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<div class="title">affine_relation.h</div> </div>
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<a href="affine__relation_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2018 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">#ifndef OR_TOOLS_UTIL_AFFINE_RELATION_H_</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#define OR_TOOLS_UTIL_AFFINE_RELATION_H_</span></div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>  </div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include <vector></span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>  </div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include "<a class="code" href="iterator__adaptors_8h.html">ortools/base/iterator_adaptors.h</a>"</span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include "<a class="code" href="base_2logging_8h.html">ortools/base/logging.h</a>"</span></div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include "<a class="code" href="macros_8h.html">ortools/base/macros.h</a>"</span></div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  </div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</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="l00024"></a><span class="lineno"> 24</span>  </div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">// Union-Find algorithm to maintain "representative" for relations of the form:</span></div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">// x = coeff * y + offset, where "coeff" and "offset" are integers. The variable</span></div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// x and y are represented by non-negative integer indices. The idea is to</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// express variables in affine relation using as little different variables as</span></div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">// possible (the representatives).</span></div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// IMPORTANT: If there are relations with std::abs(coeff) != 1, then some</span></div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// relations might be ignored. See TryAdd() for more details.</span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// TODO(user): it might be possible to do something fancier and drop less</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// relations if all the affine relations are given before hand.</span></div>
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<div class="line"><a name="l00036"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_affine_relation.html"> 36</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1_affine_relation.html">AffineRelation</a> {</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00038"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_affine_relation.html#a430114d1f3d055605606f93cc0a195e0"> 38</a></span>  <a class="code" href="classoperations__research_1_1_affine_relation.html#a430114d1f3d055605606f93cc0a195e0">AffineRelation</a>() : num_relations_(0) {}</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>  <span class="comment">// Returns the number of relations added to the class and not ignored.</span></div>
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<div class="line"><a name="l00041"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_affine_relation.html#acee7699cd3aad1b8ce9721e4952b36e7"> 41</a></span>  <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1_affine_relation.html#acee7699cd3aad1b8ce9721e4952b36e7">NumRelations</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_relations_; }</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">// Adds the relation x = coeff * y + offset to the class.</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="comment">// Returns true if it wasn't ignored.</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">// This relation will only be taken into account if the representative of x</span></div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="comment">// and the one of y are different and if the relation can be transformed into</span></div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="comment">// a similar relation with integer coefficient between the two</span></div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="comment">// representatives.</span></div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="comment">// That is, given that:</span></div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">// - x = coeff_x * representative_x + offset_x</span></div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="comment">// - y = coeff_y * representative_y + offset_y</span></div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="comment">// we have:</span></div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="comment">// coeff_x * representative_x + offset_x =</span></div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="comment">// coeff * coeff_y * representative_y + coeff * offset_y + offset.</span></div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="comment">// Which can be simplified with the introduction of new variables to:</span></div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="comment">// coeff_x * representative_x = new_coeff * representative_y + new_offset.</span></div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="comment">// And we can merge the two if:</span></div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="comment">// - new_coeff and new_offset are divisible by coeff_x.</span></div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="comment">// - OR coeff_x and new_offset are divisible by new_coeff.</span></div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="comment">// Checked preconditions: x >=0, y >= 0, coeff != 0 and x != y.</span></div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="comment">// IMPORTANT: we do not check for integer overflow, but that could be added</span></div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="comment">// if it is needed.