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<a href="sat_2util_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_SAT_UTIL_H_</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#define OR_TOOLS_SAT_UTIL_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 <cstdint></span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#include <deque></span></div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> </div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include "absl/random/bit_gen_ref.h"</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include "absl/random/random.h"</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include "<a class="code" href="sat_2model_8h.html">ortools/sat/model.h</a>"</span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#include "<a class="code" href="sat__base_8h.html">ortools/sat/sat_base.h</a>"</span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#include "<a class="code" href="sat__parameters_8pb_8h.html">ortools/sat/sat_parameters.pb.h</a>"</span></div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#include "<a class="code" href="random__engine_8h.html">ortools/util/random_engine.h</a>"</span></div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include "<a class="code" href="time__limit_8h.html">ortools/util/time_limit.h</a>"</span></div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span> </div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#if !defined(__PORTABLE_PLATFORM__)</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include "google/protobuf/descriptor.h"</span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#endif // __PORTABLE_PLATFORM__</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> </div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="keyword">namespace </span>sat {</div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> </div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// Returns a in [0, m) such that a * x = 1 modulo m.</span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// If gcd(x, m) != 1, there is no inverse, and it returns 0.</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">//</span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// This DCHECK that x is in [0, m).</span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// This is integer overflow safe.</span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">//</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// Note(user): I didn't find this in a easily usable standard library.</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span> int64_t <a class="code" href="namespaceoperations__research_1_1sat.html#abbbb4c91f9a3d6eb290709745f5b661c">ModularInverse</a>(int64_t x, int64_t m);</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> </div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// Just returns x % m but with a result always in [0, m).</span></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> int64_t <a class="code" href="namespaceoperations__research_1_1sat.html#a629c989df2521428c30722f175874774">PositiveMod</a>(int64_t x, int64_t m);</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> </div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// If we know that X * coeff % mod = rhs % mod, this returns c such that</span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// PositiveMod(X, mod) = c.</span></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">//</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// This requires coeff != 0, mod !=0 and gcd(coeff, mod) == 1.</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// The result will be in [0, mod) but there is no other condition on the sign or</span></div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// magnitude of a and b.</span></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">//</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// This is overflow safe, and when rhs == 0 or abs(mod) == 1, it returns 0.</span></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> int64_t <a class="code" href="namespaceoperations__research_1_1sat.html#ac015d81b88379719f680eadc2aad1508">ProductWithModularInverse</a>(int64_t coeff, int64_t mod, int64_t rhs);</div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span> </div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// Returns true if the equation a * X + b * Y = cte has some integer solutions.</span></div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// For now, we check that a and b are different from 0 and from int64_t min.</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment">//</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// There is actually always a solution if cte % gcd(|a|, |b|) == 0. And because</span></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// a, b and cte fit on an int64_t, if there is a solution, there is one with X</span></div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// and Y fitting on an int64_t.</span></div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment">//</span></div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// We will divide everything by gcd(a, b) first, so it is why we take reference</span></div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// and the equation can change.</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">//</span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// If there are solutions, we return one of them (x0, y0).</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// From any such solution, the set of all solutions is given for Z integer by:</span></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// X = x0 + b * Z;</span></div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// Y = y0 - a * Z;</span></div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment">//</span></div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// Given a domain for X and Y, it is possible to compute the "exact" domain of Z</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// with our Domain functions. Note however that this will only compute solution</span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// where both x-x0 and y-y0 do fit on an int64_t:</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// DomainOf(x).SubtractionWith(x0).InverseMultiplicationBy(b).IntersectionWith(</span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// DomainOf(y).SubtractionWith(y0).InverseMultiplicationBy(-a))</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a852a51b53f6217d6bfd1aef455f53f8c">SolveDiophantineEquationOfSizeTwo</a>(int64_t& <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, int64_t& <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, int64_t& cte,</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  int64_t& x0, int64_t& y0);</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span> </div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// The argument must be non-negative.