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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 id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" 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>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#ifndef OR_TOOLS_SAT_UTIL_H_</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#define OR_TOOLS_SAT_UTIL_H_</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <cstdint></span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <deque></span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> </div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include "<a class="code" href="base_2logging_8h.html">ortools/base/logging.h</a>"</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#if !defined(__PORTABLE_PLATFORM__)</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include "google/protobuf/descriptor.h"</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#endif </span><span class="comment">// __PORTABLE_PLATFORM__</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include "absl/container/btree_set.h"</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include "absl/random/bit_gen_ref.h"</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include "absl/random/random.h"</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="preprocessor">#include "absl/types/span.h"</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="preprocessor">#include "<a class="code" href="sat_2model_8h.html">ortools/sat/model.h</a>"</span></div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="preprocessor">#include "<a class="code" href="sat__base_8h.html">ortools/sat/sat_base.h</a>"</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="preprocessor">#include "ortools/sat/sat_parameters.pb.h"</span></div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="preprocessor">#include "<a class="code" href="random__engine_8h.html">ortools/util/random_engine.h</a>"</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor">#include "<a class="code" href="time__limit_8h.html">ortools/util/time_limit.h</a>"</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> </div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="keyword">namespace </span>sat {</div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">// Returns a in [0, m) such that a * x = 1 modulo m.</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// If gcd(x, m) != 1, there is no inverse, and it returns 0.</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">//</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// This DCHECK that x is in [0, m).</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">// This is integer overflow safe.</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">//</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// Note(user): I didn't find this in a easily usable standard library.</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span>int64_t <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#abbbb4c91f9a3d6eb290709745f5b661c">ModularInverse</a>(int64_t x, int64_t m);</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment">// Just returns x % m but with a result always in [0, m).</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span>int64_t <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a629c989df2521428c30722f175874774">PositiveMod</a>(int64_t x, int64_t m);</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">// If we know that X * coeff % mod = rhs % mod, this returns c such that</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// PositiveMod(X, mod) = c.</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">//</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">// This requires coeff != 0, mod !=0 and gcd(coeff, mod) == 1.</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment">// The result will be in [0, mod) but there is no other condition on the sign or</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment">// magnitude of a and b.</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment">//</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment">// This is overflow safe, and when rhs == 0 or abs(mod) == 1, it returns 0.</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span>int64_t <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ac015d81b88379719f680eadc2aad1508">ProductWithModularInverse</a>(int64_t <a class="code hl_variable" href="variable__and__expressions_8cc.html#a2091cd7d80fdd31762020bce86138587">coeff</a>, int64_t mod, int64_t rhs);</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">// Returns true if the equation a * X + b * Y = cte has some integer solutions.</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment">// For now, we check that a and b are different from 0 and from int64_t min.</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="comment">//</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="comment">// There is actually always a solution if cte % gcd(|a|, |b|) == 0. And because</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</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>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="comment">// and Y fitting on an int64_t.</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment">//</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment">// We will divide everything by gcd(a, b) first, so it is why we take reference</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="comment">// and the equation can change.</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="comment">//</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="comment">// If there are solutions, we return one of them (x0, y0).</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="comment">// From any such solution, the set of all solutions is given for Z integer by:</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span><span class="comment">// X = x0 + b * Z;</span></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="comment">// Y = y0 - a * Z;</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="comment">//</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span><span class="comment">// Given a domain for X and Y, it is possible to compute the "exact" domain of Z</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="comment">// with our Domain functions. Note however that this will only compute solution</span></div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span><span class="comment">// where both x-x0 and y-y0 do fit on an int64_t:</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="comment">// DomainOf(x).SubtractionWith(x0).InverseMultiplicationBy(b).IntersectionWith(</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="comment">// DomainOf(y).SubtractionWith(y0).InverseMultiplicationBy(-a))</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="keywordtype">bool</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a852a51b53f6217d6bfd1aef455f53f8c">SolveDiophantineEquationOfSizeTwo</a>(int64_t& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>, int64_t& <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>, int64_t& cte,</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> int64_t& x0, int64_t& y0);</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="comment">// The argument must be non-negative.