</span></div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_affine_relation.html#ab00901a89f35f3d9c663aac94cbcc77d">TryAdd</a>(<span class="keywordtype">int</span> x, <span class="keywordtype">int</span> y, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> coeff, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> offset);</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  </div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">// Same as TryAdd() with the option to disallow the use of a given</span></div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">// representative.</span></div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_affine_relation.html#ab00901a89f35f3d9c663aac94cbcc77d">TryAdd</a>(<span class="keywordtype">int</span> x, <span class="keywordtype">int</span> y, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> coeff, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> offset, <span class="keywordtype">bool</span> allow_rep_x,</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keywordtype">bool</span> allow_rep_y);</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  </div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="comment">// Returns a valid relation of the form x = coeff * representative + offset.</span></div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="comment">// Note that this can return x = x. Non-const because of path-compression.</span></div>
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<div class="line"><a name="l00076"></a><span class="lineno"><a class="line" href="structoperations__research_1_1_affine_relation_1_1_relation.html"> 76</a></span>  <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html">Relation</a> {</div>
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<div class="line"><a name="l00077"></a><span class="lineno"><a class="line" href="structoperations__research_1_1_affine_relation_1_1_relation.html#af5eb1e0745f18d589b9c552215bef515"> 77</a></span>  <span class="keywordtype">int</span> <a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#af5eb1e0745f18d589b9c552215bef515">representative</a>;</div>
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<div class="line"><a name="l00078"></a><span class="lineno"><a class="line" href="structoperations__research_1_1_affine_relation_1_1_relation.html#a03e44d5423c90c458e450c3230d71045"> 78</a></span>  <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#a03e44d5423c90c458e450c3230d71045">coeff</a>;</div>
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<div class="line"><a name="l00079"></a><span class="lineno"><a class="line" href="structoperations__research_1_1_affine_relation_1_1_relation.html#ae8ffb22e2a632e0a84779dcbc47ae96b"> 79</a></span>  <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> <a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#ae8ffb22e2a632e0a84779dcbc47ae96b">offset</a>;</div>
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<div class="line"><a name="l00080"></a><span class="lineno"><a class="line" href="structoperations__research_1_1_affine_relation_1_1_relation.html#ac171e416d4eda7ca9dc4d9cfe9c383ce"> 80</a></span>  <a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#ac171e416d4eda7ca9dc4d9cfe9c383ce">Relation</a>(<span class="keywordtype">int</span> r, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> c, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> o)</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  : <a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#af5eb1e0745f18d589b9c552215bef515">representative</a>(r), <a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#a03e44d5423c90c458e450c3230d71045">coeff</a>(c), <a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#ae8ffb22e2a632e0a84779dcbc47ae96b">offset</a>(o) {}</div>
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<div class="line"><a name="l00082"></a><span class="lineno"><a class="line" href="structoperations__research_1_1_affine_relation_1_1_relation.html#a835ae9099bb043e279d56804f48ef2fa"> 82</a></span>  <span class="keyword">const</span> <span class="keywordtype">bool</span> <a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#a835ae9099bb043e279d56804f48ef2fa">operator==</a>(<span class="keyword">const</span> <a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html">Relation</a>& other)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">return</span> <a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#af5eb1e0745f18d589b9c552215bef515">representative</a> == other.<a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#af5eb1e0745f18d589b9c552215bef515">representative</a> && <a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#a03e44d5423c90c458e450c3230d71045">coeff</a> == other.<a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#a03e44d5423c90c458e450c3230d71045">coeff</a> &&</div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#ae8ffb22e2a632e0a84779dcbc47ae96b">offset</a> == other.<a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#ae8ffb22e2a632e0a84779dcbc47ae96b">offset</a>;</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  }</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  };</div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  Relation <a class="code" href="classoperations__research_1_1_affine_relation.html#ac776696766f8c91ca8abc02f41d5854b">Get</a>(<span class="keywordtype">int</span> x) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  </div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="comment">// Advanced usage. This is a bit hacky and will just decrease the class size</span></div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="comment">// of a variable without any extra checks. Use with care. In particular when</span></div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="comment">// this is called, then x should never be used anymore in any of the non const</span></div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="comment">// calls of this class.</span></div>
