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<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 name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2018 Google LLC</span></div>
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<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div>
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<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  </div>
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<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#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 name="l00015"></a><span class="lineno"> 15</span>  </div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</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 name="l00017"></a><span class="lineno"> 17</span>  </div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="keyword">namespace </span>sat {</div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  </div>
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<div class="line"><a name="l00021"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#ae4be5fcdd40601e7d3862a5c9ab06915"> 21</a></span> std::vector<std::vector<int>> <a class="code" href="namespaceoperations__research_1_1sat.html#ae4be5fcdd40601e7d3862a5c9ab06915">BasicOrbitopeExtraction</a>(</div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  <span class="keyword">const</span> std::vector<std::unique_ptr<SparsePermutation>>& generators) {</div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</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 name="l00024"></a><span class="lineno"> 24</span>  <span class="comment">// regroup them according to the number of cycles.</span></div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  std::vector<std::vector<int>> num_cycles_to_2cyclers;</div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</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 name="l00027"></a><span class="lineno"> 27</span>  <span class="keyword">const</span> std::unique_ptr<SparsePermutation>& perm = generators[g];</div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  <span class="keywordtype">bool</span> contain_only_2cycles = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> num_cycles = perm->NumCycles();</div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</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 name="l00031"></a><span class="lineno"> 31</span>  <span class="keywordflow">if</span> (perm->Cycle(i).size() != 2) {</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  contain_only_2cycles = <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keywordflow">break</span>;</div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  }</div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  }</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordflow">if</span> (!contain_only_2cycles) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keywordflow">if</span> (num_cycles >= num_cycles_to_2cyclers.size()) {</div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  num_cycles_to_2cyclers.resize(num_cycles + 1);</div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  }</div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  num_cycles_to_2cyclers[num_cycles].push_back(g);</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  }</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  </div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</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 name="l00044"></a><span class="lineno"> 44</span>  <span class="comment">// fixing variables.</span></div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</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 name="l00047"></a><span class="lineno"> 47</span>  <span class="keywordtype">int</span> best = -1;</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keywordtype">int</span> best_score = 0;</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</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 name="l00050"></a><span class="lineno"> 50</span>  <span class="keywordflow">if</span> (num_cycles_to_2cyclers[i].size() > 1) {</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</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 name="l00052"></a><span class="lineno"> 52</span>  <a class="code" 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 name="l00053"></a><span class="lineno"> 53</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> score = <a class="code" href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">std::min</a>(i, num_perms);</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordflow">if</span> (score > best_score) {</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  best = i;</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  best_score = score;</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  }</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  }</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  }</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  </div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  std::vector<std::vector<int>> orbitope;</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordflow">if</span> (best == -1) <span class="keywordflow">return</span> orbitope;</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  </div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <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 name="l00065"></a><span class="lineno"> 65</span>  std::vector<bool> in_matrix;</div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  </div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="comment">// Greedily grow the orbitope.</span></div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  orbitope.resize(best);</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</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 name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">// Start using the first permutation.</span></div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keywordflow">if</span> (orbitope[0].empty()) {</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keyword">const</span> std::unique_ptr<SparsePermutation>& perm = generators[g];</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> num_cycles = perm->NumCycles();</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</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 name="l00075"></a><span class="lineno"> 75</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 name="l00076"></a><span class="lineno"> 76</span>  orbitope[i].push_back(x);</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</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 name="l00078"></a><span class="lineno"> 78</span>  in_matrix[x] = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  }</div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  }</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  }</div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  </div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</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 name="l00085"></a><span class="lineno"> 85</span>  <span class="comment">// in the orbitope matrix.