</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span>int64_t <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#aa7497b495a7fbfddaea40d45861680c5">FloorSquareRoot</a>(int64_t <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>);</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span>int64_t <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a72e9fb9c1d4b0649782f8696e85cbbaa">CeilSquareRoot</a>(int64_t <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>);</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="comment">// Returns the multiple of base closest to value. If there is a tie, we return</span></div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="comment">// the one closest to zero. This way we have ClosestMultiple(x) =</span></div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span><span class="comment">// -ClosestMultiple(-x) which is important for how this is used.</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span>int64_t <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a2269a7a6f3b17cbd10a8d8a3914d8b51">ClosestMultiple</a>(int64_t <a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>, int64_t base);</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span><span class="comment">// Given a linear equation "sum coeff_i * X_i <= rhs. We can rewrite it using</span></div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span><span class="comment">// ClosestMultiple() as "base * new_terms + error <= rhs" where error can be</span></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span><span class="comment">// bounded using the provided bounds on each variables. This will return true if</span></div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span><span class="comment">// the error can be ignored and this equation is completely equivalent to</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="comment">// new_terms <= new_rhs.</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment">//</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment">// This is useful for cases like 9'999 X + 10'0001 Y <= 155'000 where we have</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="comment">// weird coefficient (maybe due to scaling). With a base of 10K, this is</span></div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span><span class="comment">// equivalent to X + Y <= 15.</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span><span class="comment">//</span></div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span><span class="comment">// Preconditions: All coeffs are assumed to be positive. You can easily negate</span></div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span><span class="comment">// all the negative coeffs and corresponding bounds before calling this.</span></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span><span class="keywordtype">bool</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#af20de3e143682d110b863c2e9435f050">LinearInequalityCanBeReducedWithClosestMultiple</a>(</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> int64_t base, <span class="keyword">const</span> std::vector<int64_t>& coeffs,</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keyword">const</span> std::vector<int64_t>& lbs, <span class="keyword">const</span> std::vector<int64_t>& ubs,</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> int64_t rhs, int64_t* new_rhs);</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span><span class="comment">// The model "singleton" random engine used in the solver.</span></div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span><span class="comment">//</span></div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span><span class="comment">// In test, we usually set use_absl_random() so that the sequence is changed at</span></div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span><span class="comment">// each invocation. This way, clients do not relly on the wrong assumption that</span></div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span><span class="comment">// a particular optimal solution will be returned if they are many equivalent</span></div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span><span class="comment">// ones.</span></div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_model_random_generator.html"> 115</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1sat_1_1_model_random_generator.html">ModelRandomGenerator</a> : <span class="keyword">public</span> absl::BitGenRef {</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// We seed the strategy at creation only. This should be enough for our use</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="comment">// case since the SatParameters is set first before the solver is created. We</span></div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="comment">// also never really need to change the seed afterwards, it is just used to</span></div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="comment">// diversify solves with identical parameters on different Model objects.</span></div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_model_random_generator.html#a01d0fd84c6567d5a7628deeac9a8ab23"> 121</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_model_random_generator.html#a01d0fd84c6567d5a7628deeac9a8ab23">ModelRandomGenerator</a>(<a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>)</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> : <a class="code hl_namespace" href="namespaceabsl.html">absl</a>::BitGenRef(deterministic_random_) {</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keyword">const</span> <span class="keyword">auto</span>& params = *<a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>->GetOrCreate<SatParameters>();</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> deterministic_random_.seed(params.random_seed());</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordflow">if</span> (params.use_absl_random()) {</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> absl_random_ = absl::BitGen(absl::SeedSeq({params.random_seed()}));</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> absl::BitGenRef::operator=(absl::BitGenRef(absl_random_));</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> }</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> }</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> </div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="comment">// This is just used to display ABSL_RANDOM_SALT_OVERRIDE in the log so that</span></div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="comment">// it is possible to reproduce a failure more easily while looking at a solver</span></div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="comment">// log.</span></div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="comment">// TODO(user): I didn't find a cleaner way to log this.</span></div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_model_random_generator.html#a7302efe7585eecd121c7c0a6113c8ae4"> 136</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_model_random_generator.html#a7302efe7585eecd121c7c0a6113c8ae4">LogSalt</a>()<span class="keyword"> const </span>{}</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> </div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a6743e8c90bbb85a1017486ed70c7d29b">random_engine_t</a> deterministic_random_;</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> absl::BitGen absl_random_;</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span>};</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> </div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="comment">// The model "singleton" shared time limit.