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<a href="cp__model__symmetries_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span>&#160;<span class="comment">// Copyright 2010-2018 Google LLC</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span>&#160;<span class="comment">// Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span>&#160;<span class="comment">// you may not use this file except in compliance with the License.</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span>&#160;<span class="comment">// You may obtain a copy of the License at</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span>&#160;<span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span>&#160;<span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span>&#160;<span class="comment">// distributed under the License is distributed on an &quot;AS IS&quot; BASIS,</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span>&#160;<span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span>&#160;<span class="comment">// See the License for the specific language governing permissions and</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span>&#160;<span class="comment">// limitations under the License.</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="cp__model__symmetries_8h.html">ortools/sat/cp_model_symmetries.h</a>&quot;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>&#160;<span class="preprocessor">#include &lt;memory&gt;</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160; </div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="preprocessor">#include &quot;absl/container/flat_hash_map.h&quot;</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160;<span class="preprocessor">#include &quot;absl/memory/memory.h&quot;</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160;<span class="preprocessor">#include &quot;google/protobuf/repeated_field.h&quot;</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="find__graph__symmetries_8h.html">ortools/algorithms/find_graph_symmetries.h</a>&quot;</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="hash_8h.html">ortools/base/hash.h</a>&quot;</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="map__util_8h.html">ortools/base/map_util.h</a>&quot;</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="cp__model__utils_8h.html">ortools/sat/cp_model_utils.h</a>&quot;</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; </div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160;<span class="keyword">namespace </span>sat {</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; </div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160;<span class="keyword">namespace </span>{</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160;<span class="keyword">struct </span>VectorHash {</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; std::size_t operator()(<span class="keyword">const</span> std::vector&lt;int64&gt;&amp; values)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <span class="keywordtype">size_t</span> <a class="code" href="matrix__utils_8cc.html#ad96c5e641806a06a23e5d5b9fca20e89">hash</a> = 0;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a> : values) {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <a class="code" href="matrix__utils_8cc.html#ad96c5e641806a06a23e5d5b9fca20e89">hash</a> = <a class="code" href="namespaceutil__hash.html#aa2ba7114404f5416e797636b0e1eddcd">util_hash::Hash</a>(<a class="code" href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a>, <a class="code" href="matrix__utils_8cc.html#ad96c5e641806a06a23e5d5b9fca20e89">hash</a>);</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; }</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">return</span> <a class="code" href="matrix__utils_8cc.html#ad96c5e641806a06a23e5d5b9fca20e89">hash</a>;</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; }</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160;};</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; </div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160;<span class="comment">// A simple class to generate equivalence class number for</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160;<span class="comment">// GenerateGraphForSymmetryDetection().</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160;<span class="keyword">class </span>IdGenerator {</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; IdGenerator() {}</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="comment">// If the key was never seen before, then generate a new id, otherwise return</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="comment">// the previously generated id.</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="keywordtype">int</span> GetId(<span class="keyword">const</span> std::vector&lt;int64&gt;&amp; key) {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="keywordflow">return</span> <a class="code" href="namespacegtl.html#a7a0f8dc4187504b814d8a8be463b517c">gtl::LookupOrInsert</a>(&amp;id_map_, key, id_map_.size());</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; }</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="keyword">private</span>:</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; absl::flat_hash_map&lt;std::vector&lt;int64&gt;, int, VectorHash&gt; id_map_;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160;};</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160;<span class="comment">// Appends values in `repeated_field` to `vector`.</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;<span class="comment">// We use a template as proto int64 != C++ int64 in open source.</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> FieldInt64Type&gt;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160;<span class="keywordtype">void</span> Append(</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="keyword">const</span> google::protobuf::RepeatedField&lt;FieldInt64Type&gt;&amp; repeated_field,</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; std::vector&lt;int64&gt;* vector) {</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; CHECK(vector != <span class="keyword">nullptr</span>);</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> FieldInt64Type <a class="code" href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a> : repeated_field) {</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; vector-&gt;push_back(<a class="code" href="demon__profiler_8cc.html#a21edc7ca4cc5802c8779d68556bc09cf">value</a>);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; }</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160;}</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; </div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160;<span class="comment">// Returns a graph whose automorphisms can be mapped back to the symmetries of</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160;<span class="comment">// the model described in the given CpModelProto.