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<div class="line"><a name="l00093"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_affine_relation.html#a2dfbb2acebf03bbb98cc1c54256fdead"> 93</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_affine_relation.html#a2dfbb2acebf03bbb98cc1c54256fdead">IgnoreFromClassSize</a>(<span class="keywordtype">int</span> x) {</div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordflow">if</span> (x >= size_.size()) <span class="keywordflow">return</span>; <span class="comment">// never seen here.</span></div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <a class="code" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(size_[x], kSizeForRemovedEntry) << x;</div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> r = <a class="code" href="classoperations__research_1_1_affine_relation.html#ac776696766f8c91ca8abc02f41d5854b">Get</a>(x).<a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#af5eb1e0745f18d589b9c552215bef515">representative</a>;</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">if</span> (r != x) {</div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <a class="code" href="base_2logging_8h.html#a7e03ec13560fa94a8fea569960d7efc6">CHECK_GT</a>(size_[r], 1);</div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  size_[r]--;</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <a class="code" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(size_[r], 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>  size_[x] = kSizeForRemovedEntry;</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  }</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  </div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="comment">// Returns the size of the class of x.</span></div>
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<div class="line"><a name="l00107"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_affine_relation.html#abc96755c0de80a81fd2730d3f2e85523"> 107</a></span>  <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1_affine_relation.html#abc96755c0de80a81fd2730d3f2e85523">ClassSize</a>(<span class="keywordtype">int</span> x)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordflow">if</span> (x >= representative_.size()) <span class="keywordflow">return</span> 1;</div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">return</span> size_[<a class="code" href="classoperations__research_1_1_affine_relation.html#ac776696766f8c91ca8abc02f41d5854b">Get</a>(x).<a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html#af5eb1e0745f18d589b9c552215bef515">representative</a>];</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  }</div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  </div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> kSizeForRemovedEntry = 0;</div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  </div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keywordtype">void</span> IncreaseSizeOfMemberVectors(<span class="keywordtype">int</span> new_size) {</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordflow">if</span> (new_size <= representative_.size()) <span class="keywordflow">return</span>;</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = representative_.size(); i < new_size; ++i) {</div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  representative_.push_back(i);</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  }</div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  offset_.resize(new_size, 0);</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  coeff_.resize(new_size, 1);</div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  size_.resize(new_size, 1);</div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  }</div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  </div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordtype">void</span> CompressPath(<span class="keywordtype">int</span> x)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <a class="code" href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a>(x, 0);</div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <a class="code" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(x, representative_.size());</div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  tmp_path_.clear();</div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keywordtype">int</span> parent = x;</div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordflow">while</span> (parent != representative_[parent]) {</div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  tmp_path_.push_back(parent);</div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  parent = representative_[parent];</div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  }</div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a> : ::<a class="code" href="namespacegtl.html#ae625b5510ffc29d1a66a422ec14809f7">gtl::reversed_view</a>(tmp_path_)) {</div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> old_parent = representative_[<a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>];</div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  offset_[<a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>] += coeff_[<a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>] * offset_[old_parent];</div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  coeff_[<a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>] *= coeff_[old_parent];</div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  representative_[<a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>] = parent;</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>  </div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keywordtype">int</span> num_relations_;</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"> 144</span>  <span class="comment">// The equivalence class representative for each variable index.</span></div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keyword">mutable</span> std::vector<int> representative_;</div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  </div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="comment">// The offset and coefficient such that</span></div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="comment">// variable[index] = coeff * variable[representative_[index]] + offset;</span></div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keyword">mutable</span> std::vector<int64> coeff_;</div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keyword">mutable</span> std::vector<int64> offset_;</div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  </div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="comment">// The size of each representative "tree", used to get a good complexity when</span></div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="comment">// we have the choice of which tree to merge into the other.