </div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div><div class="line"><a name="l00156"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a783736d86811c9bc5a68dd8ff1890192"> 156</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a783736d86811c9bc5a68dd8ff1890192">DynamicMaximum<Index>::ClearAndResize</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> n) {</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  tops_.clear();</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  threshold_ = -<a class="code" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>;</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  values_.resize(n);</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  is_candidate_.ClearAndResize(n);</div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span> }</div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span> </div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div><div class="line"><a name="l00164"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a06262520df93f238136b5f3fa7dd41ab"> 164</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a06262520df93f238136b5f3fa7dd41ab">DynamicMaximum<Index>::Remove</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> position) {</div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  is_candidate_.Clear(position);</div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span> }</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span> </div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div><div class="line"><a name="l00169"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a18ec8750a372cc4b685f043056912566"> 169</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a18ec8750a372cc4b685f043056912566">DynamicMaximum<Index>::StartDenseUpdates</a>() {</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="comment">// This disable tops_ until the next GetMaximum().</span></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  tops_.clear();</div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  threshold_ = <a class="code" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>;</div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span> }</div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span> </div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div><div class="line"><a name="l00176"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a342bfaf1266d12b6202742bb5262f5d1"> 176</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a342bfaf1266d12b6202742bb5262f5d1">DynamicMaximum<Index>::DenseAddOrUpdate</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> position,</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>) {</div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#a95879916d90daeba91c40399ae5ddcc6">IsFinite</a>(<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>));</div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(tops_.empty());</div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  is_candidate_.Set(position);</div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  values_[position] = <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>;</div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span> }</div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span> </div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div><div class="line"><a name="l00185"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a0288e565c7950baedeafd9d866f27f79"> 185</a></span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a0288e565c7950baedeafd9d866f27f79">DynamicMaximum<Index>::AddOrUpdate</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> position,</div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>) {</div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#a95879916d90daeba91c40399ae5ddcc6">IsFinite</a>(<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>));</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  is_candidate_.Set(position);</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  values_[position] = <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>;</div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="keywordflow">if</span> (<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> >= threshold_) UpdateTopK(position, <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span> }</div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span> </div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="keyword">inline</span> <a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html">DynamicMaximum<Index>::RandomizeIfManyChoices</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> best) {</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keywordflow">if</span> (equivalent_choices_.empty()) <span class="keywordflow">return</span> best;</div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  equivalent_choices_.push_back(best);</div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  stats_.random_choices.Add(equivalent_choices_.size());</div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span> </div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordflow">return</span> equivalent_choices_[std::uniform_int_distribution<int>(</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  0, equivalent_choices_.size() - 1)(random_)];</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span> }</div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span> </div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div><div class="line"><a name="l00204"></a><span class="lineno"><a class="line" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#ae9e909718fc3aa8d0c968ef9a35f495b"> 204</a></span> <span class="keyword">inline</span> <a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#ae9e909718fc3aa8d0c968ef9a35f495b">DynamicMaximum<Index>::GetMaximum</a>() {</div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <a class="code" href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a>(&stats_);</div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> best_value = -<a class="code" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>;</div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> best_position(-1);</div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  equivalent_choices_.clear();</div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span> </div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="comment">// Optimized version if the maximum is in tops_ already.</span></div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="comment">//</span></div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="comment">// We do two things here:</span></div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="comment">// 1/ Filter tops_ to only contain valid entries. This is because we never</span></div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="comment">// remove element, so the value of one of the element in tops might have</span></div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="comment">// decreased now. Note that we leave threshold_ untouched, so it</span></div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="comment">// can actually be lower than the minimum of the element in tops.</span></div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="comment">// 2/ Get the maximum of the valid elements.</span></div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">if</span> (!tops_.empty()) {</div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keywordtype">int</span> new_size = 0;</div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> HeapElement e : tops_) {</div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="comment">// The two possible sources of "invalidity".