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<div class="title">circuit.h</div> </div>
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<a href="circuit_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a 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 name="l00013"></a><span class="lineno"> 13</span>  </div>
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<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#ifndef OR_TOOLS_SAT_CIRCUIT_H_</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#define OR_TOOLS_SAT_CIRCUIT_H_</span></div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>  </div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include <functional></span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#include <memory></span></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include <vector></span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  </div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include "absl/container/flat_hash_map.h"</span></div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include "<a class="code" href="int__type_8h.html">ortools/base/int_type.h</a>"</span></div>
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<div class="line"><a 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 name="l00024"></a><span class="lineno"> 24</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 name="l00025"></a><span class="lineno"> 25</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 name="l00026"></a><span class="lineno"> 26</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 name="l00027"></a><span class="lineno"> 27</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 name="l00028"></a><span class="lineno"> 28</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 name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include "<a class="code" href="rev_8h.html">ortools/util/rev.h</a>"</span></div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  </div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="keyword">namespace </span>sat {</div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  </div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// Circuit/sub-circuit constraint.</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// Nodes that are not in the unique allowed sub-circuit must point to themseves.</span></div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// A nodes that has no self-arc must thus be inside the sub-circuit. If there is</span></div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// no self-arc at all, then this constaint forces the circuit to go through all</span></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// the nodes. Multi-arcs are NOT supported.</span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// Important: for correctness, this constraint requires that "exactly one"</span></div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// constraints have been added for all the incoming (resp. outgoing) arcs of</span></div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// each node. Also, such constraint must propagate before this one.</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_circuit_propagator.html"> 44</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1sat_1_1_circuit_propagator.html">CircuitPropagator</a> : <a class="code" href="classoperations__research_1_1sat_1_1_propagator_interface.html">PropagatorInterface</a>, <a class="code" href="classoperations__research_1_1_reversible_interface.html">ReversibleInterface</a> {</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00046"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_circuit_propagator_1_1_options.html"> 46</a></span>  <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1sat_1_1_circuit_propagator_1_1_options.html">Options</a> {</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="comment">// Hack for the VRP to allow for more than one sub-circuit and forces all</span></div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="comment">// the subcircuits to go through the node zero.</span></div>
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<div class="line"><a name="l00049"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_circuit_propagator_1_1_options.html#af1123baeaa5412b68d37d8adf43ccb7c"> 49</a></span>  <span class="keywordtype">bool</span> <a class="code" href="structoperations__research_1_1sat_1_1_circuit_propagator_1_1_options.html#af1123baeaa5412b68d37d8adf43ccb7c">multiple_subcircuit_through_zero</a> = <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  };</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  </div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">// The constraints take a sparse representation of a graph on [0, n). Each arc</span></div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="comment">// being present when the given literal is true.</span></div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <a class="code" href="classoperations__research_1_1sat_1_1_circuit_propagator.html#ab724d1b4067da7ec830cb4d1b8284ee7">CircuitPropagator</a>(<span class="keywordtype">int</span> num_nodes, <span class="keyword">const</span> std::vector<int>& tails,</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keyword">const</span> std::vector<int>& heads,</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keyword">const</span> std::vector<Literal>& literals, <a class="code" href="structoperations__research_1_1sat_1_1_circuit_propagator_1_1_options.html">Options</a> options,</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <a class="code" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  </div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_circuit_propagator.html#a176d2c659864433ccd869b5fba8d57af">SetLevel</a>(<span class="keywordtype">int</span> level) <span class="keyword">final</span>;</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1sat_1_1_circuit_propagator.html#ac1fe9b1f2b978c4283e42f12e586eb1e">Propagate</a>() final;</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1sat_1_1_circuit_propagator.html#a45321337f970685d9847db005c4b3de1">IncrementalPropagate</a>(const std::vector<<span class="keywordtype">int</span>>& watch_indices) final;</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_circuit_propagator.html#a6ee8ed57254aec3ae99d399bae5b3736">RegisterWith</a>(<a class="code" href="classoperations__research_1_1sat_1_1_generic_literal_watcher.html">GenericLiteralWatcher</a>* watcher);</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  </div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  private:</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="comment">// Updates the structures when the given arc is added to the paths.