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363 lines
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<a href="all__different_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_ALL_DIFFERENT_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_ALL_DIFFERENT_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 <functional></span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include <utility></span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> </div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include "absl/container/flat_hash_map.h"</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include "<a class="code" href="integral__types_8h.html">ortools/base/integral_types.h</a>"</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include "<a class="code" href="macros_8h.html">ortools/base/macros.h</a>"</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include "<a class="code" href="integer_8h.html">ortools/sat/integer.h</a>"</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</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="l00027" name="l00027"></a><span class="lineno"> 27</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="l00028" name="l00028"></a><span class="lineno"> 28</span> </div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</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="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="keyword">namespace </span>sat {</div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// Enforces that the given tuple of variables takes different values. This fully</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">// encodes all the variables and simply enforces a <= 1 constraint on each</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">// possible values.</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span>std::function<void(Model*)> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a9d6526e2b6f684e7c3c80172b598b7cb">AllDifferentBinary</a>(</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keyword">const</span> std::vector<IntegerVariable>& vars);</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">// Enforces that the given tuple of variables takes different values.</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// Same as AllDifferentBinary() but use a different propagator that only enforce</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// the so called "bound consistency" on the variable domains.</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">//</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">// Compared to AllDifferentBinary() this doesn't require fully encoding the</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">// variables and it is also quite fast. Note that the propagation is different,</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// this will not remove already taken values from inside a domain, but it will</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment">// propagates more the domain bounds.</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span>std::function<void(Model*)> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#aee7948e4ec576c5102f5f09028388d4c">AllDifferentOnBounds</a>(</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">const</span> std::vector<IntegerVariable>& vars);</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span>std::function<void(Model*)> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#aee7948e4ec576c5102f5f09028388d4c">AllDifferentOnBounds</a>(</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keyword">const</span> std::vector<AffineExpression>& expressions);</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// This constraint forces all variables to take different values. This is meant</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">// to be used as a complement to an alldifferent decomposition like</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">// AllDifferentBinary(): DO NOT USE WITHOUT ONE. Doing the filtering that the</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment">// decomposition can do with an appropriate algorithm should be cheaper and</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment">// yield more accurate explanations.</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">// It uses the matching algorithm described in Regin at AAAI1994:</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment">// "A filtering algorithm for constraints of difference in CSPs".</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="comment">//</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">// This will fully encode variables.</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span>std::function<void(Model*)> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a0f570bf53aae0cd9303912d273425428">AllDifferentAC</a>(</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keyword">const</span> std::vector<IntegerVariable>& variables);</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="comment">// Implementation of AllDifferentAC().</span></div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_all_different_constraint.html"> 65</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1sat_1_1_all_different_constraint.html">AllDifferentConstraint</a> : <a class="code hl_class" href="classoperations__research_1_1sat_1_1_propagator_interface.html">PropagatorInterface</a> {</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_all_different_constraint.html#aa93f9022262acc95180e6483878d95d5">AllDifferentConstraint</a>(std::vector<IntegerVariable> variables,</div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_integer_encoder.html">IntegerEncoder</a>* encoder, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_trail.html">Trail</a>* trail,</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_integer_trail.html">IntegerTrail</a>* integer_trail);</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_all_different_constraint.html#ac1fe9b1f2b978c4283e42f12e586eb1e">Propagate</a>() <span class="keyword">final</span>;</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_all_different_constraint.html#a6ee8ed57254aec3ae99d399bae5b3736">RegisterWith</a>(<a class="code hl_class" href="classoperations__research_1_1sat_1_1_generic_literal_watcher.html">GenericLiteralWatcher</a>* watcher);</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> </div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// MakeAugmentingPath() is a step in Ford-Fulkerson's augmenting path</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// algorithm. It changes its current internal state (see vectors below)</span></div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// to assign a value to the start vertex using an augmenting path.