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<li><a href="../cpp_algorithms/annotated.html">Algorithms</a></li>
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<li><a href="../cpp_sat/annotated.html">CP-SAT</a></li>
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<h1 style="color: #145A32;">C++ Reference: Graph</h1>
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<div class="title">connectivity.h</div> </div>
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<a href="connectivity_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="comment">// Graph connectivity algorithm for undirected graphs.</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// Memory consumption: O(n) where m is the number of arcs and n the number</span></div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// of nodes.</span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">// TODO(user): add depth-first-search based connectivity for directed graphs.</span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">// TODO(user): add depth-first-search based biconnectivity for directed graphs.</span></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  </div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#ifndef OR_TOOLS_GRAPH_CONNECTIVITY_H_</span></div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#define OR_TOOLS_GRAPH_CONNECTIVITY_H_</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="preprocessor">#include <vector></span></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="preprocessor">#include "ortools/base/integral_types.h"</span></div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include "ortools/base/logging.h"</span></div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include "ortools/base/macros.h"</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  </div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</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="l00030"></a><span class="lineno"> 30</span>  </div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// Template class implementing a Union-Find algorithm with path compression for</span></div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// maintaining the connected components of a graph.</span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// See Cormen et al. 2nd Edition. MIT Press, 2001. ISBN 0-262-03293-7.</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// Chapter 21: Data structures for Disjoint Sets, pp. 498-524.</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// and Tarjan (1975). Efficiency of a Good But Not Linear Set</span></div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// Union Algorithm. Journal of the ACM 22(2):215-225</span></div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// It is implemented as a template so that the size of NodeIndex can be chosen</span></div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// depending on the size of the graphs considered.</span></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// The main interest is that arcs do not need to be kept. Thus the memory</span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// complexity is O(n) where n is the number of nodes in the graph.</span></div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// The complexity of this algorithm is O(n . alpha(n)) where alpha(n) is</span></div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// the inverse Ackermann function. alpha(n) <= log(log(log(..log(log(n))..)</span></div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// In practice alpha(n) <= 5.</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// See Tarjan and van Leeuwen (1984). Worst-case analysis of set union</span></div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// algorithms. Journal of the ACM 31(2):245-281.</span></div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// Usage example:</span></div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// ConnectedComponents<int, int> components;</span></div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// components.Init(num_nodes);</span></div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// for (int arc = 0; arc < num_arcs; ++arc) {</span></div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// components.AddArc(tail[arc], head[arc]);</span></div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// }</span></div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// int num_connected_components = components.GetNumberOfConnectedComponents();</span></div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// if (num_connected_components == 1) {</span></div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// // Graph is completely connected.</span></div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// }</span></div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// // Group the nodes in the same connected component together.</span></div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// // group[class_number][i] contains the i-th node in group class_number.</span></div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// hash_map<int, vector<int> > group(num_connected_components);</span></div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// for (int node = 0; node < num_nodes; ++node) {</span></div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// group[components.GetClassRepresentative(node)].push_back(node);</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">//</span></div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// Keywords: graph, connected components.</span></div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  </div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex, <span class="keyword">typename</span> ArcIndex></div>
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<div class="line"><a name="l00067"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_connected_components.html"> 67</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1_connected_components.html">ConnectedComponents</a> {</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00069"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_connected_components.html#a04bf0bd47cf349309302338120f12465"> 69</a></span>  <a class="code" href="classoperations__research_1_1_connected_components.html#a04bf0bd47cf349309302338120f12465">ConnectedComponents</a>() : num_nodes_(0), class_(), class_size_() {}</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  </div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">// Reserves memory for num_nodes and resets the data structures.</span></div>
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<div class="line"><a name="l00072"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_connected_components.html#a8247e505912b0c7d2309f3f9eaa74080"> 72</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_connected_components.html#a8247e505912b0c7d2309f3f9eaa74080">Init</a>(<a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> num_nodes) {</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  CHECK_GE(num_nodes, 0);</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  num_nodes_ = num_nodes;</div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  class_.resize(num_nodes_);</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  class_size_.assign(num_nodes_, 1);</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> node = 0; node < num_nodes_; ++node) {</div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  class_[node] = node;</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>  </div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="comment">// Adds the information that NodeIndex tail and NodeIndex head are connected.</span></div>
