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<a href="sat_2util_8cc.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">#include "<a class="code" href="sat_2util_8h.html">ortools/sat/util.h</a>"</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#include <algorithm></span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include <cmath></span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#include <cstdint></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/numeric/int128.h"</span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include "<a class="code" href="stl__util_8h.html">ortools/base/stl_util.h</a>"</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include "<a class="code" href="saturated__arithmetic_8h.html">ortools/util/saturated_arithmetic.h</a>"</span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> </div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="keyword">namespace </span>sat {</div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> </div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="keyword">namespace </span>{</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// This will be optimized into one division. I tested that in other places:</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">//</span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">// Note that I am not 100% sure we need the indirection for the optimization</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// to kick in though, but this seemed safer given our weird r[i ^ 1] inputs.</span></div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="keywordtype">void</span> QuotientAndRemainder(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& q, int64_t& r) {</div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  q = <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a> / <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>;</div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  r = <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a> % <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>;</div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> }</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> } <span class="comment">// namespace</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> </div><div class="line"><a name="l00038"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a0441e1a54fe203c0707131e587de8fae"> 38</a></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="l00039"></a><span class="lineno"> 39</span>  <a class="code" href="classoperations__research_1_1sat_1_1_sat_parameters.html">SatParameters</a>* <a class="code" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>) {</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="preprocessor">#if !defined(__PORTABLE_PLATFORM__)</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="comment">// Random preferred variable order.</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keyword">const</span> google::protobuf::EnumDescriptor* order_d =</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <a class="code" href="classoperations__research_1_1sat_1_1_sat_parameters.html#a0e0e7b7f0e5cc8e0b535ffab534fade0">SatParameters::VariableOrder_descriptor</a>();</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <a class="code" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>-><a class="code" href="classoperations__research_1_1sat_1_1_sat_parameters.html#a7e544bdc4785ce055ed01ca1f22fca41">set_preferred_variable_order</a>(</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  static_cast<SatParameters::VariableOrder>(</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  order_d->value(absl::Uniform(random, 0, order_d->value_count()))</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  ->number()));</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> </div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="comment">// Random polarity initial value.</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keyword">const</span> google::protobuf::EnumDescriptor* polarity_d =</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <a class="code" href="classoperations__research_1_1sat_1_1_sat_parameters.html#a1e17932252915c774d68a1ba03950715">SatParameters::Polarity_descriptor</a>();</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <a class="code" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>-><a class="code" href="classoperations__research_1_1sat_1_1_sat_parameters.html#a12558bbe25af1ee14f86bab924c96709">set_initial_polarity</a>(static_cast<SatParameters::Polarity>(</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  polarity_d->value(absl::Uniform(random, 0, polarity_d->value_count()))</div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  ->number()));</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="preprocessor">#endif // __PORTABLE_PLATFORM__</span></div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="comment">// Other random parameters.</span></div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <a class="code" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>-><a class="code" href="classoperations__research_1_1sat_1_1_sat_parameters.html#ae31c8a339e7515e82ad032f6f89ace68">set_use_phase_saving</a>(absl::Bernoulli(random, 0.5));</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <a class="code" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>-><a class="code" href="classoperations__research_1_1sat_1_1_sat_parameters.html#a05528f270d7291bd49be9f8575780fcb">set_random_polarity_ratio</a>(absl::Bernoulli(random, 0.5) ? 0.01</div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  : 0.0);</div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <a class="code" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>-><a class="code" href="classoperations__research_1_1sat_1_1_sat_parameters.html#a8a7cbb53d028e253e201883124b6089e">set_random_branches_ratio</a>(absl::Bernoulli(random, 0.5) ? 0.01</div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  : 0.0);</div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span> }</div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> </div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// Using the extended Euclidian algo, we find a and b such that a x + b m = gcd.