</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// If it is not possible, it keeps variable_to_value_[start] to -1 and returns</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// false, otherwise it modifies the current assignment and returns true.</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// It uses value/variable_visited to mark the nodes it visits during its</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// search: one can use this information to generate an explanation of failure,</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="comment">// or manipulate it to create what-if scenarios without modifying successor_.</span></div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordtype">bool</span> MakeAugmentingPath(<span class="keywordtype">int</span> <a class="code hl_variable" href="sparse__submatrix_8cc.html#a9b7656b922ea4ec96097d7380c0e61fe">start</a>);</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="comment">// Accessors to the cache of literals.</span></div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keyword">inline</span> LiteralIndex VariableLiteralIndexOf(<span class="keywordtype">int</span> x, int64_t <a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> VariableHasPossibleValue(<span class="keywordtype">int</span> x, int64_t <a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>);</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> </div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// This caches all literals of the fully encoded variables.</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// Values of a given variable are 0-indexed using offsets variable_min_value_,</span></div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// the set of all values is globally offset using offset min_all_values_.</span></div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// TODO(user): compare this encoding to a sparser hash_map encoding.</span></div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_variables_;</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keyword">const</span> std::vector<IntegerVariable> variables_;</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> int64_t min_all_values_;</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> int64_t num_all_values_;</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> std::vector<int64_t> variable_min_value_;</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> std::vector<int64_t> variable_max_value_;</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> std::vector<std::vector<LiteralIndex>> variable_literal_index_;</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> </div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="comment">// Internal state of MakeAugmentingPath().</span></div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// value_to_variable_ and variable_to_value_ represent the current assignment;</span></div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// -1 means not assigned. Otherwise,</span></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="comment">// variable_to_value_[var] = value <=> value_to_variable_[value] = var.</span></div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> std::vector<std::vector<int>> successor_;</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> std::vector<bool> value_visited_;</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> std::vector<bool> variable_visited_;</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> std::vector<int> value_to_variable_;</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> std::vector<int> variable_to_value_;</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> std::vector<int> prev_matching_;</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> std::vector<int> visiting_;</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> std::vector<int> variable_visited_from_;</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> </div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="comment">// Internal state of ComputeSCCs().</span></div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// Variable nodes are indexed by [0, num_variables_),</span></div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// value nodes by [num_variables_, num_variables_ + num_all_values_),</span></div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// and a dummy node with index num_variables_ + num_all_values_ is added.</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="comment">// The graph passed to ComputeSCCs() is the residual of the possible graph</span></div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="comment">// by the current matching, i.e. its arcs are:</span></div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="comment">// _ (var, val) if val \in dom(var) and var not matched to val,</span></div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="comment">// _ (val, var) if var matched to val,</span></div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="comment">// _ (val, dummy) if val not matched to any variable,</span></div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="comment">// _ (dummy, var) for all variables.</span></div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="comment">// In the original paper, forbidden arcs are identified by detecting that they</span></div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="comment">// are not in any alternating cycle or alternating path starting at a</span></div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="comment">// free vertex. Adding the dummy node allows to factor the alternating path</span></div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// part in the alternating cycle, and filter with only the SCC decomposition.</span></div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="comment">// When num_variables_ == num_all_values_, the dummy node is useless,</span></div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="comment">// we add it anyway to simplify the code.