</span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> int64_t <a class="code" href="namespaceoperations__research_1_1sat.html#aa7497b495a7fbfddaea40d45861680c5">FloorSquareRoot</a>(int64_t <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>);</div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span> int64_t <a class="code" href="namespaceoperations__research_1_1sat.html#a72e9fb9c1d4b0649782f8696e85cbbaa">CeilSquareRoot</a>(int64_t <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>);</div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span> </div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// The model "singleton" random engine used in the solver.</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment">//</span></div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// In test, we usually set use_absl_random() so that the sequence is changed at</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// each invocation. This way, clients do not relly on the wrong assumption that</span></div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// a particular optimal solution will be returned if they are many equivalent</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// ones.</span></div><div class="line"><a name="l00090"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_model_random_generator.html"> 90</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1sat_1_1_model_random_generator.html">ModelRandomGenerator</a> : <span class="keyword">public</span> absl::BitGenRef {</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="comment">// We seed the strategy at creation only. This should be enough for our use</span></div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="comment">// case since the SatParameters is set first before the solver is created. We</span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="comment">// also never really need to change the seed afterwards, it is just used to</span></div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="comment">// diversify solves with identical parameters on different Model objects.</span></div><div class="line"><a name="l00096"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_model_random_generator.html#a01d0fd84c6567d5a7628deeac9a8ab23"> 96</a></span>  <span class="keyword">explicit</span> <a class="code" href="classoperations__research_1_1sat_1_1_model_random_generator.html#a01d0fd84c6567d5a7628deeac9a8ab23">ModelRandomGenerator</a>(<a class="code" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>)</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  : <a class="code" href="namespaceabsl.html">absl</a>::BitGenRef(deterministic_random_) {</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keyword">const</span> <span class="keyword">auto</span>& params = *<a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>->GetOrCreate<<a class="code" href="classoperations__research_1_1sat_1_1_sat_parameters.html">SatParameters</a>>();</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  deterministic_random_.seed(params.random_seed());</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keywordflow">if</span> (params.use_absl_random()) {</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  absl_random_ = absl::BitGen(absl::SeedSeq({params.random_seed()}));</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  absl::BitGenRef::operator=(absl::BitGenRef(absl_random_));</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  }</div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  }</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span> </div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="comment">// This is just used to display ABSL_RANDOM_SALT_OVERRIDE in the log so that</span></div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="comment">// it is possible to reproduce a failure more easily while looking at a solver</span></div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">// log.</span></div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="comment">//</span></div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="comment">// TODO(user): I didn't find a cleaner way to log this.</span></div><div class="line"><a name="l00111"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_model_random_generator.html#a7302efe7585eecd121c7c0a6113c8ae4"> 111</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_model_random_generator.html#a7302efe7585eecd121c7c0a6113c8ae4">LogSalt</a>()<span class="keyword"> const </span>{}</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span> </div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <a class="code" href="namespaceoperations__research.html#a6743e8c90bbb85a1017486ed70c7d29b">random_engine_t</a> deterministic_random_;</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  absl::BitGen absl_random_;</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span> };</div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span> </div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment">// The model "singleton" shared time limit.</span></div><div class="line"><a name="l00119"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_model_shared_time_limit.html"> 119</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1sat_1_1_model_shared_time_limit.html">ModelSharedTimeLimit</a> : <span class="keyword">public</span> <a class="code" href="classoperations__research_1_1_shared_time_limit.html">SharedTimeLimit</a> {</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00121"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_model_shared_time_limit.html#a79b7879c6b56eab4a6c0222adf4d6e51"> 121</a></span>  <span class="keyword">explicit</span> <a class="code" href="classoperations__research_1_1sat_1_1_model_shared_time_limit.html#a79b7879c6b56eab4a6c0222adf4d6e51">ModelSharedTimeLimit</a>(<a class="code" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>)</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  : <a class="code" href="classoperations__research_1_1_shared_time_limit.html">SharedTimeLimit</a>(<a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>->GetOrCreate<<a class="code" href="classoperations__research_1_1_time_limit.html">TimeLimit</a>>()) {}</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span> };</div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span> </div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="comment">// Randomizes the decision heuristic of the given SatParameters.