</span></div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keywordflow">if</span> (!is_candidate_[e.index]) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordflow">if</span> (values_[e.index] != e.value) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span> </div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  tops_[new_size++] = e;</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="keywordflow">if</span> (e.value >= best_value) {</div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordflow">if</span> (e.value == best_value) {</div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  equivalent_choices_.push_back(e.index);</div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  }</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  equivalent_choices_.clear();</div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  best_value = e.value;</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  best_position = e.index;</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  }</div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  }</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  tops_.resize(new_size);</div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="keywordflow">if</span> (new_size != 0) {</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  stats_.heap_size_on_hit.Add(new_size);</div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keywordflow">return</span> RandomizeIfManyChoices(best_position);</div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  }</div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  }</div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span> </div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="comment">// We need to iterate over all the candidates.</span></div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  threshold_ = -<a class="code" href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">kInfinity</a>;</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(tops_.empty());</div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> position : is_candidate_) {</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> = values_[position];</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span> </div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="comment">// TODO(user): Add a mode when we do not maintain the TopK for small sizes</span></div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="comment">// (like n < 1000) ? The gain might not be worth the extra code though.</span></div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keywordflow">if</span> (<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> < threshold_) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  UpdateTopK(position, <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span> </div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordflow">if</span> (<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> >= best_value) {</div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <span class="keywordflow">if</span> (<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> == best_value) {</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  equivalent_choices_.push_back(position);</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  }</div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  equivalent_choices_.clear();</div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  best_value = <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>;</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  best_position = position;</div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  }</div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  }</div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span> </div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keywordflow">return</span> RandomizeIfManyChoices(best_position);</div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span> }</div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span> </div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1glop_1_1_dynamic_maximum.html">DynamicMaximum<Index>::UpdateTopK</a>(<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a> position,</div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>) {</div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <span class="comment">// Note that this should only be called when an update is required.</span></div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <a class="code" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>, threshold_);</div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span> </div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="comment">// We use a compile time size of the form 2^n - 1 to have a full binary heap.</span></div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="comment">//</span></div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="comment">// TODO(user): Adapt the size depending on the problem size? Note sure it is</span></div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="comment">// worth it. To experiment more.</span></div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  constexpr <span class="keywordtype">int</span> k = 31;</div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  static_assert(((k + 1) & k) == 0, <span class="stringliteral">"k + 1 should be a power of 2."</span>);</div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span> </div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="comment">// Simply grow the vector until we hit a size of k.</span></div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keywordflow">if</span> (tops_.size() < k) {</div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  tops_.emplace_back(position, <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="keywordflow">if</span> (tops_.size() == k) {</div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  std::make_heap(tops_.begin(), tops_.end());</div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  threshold_ = tops_[0].value;</div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  }</div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keywordflow">return</span>;</div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  }</div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span> </div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="comment">// If the value is equal, we randomly replace it. Having some randomness can</span></div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <span class="comment">// also be important to increase the chance of keeping the true maximum in the</span></div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="comment">// top k set.</span></div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="comment">//</span></div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="comment">// TODO(user): use proper probability by counting the number of ties seen and</span></div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="comment">// replacing a random minimum element to get an uniform distribution? Note</span></div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="comment">// that it will never be truly uniform since once the top k structure is</span></div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="comment">// constructed, we will reuse it as much as possible, so it will be biased</span></div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="comment">// towards elements already inside.