</span></div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> std::vector<std::vector<int>> residual_graph_successors_;</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> std::vector<int> component_number_;</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> </div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_trail.html">Trail</a>* trail_;</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_integer_trail.html">IntegerTrail</a>* integer_trail_;</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span>};</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> </div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span><span class="comment">// Implements the all different bound consistent propagator with explanation.</span></div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span><span class="comment">// That is, given n affine expressions that must take different values, this</span></div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span><span class="comment">// propagates the bounds of each expression as much as possible. The key is to</span></div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span><span class="comment">// detect the so called Hall interval which are interval of size k that contains</span></div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span><span class="comment">// the domain of k expressinos. Because all the variables must take different</span></div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span><span class="comment">// values, we can deduce that the domain of the other variables cannot contains</span></div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="comment">// such Hall interval.</span></div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span><span class="comment">//</span></div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span><span class="comment">// We use a "fast" O(n log n) algorithm.</span></div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span><span class="comment">//</span></div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span><span class="comment">// TODO(user): It might be difficult to find something faster than what is</span></div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span><span class="comment">// implemented here. Some related reference:</span></div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span><span class="comment">// https://cs.uwaterloo.ca/~vanbeek/Publications/ijcai03_TR.pdf</span></div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_all_different_bounds_propagator.html"> 150</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1sat_1_1_all_different_bounds_propagator.html">AllDifferentBoundsPropagator</a> : <span class="keyword">public</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_propagator_interface.html">PropagatorInterface</a> {</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_all_different_bounds_propagator.html#a78dfacd9548d8e380a976e1034c41c13">AllDifferentBoundsPropagator</a>(<span class="keyword">const</span> std::vector<AffineExpression>& expressions,</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_integer_trail.html">IntegerTrail</a>* integer_trail);</div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> </div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_all_different_bounds_propagator.html#ac1fe9b1f2b978c4283e42f12e586eb1e">Propagate</a>() <span class="keyword">final</span>;</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_all_different_bounds_propagator.html#a6ee8ed57254aec3ae99d399bae5b3736">RegisterWith</a>(<a class="code hl_class" href="classoperations__research_1_1sat_1_1_generic_literal_watcher.html">GenericLiteralWatcher</a>* watcher);</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> </div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="comment">// We locally cache the lb/ub for faster sorting and to guarantee some</span></div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="comment">// invariant when we push bounds.</span></div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="keyword">struct </span>CachedBounds {</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_affine_expression.html">AffineExpression</a> expr;</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> IntegerValue lb;</div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> IntegerValue ub;</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> };</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> </div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="comment">// Fills integer_reason_ with the reason why we have the given hall interval.</span></div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="keywordtype">void</span> FillHallReason(IntegerValue hall_lb, IntegerValue hall_ub);</div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> </div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="comment">// Do half the job of Propagate(). This will split the variable into</span></div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <span class="comment">// independent subset, and call PropagateLowerBoundsInternal() on each of</span></div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="comment">// them.</span></div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="keywordtype">bool</span> PropagateLowerBounds();</div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="keywordtype">bool</span> PropagateLowerBoundsInternal(IntegerValue min_lb,</div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> absl::Span<CachedBounds> vars);</div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> </div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="comment">// Internally, we will maintain a set of non-consecutive integer intervals of</span></div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="comment">// the form [start, end]. Each point (i.e. IntegerValue) of such interval will</span></div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="comment">// be associated to an unique input expression and via an union-find algorithm</span></div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="comment">// point to its start. The end only make sense for representative.</span></div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// TODO(user): Because we don't use rank, we have a worst case complexity of</span></div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="comment">// O(n log n). We could try a normal Union-find data structure, but then we</span></div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="comment">// also have to maintain a start vector.