</span></div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordtype">void</span> AddArc(<span class="keywordtype">int</span> <a class="code" href="routing__flow_8cc.html#a64e7efc5529154ba56903e75f5300990">tail</a>, <span class="keywordtype">int</span> <a class="code" href="routing__flow_8cc.html#afca32f65388659a4b0956496169488b4">head</a>, LiteralIndex literal_index);</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  </div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="comment">// Clears and fills reason with the literals of the arcs that form a path from</span></div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">// the given node. The path can be a cycle, but in this case it must end at</span></div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">// start (not like a rho shape).</span></div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keywordtype">void</span> FillReasonForPath(<span class="keywordtype">int</span> start_node, std::vector<<a class="code" href="classoperations__research_1_1sat_1_1_literal.html">Literal</a>>* reason) const;</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  </div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  const <span class="keywordtype">int</span> num_nodes_;</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  const <a class="code" href="structoperations__research_1_1sat_1_1_circuit_propagator_1_1_options.html">Options</a> options_;</div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <a class="code" href="classoperations__research_1_1sat_1_1_trail.html">Trail</a>* trail_;</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  const <a class="code" href="classoperations__research_1_1sat_1_1_variables_assignment.html">VariablesAssignment</a>& assignment_;</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  </div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="comment">// We use this to query in O(1) for an arc existence. The self-arcs are</span></div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">// accessed often, so we use a more efficient std::vector<> for them. Note</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="comment">// that we do not add self-arcs to graph_.</span></div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="comment">// TODO(user): for large dense graph, using a matrix is faster and uses less</span></div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">// memory. If the need arise we can have the two implementations.</span></div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  std::vector<<a class="code" href="classoperations__research_1_1sat_1_1_literal.html">Literal</a>> self_arcs_;</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <a class="code" href="namespaceabsl.html">absl</a>::flat_hash_map<std::pair<<span class="keywordtype">int</span>, <span class="keywordtype">int</span>>, <a class="code" href="classoperations__research_1_1sat_1_1_literal.html">Literal</a>> graph_;</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  </div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="comment">// Data used to interpret the watch indices passed to IncrementalPropagate().</span></div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  struct <a class="code" href="namespaceoperations__research.html#a7deeae530369e107f9d91c1a189f451f">Arc</a> {</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keywordtype">int</span> <a class="code" href="routing__flow_8cc.html#a64e7efc5529154ba56903e75f5300990">tail</a>;</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordtype">int</span> <a class="code" href="routing__flow_8cc.html#afca32f65388659a4b0956496169488b4">head</a>;</div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  };</div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  std::vector<Literal> watch_index_to_literal_;</div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  std::vector<std::vector<Arc>> watch_index_to_arcs_;</div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  </div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="comment">// Index in trail_ up to which we propagated all the assigned Literals.</span></div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordtype">int</span> propagation_trail_index_ = 0;</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  </div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="comment">// Current partial chains of arc that are present.</span></div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  std::vector<int> next_; <span class="comment">// -1 if not assigned yet.</span></div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  std::vector<int> prev_; <span class="comment">// -1 if not assigned yet.</span></div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  std::vector<LiteralIndex> next_literal_;</div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  </div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="comment">// Backtrack support for the partial chains of arcs, level_ends_[level] is an</span></div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="comment">// index in added_arcs_;</span></div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  std::vector<int> level_ends_;</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  std::vector<Arc> added_arcs_;</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  </div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">// Reversible list of node that must be in a cycle. A node must be in a cycle</span></div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="comment">// iff self_arcs_[node] is false. This graph entry can be used as a reason.</span></div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordtype">int</span> rev_must_be_in_cycle_size_ = 0;</div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  std::vector<int> must_be_in_cycle_;</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  </div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="comment">// Temporary vectors.