</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160;<span class="comment">// Any permutation of the graph that respects the initial_equivalence_classes</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160;<span class="comment">// output can be mapped to a symmetry of the given problem simply by taking its</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160;<span class="comment">// restriction on the first num_variables nodes and interpreting its index as a</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160;<span class="comment">// variable index. In a sense, a node with a low enough index #i is in</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160;<span class="comment">// one-to-one correspondence with the variable #i (using the index</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160;<span class="comment">// representation of variables).</span></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160;<span class="comment">// The format of the initial_equivalence_classes is the same as the one</span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160;<span class="comment">// described in GraphSymmetryFinder::FindSymmetries(). The classes must be dense</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160;<span class="comment">// in [0, num_classes) and any symmetry will only map nodes with the same class</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160;<span class="comment">// between each other.</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Graph&gt;</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160;std::unique_ptr&lt;Graph&gt; <a class="code" href="namespaceoperations__research_1_1sat.html#a3f6fa74408ea28eb41f29e9696d9a9a2">GenerateGraphForSymmetryDetection</a>(</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="keyword">const</span> CpModelProto&amp; problem,</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; std::vector&lt;int&gt;* initial_equivalence_classes) {</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; CHECK(initial_equivalence_classes != <span class="keyword">nullptr</span>);</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; </div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> num_variables = problem.variables_size();</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; <span class="keyword">auto</span> graph = absl::make_unique&lt;Graph&gt;();</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; initial_equivalence_classes-&gt;clear();</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <span class="keyword">enum</span> NodeType {</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; VARIABLE_NODE,</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; CONSTRAINT_NODE,</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; CONSTRAINT_COEFFICIENT_NODE,</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; ENFORCEMENT_LITERAL</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; };</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; IdGenerator id_generator;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; </div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; <span class="comment">// For two variables to be in the same equivalence class, they need to have</span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="comment">// the same objective coefficient, and the same possible bounds.</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; std::vector&lt;int64&gt; objective_by_var(num_variables, 0);</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; problem.objective().vars_size(); ++i) {</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; objective_by_var[problem.objective().vars(i)] =</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; problem.objective().coeffs(i);</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; }</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; </div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; <span class="keyword">auto</span> new_node = [&amp;initial_equivalence_classes,</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; &amp;id_generator](<span class="keyword">const</span> std::vector&lt;int64&gt;&amp; key) {</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; <span class="comment">// Since we add nodes one by one, initial_equivalence_classes-&gt;size() gives</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; <span class="comment">// the number of nodes at any point, which we use as the next node index.</span></div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> node = initial_equivalence_classes-&gt;size();</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; initial_equivalence_classes-&gt;push_back(id_generator.GetId(key));</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; <span class="keywordflow">return</span> node;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; };</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; </div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> v = 0; v &lt; num_variables; ++v) {</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; <span class="keyword">const</span> IntegerVariableProto&amp; variable = problem.variables(v);</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; std::vector&lt;int64&gt; key = {VARIABLE_NODE, objective_by_var[v]};</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; Append(variable.domain(), &amp;key);</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; CHECK_EQ(v, new_node(key));</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; <span class="comment">// Make sure the graph contains all the variable nodes, even if no edges are</span></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160; <span class="comment">// attached to them through constraints.