</span></div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_model_shared_time_limit.html"> 144</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1sat_1_1_model_shared_time_limit.html">ModelSharedTimeLimit</a> : <span class="keyword">public</span> <a class="code hl_class" href="classoperations__research_1_1_shared_time_limit.html">SharedTimeLimit</a> {</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_model_shared_time_limit.html#a79b7879c6b56eab4a6c0222adf4d6e51"> 146</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_model_shared_time_limit.html#a79b7879c6b56eab4a6c0222adf4d6e51">ModelSharedTimeLimit</a>(<a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>)</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> : <a class="code hl_class" href="classoperations__research_1_1_shared_time_limit.html">SharedTimeLimit</a>(<a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>->GetOrCreate<<a class="code hl_class" href="classoperations__research_1_1_time_limit.html">TimeLimit</a>>()) {}</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span>};</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> </div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span><span class="comment">// Randomizes the decision heuristic of the given SatParameters.</span></div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a0441e1a54fe203c0707131e587de8fae">RandomizeDecisionHeuristic</a>(absl::BitGenRef random,</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> SatParameters* <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>);</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> </div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span><span class="comment">// Context: this function is not really generic, but required to be unit-tested.</span></div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span><span class="comment">// It is used in a clause minimization algorithm when we try to detect if any of</span></div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span><span class="comment">// the clause literals can be propagated by a subset of the other literal being</span></div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span><span class="comment">// false. For that, we want to enqueue in the solver all the subset of size n-1.</span></div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span><span class="comment">//</span></div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span><span class="comment">// This moves one of the unprocessed literal from literals to the last position.</span></div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span><span class="comment">// The function tries to do that while preserving the longest possible prefix of</span></div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span><span class="comment">// literals "amortized" through the calls assuming that we want to move each</span></div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span><span class="comment">// literal to the last position once.</span></div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span><span class="comment">//</span></div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span><span class="comment">// For a vector of size n, if we want to call this n times so that each literal</span></div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span><span class="comment">// is last at least once, the sum of the size of the changed suffixes will be</span></div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span><span class="comment">// O(n log n). If we were to use a simpler algorithm (like moving the last</span></div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span><span class="comment">// unprocessed literal to the last position), this sum would be O(n^2).</span></div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span><span class="comment">//</span></div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span><span class="comment">// Returns the size of the common prefix of literals before and after the move,</span></div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span><span class="comment">// or -1 if all the literals are already processed. The argument</span></div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span><span class="comment">// relevant_prefix_size is used as a hint when keeping more that this prefix</span></div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span><span class="comment">// size do not matter. The returned value will always be lower or equal to</span></div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span><span class="comment">// relevant_prefix_size.</span></div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span><span class="keywordtype">int</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ae1ffd76bca69ccb2e7b65dfe2cf76f2e">MoveOneUnprocessedLiteralLast</a>(</div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="keyword">const</span> absl::btree_set<LiteralIndex>& processed, <span class="keywordtype">int</span> relevant_prefix_size,</div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> std::vector<Literal>* literals);</div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> </div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span><span class="comment">// ============================================================================</span></div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span><span class="comment">// Implementation.</span></div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span><span class="comment">// ============================================================================</span></div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> </div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span><span class="comment">// Manages incremental averages.</span></div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html"> 183</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1sat_1_1_incremental_average.html">IncrementalAverage</a> {</div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="comment">// Initializes the average with 'initial_average' and number of records to 0.</span></div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html#a2f01b362e8160a5d5a3d30a09ffe280c"> 186</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_incremental_average.html#a2f01b362e8160a5d5a3d30a09ffe280c">IncrementalAverage</a>(<span class="keywordtype">double</span> initial_average)</div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> : average_(initial_average) {}</div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html#a8f4ea7664e6ea6da0bff32eac8f4a975"> 188</a></span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_incremental_average.html#a8f4ea7664e6ea6da0bff32eac8f4a975">IncrementalAverage</a>() {}</div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> </div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="comment">// Sets the number of records to 0 and average to 'reset_value'.</span></div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_incremental_average.html#adf01dcbe31fa99f0a8f9d91ba9f85b8b">Reset</a>(<span class="keywordtype">double</span> reset_value);</div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> </div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html#a6d9b473fa04b0558a8e48737f5ab9564"> 193</a></span> <span class="keywordtype">double</span> <a class="code hl_function" 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>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_incremental_average.html#a1bdd878a5252fe5eb23b9319ed5b3f35"> 194</a></span> int64_t <a class="code hl_function" 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>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> </div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_incremental_average.html#a198870bbc0f9b8d197a4c80f766ddf49">AddData</a>(<span class="keywordtype">double</span> new_record);</div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> </div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="keywordtype">double</span> average_ = 0.0;</div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> int64_t num_records_ = 0;</div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span>};</div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> </div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span><span class="comment">// Manages exponential moving averages defined as</span></div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span><span class="comment">// new_average = decaying_factor * old_average</span></div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span><span class="comment">// + (1 - decaying_factor) * new_record.