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<div class="line"><a name="l00083"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_connected_components.html#a07ef59a345df6bddab386c943af4238c"> 83</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_connected_components.html#a07ef59a345df6bddab386c943af4238c">AddArc</a>(<a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> tail, <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> head) {</div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> tail_class = <a class="code" href="classoperations__research_1_1_connected_components.html#aeaa04a98ce83a11cc8260f15b7ceb6ce">CompressPath</a>(tail);</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> head_class = <a class="code" href="classoperations__research_1_1_connected_components.html#aeaa04a98ce83a11cc8260f15b7ceb6ce">CompressPath</a>(head);</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">if</span> (tail_class != head_class) {</div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <a class="code" href="classoperations__research_1_1_connected_components.html#a047f863116aabfa88d8eeeebda5de760">MergeClasses</a>(tail_class, head_class);</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>  }</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  </div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="comment">// Adds a complete StarGraph to the object. Note that Depth-First Search</span></div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="comment">// is a better algorithm for finding connected components on graphs.</span></div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="comment">// TODO(user): implement Depth-First Search-based connected components finder.</span></div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> Graph></div>
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<div class="line"><a name="l00095"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_connected_components.html#a0f653082d74e1d7e9d8e97be437ba036"> 95</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_connected_components.html#a0f653082d74e1d7e9d8e97be437ba036">AddGraph</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph) {</div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <a class="code" href="classoperations__research_1_1_connected_components.html#a8247e505912b0c7d2309f3f9eaa74080">Init</a>(graph.num_nodes());</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> tail = 0; tail < graph.num_nodes(); ++tail) {</div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> Graph::OutgoingArcIterator it(graph, tail); it.Ok();</div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  it.Next()) {</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <a class="code" href="classoperations__research_1_1_connected_components.html#a07ef59a345df6bddab386c943af4238c">AddArc</a>(tail, graph.Head(it.Index()));</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  }</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>  }</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>  <span class="comment">// Compresses the path for node.</span></div>
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<div class="line"><a name="l00106"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_connected_components.html#aeaa04a98ce83a11cc8260f15b7ceb6ce"> 106</a></span>  <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> <a class="code" href="classoperations__research_1_1_connected_components.html#aeaa04a98ce83a11cc8260f15b7ceb6ce">CompressPath</a>(<a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> node) {</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  CheckNodeBounds(node);</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> parent = node;</div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">while</span> (parent != class_[parent]) {</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  CheckNodeBounds(class_[parent]);</div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  CheckNodeBounds(class_[class_[parent]]);</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  parent = class_[parent];</div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  }</div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keywordflow">while</span> (node != class_[node]) {</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> old_parent = class_[node];</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  class_[node] = parent;</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  node = old_parent;</div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  }</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keywordflow">return</span> parent;</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>  </div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="comment">// Returns the equivalence class representative for node.</span></div>
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<div class="line"><a name="l00123"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_connected_components.html#a874a54f45623ba735a5634b1ea9289ea"> 123</a></span>  <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> <a class="code" href="classoperations__research_1_1_connected_components.html#a874a54f45623ba735a5634b1ea9289ea">GetClassRepresentative</a>(<a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> node) {</div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keywordflow">return</span> <a class="code" href="classoperations__research_1_1_connected_components.html#aeaa04a98ce83a11cc8260f15b7ceb6ce">CompressPath</a>(node);</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  }</div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  </div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="comment">// Returns the number of connected components. Allocates num_nodes_ bits for</span></div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="comment">// the computation.</span></div>
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<div class="line"><a name="l00129"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_connected_components.html#ad93186658fbb95624b55f85af74f8ea5"> 129</a></span>  <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> <a class="code" href="classoperations__research_1_1_connected_components.html#ad93186658fbb95624b55f85af74f8ea5">GetNumberOfConnectedComponents</a>() {</div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> number = 0;</div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> node = 0; node < num_nodes_; ++node) {</div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordflow">if</span> (class_[node] == node) ++number;</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">return</span> number;</div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  }</div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  </div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="comment">// Merges the equivalence classes of node1 and node2.</span></div>
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<div class="line"><a name="l00138"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_connected_components.html#a047f863116aabfa88d8eeeebda5de760"> 138</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1_connected_components.html#a047f863116aabfa88d8eeeebda5de760">MergeClasses</a>(<a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> node1, <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> node2) {</div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="comment">// It's faster (~10%) to swap the two values and have a single piece of</span></div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="comment">// code for merging the classes.</span></div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  CheckNodeBounds(node1);</div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  CheckNodeBounds(node2);</div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keywordflow">if</span> (class_size_[node1] < class_size_[node2]) {</div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  std::swap(node1, node2);</div>