</span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160; graph-&gt;AddNode(v);</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; }</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; </div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; <span class="keyword">auto</span> add_edge = [&amp;graph](<span class="keywordtype">int</span> node_1, <span class="keywordtype">int</span> node_2) {</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; graph-&gt;AddArc(node_1, node_2);</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; graph-&gt;AddArc(node_2, node_1);</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; };</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160; <span class="keyword">auto</span> add_literal_edge = [&amp;add_edge, &amp;new_node](<span class="keywordtype">int</span> ref, <span class="keywordtype">int</span> constraint_node) {</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> variable_node = <a class="code" href="namespaceoperations__research_1_1sat.html#acdbc8ad33149d45a6e6fcd8b72fd68ed">PositiveRef</a>(ref);</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="namespaceoperations__research_1_1sat.html#a217338425de4389014563f1f24331713">RefIsPositive</a>(ref)) {</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; add_edge(variable_node, constraint_node);</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> coefficient_node = new_node({CONSTRAINT_COEFFICIENT_NODE, -1});</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160; </div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160; add_edge(variable_node, coefficient_node);</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160; add_edge(coefficient_node, constraint_node);</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160; }</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160; };</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160; </div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160; <span class="comment">// Add constraints to the graph.</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> ConstraintProto&amp; constraint : problem.constraints()) {</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> constraint_node = initial_equivalence_classes-&gt;size();</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160; std::vector&lt;int64&gt; key = {CONSTRAINT_NODE, constraint.constraint_case()};</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160; </div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160; <span class="keywordflow">switch</span> (constraint.constraint_case()) {</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160; <span class="keywordflow">case</span> ConstraintProto::kLinear: {</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160; Append(constraint.linear().domain(), &amp;key);</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160; CHECK_EQ(constraint_node, new_node(key));</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>&#160; </div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; constraint.linear().vars_size(); ++i) {</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>&#160; <span class="keywordflow">if</span> (constraint.linear().coeffs(i) == 0) <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> ref = constraint.linear().vars(i);</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> variable_node = <a class="code" href="namespaceoperations__research_1_1sat.html#acdbc8ad33149d45a6e6fcd8b72fd68ed">PositiveRef</a>(ref);</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160; <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> coeff = <a class="code" href="namespaceoperations__research_1_1sat.html#a217338425de4389014563f1f24331713">RefIsPositive</a>(ref)</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160; ? constraint.linear().coeffs(i)</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160; : -constraint.linear().coeffs(i);</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160; <span class="keywordflow">if</span> (coeff == 1) {</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160; <span class="comment">// For all coefficients equal to one, which are the most common, we</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160; <span class="comment">// can optimize the size of the graph by omitting the coefficient</span></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160; <span class="comment">// node altogether.</span></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160; add_edge(variable_node, constraint_node);</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> coefficient_node =</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160; new_node({CONSTRAINT_COEFFICIENT_NODE, coeff});</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160; </div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160; add_edge(variable_node, coefficient_node);</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160; add_edge(coefficient_node, constraint_node);</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160; }</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160; }</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160; }</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160; <span class="keywordflow">case</span> ConstraintProto::kBoolOr: {</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160; CHECK_EQ(constraint_node, new_node(key));</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> ref : constraint.bool_or().literals()) {</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160; add_literal_edge(ref, constraint_node);</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160; }</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160; }</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160; <span class="keywordflow">case</span> ConstraintProto::kBoolXor: {</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160; CHECK_EQ(constraint_node, new_node(key));</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> ref : constraint.bool_xor().literals()) {</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160; add_literal_edge(ref, constraint_node);</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160; }</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160; }</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>&#160; <span class="keywordflow">case</span> ConstraintProto::kBoolAnd: {</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>&#160; <span class="keywordflow">if</span> (constraint.enforcement_literal_size() == 0) {</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>&#160; <span class="comment">// All literals are true in this case.