</span></div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm</span></div><div class="line"><a name="l00066"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#abbbb4c91f9a3d6eb290709745f5b661c"> 66</a></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="l00067"></a><span class="lineno"> 67</span>  <a class="code" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(x, 0);</div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <a class="code" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(x, m);</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span> </div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  int64_t r[2] = {m, x};</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  int64_t t[2] = {0, 1};</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  int64_t q;</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">// We only keep the last two terms of the sequences with the "^1" trick:</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="comment">//</span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="comment">// q = r[i-2] / r[i-1]</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="comment">// r[i] = r[i-2] % r[i-1]</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="comment">// t[i] = t[i-2] - t[i-1] * q</span></div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">//</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="comment">// We always have:</span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="comment">// - gcd(r[i], r[i - 1]) = gcd(r[i - 1], r[i - 2])</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="comment">// - x * t[i] + m * t[i - 1] = r[i]</span></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordtype">int</span> i = 0;</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordflow">for</span> (; r[i ^ 1] != 0; i ^= 1) {</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  QuotientAndRemainder(r[i], r[i ^ 1], q, r[i]);</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  t[i] -= t[i ^ 1] * q;</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> </div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="comment">// If the gcd is not one, there is no inverse, we returns 0.</span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordflow">if</span> (r[i] != 1) <span class="keywordflow">return</span> 0;</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">// Correct the result so that it is in [0, m). Note that abs(t[i]) is known to</span></div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="comment">// be less than or equal to x / 2, and we have thorough unit-tests.</span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordflow">if</span> (t[i] < 0) t[i] += m;</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span> </div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordflow">return</span> t[i];</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span> }</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span> </div><div class="line"><a name="l00099"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a629c989df2521428c30722f175874774"> 99</a></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="l00100"></a><span class="lineno"> 100</span>  <span class="keyword">const</span> int64_t r = x % m;</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keywordflow">return</span> r < 0 ? r + m : r;</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> </div><div class="line"><a name="l00104"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#ac015d81b88379719f680eadc2aad1508"> 104</a></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="l00105"></a><span class="lineno"> 105</span>  <a class="code" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(coeff, 0);</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <a class="code" href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a>(mod, 0);</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span> </div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  mod = std::abs(mod);</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">if</span> (rhs == 0 || mod == 1) <span class="keywordflow">return</span> 0;</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(std::gcd(std::abs(coeff), mod), 1);</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">// Make both in [0, mod).</span></div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  coeff = <a class="code" href="namespaceoperations__research_1_1sat.html#a629c989df2521428c30722f175874774">PositiveMod</a>(coeff, mod);</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  rhs = <a class="code" href="namespaceoperations__research_1_1sat.html#a629c989df2521428c30722f175874774">PositiveMod</a>(rhs, mod);</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span> </div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="comment">// From X * coeff % mod = rhs</span></div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="comment">// We deduce that X % mod = rhs * inverse % mod</span></div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keyword">const</span> int64_t inverse = <a class="code" href="namespaceoperations__research_1_1sat.html#abbbb4c91f9a3d6eb290709745f5b661c">ModularInverse</a>(coeff, mod);</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <a class="code" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(inverse, 0);</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span> </div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="comment">// We make the operation in 128 bits to be sure not to have any overflow here.</span></div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keyword">const</span> absl::int128 p = absl::int128{inverse} * absl::int128{rhs};</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keywordflow">return</span> static_cast<int64_t>(p % absl::int128{mod});</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> </div><div class="line"><a name="l00126"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a852a51b53f6217d6bfd1aef455f53f8c"> 126</a></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="l00127"></a><span class="lineno"> 127</span>  int64_t& x0, int64_t& y0) {</div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <a class="code" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(<a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, 0);</div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <a class="code" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(<a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, 0);</div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <a class="code" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(<a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::numeric_limits<int64_t>::min</a>());</div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <a class="code" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(<a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::numeric_limits<int64_t>::min</a>());</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span> </div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keyword">const</span> int64_t gcd = std::gcd(std::abs(<a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>), std::abs(<a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>));</div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">if</span> (cte % gcd != 0) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a> /= gcd;</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a> /= gcd;</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  cte /= gcd;</div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span> </div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="comment">// The simple case where (0, 0) is a solution.