</span></div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</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 name="l00088"></a><span class="lineno"> 88</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 name="l00089"></a><span class="lineno"> 89</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 name="l00090"></a><span class="lineno"> 90</span>  <span class="comment">// of the problem should already return permutation in this canonical</span></div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="comment">// format.</span></div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  std::vector<int> grow;</div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordtype">int</span> matching_column_index = -1;</div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keyword">const</span> std::unique_ptr<SparsePermutation>& perm = generators[g];</div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> num_cycles = perm->NumCycles();</div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</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 name="l00097"></a><span class="lineno"> 97</span>  <span class="comment">// Extract the two elements of this transposition.</span></div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  std::vector<int> tmp;</div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</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 name="l00100"></a><span class="lineno"> 100</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a> = tmp[0];</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a> = tmp[1];</div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  </div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="comment">// We want one element to appear in matching_column_index and the other to</span></div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="comment">// not appear at all.</span></div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keywordtype">int</span> num_matches_a = 0;</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordtype">int</span> num_matches_b = 0;</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keywordtype">int</span> last_match_index = -1;</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</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 name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">if</span> (orbitope[i][j] == <a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>) {</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  ++num_matches_a;</div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  last_match_index = j;</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (orbitope[i][j] == <a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>) {</div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  ++num_matches_b;</div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  last_match_index = j;</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  }</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  }</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordflow">if</span> (last_match_index == -1) <span class="keywordflow">break</span>;</div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordflow">if</span> (matching_column_index == -1) {</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  matching_column_index = last_match_index;</div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  }</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</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 name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordflow">if</span> (num_matches_a == 0 && num_matches_b == 1) {</div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keywordflow">if</span> (<a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a> >= in_matrix.size() || !in_matrix[<a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>]) grow.push_back(<a class="code" href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a>);</div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</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 name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordflow">if</span> (<a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a> >= in_matrix.size() || !in_matrix[<a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>]) grow.push_back(<a class="code" href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a>);</div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordflow">break</span>;</div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  }</div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  }</div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  </div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</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 name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordflow">if</span> (grow.size() == num_cycles) {</div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</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 name="l00134"></a><span class="lineno"> 134</span>  orbitope[i].push_back(grow[i]);</div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</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 name="l00136"></a><span class="lineno"> 136</span>  in_matrix[grow[i]] = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  }</div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  }</div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  }</div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  </div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordflow">return</span> orbitope;</div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> }</div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  </div>
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<div class="line"><a name="l00144"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#ae75c184235d68cd4b3019cfba09b764d"> 144</a></span> std::vector<int> <a class="code" href="namespaceoperations__research_1_1sat.html#ae75c184235d68cd4b3019cfba09b764d">GetOrbits</a>(</div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</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 name="l00146"></a><span class="lineno"> 146</span>  <a class="code" href="classoperations__research_1_1_merging_partition.html">MergingPartition</a> union_find;</div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  union_find.<a class="code" href="classoperations__research_1_1_merging_partition.html#a50eca19efa71a0b70de25f9ad4a2a6f8">Reset</a>(n);</div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</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 name="l00149"></a><span class="lineno"> 149</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> num_cycles = perm->NumCycles();</div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</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 name="l00151"></a><span class="lineno"> 151</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 name="l00152"></a><span class="lineno"> 152</span>  <span class="keywordtype">int</span> first;</div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="keywordtype">bool</span> is_first = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</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 name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordflow">if</span> (is_first) {</div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  first = x;</div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  is_first = <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  union_find.<a class="code" href="classoperations__research_1_1_merging_partition.html#a612bd8d97219124a8d6fbac721bcdbc6">MergePartsOf</a>(first, x);</div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  }</div>