</span></div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  std::vector<bool> processed_;</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  std::vector<bool> in_current_path_;</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  </div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  DISALLOW_COPY_AND_ASSIGN(<a class="code" href="classoperations__research_1_1sat_1_1_circuit_propagator.html">CircuitPropagator</a>);</div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> };</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  </div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment">// This constraint ensures that the graph is a covering of all nodes by</span></div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="comment">// circuits and loops, such that all circuits contain exactly one distinguished</span></div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment">// node. Those distinguished nodes are meant to be depots.</span></div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="comment">// This constraint does not need ExactlyOnePerRowAndPerColumn() to be correct,</span></div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="comment">// but it does not propagate degree deductions (only fails if a node has more</span></div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment">// than one outgoing arc or more than one incoming arc), so that adding</span></div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// ExactlyOnePerRowAndPerColumn() should work better.</span></div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="comment">// TODO(user): Make distinguished nodes an array of Boolean variables,</span></div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment">// so this can be used for facility location problems.</span></div>
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<div class="line"><a name="l00131"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_circuit_covering_propagator.html"> 131</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1sat_1_1_circuit_covering_propagator.html">CircuitCoveringPropagator</a> : <a class="code" href="classoperations__research_1_1sat_1_1_propagator_interface.html">PropagatorInterface</a>, <a class="code" href="classoperations__research_1_1_reversible_interface.html">ReversibleInterface</a> {</div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <a class="code" href="classoperations__research_1_1sat_1_1_circuit_covering_propagator.html#a154741eb694fbdb51b431c9c0d404496">CircuitCoveringPropagator</a>(std::vector<std::vector<Literal>> graph,</div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keyword">const</span> std::vector<int>& distinguished_nodes,</div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <a class="code" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  </div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_circuit_covering_propagator.html#a176d2c659864433ccd869b5fba8d57af">SetLevel</a>(<span class="keywordtype">int</span> level) <span class="keyword">final</span>;</div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1sat_1_1_circuit_covering_propagator.html#ac1fe9b1f2b978c4283e42f12e586eb1e">Propagate</a>() <span class="keyword">final</span>;</div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1sat_1_1_circuit_covering_propagator.html#a45321337f970685d9847db005c4b3de1">IncrementalPropagate</a>(<span class="keyword">const</span> std::vector<int>& watch_indices) <span class="keyword">final</span>;</div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_circuit_covering_propagator.html#a6ee8ed57254aec3ae99d399bae5b3736">RegisterWith</a>(<a class="code" href="classoperations__research_1_1sat_1_1_generic_literal_watcher.html">GenericLiteralWatcher</a>* watcher);</div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  </div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="comment">// Adds all literals on the path/circuit from tail to head in the graph of</span></div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="comment">// literals set to true.</span></div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="comment">// next_[i] should be filled with a node j s.t. graph_[i][j] is true, or -1.</span></div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordtype">void</span> FillFixedPathInReason(<span class="keywordtype">int</span> start, <span class="keywordtype">int</span> end, std::vector<Literal>* reason);</div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  </div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="comment">// Input data.</span></div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keyword">const</span> std::vector<std::vector<Literal>> graph_;</div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> num_nodes_;</div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  std::vector<bool> node_is_distinguished_;</div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  </div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="comment">// SAT incremental state.</span></div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <a class="code" href="classoperations__research_1_1sat_1_1_trail.html">Trail</a>* trail_;</div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  std::vector<std::pair<int, int>> watch_index_to_arc_;</div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  std::vector<std::pair<int, int>> fixed_arcs_;</div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  std::vector<int> level_ends_;</div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  </div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="comment">// Used in Propagate() to represent paths and circuits.</span></div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  std::vector<int> next_;</div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  std::vector<int> prev_;</div>
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  std::vector<bool> visited_;</div>
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<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> };</div>
