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<a href="strongly__connected__components_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment">// This code computes the strongly connected components of a directed graph,</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment">// and presents them sorted by reverse topological order.</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment">//</span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">// It implements an efficient version of Tarjan's strongly connected components</span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">// algorithm published in: Tarjan, R. E. (1972), "Depth-first search and linear</span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment">// graph algorithms", SIAM Journal on Computing.</span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment">//</span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment">// A description can also be found here:</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment">// http://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment">//</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment">// SIMPLE EXAMPLE:</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment">//</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">// Fill a vector<vector<int>> graph; representing your graph adjacency lists.</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">// That is, graph[i] contains the nodes adjacent to node #i. The nodes must be</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">// integers in [0, num_nodes). Then just do:</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">//</span></div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">// vector<vector<int>> components;</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">// FindStronglyConnectedComponents(</span></div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// static_cast<int>(graph.size()), graph, &components);</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">//</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">// The nodes of each strongly connected components will be listed in each</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment">// subvector of components. The components appear in reverse topological order:</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment">// outgoing arcs from a component will only be towards earlier components.</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">//</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">// IMPORTANT: num_nodes will be the number of nodes of the graph. Its type</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// is the type used internally by the algorithm. It is why it is better to</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// convert it to int or even int32_t rather than using size_t which takes 64</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// bits.</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> </div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="preprocessor">#ifndef UTIL_GRAPH_STRONGLY_CONNECTED_COMPONENTS_H_</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="preprocessor">#define UTIL_GRAPH_STRONGLY_CONNECTED_COMPONENTS_H_</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="preprocessor">#include <limits></span></div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="preprocessor">#include "ortools/base/logging.h"</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="preprocessor">#include "ortools/base/macros.h"</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">// Finds the strongly connected components of a directed graph. It is templated</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">// so it can be used in many contexts. See the simple example above for the</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment">// easiest use case.</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment">//</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment">// The requirement of the different types are:</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment">// - The type NodeIndex must be an integer type representing a node of the</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment">// graph. The nodes must be in [0, num_nodes). It can be unsigned.</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="comment">// - The type Graph must provide a [] operator such that the following code</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">// iterates over the adjacency list of the given node:</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment">// for (const NodeIndex head : graph[node]) {}</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="comment">// - The type SccOutput must implement the function:</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="comment">// emplace_back(NodeIndex const* begin, NodeIndex const* end);</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="comment">// It will be called with the connected components of the given graph as they</span></div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="comment">// are found (In the reverse topological order).</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment">//</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment">// More practical details on the algorithm:</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="comment">// - It deals properly with self-loop and duplicate nodes.</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="comment">// - It is really fast! and work in O(nodes + edges).</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="comment">// - Its memory usage is also bounded by O(nodes + edges) but in practice it</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="comment">// uses less than the input graph.</span></div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span><span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex, <span class="keyword">typename</span> Graph, <span class="keyword">typename</span> SccOutput></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="keywordtype">void</span> <a class="code hl_function" href="strongly__connected__components_8h.html#aafab5785b250e1013c13511ce478f36b">FindStronglyConnectedComponents</a>(<span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> num_nodes,</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph, SccOutput* components);</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="comment">// A simple custom output class that just counts the number of SCC. Not</span></div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span><span class="comment">// allocating many vectors can save both space and speed if your graph is large.</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="comment">//</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="comment">// Note: If this matters, you probably don't want to use vector<vector<int>> as</span></div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="comment">// an input either. See StaticGraph in ortools/graph/graph.h</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span><span class="comment">// for an efficient graph data structure compatible with this algorithm.</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex></div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"><a class="line" href="struct_scc_counter_output.html"> 83</a></span><span class="keyword">struct </span><a class="code hl_struct" href="struct_scc_counter_output.html">SccCounterOutput</a> {</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"><a class="line" href="struct_scc_counter_output.html#aa1c5d9076a0daa336ed562752e6fd5a3"> 84</a></span> <span class="keywordtype">int</span> <a class="code hl_variable" href="struct_scc_counter_output.html#aa1c5d9076a0daa336ed562752e6fd5a3">number_of_components</a> = 0;</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"><a class="line" href="struct_scc_counter_output.html#ac706b4714b4a833d82f355d3c06c18af"> 85</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="struct_scc_counter_output.html#ac706b4714b4a833d82f355d3c06c18af">emplace_back</a>(<a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> <span class="keyword">const</span>* b, <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> <span class="keyword">const</span>* e) {</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> ++<a class="code hl_variable" href="struct_scc_counter_output.html#aa1c5d9076a0daa336ed562752e6fd5a3">number_of_components</a>;</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> }</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// This is just here so this class can transparently replace a code that</span></div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// use vector<vector<int>> as an SccOutput, and get its size with size().