|
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  }</div>
|
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  }</div>
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<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  }</div>
|
|
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  </div>
|
|
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keywordtype">int</span> num_parts = 0;</div>
|
|
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  std::vector<int> orbits(n, -1);</div>
|
|
<div class="line"><a name="l00167"></a><span class="lineno"> 167</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 name="l00168"></a><span class="lineno"> 168</span>  <span class="keywordflow">if</span> (union_find.<a class="code" href="classoperations__research_1_1_merging_partition.html#a3d5f7b1e62f42b574085e671ae6dfb73">NumNodesInSamePartAs</a>(i) == 1) <span class="keywordflow">continue</span>;</div>
|
|
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> root = union_find.<a class="code" href="classoperations__research_1_1_merging_partition.html#ac64dbed5d9196b941f3f53862f77309d">GetRootAndCompressPath</a>(i);</div>
|
|
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="keywordflow">if</span> (orbits[root] == -1) orbits[root] = num_parts++;</div>
|
|
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  orbits[i] = orbits[root];</div>
|
|
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  }</div>
|
|
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keywordflow">return</span> orbits;</div>
|
|
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> }</div>
|
|
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  </div>
|
|
<div class="line"><a name="l00176"></a><span class="lineno"><a class="line" href="namespaceoperations__research_1_1sat.html#a34d8ec706e23b38d955a1c902a03208e"> 176</a></span> std::vector<int> <a class="code" href="namespaceoperations__research_1_1sat.html#a34d8ec706e23b38d955a1c902a03208e">GetOrbitopeOrbits</a>(</div>
|
|
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordtype">int</span> n, <span class="keyword">const</span> std::vector<std::vector<int>>& orbitope) {</div>
|
|
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  std::vector<int> orbits(n, -1);</div>
|
|
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < orbitope.size(); ++i) {</div>
|
|
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < orbitope[i].size(); ++j) {</div>
|
|
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <a class="code" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(orbits[orbitope[i][j]], -1);</div>
|
|
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  orbits[orbitope[i][j]] = i;</div>
|
|
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  }</div>
|
|
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  }</div>
|
|
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keywordflow">return</span> orbits;</div>
|
|
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span> }</div>
|
|
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  </div>
|
|
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> } <span class="comment">// namespace sat</span></div>
|
|
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a021e695f54a13bd809c34b2f4ca87c37"><div class="ttname"><a href="alldiff__cst_8cc.html#a021e695f54a13bd809c34b2f4ca87c37">min</a></div><div class="ttdeci">int64 min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00138">alldiff_cst.cc:138</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#l00697">base/logging.h:697</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#l00978">base/logging.h:978</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#l00203">dynamic_partition.h:203</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#l00251">dynamic_partition.h:251</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#l00205">dynamic_partition.cc:205</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#l00213">dynamic_partition.cc:213</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#l00237">dynamic_partition.cc:237</a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_a344010e26426d6a13411648d988bc9b6"><div class="ttname"><a href="constraint__solver_2table_8cc.html#a344010e26426d6a13411648d988bc9b6">b</a></div><div class="ttdeci">int64 b</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00043">constraint_solver/table.cc:43</a></div></div>
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<div class="ttc" id="aconstraint__solver_2table_8cc_html_af730895c6c6ef6e03caaf6251192dfd2"><div class="ttname"><a href="constraint__solver_2table_8cc.html#af730895c6c6ef6e03caaf6251192dfd2">a</a></div><div class="ttdeci">int64 a</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_2table_8cc_source.html#l00042">constraint_solver/table.cc:42</a></div></div>
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<div class="ttc" id="adynamic__partition_8h_html"><div class="ttname"><a href="dynamic__partition_8h.html">dynamic_partition.h</a></div></div>
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<div class="ttc" id="aintegral__types_8h_html_a7cde0074dfd288f2d70c0e035dacb28a"><div class="ttname"><a href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a></div><div class="ttdeci">int64_t int64</div><div class="ttdef"><b>Definition:</b> <a href="integral__types_8h_source.html#l00034">integral_types.h:34</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a34d8ec706e23b38d955a1c902a03208e"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a34d8ec706e23b38d955a1c902a03208e">operations_research::sat::GetOrbitopeOrbits</a></div><div class="ttdeci">std::vector< int > GetOrbitopeOrbits(int n, const std::vector< std::vector< int >> &orbitope)</div><div class="ttdef"><b>Definition:</b> <a href="symmetry__util_8cc_source.html#l00176">symmetry_util.cc:176</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ae4be5fcdd40601e7d3862a5c9ab06915"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ae4be5fcdd40601e7d3862a5c9ab06915">operations_research::sat::BasicOrbitopeExtraction</a></div><div class="ttdeci">std::vector< std::vector< int > > BasicOrbitopeExtraction(const std::vector< std::unique_ptr< SparsePermutation >> &generators)</div><div class="ttdef"><b>Definition:</b> <a href="symmetry__util_8cc_source.html#l00021">symmetry_util.cc:21</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ae75c184235d68cd4b3019cfba09b764d"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ae75c184235d68cd4b3019cfba09b764d">operations_research::sat::GetOrbits</a></div><div class="ttdeci">std::vector< int > GetOrbits(int n, const std::vector< std::unique_ptr< SparsePermutation >> &generators)</div><div class="ttdef"><b>Definition:</b> <a href="symmetry__util_8cc_source.html#l00144">symmetry_util.cc:144</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">The vehicle routing library lets one model and solve generic vehicle routing problems ranging from th...</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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