</span></div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a0441e1a54fe203c0707131e587de8fae">RandomizeDecisionHeuristic</a>(absl::BitGenRef random,</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  SatParameters* <a class="code" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>);</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> <span class="comment">// Context: this function is not really generic, but required to be unit-tested.</span></div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment">// It is used in a clause minimization algorithm when we try to detect if any of</span></div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment">// the clause literals can be propagated by a subset of the other literal being</span></div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment">// false. For that, we want to enqueue in the solver all the subset of size n-1.</span></div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="comment">//</span></div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment">// This moves one of the unprocessed literal from literals to the last position.</span></div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment">// The function tries to do that while preserving the longest possible prefix of</span></div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="comment">// literals "amortized" through the calls assuming that we want to move each</span></div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment">// literal to the last position once.</span></div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment">//</span></div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment">// For a vector of size n, if we want to call this n times so that each literal</span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="comment">// is last at least once, the sum of the size of the changed suffixes will be</span></div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment">// O(n log n). If we were to use a simpler algorithm (like moving the last</span></div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment">// unprocessed literal to the last position), this sum would be O(n^2).</span></div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="comment">//</span></div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment">// Returns the size of the common prefix of literals before and after the move,</span></div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment">// or -1 if all the literals are already processed. The argument</span></div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="comment">// relevant_prefix_size is used as a hint when keeping more that this prefix</span></div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment">// size do not matter. The returned value will always be lower or equal to</span></div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="comment">// relevant_prefix_size.</span></div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="keywordtype">int</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a2ef3eb1f5fe6506a5e24115f10d724fc">MoveOneUnprocessedLiteralLast</a>(<span class="keyword">const</span> std::set<LiteralIndex>& processed,</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordtype">int</span> relevant_prefix_size,</div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  std::vector<Literal>* literals);</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span> </div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment">// ============================================================================</span></div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment">// Implementation.</span></div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment">// ============================================================================</span></div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span> </div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment">// Manages incremental averages.</span></div><div class="line"><a name="l00158"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html"> 158</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1sat_1_1_incremental_average.html">IncrementalAverage</a> {</div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="comment">// Initializes the average with 'initial_average' and number of records to 0.</span></div><div class="line"><a name="l00161"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html#a2f01b362e8160a5d5a3d30a09ffe280c"> 161</a></span>  <span class="keyword">explicit</span> <a class="code" href="classoperations__research_1_1sat_1_1_incremental_average.html#a2f01b362e8160a5d5a3d30a09ffe280c">IncrementalAverage</a>(<span class="keywordtype">double</span> initial_average)</div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  : average_(initial_average) {}</div><div class="line"><a name="l00163"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html#a8f4ea7664e6ea6da0bff32eac8f4a975"> 163</a></span>  <a class="code" href="classoperations__research_1_1sat_1_1_incremental_average.html#a8f4ea7664e6ea6da0bff32eac8f4a975">IncrementalAverage</a>() {}</div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span> </div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="comment">// Sets the number of records to 0 and average to 'reset_value'.