</span></div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="keywordflow">if</span> (<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> == tops_[0].<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>) {</div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keywordflow">if</span> (absl::Bernoulli(random_, 0.5)) {</div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  tops_[0].index = position;</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  }</div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keywordflow">return</span>;</div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  }</div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span> </div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="comment">// The code below is basically a custom implementation of this. It is however</span></div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="comment">// only slighlty faster for such a small heap. So it might not be completely</span></div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="comment">// worth it.</span></div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="keywordflow">if</span> (<span class="comment">/*DISABLES CODE*/</span> (<span class="keyword">false</span>)) {</div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  std::pop_heap(tops_.begin(), tops_.end());</div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  tops_.back() = HeapElement(position, <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  std::push_heap(tops_.begin(), tops_.end());</div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  threshold_ = tops_[0].value;</div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keywordflow">return</span>;</div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  }</div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span> </div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="comment">// To not have to do std::pop_heap() and then std::push_heap(), we code our</span></div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <span class="comment">// own update. Note that we exploit the fact that k is of the form 2^n - 1 to</span></div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="comment">// save one test per update.</span></div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keywordtype">int</span> i = 0;</div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(tops_.size(), k);</div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  constexpr <span class="keywordtype">int</span> limit = k / 2;</div><div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <span class="keywordflow">for</span> (; i < limit;) {</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> left_child = 2 * i + 1;</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code" href="arc__flow__builder_8cc.html#a37a60bd8e1de6871a556b2822884edea">right_child</a> = left_child + 1;</div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> l_value = tops_[left_child].value;</div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">Fractional</a> r_value = tops_[<a class="code" href="arc__flow__builder_8cc.html#a37a60bd8e1de6871a556b2822884edea">right_child</a>].value;</div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="keywordflow">if</span> (l_value > r_value) {</div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <span class="keywordflow">if</span> (<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> <= r_value) <span class="keywordflow">break</span>;</div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  tops_[i] = tops_[<a class="code" href="arc__flow__builder_8cc.html#a37a60bd8e1de6871a556b2822884edea">right_child</a>];</div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  i = <a class="code" href="arc__flow__builder_8cc.html#a37a60bd8e1de6871a556b2822884edea">right_child</a>;</div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordflow">if</span> (<a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> <= l_value) <span class="keywordflow">break</span>;</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  tops_[i] = tops_[left_child];</div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  i = left_child;</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  }</div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  }</div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  tops_[i] = HeapElement(position, <a class="code" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  threshold_ = tops_[0].value;</div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <a class="code" href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a>(std::is_heap(tops_.begin(), tops_.end()));</div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span> }</div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span> </div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span> } <span class="comment">// namespace glop</span></div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span> } <span class="comment">// namespace operations_research</span></div><div class="line"><a name="l00346"></a><span class="lineno"> 346</span> </div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="preprocessor">#endif // OR_TOOLS_GLOP_PRICING_H_</span></div><div class="ttc" id="classoperations__research_1_1_stats_group_html_ad3718c845372a46a063163204783b7ca"><div class="ttname"><a href="classoperations__research_1_1_stats_group.html#ad3718c845372a46a063163204783b7ca">operations_research::StatsGroup::StatsGroup</a></div><div class="ttdeci">StatsGroup(const std::string &name)</div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00138">stats.h:138</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_dynamic_maximum_html_af9bc435481ae9e6e60d66a65d5394a7f"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#af9bc435481ae9e6e60d66a65d5394a7f">operations_research::glop::DynamicMaximum::StatString</a></div><div class="ttdeci">std::string StatString() const</div><div class="ttdef"><b>Definition:</b> <a href="pricing_8h_source.html#l00093">pricing.h:93</a></div></div>
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<div class="ttc" id="stats_8h_html_a9995704aaaf45fc21e08c847551a8d04"><div class="ttname"><a href="stats_8h.html#a9995704aaaf45fc21e08c847551a8d04">SCOPED_TIME_STAT</a></div><div class="ttdeci">#define SCOPED_TIME_STAT(stats)</div><div class="ttdef"><b>Definition:</b> <a href="stats_8h_source.html#l00438">stats.h:438</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a733947145e3e1631165b618b05c9ccb7"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a733947145e3e1631165b618b05c9ccb7">operations_research::glop::Fractional</a></div><div class="ttdeci">double Fractional</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00078">lp_types.h:78</a></div></div>
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<div class="ttc" id="arc__flow__builder_8cc_html_a37a60bd8e1de6871a556b2822884edea"><div class="ttname"><a href="arc__flow__builder_8cc.html#a37a60bd8e1de6871a556b2822884edea">right_child</a></div><div class="ttdeci">int right_child</div><div class="ttdef"><b>Definition:</b> <a href="arc__flow__builder_8cc_source.html#l00064">arc_flow_builder.cc:64</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_a95879916d90daeba91c40399ae5ddcc6"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#a95879916d90daeba91c40399ae5ddcc6">operations_research::glop::IsFinite</a></div><div class="ttdeci">bool IsFinite(Fractional value)</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00091">lp_types.h:91</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_bitset64_html"><div class="ttname"><a href="classoperations__research_1_1_bitset64.html">operations_research::Bitset64< Index ></a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_dynamic_maximum_html_ae9e909718fc3aa8d0c968ef9a35f495b"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#ae9e909718fc3aa8d0c968ef9a35f495b">operations_research::glop::DynamicMaximum::GetMaximum</a></div><div class="ttdeci">Index GetMaximum()</div><div class="ttdef"><b>Definition:</b> <a href="pricing_8h_source.html#l00204">pricing.h:204</a></div></div>