</span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordflow">if</span> (cte == 0) {</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  x0 = y0 = 0;</div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  }</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span> </div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="comment">// We solve a * X + b * Y = cte</span></div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="comment">// We take a valid x0 in [0, b) by considering the equation mod b.</span></div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  x0 = <a class="code" href="namespaceoperations__research_1_1sat.html#ac015d81b88379719f680eadc2aad1508">ProductWithModularInverse</a>(<a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, <a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, cte);</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span> </div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="comment">// We choose x0 of the same sign as cte.</span></div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordflow">if</span> (cte < 0 && x0 != 0) x0 -= std::abs(<a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>);</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>  <span class="comment">// By plugging X = x0 + b * Z</span></div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="comment">// We have a * (x0 + b * Z) + b * Y = cte</span></div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="comment">// so a * b * Z + b * Y = cte - a * x0;</span></div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="comment">// and y0 = (cte - a * x0) / b (with an exact division by construction).</span></div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keyword">const</span> absl::int128 t = absl::int128{cte} - absl::int128{<a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>} * absl::int128{x0};</div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <a class="code" href="base_2logging_8h.html#ae89df3243bbb8341130c7b3f44145ea0">DCHECK_EQ</a>(t % absl::int128{<a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>}, absl::int128{0});</div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span> </div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="comment">// Overflow-wise, there is two cases for cte > 0:</span></div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="comment">// - a * x0 <= cte, in this case y0 will not overflow (<= cte).</span></div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="comment">// - a * x0 > cte, in this case y0 will be in (-a, 0].</span></div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keyword">const</span> absl::int128 r = t / absl::int128{<a class="code" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>};</div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <a class="code" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(r, absl::int128{<a class="code" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::numeric_limits<int64_t>::max</a>()});</div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <a class="code" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(r, absl::int128{<a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::numeric_limits<int64_t>::min</a>()});</div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span> </div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  y0 = static_cast<int64_t>(r);</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span> }</div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span> </div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment">// TODO(user): Find better implementation? In pratice passing via double is</span></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment">// almost always correct, but the CapProd() might be a bit slow. However this</span></div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment">// is only called when we do propagate something.</span></div><div class="line"><a name="l00173"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#aa7497b495a7fbfddaea40d45861680c5"> 173</a></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="l00174"></a><span class="lineno"> 174</span>  int64_t result =</div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  static_cast<int64_t>(std::floor(std::sqrt(static_cast<double>(<a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>))));</div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="keywordflow">while</span> (<a class="code" href="namespaceoperations__research.html#aa64bf49d041052c7cb3f40f7496d7534">CapProd</a>(result, result) > <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>) --result;</div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordflow">while</span> (<a class="code" href="namespaceoperations__research.html#aa64bf49d041052c7cb3f40f7496d7534">CapProd</a>(result + 1, result + 1) <= <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>) ++result;</div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keywordflow">return</span> result;</div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span> }</div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span> </div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment">// TODO(user): Find better implementation?</span></div><div class="line"><a name="l00182"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a72e9fb9c1d4b0649782f8696e85cbbaa"> 182</a></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="l00183"></a><span class="lineno"> 183</span>  int64_t result =</div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  static_cast<int64_t>(std::ceil(std::sqrt(static_cast<double>(<a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>))));</div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keywordflow">while</span> (<a class="code" href="namespaceoperations__research.html#aa64bf49d041052c7cb3f40f7496d7534">CapProd</a>(result, result) < <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>) ++result;</div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keywordflow">while</span> ((result - 1) * (result - 1) >= <a class="code" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>) --result;</div><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keywordflow">return</span> result;</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"><a class="line" href="namespaceoperations__research_1_1sat.html#a2ef3eb1f5fe6506a5e24115f10d724fc"> 190</a></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="l00191"></a><span class="lineno"> 191</span>  <span class="keywordtype">int</span> relevant_prefix_size,</div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  std::vector<Literal>* literals) {</div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordflow">if</span> (literals->empty()) <span class="keywordflow">return</span> -1;</div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keywordflow">if</span> (!<a class="code" href="namespacegtl.html#aae28e97bd1fa93cb0032642550da7455">gtl::ContainsKey</a>(processed, literals->back().Index())) {</div><div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keywordflow">return</span> std::min<int>(relevant_prefix_size, literals->size());</div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  }</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="comment">// To get O(n log n) size of suffixes, we will first process the last n/2</span></div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="comment">// literals, we then move all of them first and process the n/2 literals left.