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321 lines
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<div class="headertitle"><div class="title">symmetry_util.cc</div></div>
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<a href="symmetry__util_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include "<a class="code" href="symmetry__util_8h.html">ortools/sat/symmetry_util.h</a>"</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include <algorithm></span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <cstdint></span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <memory></span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> </div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include "<a class="code" href="dynamic__partition_8h.html">ortools/algorithms/dynamic_partition.h</a>"</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include "<a class="code" href="sparse__permutation_8h.html">ortools/algorithms/sparse_permutation.h</a>"</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include "<a class="code" href="base_2logging_8h.html">ortools/base/logging.h</a>"</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> </div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="keyword">namespace </span>sat {</div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> </div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#ae1ba8d73886e6e6403805d215aa0fd16"> 28</a></span>std::vector<std::vector<int>> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ae1ba8d73886e6e6403805d215aa0fd16">BasicOrbitopeExtraction</a>(</div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keyword">const</span> std::vector<std::unique_ptr<SparsePermutation>>& generators) {</div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="comment">// Count the number of permutations that are compositions of 2-cycle and</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// regroup them according to the number of cycles.</span></div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> std::vector<std::vector<int>> num_cycles_to_2cyclers;</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> g = 0; g < generators.size(); ++g) {</div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keyword">const</span> std::unique_ptr<SparsePermutation>& perm = generators[g];</div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordtype">bool</span> contain_only_2cycles = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_cycles = perm->NumCycles();</div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_cycles; ++i) {</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">if</span> (perm->Cycle(i).size() != 2) {</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> contain_only_2cycles = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> }</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> }</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">if</span> (!contain_only_2cycles) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">if</span> (num_cycles >= num_cycles_to_2cyclers.size()) {</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> num_cycles_to_2cyclers.resize(num_cycles + 1);</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> }</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> num_cycles_to_2cyclers[num_cycles].push_back(g);</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> }</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// Heuristic: we try to grow the orbitope that has the most potential for</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// fixing variables.</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// TODO(user): We could grow each and keep the real maximum.</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordtype">int</span> best = -1;</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordtype">int</span> best_score = 0;</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_cycles_to_2cyclers.size(); ++i) {</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordflow">if</span> (num_cycles_to_2cyclers[i].size() > 1) {</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_perms = num_cycles_to_2cyclers[i].size() + 1;</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <a class="code hl_define" href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a>(1) << <span class="stringliteral">"Potential orbitope: "</span> << i << <span class="stringliteral">" x "</span> << num_perms;</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keyword">const</span> int64_t score = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(i, num_perms);</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">if</span> (score > best_score) {</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> best = i;</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> best_score = score;</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> }</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> }</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> }</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> std::vector<std::vector<int>> orbitope;</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">if</span> (best == -1) <span class="keywordflow">return</span> orbitope;</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// We will track the element already added so we never have duplicates.</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> std::vector<bool> in_matrix;</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> </div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// Greedily grow the orbitope.</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> orbitope.resize(best);</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> g : num_cycles_to_2cyclers[best]) {</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// Start using the first permutation.</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordflow">if</span> (orbitope[0].empty()) {</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keyword">const</span> std::unique_ptr<SparsePermutation>& perm = generators[g];</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_cycles = perm->NumCycles();</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_cycles; ++i) {</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> x : perm->Cycle(i)) {</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> orbitope[i].push_back(x);</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordflow">if</span> (x >= in_matrix.size()) in_matrix.resize(x + 1, <span class="keyword">false</span>);</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> in_matrix[x] = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> }</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> }</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> }</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// We want to find a column such that g sends it to variables not already</span></div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// in the orbitope matrix.