</span></div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="comment">// Note that during the execution of the algorithm we start from empty</span></div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="comment">// intervals and finish with a set of points of size num_vars.</span></div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <span class="comment">// The list of all points are maintained in the dense vectors index_to_*_</span></div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="comment">// where we have remapped values to indices (with GetIndex()) to make sure it</span></div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="comment">// always fall into the correct range.</span></div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="keywordtype">int</span> FindStartIndexAndCompressPath(<span class="keywordtype">int</span> <a class="code hl_variable" href="pack_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>);</div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> </div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keywordtype">int</span> GetIndex(IntegerValue <a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <a class="code hl_define" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(<a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>, base_);</div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <a class="code hl_define" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(<a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> - base_, index_to_start_index_.size());</div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <span class="keywordflow">return</span> (<a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> - base_).value();</div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> }</div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> </div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> IntegerValue GetValue(<span class="keywordtype">int</span> <a class="code hl_variable" href="pack_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> base_ + IntegerValue(<a class="code hl_variable" href="pack_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>); }</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> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_integer_trail.html">IntegerTrail</a>* integer_trail_;</div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> </div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="comment">// These vector will be either sorted by lb or by -ub.</span></div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> std::vector<CachedBounds> bounds_;</div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> std::vector<CachedBounds> negated_bounds_;</div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> </div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="comment">// The list of Hall intervalls detected so far, sorted.</span></div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> std::vector<IntegerValue> hall_starts_;</div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> std::vector<IntegerValue> hall_ends_;</div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> </div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="comment">// Non-consecutive intervals related data-structures.</span></div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> IntegerValue base_;</div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> std::vector<int> indices_to_clear_;</div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> std::vector<int> index_to_start_index_;</div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> std::vector<int> index_to_end_index_;</div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> std::vector<bool> index_is_present_;</div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> std::vector<AffineExpression> index_to_expr_;</div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> </div>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="comment">// Temporary integer reason.</span></div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> std::vector<IntegerLiteral> integer_reason_;</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> DISALLOW_COPY_AND_ASSIGN(<a class="code hl_class" href="classoperations__research_1_1sat_1_1_all_different_bounds_propagator.html">AllDifferentBoundsPropagator</a>);</div>
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<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span>};</div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> </div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span>} <span class="comment">// namespace sat</span></div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span>} <span class="comment">// namespace operations_research</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="preprocessor">#endif </span><span class="comment">// OR_TOOLS_SAT_ALL_DIFFERENT_H_</span></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#l00894">base/logging.h:894</a></div></div>
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<div class="ttc" id="abase_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="aclassoperations__research_1_1sat_1_1_all_different_bounds_propagator_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_all_different_bounds_propagator.html">operations_research::sat::AllDifferentBoundsPropagator</a></div><div class="ttdef"><b>Definition:</b> <a href="all__different_8h_source.html#l00150">all_different.h:150</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_all_different_bounds_propagator_html_a6ee8ed57254aec3ae99d399bae5b3736"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_all_different_bounds_propagator.html#a6ee8ed57254aec3ae99d399bae5b3736">operations_research::sat::AllDifferentBoundsPropagator::RegisterWith</a></div><div class="ttdeci">void RegisterWith(GenericLiteralWatcher *watcher)</div><div class="ttdef"><b>Definition:</b> <a href="all__different_8cc_source.html#l00656">all_different.cc:656</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_all_different_bounds_propagator_html_a78dfacd9548d8e380a976e1034c41c13"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_all_different_bounds_propagator.html#a78dfacd9548d8e380a976e1034c41c13">operations_research::sat::AllDifferentBoundsPropagator::AllDifferentBoundsPropagator</a></div><div class="ttdeci">AllDifferentBoundsPropagator(const std::vector< AffineExpression > &expressions, IntegerTrail *integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="all__different_8cc_source.html#l00436">all_different.cc:436</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_all_different_bounds_propagator_html_ac1fe9b1f2b978c4283e42f12e586eb1e"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_all_different_bounds_propagator.html#ac1fe9b1f2b978c4283e42f12e586eb1e">operations_research::sat::AllDifferentBoundsPropagator::Propagate</a></div><div