</span></div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span><span class="comment">// where 0 < decaying_factor < 1.</span></div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html"> 207</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html">ExponentialMovingAverage</a> {</div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a5e3f98a369b372eb5521317e3eb3a4a0"> 209</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a5e3f98a369b372eb5521317e3eb3a4a0">ExponentialMovingAverage</a>(<span class="keywordtype">double</span> decaying_factor)</div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> : decaying_factor_(decaying_factor) {</div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <a class="code hl_define" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(decaying_factor, 0.0);</div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <a class="code hl_define" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(decaying_factor, 1.0);</div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> }</div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> </div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="comment">// Returns exponential moving average for all the added data so far.</span></div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a6d9b473fa04b0558a8e48737f5ab9564"> 216</a></span> <span class="keywordtype">double</span> <a class="code hl_function" 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>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> </div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="comment">// Returns the total number of added records so far.</span></div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a1bdd878a5252fe5eb23b9319ed5b3f35"> 219</a></span> int64_t <a class="code hl_function" 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>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> </div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_exponential_moving_average.html#a198870bbc0f9b8d197a4c80f766ddf49">AddData</a>(<span class="keywordtype">double</span> new_record);</div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> </div>
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<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> <span class="keywordtype">double</span> average_ = 0.0;</div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> int64_t num_records_ = 0;</div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="keyword">const</span> <span class="keywordtype">double</span> decaying_factor_;</div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span>};</div>
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<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> </div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span><span class="comment">// Utility to calculate percentile (First variant) for limited number of</span></div>
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span><span class="comment">// records. Reference: https://en.wikipedia.org/wiki/Percentile</span></div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span><span class="comment">//</span></div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span><span class="comment">// After the vector is sorted, we assume that the element with index i</span></div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span><span class="comment">// correspond to the percentile 100*(i+0.5)/size. For percentiles before the</span></div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span><span class="comment">// first element (resp. after the last one) we return the first element (resp.</span></div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span><span class="comment">// the last). And otherwise we do a linear interpolation between the two element</span></div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span><span class="comment">// around the asked percentile.</span></div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_percentile.html"> 237</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1sat_1_1_percentile.html">Percentile</a> {</div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_percentile.html#aae45e57e2fc34863a5272f4ec3ec2bef"> 239</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_percentile.html#aae45e57e2fc34863a5272f4ec3ec2bef">Percentile</a>(<span class="keywordtype">int</span> record_limit) : record_limit_(record_limit) {}</div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> </div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_percentile.html#adfcf2b433605c03210cbd06e28ce9d97">AddRecord</a>(<span class="keywordtype">double</span> record);</div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> </div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="comment">// Returns number of stored records.</span></div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_percentile.html#a1bdd878a5252fe5eb23b9319ed5b3f35"> 244</a></span> int64_t <a class="code hl_function" 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>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> </div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="comment">// Note that this is not fast and runs in O(n log n) for n records.</span></div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="keywordtype">double</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_percentile.html#a006c3e4f212cee5414d510a9ded6eedb">GetPercentile</a>(<span class="keywordtype">double</span> percent);</div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> </div>
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> std::deque<double> records_;</div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="keyword">const</span> <span class="keywordtype">int</span> record_limit_;</div>
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span>};</div>
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<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> </div>
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<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span><span class="comment">// This method tries to compress a list of tuples by merging complementary</span></div>
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span><span class="comment">// tuples, that is a set of tuples that only differ on one variable, and that</span></div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span><span class="comment">// cover the domain of the variable. In that case, it will keep only one tuple,</span></div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span><span class="comment">// and replace the value for variable by any_value, the equivalent of '*' in</span></div>
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<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span><span class="comment">// regexps.</span></div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span><span class="comment">//</span></div>
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<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span><span class="comment">// This method is exposed for testing purposes.</span></div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a3e5f39b52251ad02e571592493b4d39f">CompressTuples</a>(absl::Span<const int64_t> domain_sizes, int64_t any_value,</div>