</span></div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_incremental_average.html#adf01dcbe31fa99f0a8f9d91ba9f85b8b">Reset</a>(<span class="keywordtype">double</span> reset_value);</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span> </div><div class="line"><a name="l00168"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html#a6d9b473fa04b0558a8e48737f5ab9564"> 168</a></span>  <span class="keywordtype">double</span> <a class="code" href="classoperations__research_1_1sat_1_1_incremental_average.html#a6d9b473fa04b0558a8e48737f5ab9564">CurrentAverage</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> average_; }</div><div class="line"><a name="l00169"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html#a1bdd878a5252fe5eb23b9319ed5b3f35"> 169</a></span>  int64_t <a class="code" href="classoperations__research_1_1sat_1_1_incremental_average.html#a1bdd878a5252fe5eb23b9319ed5b3f35">NumRecords</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_records_; }</div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span> </div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_incremental_average.html#a198870bbc0f9b8d197a4c80f766ddf49">AddData</a>(<span class="keywordtype">double</span> new_record);</div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span> </div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keywordtype">double</span> average_ = 0.0;</div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  int64_t num_records_ = 0;</div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span> };</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span> </div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment">// Manages exponential moving averages defined as</span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment">// new_average = decaying_factor * old_average</span></div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="comment">// + (1 - decaying_factor) * new_record.</span></div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment">// where 0 < decaying_factor < 1.</span></div><div class="line"><a name="l00182"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html"> 182</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html">ExponentialMovingAverage</a> {</div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00184"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a5e3f98a369b372eb5521317e3eb3a4a0"> 184</a></span>  <span class="keyword">explicit</span> <a class="code" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a5e3f98a369b372eb5521317e3eb3a4a0">ExponentialMovingAverage</a>(<span class="keywordtype">double</span> decaying_factor)</div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  : decaying_factor_(decaying_factor) {</div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <a class="code" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(decaying_factor, 0.0);</div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <a class="code" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(decaying_factor, 1.0);</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  }</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span> </div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="comment">// Returns exponential moving average for all the added data so far.</span></div><div class="line"><a name="l00191"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a6d9b473fa04b0558a8e48737f5ab9564"> 191</a></span>  <span class="keywordtype">double</span> <a class="code" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a6d9b473fa04b0558a8e48737f5ab9564">CurrentAverage</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> average_; }</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="comment">// Returns the total number of added records so far.</span></div><div class="line"><a name="l00194"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a1bdd878a5252fe5eb23b9319ed5b3f35"> 194</a></span>  int64_t <a class="code" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a1bdd878a5252fe5eb23b9319ed5b3f35">NumRecords</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_records_; }</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span> </div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a198870bbc0f9b8d197a4c80f766ddf49">AddData</a>(<span class="keywordtype">double</span> new_record);</div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span> </div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordtype">double</span> average_ = 0.0;</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  int64_t num_records_ = 0;</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> decaying_factor_;</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> </div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="comment">// Utility to calculate percentile (First variant) for limited number of</span></div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment">// records. Reference: https://en.wikipedia.org/wiki/Percentile</span></div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment">//</span></div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment">// After the vector is sorted, we assume that the element with index i</span></div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="comment">// correspond to the percentile 100*(i+0.5)/size. For percentiles before the</span></div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment">// first element (resp. after the last one) we return the first element (resp.</span></div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="comment">// the last). And otherwise we do a linear interpolation between the two element</span></div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="comment">// around the asked percentile.</span></div><div class="line"><a name="l00212"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_percentile.html"> 212</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1sat_1_1_percentile.html">Percentile</a> {</div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00214"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_percentile.html#aae45e57e2fc34863a5272f4ec3ec2bef"> 214</a></span>  <span class="keyword">explicit</span> <a class="code" href="classoperations__research_1_1sat_1_1_percentile.html#aae45e57e2fc34863a5272f4ec3ec2bef">Percentile</a>(<span class="keywordtype">int</span> record_limit) : record_limit_(record_limit) {}</div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span> </div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_percentile.html#adfcf2b433605c03210cbd06e28ce9d97">AddRecord</a>(<span class="keywordtype">double</span> record);</div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span> </div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="comment">// Returns number of stored records.</span></div><div class="line"><a name="l00219"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_percentile.html#a1bdd878a5252fe5eb23b9319ed5b3f35"> 219</a></span>  int64_t <a class="code" href="classoperations__research_1_1sat_1_1_percentile.html#a1bdd878a5252fe5eb23b9319ed5b3f35">NumRecords</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> records_.size(); }</div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span> </div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="comment">// Note that this is not fast and runs in O(n log n) for n records.