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<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  </div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment">// Changes the node indices so that we get a graph in [0, num_nodes) where every</span></div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="comment">// node has at least one incoming or outgoing arc. Returns the number of nodes.</span></div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="keyword">template</span> <<span class="keyword">class</span> IntContainer></div>
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<div class="line"><a name="l00168"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a8f4f9889ab3527ce5381ed32e2fae25a"> 168</a></span> <span class="keywordtype">int</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a8f4f9889ab3527ce5381ed32e2fae25a">ReindexArcs</a>(IntContainer* tails, IntContainer* heads) {</div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> num_arcs = tails->size();</div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="keywordflow">if</span> (num_arcs == 0) <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  </div>
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<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="comment">// Put all nodes in a set.</span></div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  std::set<int> <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>;</div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> arc = 0; arc < num_arcs; ++arc) {</div>
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<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>.insert((*tails)[arc]);</div>
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<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>.insert((*heads)[arc]);</div>
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<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  }</div>
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<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  </div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="comment">// Compute the new indices while keeping a stable order.</span></div>
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<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keywordtype">int</span> new_index = 0;</div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  absl::flat_hash_map<int, int> mapping;</div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> node : <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>) {</div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  mapping[node] = new_index++;</div>
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  }</div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  </div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="comment">// Remap the arcs.</span></div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> arc = 0; arc < num_arcs; ++arc) {</div>
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<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  (*tails)[arc] = mapping[(*tails)[arc]];</div>
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<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  (*heads)[arc] = mapping[(*heads)[arc]];</div>
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<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  }</div>
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<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keywordflow">return</span> <a class="code" href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a>.size();</div>
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<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> }</div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  </div>
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="comment">// ============================================================================</span></div>
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<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="comment">// Model based functions.</span></div>
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<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment">// ============================================================================</span></div>
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  </div>
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<div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="comment">// This just wraps CircuitPropagator. See the comment there to see what this</span></div>
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<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment">// does. Note that any nodes with no outoing or no incoming arc will cause the</span></div>
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<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment">// problem to be UNSAT. One can call ReindexArcs() first to ignore such nodes.</span></div>
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<div class="line"><a name="l00201"></a><span class="lineno"> 201</span> std::function<void(Model*)> <a class="code" href="namespaceoperations__research_1_1sat.html#a3c25e2ace66c05a1078d9d8128ca33c3">SubcircuitConstraint</a>(</div>
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<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keywordtype">int</span> num_nodes, <span class="keyword">const</span> std::vector<int>& tails, <span class="keyword">const</span> std::vector<int>& heads,</div>
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<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keyword">const</span> std::vector<Literal>& literals,</div>
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<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keywordtype">bool</span> multiple_subcircuit_through_zero = <span class="keyword">false</span>);</div>
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<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  </div>
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<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment">// TODO(user): Change to a sparse API like for the function above.</span></div>
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<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> std::function<void(Model*)> <a class="code" href="namespaceoperations__research_1_1sat.html#a505d58583f35441cea048e6a69453099">ExactlyOnePerRowAndPerColumn</a>(</div>
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<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keyword">const</span> std::vector<std::vector<Literal>>& graph);</div>