</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>&#160; CHECK_EQ(constraint_node, new_node(key));</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> ref : constraint.bool_and().literals()) {</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>&#160; add_literal_edge(ref, constraint_node);</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160; }</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160; }</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>&#160; </div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>&#160; <span class="comment">// To make the BoolAnd constraint more generic in the graph, we expand</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>&#160; <span class="comment">// it into a set of BoolOr constraints where</span></div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>&#160; <span class="comment">// not(enforcement_literal) OR literal = true</span></div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>&#160; <span class="comment">// for all constraint&#39;s literals. This is equivalent to</span></div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>&#160; <span class="comment">// enforcement_literal =&gt; literal</span></div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160; <span class="comment">// for all literals.</span></div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>&#160; std::vector&lt;int64&gt; key = {CONSTRAINT_NODE, ConstraintProto::kBoolOr};</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> non_enforcement_literal =</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>&#160; <a class="code" href="namespaceoperations__research_1_1sat.html#ae0803b8198728cd4f6e58498d9c60091">NegatedRef</a>(constraint.enforcement_literal(0));</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code" href="optimization_8cc.html#af63dcc00f2023fdf498e0829e6fb8a6b">literal</a> : constraint.bool_and().literals()) {</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> constraint_node = new_node(key);</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>&#160; add_literal_edge(non_enforcement_literal, constraint_node);</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>&#160; add_literal_edge(<a class="code" href="optimization_8cc.html#af63dcc00f2023fdf498e0829e6fb8a6b">literal</a>, constraint_node);</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>&#160; }</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>&#160; }</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>&#160; <span class="keywordflow">default</span>: {</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>&#160; <span class="comment">// If the model contains any non-supported constraints, return an empty</span></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>&#160; <span class="comment">// graph.</span></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>&#160; <span class="comment">// TODO(user): support other types of constraints.</span></div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>&#160; LOG(ERROR) &lt;&lt; <span class="stringliteral">&quot;Unsupported constraint type &quot;</span></div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>&#160; &lt;&lt; constraint.constraint_case();</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>&#160; <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>&#160; }</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>&#160; }</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>&#160; </div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>&#160; <span class="keywordflow">if</span> (constraint.constraint_case() != ConstraintProto::kBoolAnd &amp;&amp;</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>&#160; constraint.enforcement_literal_size() &gt; 0) {</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> ref = constraint.enforcement_literal(0);</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> enforcement_literal_node = <a class="code" href="namespaceoperations__research_1_1sat.html#acdbc8ad33149d45a6e6fcd8b72fd68ed">PositiveRef</a>(ref);</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> enforcement_type_node =</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>&#160; new_node({ENFORCEMENT_LITERAL, <a class="code" href="namespaceoperations__research_1_1sat.html#a217338425de4389014563f1f24331713">RefIsPositive</a>(ref)});</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>&#160; </div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>&#160; add_edge(constraint_node, enforcement_type_node);</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>&#160; add_edge(enforcement_type_node, enforcement_literal_node);</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>&#160; }</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>&#160; }</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>&#160; </div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>&#160; graph-&gt;Build();</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>&#160; DCHECK_EQ(graph-&gt;num_nodes(), initial_equivalence_classes-&gt;size());</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>&#160; <span class="keywordflow">return</span> graph;</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>&#160;}</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>&#160;} <span class="comment">// namespace</span></div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>&#160; </div>
<div class="line"><a name="l00243"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a418890b4cbc1a5c377cd8e6a7a6bc881"> 243</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a418890b4cbc1a5c377cd8e6a7a6bc881">FindCpModelSymmetries</a>(</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>&#160; <span class="keyword">const</span> CpModelProto&amp; problem,</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>&#160; std::vector&lt;std::unique_ptr&lt;SparsePermutation&gt;&gt;* generators,</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>&#160; <span class="keywordtype">double</span> time_limit_seconds) {</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>&#160; CHECK(generators != <span class="keyword">nullptr</span>);</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>&#160; generators-&gt;clear();</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>&#160; </div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>&#160; <span class="keyword">typedef</span> <a class="code" href="classutil_1_1StaticGraph.html">GraphSymmetryFinder::Graph</a> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>;</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>&#160; </div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>&#160; std::vector&lt;int&gt; equivalence_classes;</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>&#160; std::unique_ptr&lt;Graph&gt; graph(</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>&#160; GenerateGraphForSymmetryDetection&lt;Graph&gt;(problem, &amp;equivalence_classes));</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>&#160; <span class="keywordflow">if</span> (graph == <span class="keyword">nullptr</span>) <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>&#160; </div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>&#160; LOG(INFO) &lt;&lt; <span class="stringliteral">&quot;Graph has &quot;</span> &lt;&lt; graph-&gt;num_nodes() &lt;&lt; <span class="stringliteral">&quot; nodes and &quot;</span></div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>&#160; &lt;&lt; graph-&gt;num_arcs() / 2 &lt;&lt; <span class="stringliteral">&quot; edges.