</span></div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="comment">// TODO(user): Using a "rank" might be faster, but because we sometimes</span></div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="comment">// need to merge the bad subtree into the better one, it is trickier to</span></div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="comment">// maintain than in the classic union-find algorihtm.</span></div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  std::vector<int> size_;</div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  </div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="comment">// Used by CompressPath() to maintain the coeff/offset during compression.</span></div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keyword">mutable</span> std::vector<int> tmp_path_;</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>
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<div class="line"><a name="l00164"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_affine_relation.html#ab00901a89f35f3d9c663aac94cbcc77d"> 164</a></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_affine_relation.html#ab00901a89f35f3d9c663aac94cbcc77d">AffineRelation::TryAdd</a>(<span class="keywordtype">int</span> x, <span class="keywordtype">int</span> y, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> coeff, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> offset) {</div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_affine_relation.html#ab00901a89f35f3d9c663aac94cbcc77d">TryAdd</a>(x, y, coeff, offset, <span class="keyword">true</span>, <span class="keyword">true</span>);</div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> }</div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  </div>
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<div class="line"><a name="l00168"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_affine_relation.html#aba26716b3a9435aa1a8d9af046abb970"> 168</a></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1_affine_relation.html#ab00901a89f35f3d9c663aac94cbcc77d">AffineRelation::TryAdd</a>(<span class="keywordtype">int</span> x, <span class="keywordtype">int</span> y, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> coeff, <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> offset,</div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keywordtype">bool</span> allow_rep_x, <span class="keywordtype">bool</span> allow_rep_y) {</div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <a class="code" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(coeff, 0);</div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <a class="code" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(x, y);</div>
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<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <a class="code" href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a>(x, 0);</div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <a class="code" href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a>(y, 0);</div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  IncreaseSizeOfMemberVectors(<a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">std::max</a>(x, y) + 1);</div>
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<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <a class="code" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(size_[x], kSizeForRemovedEntry) << x;</div>
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<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <a class="code" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(size_[y], kSizeForRemovedEntry) << y;</div>
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<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  CompressPath(x);</div>
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<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  CompressPath(y);</div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> rep_x = representative_[x];</div>
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<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> rep_y = representative_[y];</div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keywordflow">if</span> (rep_x == rep_y) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  </div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="comment">// TODO(user): It should be possible to optimize this code block a bit, for</span></div>
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="comment">// instance depending on the magnitude of new_coeff vs coeff_x, we may already</span></div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="comment">// know that one of the two merge is not possible.</span></div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> coeff_x = coeff_[x];</div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> new_coeff = coeff * coeff_[y];</div>
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<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keyword">const</span> <a class="code" href="integral__types_8h.html#a7cde0074dfd288f2d70c0e035dacb28a">int64</a> new_offset = coeff * offset_[y] + offset - offset_[x];</div>
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<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <span class="keyword">const</span> <span class="keywordtype">bool</span> condition1 =</div>
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<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  allow_rep_y && (new_coeff % coeff_x == 0) && (new_offset % coeff_x == 0);</div>
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<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keyword">const</span> <span class="keywordtype">bool</span> condition2 = allow_rep_x && (coeff_x % new_coeff == 0) &&</div>
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<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  (new_offset % new_coeff == 0);</div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordflow">if</span> (condition1 && (!condition2 || size_[x] <= size_[y])) {</div>