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<div class="ttc" id="stats_8h_html"><div class="ttname"><a href="stats_8h.html">stats.h</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_dynamic_maximum_html_a647917658f096ec35e9a14eaf4e1a7e3"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a647917658f096ec35e9a14eaf4e1a7e3">operations_research::glop::DynamicMaximum::Size</a></div><div class="ttdeci">Index Size() const</div><div class="ttdef"><b>Definition:</b> <a href="pricing_8h_source.html#l00090">pricing.h:90</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_dynamic_maximum_html_a18ec8750a372cc4b685f043056912566"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a18ec8750a372cc4b685f043056912566">operations_research::glop::DynamicMaximum::StartDenseUpdates</a></div><div class="ttdeci">void StartDenseUpdates()</div><div class="ttdef"><b>Definition:</b> <a href="pricing_8h_source.html#l00169">pricing.h:169</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_dynamic_maximum_html_a06262520df93f238136b5f3fa7dd41ab"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a06262520df93f238136b5f3fa7dd41ab">operations_research::glop::DynamicMaximum::Remove</a></div><div class="ttdeci">void Remove(Index position)</div><div class="ttdef"><b>Definition:</b> <a href="pricing_8h_source.html#l00164">pricing.h:164</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_dynamic_maximum_html_a0288e565c7950baedeafd9d866f27f79"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a0288e565c7950baedeafd9d866f27f79">operations_research::glop::DynamicMaximum::AddOrUpdate</a></div><div class="ttdeci">void AddOrUpdate(Index position, Fractional value)</div><div class="ttdef"><b>Definition:</b> <a href="pricing_8h_source.html#l00185">pricing.h:185</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_af9a790b7e8c5b0c6d55b336177378e78"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#af9a790b7e8c5b0c6d55b336177378e78">operations_research::glop::kInfinity</a></div><div class="ttdeci">const double kInfinity</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00084">lp_types.h:84</a></div></div>
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<div class="ttc" id="pack_8cc_html_a750b5d744c39a06bfb13e6eb010e35d0"><div class="ttname"><a href="pack_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a></div><div class="ttdeci">int index</div><div class="ttdef"><b>Definition:</b> <a href="pack_8cc_source.html#l00509">pack.cc:509</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_aae2dc65d9ea248d54bf39daa986dd295"><div class="ttname"><a href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a></div><div class="ttdeci">#define DCHECK_GE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00894">base/logging.h:894</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_strict_i_t_i_vector_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html">operations_research::glop::StrictITIVector< Index, Fractional ></a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_dynamic_maximum_html_a342bfaf1266d12b6202742bb5262f5d1"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a342bfaf1266d12b6202742bb5262f5d1">operations_research::glop::DynamicMaximum::DenseAddOrUpdate</a></div><div class="ttdeci">void DenseAddOrUpdate(Index position, Fractional value)</div><div class="ttdef"><b>Definition:</b> <a href="pricing_8h_source.html#l00176">pricing.h:176</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_ae17f8119c108cf3070bad3449c7e0006"><div class="ttname"><a href="base_2logging_8h.html#ae17f8119c108cf3070bad3449c7e0006">DCHECK</a></div><div class="ttdeci">#define DCHECK(condition)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00889">base/logging.h:889</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_dynamic_maximum_html"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dynamic_maximum.html">operations_research::glop::DynamicMaximum</a></div><div class="ttdef"><b>Definition:</b> <a href="pricing_8h_source.html#l00056">pricing.h:56</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_ae89df3243bbb8341130c7b3f44145ea0"><div class="ttname"><a href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a></div><div class="ttdeci">#define DCHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00890">base/logging.h:890</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_dynamic_maximum_html_aa71d36872f416feaa853788a7a7a7ef8"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#aa71d36872f416feaa853788a7a7a7ef8">operations_research::glop::DynamicMaximum::Clear</a></div><div class="ttdeci">void Clear()</div><div class="ttdef"><b>Definition:</b> <a href="pricing_8h_source.html#l00089">pricing.h:89</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_dynamic_maximum_html_a2b42bfa1c96806cf7504a5e8890fd56f"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a2b42bfa1c96806cf7504a5e8890fd56f">operations_research::glop::DynamicMaximum::DynamicMaximum</a></div><div class="ttdeci">DynamicMaximum(absl::BitGenRef random)</div><div class="ttdef"><b>Definition:</b> <a href="pricing_8h_source.html#l00059">pricing.h:59</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_dynamic_maximum_html_a783736d86811c9bc5a68dd8ff1890192"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_dynamic_maximum.html#a783736d86811c9bc5a68dd8ff1890192">operations_research::glop::DynamicMaximum::ClearAndResize</a></div><div class="ttdeci">void ClearAndResize(Index n)</div><div class="ttdef"><b>Definition:</b> <a href="pricing_8h_source.html#l00156">pricing.h:156</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="bitset_8h_html"><div class="ttname"><a href="bitset_8h.html">bitset.h</a></div></div>
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<div class="ttc" id="classoperations__research_1_1glop_1_1_strict_i_t_i_vector_html_a967a5c081ad4195a30c78dc2c0bcabf5"><div class="ttname"><a href="classoperations__research_1_1glop_1_1_strict_i_t_i_vector.html#a967a5c081ad4195a30c78dc2c0bcabf5">operations_research::glop::StrictITIVector::size</a></div><div class="ttdeci">IntType size() const</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00280">lp_types.h:280</a></div></div>
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<div class="ttc" id="lp__types_8h_html"><div class="ttname"><a href="lp__types_8h.html">lp_types.h</a></div></div>
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<div class="ttc" id="demon__profiler_8cc_html_ac072af30c4ffbc834bb4c681f6ecb514"><div class="ttname"><a href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a></div><div class="ttdeci">int64_t value</div><div class="ttdef"><b>Definition:</b> <a href="demon__profiler_8cc_source.html#l00044">demon_profiler.cc:44</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1glop_html_ac89c7b45754e9a6bdabc08bea586fc4e"><div class="ttname"><a href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">operations_research::glop::Index</a></div><div class="ttdeci">int32_t Index</div><div class="ttdef"><b>Definition:</b> <a href="lp__types_8h_source.html#l00038">lp_types.h:38</a></div></div>
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