&quot;</span>;</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>&#160; </div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>&#160; <a class="code" href="classoperations__research_1_1GraphSymmetryFinder.html">GraphSymmetryFinder</a> symmetry_finder(*graph, <span class="comment">/*is_undirected=*/</span><span class="keyword">true</span>);</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>&#160; std::vector&lt;int&gt; factorized_automorphism_group_size;</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>&#160; <a class="code" href="base_2logging_8h.html#a9f96ed9f06763f0821fdbb4d29031d8d">CHECK_OK</a>(symmetry_finder.<a class="code" href="classoperations__research_1_1GraphSymmetryFinder.html#a3a3796326515a59739024432c5dff6d8">FindSymmetries</a>(time_limit_seconds,</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>&#160; &amp;equivalence_classes, generators,</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>&#160; &amp;factorized_automorphism_group_size));</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>&#160; </div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>&#160; <span class="comment">// Remove from the permutations the part not concerning the variables.</span></div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>&#160; <span class="comment">// Note that some permutations may become empty, which means that we had</span></div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>&#160; <span class="comment">// duplicate constraints.</span></div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>&#160; <span class="keywordtype">double</span> average_support_size = 0.0;</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>&#160; <span class="keywordtype">int</span> num_generators = 0;</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; generators-&gt;size(); ++i) {</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>&#160; <a class="code" href="classoperations__research_1_1SparsePermutation.html">SparsePermutation</a>* permutation = (*generators)[i].get();</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>&#160; std::vector&lt;int&gt; to_delete;</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; permutation-&gt;<a class="code" href="classoperations__research_1_1SparsePermutation.html#a8c5fc5af6e649a82d169f61e4dab5e33">NumCycles</a>(); ++j) {</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>&#160; <span class="comment">// Because variable nodes are in a separate equivalence class than any</span></div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>&#160; <span class="comment">// other node, a cycle can either contain only variable nodes or none, so</span></div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>&#160; <span class="comment">// we just need to check one element of the cycle.</span></div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>&#160; <span class="keywordflow">if</span> (*(permutation-&gt;<a class="code" href="classoperations__research_1_1SparsePermutation.html#af567b4e287e268eb9ecee908f63e5b64">Cycle</a>(j).<a class="code" href="structoperations__research_1_1SparsePermutation_1_1Iterator.html#a8497b34029ee966694083aa34c9022b5">begin</a>()) &gt;= problem.variables_size()) {</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>&#160; to_delete.push_back(j);</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="macros_8h.html#a7f536a3b33f9bed8f75734e035d30725">DEBUG_MODE</a>) {</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>&#160; <span class="comment">// Verify that the cycle&#39;s entire support does not touch any variable.</span></div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> node : permutation-&gt;<a class="code" href="classoperations__research_1_1SparsePermutation.html#af567b4e287e268eb9ecee908f63e5b64">Cycle</a>(j)) {</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>&#160; DCHECK_GE(node, problem.variables_size());</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>&#160; }</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>&#160; }</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>&#160; }</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>&#160; }</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>&#160; permutation-&gt;<a class="code" href="classoperations__research_1_1SparsePermutation.html#a9add43490c45e4334099bb15b6e6eab0">RemoveCycles</a>(to_delete);</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>&#160; <span class="keywordflow">if</span> (!permutation-&gt;<a class="code" href="classoperations__research_1_1SparsePermutation.html#ab601acb5aed920b1e61210d497462976">Support</a>().empty()) {</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>&#160; average_support_size += permutation-&gt;<a class="code" href="classoperations__research_1_1SparsePermutation.html#ab601acb5aed920b1e61210d497462976">Support</a>().size();</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>&#160; swap((*generators)[num_generators], (*generators)[i]);</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>&#160; ++num_generators;</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>&#160; LOG(INFO) &lt;&lt; <span class="stringliteral">&quot;The model contains duplicate constraints!&quot;</span>;</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>&#160; }</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>&#160; }</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>&#160; generators-&gt;resize(num_generators);</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>&#160; average_support_size /= num_generators;</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>&#160; LOG(INFO) &lt;&lt; <span class="stringliteral">&quot;# of generators: &quot;</span> &lt;&lt; num_generators;</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>&#160; LOG(INFO) &lt;&lt; <span class="stringliteral">&quot;Average support size: &quot;</span> &lt;&lt; average_support_size;</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>&#160;}</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>&#160; </div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>&#160;} <span class="comment">// namespace sat</span></div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>&#160;} <span class="comment">// namespace operations_research</span></div>
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