</span></div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="comment">//</span></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// Note(user): This relies on the cycle in each permutation to be ordered by</span></div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="comment">// smaller element first. This way we don't have to account any row</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// permutation of the orbitope matrix. The code that detect the symmetries</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// of the problem should already return permutation in this canonical</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// format.</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> std::vector<int> grow;</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordtype">int</span> matching_column_index = -1;</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keyword">const</span> std::unique_ptr<SparsePermutation>& perm = generators[g];</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_cycles = perm->NumCycles();</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_cycles; ++i) {</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="comment">// Extract the two elements of this transposition.</span></div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> std::vector<int> tmp;</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> x : perm->Cycle(i)) tmp.push_back(x);</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a> = tmp[0];</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a> = tmp[1];</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> </div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="comment">// We want one element to appear in matching_column_index and the other to</span></div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// not appear at all.</span></div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordtype">int</span> num_matches_a = 0;</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keywordtype">int</span> num_matches_b = 0;</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keywordtype">int</span> last_match_index = -1;</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < orbitope[i].size(); ++j) {</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keywordflow">if</span> (orbitope[i][j] == <a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>) {</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> ++num_matches_a;</div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> last_match_index = j;</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (orbitope[i][j] == <a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>) {</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> ++num_matches_b;</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> last_match_index = j;</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> }</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> }</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordflow">if</span> (last_match_index == -1) <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordflow">if</span> (matching_column_index == -1) {</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> matching_column_index = last_match_index;</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> }</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keywordflow">if</span> (matching_column_index != last_match_index) <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">if</span> (num_matches_a == 0 && num_matches_b == 1) {</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a> >= in_matrix.size() || !in_matrix[<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>]) grow.push_back(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#acb18315d548212835cd8ed4287e6c0b6">a</a>);</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (num_matches_a == 1 && num_matches_b == 0) {</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a> >= in_matrix.size() || !in_matrix[<a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>]) grow.push_back(<a class="code hl_variable" href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a>);</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> }</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> }</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> </div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="comment">// If grow is of full size, we can extend the orbitope.</span></div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordflow">if</span> (grow.size() == num_cycles) {</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < orbitope.size(); ++i) {</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> orbitope[i].push_back(grow[i]);</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="keywordflow">if</span> (grow[i] >= in_matrix.size()) in_matrix.resize(grow[i] + 1, <span class="keyword">false</span>);</div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> in_matrix[grow[i]] = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> }</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> }</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> }</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> </div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="keywordflow">return</span> orbitope;</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span>}</div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> </div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#ae177cbcee937152b1230499662441902"> 151</a></span>std::vector<int> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ae177cbcee937152b1230499662441902">GetOrbits</a>(</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordtype">int</span> n, <span class="keyword">const</span> std::vector<std::unique_ptr<SparsePermutation>>& generators) {</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <a class="code hl_class" href="classoperations__research_1_1_merging_partition.html">MergingPartition</a> union_find;</div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> union_find.<a class="code hl_function" href="classoperations__research_1_1_merging_partition.html#a50eca19efa71a0b70de25f9ad4a2a6f8">Reset</a>(n);</div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> std::unique_ptr<SparsePermutation>& perm : generators) {</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_cycles = perm->NumCycles();</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_cycles; ++i) {</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="comment">// Note that there is currently no random access api like cycle[j].</span></div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keywordtype">int</span> first;</div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="keywordtype">bool</span> <a class="code hl_variable" href="variable__and__expressions_8cc.html#a9b151b7823afeaec2e767a5190d864df">is_first</a> = <span class="keyword">true</span>;</div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> x : perm->Cycle(i)) {</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="variable__and__expressions_8cc.html#a9b151b7823afeaec2e767a5190d864df">is_first</a>) {</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> first = x;</div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <a class="code hl_variable" href="variable__and__expressions_8cc.html#a9b151b7823afeaec2e767a5190d864df">is_first</a> = <span class="keyword">false</span>;</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> union_find.