</span></div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keywordtype">double</span> <a class="code" href="classoperations__research_1_1sat_1_1_percentile.html#a006c3e4f212cee5414d510a9ded6eedb">GetPercentile</a>(<span class="keywordtype">double</span> percent);</div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span> </div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  std::deque<double> records_;</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> record_limit_;</div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span> };</div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span> </div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="comment">// This method tries to compress a list of tuples by merging complementary</span></div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="comment">// tuples, that is a set of tuples that only differ on one variable, and that</span></div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="comment">// cover the domain of the variable. In that case, it will keep only one tuple,</span></div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="comment">// and replace the value for variable by any_value, the equivalent of '*' in</span></div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="comment">// regexps.</span></div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="comment">//</span></div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="comment">// This method is exposed for testing purposes.</span></div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a441a154d125df2eb884a44be77e2bfc0">CompressTuples</a>(absl::Span<const int64_t> domain_sizes, int64_t any_value,</div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  std::vector<std::vector<int64_t>>* tuples);</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span> </div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span> } <span class="comment">// namespace sat</span></div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span> } <span class="comment">// namespace operations_research</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> <span class="preprocessor">#endif // OR_TOOLS_SAT_UTIL_H_</span></div><div class="ttc" id="classoperations__research_1_1sat_1_1_percentile_html_a1bdd878a5252fe5eb23b9319ed5b3f35"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_percentile.html#a1bdd878a5252fe5eb23b9319ed5b3f35">operations_research::sat::Percentile::NumRecords</a></div><div class="ttdeci">int64_t NumRecords() const</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00219">sat/util.h:219</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_exponential_moving_average_html_a5e3f98a369b372eb5521317e3eb3a4a0"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a5e3f98a369b372eb5521317e3eb3a4a0">operations_research::sat::ExponentialMovingAverage::ExponentialMovingAverage</a></div><div class="ttdeci">ExponentialMovingAverage(double decaying_factor)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00184">sat/util.h:184</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_time_limit_html"><div class="ttname"><a href="classoperations__research_1_1_time_limit.html">operations_research::TimeLimit</a></div><div class="ttdoc">A simple class to enforce both an elapsed time limit and a deterministic time limit in the same threa...</div><div class="ttdef"><b>Definition:</b> <a href="time__limit_8h_source.html#l00106">time_limit.h:106</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1sat_html_a0441e1a54fe203c0707131e587de8fae"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a0441e1a54fe203c0707131e587de8fae">operations_research::sat::RandomizeDecisionHeuristic</a></div><div class="ttdeci">void RandomizeDecisionHeuristic(absl::BitGenRef random, SatParameters *parameters)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00038">sat/util.cc:38</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_model_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_model.html">operations_research::sat::Model</a></div><div class="ttdoc">Class that owns everything related to a particular optimization model.</div><div class="ttdef"><b>Definition:</b> <a href="sat_2model_8h_source.html#l00038">sat/model.h:38</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1sat_html_a72e9fb9c1d4b0649782f8696e85cbbaa"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a72e9fb9c1d4b0649782f8696e85cbbaa">operations_research::sat::CeilSquareRoot</a></div><div class="ttdeci">int64_t CeilSquareRoot(int64_t a)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00182">sat/util.cc:182</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_percentile_html_adfcf2b433605c03210cbd06e28ce9d97"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_percentile.html#adfcf2b433605c03210cbd06e28ce9d97">operations_research::sat::Percentile::AddRecord</a></div><div class="ttdeci">void AddRecord(double record)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00246">sat/util.cc:246</a></div></div>
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<div class="ttc" id="random__engine_8h_html"><div class="ttname"><a href="random__engine_8h.html">random_engine.h</a></div></div>
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<div class="ttc" id="sat_2model_8h_html"><div class="ttname"><a href="sat_2model_8h.html">model.h</a></div></div>
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<div class="ttc" id="time__limit_8h_html"><div class="ttname"><a href="time__limit_8h.html">time_limit.h</a></div></div>
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<div class="ttc" id="gurobi__interface_8cc_html_a0728f23c9a47655d38e0bf1a2f200bcf"><div class="ttname"><a href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a></div><div class="ttdeci">GRBmodel * model</div><div class="ttdef"><b>Definition:</b> <a href="gurobi__interface_8cc_source.html#l00274">gurobi_interface.cc:274</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_incremental_average_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_incremental_average.html">operations_research::sat::IncrementalAverage</a></div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00158">sat/util.h:158</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_incremental_average_html_a198870bbc0f9b8d197a4c80f766ddf49"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_incremental_average.html#a198870bbc0f9b8d197a4c80f766ddf49">operations_research::sat::IncrementalAverage::AddData</a></div><div class="ttdeci">void AddData(double new_record)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00234">sat/util.cc:234</a></div></div>