</span></div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="comment">// We use the same algorithm recursively. The sum of the suffixes' size S(n)</span></div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="comment">// is thus S(n/2) + n + S(n/2). That gives us the correct complexity. The code</span></div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="comment">// below simulates one step of this algorithm and is made to be "robust" when</span></div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="comment">// from one call to the next, some literals have been removed (but the order</span></div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="comment">// of literals is preserved).</span></div><div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keywordtype">int</span> num_processed = 0;</div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keywordtype">int</span> num_not_processed = 0;</div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keywordtype">int</span> target_prefix_size = literals->size() - 1;</div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = literals->size() - 1; i >= 0; i--) {</div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="keywordflow">if</span> (<a class="code" href="namespacegtl.html#aae28e97bd1fa93cb0032642550da7455">gtl::ContainsKey</a>(processed, (*literals)[i].<a class="code" href="namespaceoperations__research_1_1glop.html#ac89c7b45754e9a6bdabc08bea586fc4e">Index</a>())) {</div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  ++num_processed;</div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  ++num_not_processed;</div><div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  target_prefix_size = i;</div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  }</div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keywordflow">if</span> (num_not_processed >= num_processed) <span class="keywordflow">break</span>;</div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  }</div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keywordflow">if</span> (num_not_processed == 0) <span class="keywordflow">return</span> -1;</div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  target_prefix_size = <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(target_prefix_size, relevant_prefix_size);</div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span> </div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="comment">// Once a prefix size has been decided, it is always better to</span></div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="comment">// enqueue the literal already processed first.</span></div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  std::stable_partition(literals->begin() + target_prefix_size, literals->end(),</div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  [&processed](<a class="code" href="classoperations__research_1_1sat_1_1_literal.html">Literal</a> l) {</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">return</span> <a class="code" href="namespacegtl.html#aae28e97bd1fa93cb0032642550da7455">gtl::ContainsKey</a>(processed, l.Index());</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  });</div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="keywordflow">return</span> target_prefix_size;</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"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html#adf01dcbe31fa99f0a8f9d91ba9f85b8b"> 229</a></span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_incremental_average.html#adf01dcbe31fa99f0a8f9d91ba9f85b8b">IncrementalAverage::Reset</a>(<span class="keywordtype">double</span> reset_value) {</div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  num_records_ = 0;</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  average_ = reset_value;</div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span> }</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span> </div><div class="line"><a name="l00234"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html#a198870bbc0f9b8d197a4c80f766ddf49"> 234</a></span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_incremental_average.html#a198870bbc0f9b8d197a4c80f766ddf49">IncrementalAverage::AddData</a>(<span class="keywordtype">double</span> new_record) {</div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  num_records_++;</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  average_ += (new_record - average_) / num_records_;</div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span> }</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span> </div><div class="line"><a name="l00239"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a198870bbc0f9b8d197a4c80f766ddf49"> 239</a></span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a198870bbc0f9b8d197a4c80f766ddf49">ExponentialMovingAverage::AddData</a>(<span class="keywordtype">double</span> new_record) {</div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  num_records_++;</div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  average_ = (num_records_ == 1)</div><div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  ? new_record</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  : (new_record + decaying_factor_ * (average_ - new_record));</div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span> }</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span> </div><div class="line"><a name="l00246"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_percentile.html#adfcf2b433605c03210cbd06e28ce9d97"> 246</a></span> <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_percentile.html#adfcf2b433605c03210cbd06e28ce9d97">Percentile::AddRecord</a>(<span class="keywordtype">double</span> record) {</div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  records_.push_front(record);</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="keywordflow">if</span> (records_.size() > record_limit_) {</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  records_.pop_back();</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  }</div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span> }</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span> </div><div class="line"><a name="l00253"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_percentile.html#a006c3e4f212cee5414d510a9ded6eedb"> 253</a></span> <span class="keywordtype">double</span> <a class="code" href="classoperations__research_1_1sat_1_1_percentile.html#a006c3e4f212cee5414d510a9ded6eedb">Percentile::GetPercentile</a>(<span class="keywordtype">double</span> percent) {</div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <a class="code" href="base_2logging_8h.html#a7e03ec13560fa94a8fea569960d7efc6">CHECK_GT</a>(records_.size(), 0);</div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <a class="code" href="base_2logging_8h.html#ae4db23f10f5d4aad6d735f5a74cd6f8c">CHECK_LE</a>(percent, 100.0);</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <a class="code" href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a>(percent, 0.0);</div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  std::vector<double> sorted_records(records_.begin(), records_.end());</div><div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  std::sort(sorted_records.begin(), sorted_records.end());</div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> num_records = sorted_records.size();</div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span> </div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> percentile_rank =</div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  static_cast<double>(num_records) * percent / 100.0 - 0.5;</div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keywordflow">if</span> (percentile_rank <= 0) {</div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <span class="keywordflow">return</span> sorted_records.front();</div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (percentile_rank >= num_records - 1) {</div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keywordflow">return</span> sorted_records.back();</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="comment">// Interpolate.</span></div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <a class="code" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(num_records, 2);</div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <a class="code" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(percentile_rank, num_records - 1);</div><div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> lower_rank = static_cast<int>(std::floor(percentile_rank));</div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <a class="code" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(lower_rank, num_records - 1);</div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <span class="keywordflow">return</span> sorted_records[lower_rank] +</div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  (percentile_rank - lower_rank) *</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  (sorted_records[lower_rank + 1] - sorted_records[lower_rank]);</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span> }</div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span> </div><div class="line"><a name="l00278"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a441a154d125df2eb884a44be77e2bfc0"> 278</a></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="l00279"></a><span class="lineno"> 279</span>  std::vector<std::vector<int64_t>>* tuples) {</div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="keywordflow">if</span> (tuples->empty()) <span class="keywordflow">return</span>;</div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span> </div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="comment">// Remove duplicates if any.</span></div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <a class="code" href="namespacegtl.html#a288a1dc92da5d3ad62d4bc4cec9e8b1d">gtl::STLSortAndRemoveDuplicates</a>(tuples);</div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span> </div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> num_vars = (*tuples)[0].size();</div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span> </div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  std::vector<int> to_remove;</div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  std::vector<int64_t> tuple_minus_var_i(num_vars - 1);</div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_vars; ++i) {</div><div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> domain_size = domain_sizes[i];</div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="keywordflow">if</span> (domain_size == 1) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  absl::flat_hash_map<const std::vector<int64_t>, std::vector<int>></div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  masked_tuples_to_indices;</div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> t = 0; t < tuples->size(); ++t) {</div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="keywordtype">int</span> out = 0;</div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < num_vars; ++j) {</div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordflow">if</span> (i == j) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  tuple_minus_var_i[out++] = (*tuples)[t][j];</div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  }</div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  masked_tuples_to_indices[tuple_minus_var_i].push_back(t);</div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  }</div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  to_remove.clear();</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& it : masked_tuples_to_indices) {</div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keywordflow">if</span> (it.second.size() != domain_size) <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  (*tuples)[it.second.front()][i] = any_value;</div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  to_remove.insert(to_remove.end(), it.second.begin() + 1, it.second.end());</div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  }</div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  std::sort(to_remove.begin(), to_remove.end(), std::greater<int>());</div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> t : to_remove) {</div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  (*tuples)[t] = tuples->back();</div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  tuples->pop_back();</div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  }</div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  }</div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span> }</div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span> </div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span> } <span class="comment">// namespace sat</span></div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span> } <span class="comment">// namespace operations_research</span></div><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="alldiff__cst_8cc_html_ad10edae0a852d72fb76afb1c77735045"><div class="ttname"><a href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a></div><div class="ttdeci">int64_t min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_a7cc25402ecd7591b4c39934dd656b1f9"><div class="ttname"><a href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a></div><div class="ttdeci">#define CHECK_GE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00706">base/logging.h:706</a></div></div>