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<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> std::vector<std::vector<int64_t>>* tuples);</div>
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<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> </div>
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span>} <span class="comment">// namespace sat</span></div>
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<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> </div>
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_SAT_UTIL_H_</span></div>
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<div class="ttc" id="abase_2logging_8h_html"><div class="ttname"><a href="base_2logging_8h.html">logging.h</a></div></div>
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<div class="ttc" id="abase_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#l00893">base/logging.h:893</a></div></div>
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<div class="ttc" id="abase_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#l00895">base/logging.h:895</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00352">time_limit.h:352</a></div></div>
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<div class="ttc" id="aclassoperations__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="aclassoperations__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#l00207">sat/util.h:207</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00331">sat/util.cc:331</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00219">sat/util.h:219</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00209">sat/util.h:209</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00216">sat/util.h:216</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00183">sat/util.h:183</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00326">sat/util.cc:326</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00194">sat/util.h:194</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00186">sat/util.h:186</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00193">sat/util.h:193</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00188">sat/util.h:188</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00321">sat/util.cc:321</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00042">sat/model.h:42</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00115">sat/util.h:115</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00121">sat/util.h:121</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00136">sat/util.h:136</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00144">sat/util.h:144</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00146">sat/util.h:146</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00237">sat/util.h:237</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00345">sat/util.cc:345</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00244">sat/util.h:244</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00239">sat/util.h:239</a></div></div>
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<div class="ttc" id="aclassoperations__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#l00338">sat/util.cc:338</a></div></div>
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<div class="ttc" id="aconstraint__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="aconstraint__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="acp__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#l00119">cp_model_fz_solver.cc:119</a></div></div>
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<div class="ttc" id="ademon__profiler_8cc_html_ac072af30c4ffbc834bb4c681f6ecb514"><div class="ttname"><a href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a></div><div class="ttdeci">int64_t value</div><div class="ttdef"><b>Definition:</b> <a href="demon__profiler_8cc_source.html#l00044">demon_profiler.cc:44</a></div></div>
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<div class="ttc" id="agurobi__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="anamespaceabsl_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="anamespaceoperations__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#l00059">sat/util.cc:59</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a2269a7a6f3b17cbd10a8d8a3914d8b51"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a2269a7a6f3b17cbd10a8d8a3914d8b51">operations_research::sat::ClosestMultiple</a></div><div class="ttdeci">int64_t ClosestMultiple(int64_t value, int64_t base)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00211">sat/util.cc:211</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a3e5f39b52251ad02e571592493b4d39f"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a3e5f39b52251ad02e571592493b4d39f">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#l00370">sat/util.cc:370</a></div></div>
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<div class="ttc" id="anamespaceoperations__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#l00120">sat/util.cc:120</a></div></div>
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<div class="ttc" id="anamespaceoperations__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#l00203">sat/util.cc:203</a></div></div>
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<div class="ttc" id="anamespaceoperations__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#l00147">sat/util.cc:147</a></div></div>
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<div class="ttc" id="anamespaceoperations__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#l00194">sat/util.cc:194</a></div></div>
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<div class="ttc" id="anamespaceoperations__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#l00087">sat/util.cc:87</a></div></div>
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<div class="ttc" id="anamespaceoperations__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#l00125">sat/util.cc:125</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ae1ffd76bca69ccb2e7b65dfe2cf76f2e"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ae1ffd76bca69ccb2e7b65dfe2cf76f2e">operations_research::sat::MoveOneUnprocessedLiteralLast</a></div><div class="ttdeci">int MoveOneUnprocessedLiteralLast(const absl::btree_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#l00282">sat/util.cc:282</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_af20de3e143682d110b863c2e9435f050"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#af20de3e143682d110b863c2e9435f050">operations_research::sat::LinearInequalityCanBeReducedWithClosestMultiple</a></div><div class="ttdeci">bool LinearInequalityCanBeReducedWithClosestMultiple(int64_t base, const std::vector< int64_t > &coeffs, const std::vector< int64_t > &lbs, const std::vector< int64_t > &ubs, int64_t rhs, int64_t *new_rhs)</div><div class="ttdef"><b>Definition:</b> <a href="sat_2util_8cc_source.html#l00218">sat/util.cc:218</a></div></div>
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<div class="ttc" id="anamespaceoperations__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="anamespaceoperations__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="arandom__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="asat_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="asat__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="atime__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="avariable__and__expressions_8cc_html_a2091cd7d80fdd31762020bce86138587"><div class="ttname"><a href="variable__and__expressions_8cc.html#a2091cd7d80fdd31762020bce86138587">coeff</a></div><div class="ttdeci">const double coeff</div><div class="ttdef"><b>Definition:</b> <a href="variable__and__expressions_8cc_source.html#l00105">variable_and_expressions.cc:105</a></div></div>
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