class="ttdeci">bool Propagate() final</div><div class="ttdef"><b>Definition:</b> <a href="all__different_8cc_source.html#l00455">all_different.cc:455</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_all_different_constraint_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_all_different_constraint.html">operations_research::sat::AllDifferentConstraint</a></div><div class="ttdef"><b>Definition:</b> <a href="all__different_8h_source.html#l00065">all_different.h:65</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_all_different_constraint_html_a6ee8ed57254aec3ae99d399bae5b3736"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_all_different_constraint.html#a6ee8ed57254aec3ae99d399bae5b3736">operations_research::sat::AllDifferentConstraint::RegisterWith</a></div><div class="ttdeci">void RegisterWith(GenericLiteralWatcher *watcher)</div><div class="ttdef"><b>Definition:</b> <a href="all__different_8cc_source.html#l00166">all_different.cc:166</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_all_different_constraint_html_aa93f9022262acc95180e6483878d95d5"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_all_different_constraint.html#aa93f9022262acc95180e6483878d95d5">operations_research::sat::AllDifferentConstraint::AllDifferentConstraint</a></div><div class="ttdeci">AllDifferentConstraint(std::vector< IntegerVariable > variables, IntegerEncoder *encoder, Trail *trail, IntegerTrail *integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="all__different_8cc_source.html#l00107">all_different.cc:107</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_all_different_constraint_html_ac1fe9b1f2b978c4283e42f12e586eb1e"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_all_different_constraint.html#ac1fe9b1f2b978c4283e42f12e586eb1e">operations_research::sat::AllDifferentConstraint::Propagate</a></div><div class="ttdeci">bool Propagate() final</div><div class="ttdef"><b>Definition:</b> <a href="all__different_8cc_source.html#l00255">all_different.cc:255</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_generic_literal_watcher_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_generic_literal_watcher.html">operations_research::sat::GenericLiteralWatcher</a></div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l01221">integer.h:1221</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_integer_encoder_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_integer_encoder.html">operations_research::sat::IntegerEncoder</a></div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00356">integer.h:356</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_integer_trail_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_integer_trail.html">operations_research::sat::IntegerTrail</a></div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00613">integer.h:613</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_propagator_interface_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_propagator_interface.html">operations_research::sat::PropagatorInterface</a></div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l01173">integer.h:1173</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_trail_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_trail.html">operations_research::sat::Trail</a></div><div class="ttdef"><b>Definition:</b> <a href="sat__base_8h_source.html#l00235">sat_base.h:235</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="ainteger_8h_html"><div class="ttname"><a href="integer_8h.html">integer.h</a></div></div>
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<div class="ttc" id="aintegral__types_8h_html"><div class="ttname"><a href="integral__types_8h.html">integral_types.h</a></div></div>
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<div class="ttc" id="amacros_8h_html"><div class="ttname"><a href="macros_8h.html">macros.h</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a0f570bf53aae0cd9303912d273425428"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a0f570bf53aae0cd9303912d273425428">operations_research::sat::AllDifferentAC</a></div><div class="ttdeci">std::function< void(Model *)> AllDifferentAC(const std::vector< IntegerVariable > &variables)</div><div class="ttdef"><b>Definition:</b> <a href="all__different_8cc_source.html#l00094">all_different.cc:94</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a9d6526e2b6f684e7c3c80172b598b7cb"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a9d6526e2b6f684e7c3c80172b598b7cb">operations_research::sat::AllDifferentBinary</a></div><div class="ttdeci">std::function< void(Model *)> AllDifferentBinary(const std::vector< IntegerVariable > &vars)</div><div class="ttdef"><b>Definition:</b> <a href="all__different_8cc_source.html#l00033">all_different.cc:33</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_aee7948e4ec576c5102f5f09028388d4c"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#aee7948e4ec576c5102f5f09028388d4c">operations_research::sat::AllDifferentOnBounds</a></div><div class="ttdeci">std::function< void(Model *)> AllDifferentOnBounds(const std::vector< AffineExpression > &expressions)</div><div class="ttdef"><b>Definition:</b> <a href="all__different_8cc_source.html#l00067">all_different.cc:67</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="apack_8cc_html_a750b5d744c39a06bfb13e6eb010e35d0"><div class="ttname"><a href="pack_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a></div><div class="ttdeci">int index</div><div class="ttdef"><b>Definition:</b> <a href="pack_8cc_source.html#l00509">pack.cc:509</a></div></div>
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<div class="ttc" id="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="asparse__submatrix_8cc_html_a9b7656b922ea4ec96097d7380c0e61fe"><div class="ttname"><a href="sparse__submatrix_8cc.html#a9b7656b922ea4ec96097d7380c0e61fe">start</a></div><div class="ttdeci">int64_t start</div><div class="ttdef"><b>Definition:</b> <a href="sparse__submatrix_8cc_source.html#l00035">sparse_submatrix.cc:35</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_affine_expression_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_affine_expression.html">operations_research::sat::AffineExpression</a></div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00227">integer.h:227</a></div></div>
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