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<div class="ttc" id="stl__util_8h_html"><div class="ttname"><a href="stl__util_8h.html">stl_util.h</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_sat_parameters_html_ae31c8a339e7515e82ad032f6f89ace68"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#ae31c8a339e7515e82ad032f6f89ace68">operations_research::sat::SatParameters::set_use_phase_saving</a></div><div class="ttdeci">void set_use_phase_saving(bool value)</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l03593">sat_parameters.pb.h:3593</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="base_2logging_8h_html_a7e03ec13560fa94a8fea569960d7efc6"><div class="ttname"><a href="base_2logging_8h.html#a7e03ec13560fa94a8fea569960d7efc6">CHECK_GT</a></div><div class="ttdeci">#define CHECK_GT(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00707">base/logging.h:707</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_sat_parameters_html_a8a7cbb53d028e253e201883124b6089e"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#a8a7cbb53d028e253e201883124b6089e">operations_research::sat::SatParameters::set_random_branches_ratio</a></div><div class="ttdeci">void set_random_branches_ratio(double value)</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l03677">sat_parameters.pb.h:3677</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_literal_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_literal.html">operations_research::sat::Literal</a></div><div class="ttdef"><b>Definition:</b> <a href="sat__base_8h_source.html#l00066">sat_base.h:66</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_aa64bf49d041052c7cb3f40f7496d7534"><div class="ttname"><a href="namespaceoperations__research.html#aa64bf49d041052c7cb3f40f7496d7534">operations_research::CapProd</a></div><div class="ttdeci">int64_t CapProd(int64_t x, int64_t y)</div><div class="ttdef"><b>Definition:</b> <a href="saturated__arithmetic_8h_source.html#l00235">saturated_arithmetic.h:235</a></div></div>
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<div class="ttc" id="namespacegtl_html_a288a1dc92da5d3ad62d4bc4cec9e8b1d"><div class="ttname"><a href="namespacegtl.html#a288a1dc92da5d3ad62d4bc4cec9e8b1d">gtl::STLSortAndRemoveDuplicates</a></div><div class="ttdeci">void STLSortAndRemoveDuplicates(T *v, const LessFunc &less_func)</div><div class="ttdef"><b>Definition:</b> <a href="stl__util_8h_source.html#l00058">stl_util.h:58</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="alldiff__cst_8cc_html_a26e6db9bcc64b584051ecc28171ed11f"><div class="ttname"><a href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a></div><div class="ttdeci">int64_t max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00140">alldiff_cst.cc:140</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_a46e69120fbd3b36e6960e096d23b66f0"><div class="ttname"><a href="base_2logging_8h.html#a46e69120fbd3b36e6960e096d23b66f0">DCHECK_NE</a></div><div class="ttdeci">#define DCHECK_NE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00891">base/logging.h:891</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_ae4db23f10f5d4aad6d735f5a74cd6f8c"><div class="ttname"><a href="base_2logging_8h.html#ae4db23f10f5d4aad6d735f5a74cd6f8c">CHECK_LE</a></div><div class="ttdeci">#define CHECK_LE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00704">base/logging.h:704</a></div></div>
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<div class="ttc" id="namespacegtl_html_aae28e97bd1fa93cb0032642550da7455"><div class="ttname"><a href="namespacegtl.html#aae28e97bd1fa93cb0032642550da7455">gtl::ContainsKey</a></div><div class="ttdeci">bool ContainsKey(const Collection &collection, const Key &key)</div><div class="ttdef"><b>Definition:</b> <a href="map__util_8h_source.html#l00200">map_util.h:200</a></div></div>
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<div class="ttc" id="classoperations__research_1_1sat_1_1_sat_parameters_html_a05528f270d7291bd49be9f8575780fcb"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#a05528f270d7291bd49be9f8575780fcb">operations_research::sat::SatParameters::set_random_polarity_ratio</a></div><div class="ttdeci">void set_random_polarity_ratio(double value)</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l03649">sat_parameters.pb.h:3649</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="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_sat_parameters_html_a12558bbe25af1ee14f86bab924c96709"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#a12558bbe25af1ee14f86bab924c96709">operations_research::sat::SatParameters::set_initial_polarity</a></div><div class="ttdeci">void set_initial_polarity(::operations_research::sat::SatParameters_Polarity value)</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l03565">sat_parameters.pb.h:3565</a></div></div>
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<div class="ttc" id="saturated__arithmetic_8h_html"><div class="ttname"><a href="saturated__arithmetic_8h.html">saturated_arithmetic.h</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_2util_8h_html"><div class="ttname"><a href="sat_2util_8h.html">util.h</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="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_1sat_1_1_sat_parameters_html_a1e17932252915c774d68a1ba03950715"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#a1e17932252915c774d68a1ba03950715">operations_research::sat::SatParameters::Polarity_descriptor</a></div><div class="ttdeci">static const ::PROTOBUF_NAMESPACE_ID::EnumDescriptor * Polarity_descriptor()</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l00526">sat_parameters.pb.h:526</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_sat_parameters_html_a0e0e7b7f0e5cc8e0b535ffab534fade0"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#a0e0e7b7f0e5cc8e0b535ffab534fade0">operations_research::sat::SatParameters::VariableOrder_descriptor</a></div><div class="ttdeci">static const ::PROTOBUF_NAMESPACE_ID::EnumDescriptor * VariableOrder_descriptor()</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l00490">sat_parameters.pb.h:490</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="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_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_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="base_2logging_8h_html_ab25e01a2942b821d66371fc68d53f2eb"><div class="ttname"><a href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a></div><div class="ttdeci">#define CHECK_NE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00703">base/logging.h:703</a></div></div>
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<div class="ttc" id="base_2logging_8h_html_ab62f5ed8f2d48e29802be0cbbcd1359a"><div class="ttname"><a href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a></div><div class="ttdeci">#define DCHECK_LT(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00893">base/logging.h:893</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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<div class="ttc" id="classoperations__research_1_1sat_1_1_sat_parameters_html_a7e544bdc4785ce055ed01ca1f22fca41"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_sat_parameters.html#a7e544bdc4785ce055ed01ca1f22fca41">operations_research::sat::SatParameters::set_preferred_variable_order</a></div><div class="ttdeci">void set_preferred_variable_order(::operations_research::sat::SatParameters_VariableOrder value)</div><div class="ttdef"><b>Definition:</b> <a href="sat__parameters_8pb_8h_source.html#l03536">sat_parameters.pb.h:3536</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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