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<div class="ttc" id="constraint__solver_2table_8cc_html_a9293e4d29cac928301645070dd307683"><div class="ttname"><a href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a></div><div class="ttdeci">int64_t b</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00047">constraint_solver/table.cc:47</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_model_random_generator_html_a01d0fd84c6567d5a7628deeac9a8ab23"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_model_random_generator.html#a01d0fd84c6567d5a7628deeac9a8ab23">operations_research::sat::ModelRandomGenerator::ModelRandomGenerator</a></div><div class="ttdeci">ModelRandomGenerator(Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00096">sat/util.h:96</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_model_random_generator_html_a7302efe7585eecd121c7c0a6113c8ae4"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_model_random_generator.html#a7302efe7585eecd121c7c0a6113c8ae4">operations_research::sat::ModelRandomGenerator::LogSalt</a></div><div class="ttdeci">void LogSalt() const</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00111">sat/util.h:111</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_percentile_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_percentile.html">operations_research::sat::Percentile</a></div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00212">sat/util.h:212</a></div></div>
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<div class="ttc" id="namespaceabsl_html"><div class="ttname"><a href="namespaceabsl.html">absl</a></div><div class="ttdef"><b>Definition:</b> <a href="cleanup_8h_source.html#l00022">cleanup.h:22</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_percentile_html_aae45e57e2fc34863a5272f4ec3ec2bef"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_percentile.html#aae45e57e2fc34863a5272f4ec3ec2bef">operations_research::sat::Percentile::Percentile</a></div><div class="ttdeci">Percentile(int record_limit)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00214">sat/util.h:214</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_exponential_moving_average_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_exponential_moving_average.html">operations_research::sat::ExponentialMovingAverage</a></div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00182">sat/util.h:182</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_a6743e8c90bbb85a1017486ed70c7d29b"><div class="ttname"><a href="namespaceoperations__research.html#a6743e8c90bbb85a1017486ed70c7d29b">operations_research::random_engine_t</a></div><div class="ttdeci">std::mt19937 random_engine_t</div><div class="ttdef"><b>Definition:</b> <a href="random__engine_8h_source.html#l00023">random_engine.h:23</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_model_random_generator_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_model_random_generator.html">operations_research::sat::ModelRandomGenerator</a></div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00090">sat/util.h:90</a></div></div>
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<div class="ttc" id="classoperations__research_1_1_shared_time_limit_html"><div class="ttname"><a href="classoperations__research_1_1_shared_time_limit.html">operations_research::SharedTimeLimit</a></div><div class="ttdef"><b>Definition:</b> <a href="time__limit_8h_source.html#l00340">time_limit.h:340</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_1sat_1_1_exponential_moving_average_html_a1bdd878a5252fe5eb23b9319ed5b3f35"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a1bdd878a5252fe5eb23b9319ed5b3f35">operations_research::sat::ExponentialMovingAverage::NumRecords</a></div><div class="ttdeci">int64_t NumRecords() const</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00194">sat/util.h:194</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1sat_html_a852a51b53f6217d6bfd1aef455f53f8c"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a852a51b53f6217d6bfd1aef455f53f8c">operations_research::sat::SolveDiophantineEquationOfSizeTwo</a></div><div class="ttdeci">bool SolveDiophantineEquationOfSizeTwo(int64_t &a, int64_t &b, int64_t &cte, int64_t &x0, int64_t &y0)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00126">sat/util.cc:126</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_exponential_moving_average_html_a198870bbc0f9b8d197a4c80f766ddf49"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a198870bbc0f9b8d197a4c80f766ddf49">operations_research::sat::ExponentialMovingAverage::AddData</a></div><div class="ttdeci">void AddData(double new_record)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00239">sat/util.cc:239</a></div></div>
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<div class="ttc" id="sat__base_8h_html"><div class="ttname"><a href="sat__base_8h.html">sat_base.h</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_exponential_moving_average_html_a6d9b473fa04b0558a8e48737f5ab9564"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a6d9b473fa04b0558a8e48737f5ab9564">operations_research::sat::ExponentialMovingAverage::CurrentAverage</a></div><div class="ttdeci">double CurrentAverage() const</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00191">sat/util.h:191</a></div></div>