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  representative_[rep_x] = rep_y;</div>
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<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  size_[rep_y] += size_[rep_x];</div>
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<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  coeff_[rep_x] = new_coeff / coeff_x;</div>
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  offset_[rep_x] = new_offset / coeff_x;</div>
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<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (condition2) {</div>
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<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  representative_[rep_y] = rep_x;</div>
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<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  size_[rep_x] += size_[rep_y];</div>
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<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  coeff_[rep_y] = coeff_x / new_coeff;</div>
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<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  offset_[rep_y] = -new_offset / new_coeff;</div>
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<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  }</div>
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<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  ++num_relations_;</div>
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<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00208"></a><span class="lineno"> 208</span> }</div>
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<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  </div>
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<div class="line"><a name="l00210"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_affine_relation.html#ac776696766f8c91ca8abc02f41d5854b"> 210</a></span> <span class="keyword">inline</span> <a class="code" href="structoperations__research_1_1_affine_relation_1_1_relation.html">AffineRelation::Relation</a> <a class="code" href="classoperations__research_1_1_affine_relation.html#ac776696766f8c91ca8abc02f41d5854b">AffineRelation::Get</a>(<span class="keywordtype">int</span> x)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="keywordflow">if</span> (x >= representative_.size() || representative_[x] == x) <span class="keywordflow">return</span> {x, 1, 0};</div>
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<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  CompressPath(x);</div>
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<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keywordflow">return</span> {representative_[x], coeff_[x], offset_[x]};</div>
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<div class="line"><a name="l00214"></a><span class="lineno"> 214</span> }</div>
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<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  </div>
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<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  </div>
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<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="preprocessor">#endif // OR_TOOLS_UTIL_AFFINE_RELATION_H_</span></div>
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</div><!-- fragment --></div><!-- contents -->
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</div><!-- doc-content -->
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<div class="ttc" id="astructoperations__research_1_1_affine_relation_1_1_relation_html_a03e44d5423c90c458e450c3230d71045"><div class="ttname"><a href="structoperations__research_1_1_affine_relation_1_1_relation.html#a03e44d5423c90c458e450c3230d71045">operations_research::AffineRelation::Relation::coeff</a></div><div class="ttdeci">int64 coeff</div><div class="ttdef"><b>Definition:</b> <a href="affine__relation_8h_source.html#l00078">affine_relation.h:78</a></div></div>
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<div class="ttc" id="aexpr__array_8cc_html_a472a99923cbe11ae7b5a5d157d9ad465"><div class="ttname"><a href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a></div><div class="ttdeci">IntVar * var</div><div class="ttdef"><b>Definition:</b> <a href="expr__array_8cc_source.html#l01858">expr_array.cc:1858</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_ab62f5ed8f2d48e29802be0cbbcd1359a"><div class="ttname"><a href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a></div><div class="ttdeci">#define DCHECK_LT(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00888">base/logging.h:888</a></div></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a9d0c202d5fdd62f4fa2c613339ff168a"><div class="ttname"><a href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">max</a></div><div class="ttdeci">int64 max</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="aclassoperations__research_1_1_affine_relation_html_ac776696766f8c91ca8abc02f41d5854b"><div class="ttname"><a href="classoperations__research_1_1_affine_relation.html#ac776696766f8c91ca8abc02f41d5854b">operations_research::AffineRelation::Get</a></div><div class="ttdeci">Relation Get(int x) const</div><div class="ttdef"><b>Definition:</b> <a href="affine__relation_8h_source.html#l00210">affine_relation.h:210</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_a7cc25402ecd7591b4c39934dd656b1f9"><div class="ttname"><a href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a></div><div class="ttdeci">#define CHECK_GE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00701">base/logging.h:701</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="aclassoperations__research_1_1_affine_relation_html_abc96755c0de80a81fd2730d3f2e85523"><div class="ttname"><a href="classoperations__research_1_1_affine_relation.html#abc96755c0de80a81fd2730d3f2e85523">operations_research::AffineRelation::ClassSize</a></div><div class="ttdeci">int ClassSize(int x) const</div><div class="ttdef"><b>Definition:</b> <a href="affine__relation_8h_source.html#l00107">affine_relation.h:107</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_a7e03ec13560fa94a8fea569960d7efc6"><div class="ttname"><a href="base_2logging_8h.html#a7e03ec13560fa94a8fea569960d7efc6">CHECK_GT</a></div><div class="ttdeci">#define CHECK_GT(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00702">base/logging.h:702</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_affine_relation_html_ab00901a89f35f3d9c663aac94cbcc77d"><div class="ttname"><a href="classoperations__research_1_1_affine_relation.html#ab00901a89f35f3d9c663aac94cbcc77d">operations_research::AffineRelation::TryAdd</a></div><div class="ttdeci">bool TryAdd(int x, int y, int64 coeff, int64 offset)</div><div class="ttdef"><b>Definition:</b> <a href="affine__relation_8h_source.html#l00164">affine_relation.h:164</a></div></div>