<a class="code hl_function" href="classoperations__research_1_1_merging_partition.html#a612bd8d97219124a8d6fbac721bcdbc6">MergePartsOf</a>(first, x);</div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> }</div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> }</div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> }</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> }</div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> </div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="keywordtype">int</span> num_parts = 0;</div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> std::vector<int> orbits(n, -1);</div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < n; ++i) {</div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="keywordflow">if</span> (union_find.<a class="code hl_function" href="classoperations__research_1_1_merging_partition.html#a3d5f7b1e62f42b574085e671ae6dfb73">NumNodesInSamePartAs</a>(i) == 1) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="keyword">const</span> <span class="keywordtype">int</span> root = union_find.<a class="code hl_function" href="classoperations__research_1_1_merging_partition.html#ac64dbed5d9196b941f3f53862f77309d">GetRootAndCompressPath</a>(i);</div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="keywordflow">if</span> (orbits[root] == -1) orbits[root] = num_parts++;</div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> orbits[i] = orbits[root];</div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> }</div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="keywordflow">return</span> orbits;</div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span>}</div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> </div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a1e331438c0fc60e8b00aebd0b66ce658"> 183</a></span>std::vector<int> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a1e331438c0fc60e8b00aebd0b66ce658">GetOrbitopeOrbits</a>(</div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="keywordtype">int</span> n, <span class="keyword">const</span> std::vector<std::vector<int>>& orbitope) {</div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> std::vector<int> orbits(n, -1);</div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < orbitope.size(); ++i) {</div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < orbitope[i].size(); ++j) {</div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <a class="code hl_define" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(orbits[orbitope[i][j]], -1);</div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> orbits[orbitope[i][j]] = i;</div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> }</div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> }</div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="keywordflow">return</span> orbits;</div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span>}</div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> </div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span>} <span class="comment">// namespace sat</span></div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_ad10edae0a852d72fb76afb1c77735045"><div class="ttname"><a href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a></div><div class="ttdeci">int64_t min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html"><div class="ttname"><a href="base_2logging_8h.html">logging.h</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_a7c0ce053b28d53aa4eaf3eb7fb71663b"><div class="ttname"><a href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a></div><div class="ttdeci">#define CHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00703">base/logging.h:703</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_afcaa7cadd41741bb855c2ada1d2ef927"><div class="ttname"><a href="base_2logging_8h.html#afcaa7cadd41741bb855c2ada1d2ef927">VLOG</a></div><div class="ttdeci">#define VLOG(verboselevel)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00984">base/logging.h:984</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_merging_partition_html"><div class="ttname"><a href="classoperations__research_1_1_merging_partition.html">operations_research::MergingPartition</a></div><div class="ttdef"><b>Definition:</b> <a href="dynamic__partition_8h_source.html#l00204">dynamic_partition.h:204</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_merging_partition_html_a3d5f7b1e62f42b574085e671ae6dfb73"><div class="ttname"><a href="classoperations__research_1_1_merging_partition.html#a3d5f7b1e62f42b574085e671ae6dfb73">operations_research::MergingPartition::NumNodesInSamePartAs</a></div><div class="ttdeci">int NumNodesInSamePartAs(int node)</div><div class="ttdef"><b>Definition:</b> <a href="dynamic__partition_8h_source.html#l00252">dynamic_partition.h:252</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_merging_partition_html_a50eca19efa71a0b70de25f9ad4a2a6f8"><div class="ttname"><a href="classoperations__research_1_1_merging_partition.html#a50eca19efa71a0b70de25f9ad4a2a6f8">operations_research::MergingPartition::Reset</a></div><div class="ttdeci">void Reset(int num_nodes)</div><div class="ttdef"><b>Definition:</b> <a href="dynamic__partition_8cc_source.html#l00206">dynamic_partition.cc:206</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_merging_partition_html_a612bd8d97219124a8d6fbac721bcdbc6"><div class="ttname"><a href="classoperations__research_1_1_merging_partition.html#a612bd8d97219124a8d6fbac721bcdbc6">operations_research::MergingPartition::MergePartsOf</a></div><div class="ttdeci">int MergePartsOf(int node1, int node2)</div><div class="ttdef"><b>Definition:</b> <a href="dynamic__partition_8cc_source.html#l00214">dynamic_partition.cc:214</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_merging_partition_html_ac64dbed5d9196b941f3f53862f77309d"><div class="ttname"><a href="classoperations__research_1_1_merging_partition.html#ac64dbed5d9196b941f3f53862f77309d">operations_research::MergingPartition::GetRootAndCompressPath</a></div><div class="ttdeci">int GetRootAndCompressPath(int node)</div><div class="ttdef"><b>Definition:</b> <a href="dynamic__partition_8cc_source.html#l00238">dynamic_partition.cc:238</a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_a9293e4d29cac928301645070dd307683"><div class="ttname"><a href="constraint__solver_2table_8cc.html#a9293e4d29cac928301645070dd307683">b</a></div><div class="ttdeci">int64_t b</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00047">constraint_solver/table.cc:47</a></div></div>
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<div class="ttc" id="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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