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<div class="ttc" id="sat__parameters_8pb_8h_html"><div class="ttname"><a href="sat__parameters_8pb_8h.html">sat_parameters.pb.h</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_model_shared_time_limit_html_a79b7879c6b56eab4a6c0222adf4d6e51"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_model_shared_time_limit.html#a79b7879c6b56eab4a6c0222adf4d6e51">operations_research::sat::ModelSharedTimeLimit::ModelSharedTimeLimit</a></div><div class="ttdeci">ModelSharedTimeLimit(Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00121">sat/util.h:121</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1sat_html_aa7497b495a7fbfddaea40d45861680c5"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#aa7497b495a7fbfddaea40d45861680c5">operations_research::sat::FloorSquareRoot</a></div><div class="ttdeci">int64_t FloorSquareRoot(int64_t a)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00173">sat/util.cc:173</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1sat_html_ac015d81b88379719f680eadc2aad1508"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ac015d81b88379719f680eadc2aad1508">operations_research::sat::ProductWithModularInverse</a></div><div class="ttdeci">int64_t ProductWithModularInverse(int64_t coeff, int64_t mod, int64_t rhs)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00104">sat/util.cc:104</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_a4395e95bab44e222cb2e77251017a0e2"><div class="ttname"><a href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a></div><div class="ttdeci">#define DCHECK_LE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00892">base/logging.h:892</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_incremental_average_html_a1bdd878a5252fe5eb23b9319ed5b3f35"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_incremental_average.html#a1bdd878a5252fe5eb23b9319ed5b3f35">operations_research::sat::IncrementalAverage::NumRecords</a></div><div class="ttdeci">int64_t NumRecords() const</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00169">sat/util.h:169</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="cp__model__fz__solver_8cc_html_a10a1eab179b472c030bdc2a2efef7219"><div class="ttname"><a href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a></div><div class="ttdeci">SatParameters parameters</div><div class="ttdef"><b>Definition:</b> <a href="cp__model__fz__solver_8cc_source.html#l00120">cp_model_fz_solver.cc:120</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_incremental_average_html_a2f01b362e8160a5d5a3d30a09ffe280c"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_incremental_average.html#a2f01b362e8160a5d5a3d30a09ffe280c">operations_research::sat::IncrementalAverage::IncrementalAverage</a></div><div class="ttdeci">IncrementalAverage(double initial_average)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00161">sat/util.h:161</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_incremental_average_html_a6d9b473fa04b0558a8e48737f5ab9564"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_incremental_average.html#a6d9b473fa04b0558a8e48737f5ab9564">operations_research::sat::IncrementalAverage::CurrentAverage</a></div><div class="ttdeci">double CurrentAverage() const</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00168">sat/util.h:168</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1sat_html_a441a154d125df2eb884a44be77e2bfc0"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a441a154d125df2eb884a44be77e2bfc0">operations_research::sat::CompressTuples</a></div><div class="ttdeci">void CompressTuples(absl::Span< const int64_t > domain_sizes, int64_t any_value, std::vector< std::vector< int64_t >> *tuples)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00278">sat/util.cc:278</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1sat_html_a2ef3eb1f5fe6506a5e24115f10d724fc"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a2ef3eb1f5fe6506a5e24115f10d724fc">operations_research::sat::MoveOneUnprocessedLiteralLast</a></div><div class="ttdeci">int MoveOneUnprocessedLiteralLast(const std::set< LiteralIndex > &processed, int relevant_prefix_size, std::vector< Literal > *literals)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00190">sat/util.cc:190</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_incremental_average_html_a8f4ea7664e6ea6da0bff32eac8f4a975"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_incremental_average.html#a8f4ea7664e6ea6da0bff32eac8f4a975">operations_research::sat::IncrementalAverage::IncrementalAverage</a></div><div class="ttdeci">IncrementalAverage()</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00163">sat/util.h:163</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_percentile_html_a006c3e4f212cee5414d510a9ded6eedb"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_percentile.html#a006c3e4f212cee5414d510a9ded6eedb">operations_research::sat::Percentile::GetPercentile</a></div><div class="ttdeci">double GetPercentile(double percent)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00253">sat/util.cc:253</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_model_shared_time_limit_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_model_shared_time_limit.html">operations_research::sat::ModelSharedTimeLimit</a></div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8h_source.html#l00119">sat/util.h:119</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_sat_parameters_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html">operations_research::sat::SatParameters</a></div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l00347">sat_parameters.pb.h:347</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_incremental_average_html_adf01dcbe31fa99f0a8f9d91ba9f85b8b"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_incremental_average.html#adf01dcbe31fa99f0a8f9d91ba9f85b8b">operations_research::sat::IncrementalAverage::Reset</a></div><div class="ttdeci">void Reset(double reset_value)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00229">sat/util.cc:229</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1sat_html_a629c989df2521428c30722f175874774"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a629c989df2521428c30722f175874774">operations_research::sat::PositiveMod</a></div><div class="ttdeci">int64_t PositiveMod(int64_t x, int64_t m)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00099">sat/util.cc:99</a></div></div>
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<div class="ttc" id="constraint__solver_2table_8cc_html_acb18315d548212835cd8ed4287e6c0b6"><div class="ttname"><a href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a></div><div class="ttdeci">int64_t a</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00046">constraint_solver/table.cc:46</a></div></div>
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<div class="ttc" id="namespaceoperations__research_1_1sat_html_abbbb4c91f9a3d6eb290709745f5b661c"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#abbbb4c91f9a3d6eb290709745f5b661c">operations_research::sat::ModularInverse</a></div><div class="ttdeci">int64_t ModularInverse(int64_t x, int64_t m)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00066">sat/util.cc:66</a></div></div>
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