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<div class="ttc" id="amacros_8h_html"><div class="ttname"><a href="macros_8h.html">macros.h</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_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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<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="aclassoperations__research_1_1_affine_relation_html_a430114d1f3d055605606f93cc0a195e0"><div class="ttname"><a href="classoperations__research_1_1_affine_relation.html#a430114d1f3d055605606f93cc0a195e0">operations_research::AffineRelation::AffineRelation</a></div><div class="ttdeci">AffineRelation()</div><div class="ttdef"><b>Definition:</b> <a href="affine__relation_8h_source.html#l00038">affine_relation.h:38</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_affine_relation_html_acee7699cd3aad1b8ce9721e4952b36e7"><div class="ttname"><a href="classoperations__research_1_1_affine_relation.html#acee7699cd3aad1b8ce9721e4952b36e7">operations_research::AffineRelation::NumRelations</a></div><div class="ttdeci">int NumRelations() const</div><div class="ttdef"><b>Definition:</b> <a href="affine__relation_8h_source.html#l00041">affine_relation.h:41</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1_affine_relation_1_1_relation_html"><div class="ttname"><a href="structoperations__research_1_1_affine_relation_1_1_relation.html">operations_research::AffineRelation::Relation</a></div><div class="ttdef"><b>Definition:</b> <a href="affine__relation_8h_source.html#l00076">affine_relation.h:76</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="astructoperations__research_1_1_affine_relation_1_1_relation_html_ac171e416d4eda7ca9dc4d9cfe9c383ce"><div class="ttname"><a href="structoperations__research_1_1_affine_relation_1_1_relation.html#ac171e416d4eda7ca9dc4d9cfe9c383ce">operations_research::AffineRelation::Relation::Relation</a></div><div class="ttdeci">Relation(int r, int64 c, int64 o)</div><div class="ttdef"><b>Definition:</b> <a href="affine__relation_8h_source.html#l00080">affine_relation.h:80</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1_affine_relation_1_1_relation_html_ae8ffb22e2a632e0a84779dcbc47ae96b"><div class="ttname"><a href="structoperations__research_1_1_affine_relation_1_1_relation.html#ae8ffb22e2a632e0a84779dcbc47ae96b">operations_research::AffineRelation::Relation::offset</a></div><div class="ttdeci">int64 offset</div><div class="ttdef"><b>Definition:</b> <a href="affine__relation_8h_source.html#l00079">affine_relation.h:79</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_aae2dc65d9ea248d54bf39daa986dd295"><div class="ttname"><a href="base_2logging_8h.html#aae2dc65d9ea248d54bf39daa986dd295">DCHECK_GE</a></div><div class="ttdeci">#define DCHECK_GE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00889">base/logging.h:889</a></div></div>
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<div class="ttc" id="anamespacegtl_html_ae625b5510ffc29d1a66a422ec14809f7"><div class="ttname"><a href="namespacegtl.html#ae625b5510ffc29d1a66a422ec14809f7">gtl::reversed_view</a></div><div class="ttdeci">ReverseView< Container > reversed_view(const Container &c)</div><div class="ttdef"><b>Definition:</b> <a href="iterator__adaptors_8h_source.html#l00033">iterator_adaptors.h:33</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1_affine_relation_1_1_relation_html_af5eb1e0745f18d589b9c552215bef515"><div class="ttname"><a href="structoperations__research_1_1_affine_relation_1_1_relation.html#af5eb1e0745f18d589b9c552215bef515">operations_research::AffineRelation::Relation::representative</a></div><div class="ttdeci">int representative</div><div class="ttdef"><b>Definition:</b> <a href="affine__relation_8h_source.html#l00077">affine_relation.h:77</a></div></div>
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<div class="ttc" id="aiterator__adaptors_8h_html"><div class="ttname"><a href="iterator__adaptors_8h.html">iterator_adaptors.h</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_affine_relation_html_a2dfbb2acebf03bbb98cc1c54256fdead"><div class="ttname"><a href="classoperations__research_1_1_affine_relation.html#a2dfbb2acebf03bbb98cc1c54256fdead">operations_research::AffineRelation::IgnoreFromClassSize</a></div><div class="ttdeci">void IgnoreFromClassSize(int x)</div><div class="ttdef"><b>Definition:</b> <a href="affine__relation_8h_source.html#l00093">affine_relation.h:93</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_ab25e01a2942b821d66371fc68d53f2eb"><div class="ttname"><a href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a></div><div class="ttdeci">#define CHECK_NE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00698">base/logging.h:698</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1_affine_relation_1_1_relation_html_a835ae9099bb043e279d56804f48ef2fa"><div class="ttname"><a href="structoperations__research_1_1_affine_relation_1_1_relation.html#a835ae9099bb043e279d56804f48ef2fa">operations_research::AffineRelation::Relation::operator==</a></div><div class="ttdeci">const bool operator==(const Relation &other) const</div><div class="ttdef"><b>Definition:</b> <a href="affine__relation_8h_source.html#l00082">affine_relation.h:82</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_affine_relation_html"><div class="ttname"><a href="classoperations__research_1_1_affine_relation.html">operations_research::AffineRelation</a></div><div class="ttdef"><b>Definition:</b> <a href="affine__relation_8h_source.html#l00036">affine_relation.h:36</a></div></div>
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