|
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  }</div>
|
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  class_[node2] = node1;</div>
|
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  class_size_[node1] += class_size_[node2];</div>
|
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  }</div>
|
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  </div>
|
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="keywordtype">void</span> CheckNodeBounds(<a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> node_index) {</div>
|
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  DCHECK_LE(0, node_index);</div>
|
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  DCHECK_LT(node_index, num_nodes_);</div>
|
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  }</div>
|
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="comment">// The exact number of nodes in the graph.</span></div>
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|
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> num_nodes_;</div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  </div>
|
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="comment">// The equivalence class representative for each node.</span></div>
|
|
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  std::vector<NodeIndex> class_;</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>  <span class="comment">// The size of each equivalence class of each node. Used to compress the paths</span></div>
|
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="comment">// and therefore achieve better time complexity.</span></div>
|
|
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  std::vector<NodeIndex> class_size_;</div>
|
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<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  </div>
|
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  DISALLOW_COPY_AND_ASSIGN(<a class="code" href="classoperations__research_1_1_connected_components.html#a04bf0bd47cf349309302338120f12465">ConnectedComponents</a>);</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"> 168</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  </div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="preprocessor">#endif // OR_TOOLS_GRAPH_CONNECTIVITY_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="aclassoperations__research_1_1_connected_components_html"><div class="ttname"><a href="classoperations__research_1_1_connected_components.html">operations_research::ConnectedComponents</a></div><div class="ttdef"><b>Definition:</b> <a href="connectivity_8h_source.html#l00067">connectivity.h:67</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_connected_components_html_ad93186658fbb95624b55f85af74f8ea5"><div class="ttname"><a href="classoperations__research_1_1_connected_components.html#ad93186658fbb95624b55f85af74f8ea5">operations_research::ConnectedComponents::GetNumberOfConnectedComponents</a></div><div class="ttdeci">NodeIndex GetNumberOfConnectedComponents()</div><div class="ttdef"><b>Definition:</b> <a href="connectivity_8h_source.html#l00129">connectivity.h:129</a></div></div>
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<div class="ttc" id="anamespaceutil_html_a2f76166dbe0c4055a1f256235ad00478"><div class="ttname"><a href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">util::Graph</a></div><div class="ttdeci">ListGraph Graph</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l02354">graph.h:2354</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="ttdef"><b>Definition:</b> <a href="christofides_8h_source.html#l00033">christofides.h:33</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_connected_components_html_a04bf0bd47cf349309302338120f12465"><div class="ttname"><a href="classoperations__research_1_1_connected_components.html#a04bf0bd47cf349309302338120f12465">operations_research::ConnectedComponents::ConnectedComponents</a></div><div class="ttdeci">ConnectedComponents()</div><div class="ttdef"><b>Definition:</b> <a href="connectivity_8h_source.html#l00069">connectivity.h:69</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_connected_components_html_a8247e505912b0c7d2309f3f9eaa74080"><div class="ttname"><a href="classoperations__research_1_1_connected_components.html#a8247e505912b0c7d2309f3f9eaa74080">operations_research::ConnectedComponents::Init</a></div><div class="ttdeci">void Init(NodeIndex num_nodes)</div><div class="ttdef"><b>Definition:</b> <a href="connectivity_8h_source.html#l00072">connectivity.h:72</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_connected_components_html_aeaa04a98ce83a11cc8260f15b7ceb6ce"><div class="ttname"><a href="classoperations__research_1_1_connected_components.html#aeaa04a98ce83a11cc8260f15b7ceb6ce">operations_research::ConnectedComponents::CompressPath</a></div><div class="ttdeci">NodeIndex CompressPath(NodeIndex node)</div><div class="ttdef"><b>Definition:</b> <a href="connectivity_8h_source.html#l00106">connectivity.h:106</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_connected_components_html_a047f863116aabfa88d8eeeebda5de760"><div class="ttname"><a href="classoperations__research_1_1_connected_components.html#a047f863116aabfa88d8eeeebda5de760">operations_research::ConnectedComponents::MergeClasses</a></div><div class="ttdeci">void MergeClasses(NodeIndex node1, NodeIndex node2)</div><div class="ttdef"><b>Definition:</b> <a href="connectivity_8h_source.html#l00138">connectivity.h:138</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_connected_components_html_a874a54f45623ba735a5634b1ea9289ea"><div class="ttname"><a href="classoperations__research_1_1_connected_components.html#a874a54f45623ba735a5634b1ea9289ea">operations_research::ConnectedComponents::GetClassRepresentative</a></div><div class="ttdeci">NodeIndex GetClassRepresentative(NodeIndex node)</div><div class="ttdef"><b>Definition:</b> <a href="connectivity_8h_source.html#l00123">connectivity.h:123</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_connected_components_html_a0f653082d74e1d7e9d8e97be437ba036"><div class="ttname"><a href="classoperations__research_1_1_connected_components.html#a0f653082d74e1d7e9d8e97be437ba036">operations_research::ConnectedComponents::AddGraph</a></div><div class="ttdeci">void AddGraph(const Graph &graph)</div><div class="ttdef"><b>Definition:</b> <a href="connectivity_8h_source.html#l00095">connectivity.h:95</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a272bcc4d6ee0e87a7fc430a5cb13c582"><div class="ttname"><a href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">operations_research::NodeIndex</a></div><div class="ttdeci">int32 NodeIndex</div><div class="ttdef"><b>Definition:</b> <a href="ebert__graph_8h_source.html#l00200">ebert_graph.h:192</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_connected_components_html_a07ef59a345df6bddab386c943af4238c"><div class="ttname"><a href="classoperations__research_1_1_connected_components.html#a07ef59a345df6bddab386c943af4238c">operations_research::ConnectedComponents::AddArc</a></div><div class="ttdeci">void AddArc(NodeIndex tail, NodeIndex head)</div><div class="ttdef"><b>Definition:</b> <a href="connectivity_8h_source.html#l00083">connectivity.h:83</a></div></div>
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