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<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> std::function<void(Model*)> <a class="code" href="namespaceoperations__research_1_1sat.html#a42094dcdae62a62bd5d269e1223f7f30">CircuitCovering</a>(</div>
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<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keyword">const</span> std::vector<std::vector<Literal>>& graph,</div>
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<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="keyword">const</span> std::vector<int>& distinguished_nodes);</div>
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<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  </div>
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<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> } <span class="comment">// namespace sat</span></div>
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<div class="line"><a name="l00214"></a><span class="lineno"> 214</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  </div>
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<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_SAT_CIRCUIT_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="aclassoperations__research_1_1_reversible_interface_html"><div class="ttname"><a href="classoperations__research_1_1_reversible_interface.html">operations_research::ReversibleInterface</a></div><div class="ttdef"><b>Definition:</b> <a href="rev_8h_source.html#l00029">rev.h:29</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_circuit_covering_propagator_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_circuit_covering_propagator.html">operations_research::sat::CircuitCoveringPropagator</a></div><div class="ttdef"><b>Definition:</b> <a href="circuit_8h_source.html#l00131">circuit.h:131</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_circuit_covering_propagator_html_a154741eb694fbdb51b431c9c0d404496"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_circuit_covering_propagator.html#a154741eb694fbdb51b431c9c0d404496">operations_research::sat::CircuitCoveringPropagator::CircuitCoveringPropagator</a></div><div class="ttdeci">CircuitCoveringPropagator(std::vector< std::vector< Literal >> graph, const std::vector< int > &distinguished_nodes, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8cc_source.html#l00308">circuit.cc:308</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_circuit_covering_propagator_html_a176d2c659864433ccd869b5fba8d57af"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_circuit_covering_propagator.html#a176d2c659864433ccd869b5fba8d57af">operations_research::sat::CircuitCoveringPropagator::SetLevel</a></div><div class="ttdeci">void SetLevel(int level) final</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8cc_source.html#l00340">circuit.cc:340</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_circuit_covering_propagator_html_a45321337f970685d9847db005c4b3de1"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_circuit_covering_propagator.html#a45321337f970685d9847db005c4b3de1">operations_research::sat::CircuitCoveringPropagator::IncrementalPropagate</a></div><div class="ttdeci">bool IncrementalPropagate(const std::vector< int > &watch_indices) final</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8cc_source.html#l00353">circuit.cc:353</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_circuit_covering_propagator_html_a6ee8ed57254aec3ae99d399bae5b3736"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_circuit_covering_propagator.html#a6ee8ed57254aec3ae99d399bae5b3736">operations_research::sat::CircuitCoveringPropagator::RegisterWith</a></div><div class="ttdeci">void RegisterWith(GenericLiteralWatcher *watcher)</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8cc_source.html#l00320">circuit.cc:320</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_circuit_covering_propagator_html_ac1fe9b1f2b978c4283e42f12e586eb1e"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_circuit_covering_propagator.html#ac1fe9b1f2b978c4283e42f12e586eb1e">operations_research::sat::CircuitCoveringPropagator::Propagate</a></div><div class="ttdeci">bool Propagate() final</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8cc_source.html#l00374">circuit.cc:374</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_circuit_propagator_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_circuit_propagator.html">operations_research::sat::CircuitPropagator</a></div><div class="ttdef"><b>Definition:</b> <a href="circuit_8h_source.html#l00044">circuit.h:44</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_circuit_propagator_html_a176d2c659864433ccd869b5fba8d57af"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_circuit_propagator.html#a176d2c659864433ccd869b5fba8d57af">operations_research::sat::CircuitPropagator::SetLevel</a></div><div class="ttdeci">void SetLevel(int level) final</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8cc_source.html#l00108">circuit.cc:108</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_circuit_propagator_html_a45321337f970685d9847db005c4b3de1"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_circuit_propagator.html#a45321337f970685d9847db005c4b3de1">operations_research::sat::CircuitPropagator::IncrementalPropagate</a></div><div class="ttdeci">bool IncrementalPropagate(const std::vector< int > &watch_indices) final</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8cc_source.html#l00153">circuit.cc:153</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_circuit_propagator_html_a6ee8ed57254aec3ae99d399bae5b3736"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_circuit_propagator.html#a6ee8ed57254aec3ae99d399bae5b3736">operations_research::sat::CircuitPropagator::RegisterWith</a></div><div class="ttdeci">void RegisterWith(GenericLiteralWatcher *watcher)</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8cc_source.html#l00092">circuit.cc:92</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_circuit_propagator_html_ab724d1b4067da7ec830cb4d1b8284ee7"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_circuit_propagator.html#ab724d1b4067da7ec830cb4d1b8284ee7">operations_research::sat::CircuitPropagator::CircuitPropagator</a></div><div class="ttdeci">CircuitPropagator(int num_nodes, const std::vector< int > &tails, const std::vector< int > &heads, const std::vector< Literal > &literals, Options options, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8cc_source.html#l00025">circuit.cc:25</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_circuit_propagator_html_ac1fe9b1f2b978c4283e42f12e586eb1e"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_circuit_propagator.html#ac1fe9b1f2b978c4283e42f12e586eb1e">operations_research::sat::CircuitPropagator::Propagate</a></div><div class="ttdeci">bool Propagate() final</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8cc_source.html#l00197">circuit.cc:197</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#l01113">integer.h:1113</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_literal_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_literal.html">operations_research::sat::Literal</a></div><div class="ttdef"><b>Definition:</b> <a href="sat__base_8h_source.html#l00065">sat_base.h:65</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#l00038">sat/model.h:38</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#l01065">integer.h:1065</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#l00234">sat_base.h:234</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_variables_assignment_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_variables_assignment.html">operations_research::sat::VariablesAssignment</a></div><div class="ttdef"><b>Definition:</b> <a href="sat__base_8h_source.html#l00123">sat_base.h:123</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#l00273">gurobi_interface.cc:273</a></div></div>
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<div class="ttc" id="aint__type_8h_html"><div class="ttname"><a href="int__type_8h.html">int_type.h</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="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_a3c25e2ace66c05a1078d9d8128ca33c3"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a3c25e2ace66c05a1078d9d8128ca33c3">operations_research::sat::SubcircuitConstraint</a></div><div class="ttdeci">std::function< void(Model *)> SubcircuitConstraint(int num_nodes, const std::vector< int > &tails, const std::vector< int > &heads, const std::vector< Literal > &literals, bool multiple_subcircuit_through_zero)</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8cc_source.html#l00471">circuit.cc:471</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a42094dcdae62a62bd5d269e1223f7f30"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a42094dcdae62a62bd5d269e1223f7f30">operations_research::sat::CircuitCovering</a></div><div class="ttdeci">std::function< void(Model *)> CircuitCovering(const std::vector< std::vector< Literal >> &graph, const std::vector< int > &distinguished_nodes)</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8cc_source.html#l00513">circuit.cc:513</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a505d58583f35441cea048e6a69453099"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a505d58583f35441cea048e6a69453099">operations_research::sat::ExactlyOnePerRowAndPerColumn</a></div><div class="ttdeci">std::function< void(Model *)> ExactlyOnePerRowAndPerColumn(const std::vector< std::vector< Literal >> &graph)</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8cc_source.html#l00452">circuit.cc:452</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a8f4f9889ab3527ce5381ed32e2fae25a"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a8f4f9889ab3527ce5381ed32e2fae25a">operations_research::sat::ReindexArcs</a></div><div class="ttdeci">int ReindexArcs(IntContainer *tails, IntContainer *heads)</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8h_source.html#l00168">circuit.h:168</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_a7deeae530369e107f9d91c1a189f451f"><div class="ttname"><a href="namespaceoperations__research.html#a7deeae530369e107f9d91c1a189f451f">operations_research::Arc</a></div><div class="ttdeci">std::pair< int64_t, int64_t > Arc</div><div class="ttdef"><b>Definition:</b> <a href="search_8cc_source.html#l03383">search.cc:3383</a></div></div>
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<div class="ttc" id="arev_8h_html"><div class="ttname"><a href="rev_8h.html">rev.h</a></div></div>
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<div class="ttc" id="arouting__flow_8cc_html_a64e7efc5529154ba56903e75f5300990"><div class="ttname"><a href="routing__flow_8cc.html#a64e7efc5529154ba56903e75f5300990">tail</a></div><div class="ttdeci">int64_t tail</div><div class="ttdef"><b>Definition:</b> <a href="routing__flow_8cc_source.html#l00149">routing_flow.cc:149</a></div></div>
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<div class="ttc" id="arouting__flow_8cc_html_afca32f65388659a4b0956496169488b4"><div class="ttname"><a href="routing__flow_8cc.html#afca32f65388659a4b0956496169488b4">head</a></div><div class="ttdeci">int64_t head</div><div class="ttdef"><b>Definition:</b> <a href="routing__flow_8cc_source.html#l00150">routing_flow.cc:150</a></div></div>
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<div class="ttc" id="arouting__search_8cc_html_a6b7983ccd32c86cbbc3d4d9cda4cac17"><div class="ttname"><a href="routing__search_8cc.html#a6b7983ccd32c86cbbc3d4d9cda4cac17">nodes</a></div><div class="ttdeci">int nodes</div><div class="ttdef"><b>Definition:</b> <a href="routing__search_8cc_source.html#l03686">routing_search.cc:3686</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="astructoperations__research_1_1sat_1_1_circuit_propagator_1_1_options_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_circuit_propagator_1_1_options.html">operations_research::sat::CircuitPropagator::Options</a></div><div class="ttdef"><b>Definition:</b> <a href="circuit_8h_source.html#l00046">circuit.h:46</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_circuit_propagator_1_1_options_html_af1123baeaa5412b68d37d8adf43ccb7c"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_circuit_propagator_1_1_options.html#af1123baeaa5412b68d37d8adf43ccb7c">operations_research::sat::CircuitPropagator::Options::multiple_subcircuit_through_zero</a></div><div class="ttdeci">bool multiple_subcircuit_through_zero</div><div class="ttdef"><b>Definition:</b> <a href="circuit_8h_source.html#l00049">circuit.h:49</a></div></div>
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