</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"><a class="line" href="struct_scc_counter_output.html#af9593d4a5ff4274efaf429cb4f9e57cc"> 90</a></span> <span class="keywordtype">int</span> <a class="code hl_function" href="struct_scc_counter_output.html#af9593d4a5ff4274efaf429cb4f9e57cc">size</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code hl_variable" href="struct_scc_counter_output.html#aa1c5d9076a0daa336ed562752e6fd5a3">number_of_components</a>; }</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span>};</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> </div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span><span class="comment">// This implementation is slightly different than a classical iterative version</span></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span><span class="comment">// of Tarjan's strongly connected components algorithm. But basically it is</span></div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span><span class="comment">// still an iterative DFS. We use a class so memory can be reused if one needs</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="comment">// to compute many SCC in a row. It also allows more complex behavior in the</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment">// Graph or SccOutput class that might inspect the current state of the</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment">// algorithm.</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="comment">//</span></div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span><span class="comment">// TODO(user): Possible optimizations:</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span><span class="comment">// - Try to reserve the vectors which sizes are bounded by num_nodes.</span></div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span><span class="comment">// - Use an index rather than doing push_back(), pop_back() on them.</span></div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span><span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex, <span class="keyword">typename</span> Graph, <span class="keyword">typename</span> SccOutput></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"><a class="line" href="class_strongly_connected_components_finder.html"> 104</a></span><span class="keyword">class </span><a class="code hl_class" href="class_strongly_connected_components_finder.html">StronglyConnectedComponentsFinder</a> {</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"><a class="line" href="class_strongly_connected_components_finder.html#ae578e6662172f4c25bb8ad068a597ba5"> 106</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="class_strongly_connected_components_finder.html#ae578e6662172f4c25bb8ad068a597ba5">FindStronglyConnectedComponents</a>(<span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> num_nodes,</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph,</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> SccOutput* components) {</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// Reset the class fields.</span></div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> scc_stack_.clear();</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> scc_start_index_.clear();</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> node_index_.assign(num_nodes, 0);</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> node_to_process_.clear();</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> </div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// Optimization. This will always be equal to scc_start_index_.back() except</span></div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// when scc_stack_ is empty, in which case its value does not matter.</span></div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> current_scc_start = 0;</div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> </div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="comment">// Loop over all the nodes not yet settled and start a DFS from each of</span></div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="comment">// them.</span></div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keywordflow">for</span> (<a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> base_node = 0; base_node < num_nodes; ++base_node) {</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordflow">if</span> (node_index_[base_node] != 0) <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> DCHECK_EQ(0, node_to_process_.size());</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> node_to_process_.push_back(base_node);</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordflow">do</span> {</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node = node_to_process_.back();</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> index = node_index_[node];</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keywordflow">if</span> (index == 0) {</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="comment">// We continue the dfs from this node and set its 1-based index.</span></div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> scc_stack_.push_back(node);</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> current_scc_start = scc_stack_.size();</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> node_index_[node] = current_scc_start;</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> scc_start_index_.push_back(current_scc_start);</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> </div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="comment">// Enqueue all its adjacent nodes.</span></div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> min_head_index = kSettledIndex;</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> head : graph[node]) {</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> head_index = node_index_[head];</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordflow">if</span> (head_index == 0) {</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> node_to_process_.push_back(head);</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="comment">// Note that if head_index == kSettledIndex, nothing happens.</span></div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> min_head_index = std::min(min_head_index, head_index);</div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> }</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> }</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> </div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="comment">// Update the start of this strongly connected component.</span></div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="comment">// Note that scc_start_index_ can never be empty since it first</span></div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="comment">// element is 1 and by definition min_head_index is 1-based and can't</span></div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="comment">// be 0.</span></div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keywordflow">while</span> (current_scc_start > min_head_index) {</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> scc_start_index_.pop_back();</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> current_scc_start = scc_start_index_.back();</div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> }</div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> node_to_process_.pop_back();</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keywordflow">if</span> (current_scc_start == index) {</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="comment">// We found a strongly connected component.</span></div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> components->emplace_back(&scc_stack_[current_scc_start - 1],</div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> &scc_stack_[0] + scc_stack_.size());</div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = current_scc_start - 1; i < scc_stack_.size(); ++i) {</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> node_index_[scc_stack_[i]] = kSettledIndex;</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> }</div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> scc_stack_.resize(current_scc_start - 1);</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> scc_start_index_.pop_back();</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> current_scc_start =</div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> scc_start_index_.empty() ? 0 : scc_start_index_.back();</div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> }</div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> }</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> } <span class="keywordflow">while</span> (!node_to_process_.empty());</div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> }</div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> }</div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> </div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="comment">// Advanced usage. This can be used in either the Graph or SccOutput template</span></div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="comment">// class to query the current state of the algorithm. It allows to build more</span></div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="comment">// complex variant based on the core DFS algo.</span></div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"><a class="line" href="class_strongly_connected_components_finder.html#a4db5c4e5c0437428c74f692ac4601af7"> 177</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" href="class_strongly_connected_components_finder.html#a4db5c4e5c0437428c74f692ac4601af7">NodeIsInCurrentDfsPath</a>(<a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="keywordflow">return</span> node_index_[node] > 0 && node_index_[node] < kSettledIndex;</div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> }</div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> </div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="keyword">static</span> <span class="keyword">constexpr</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> kSettledIndex =</div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> std::numeric_limits<NodeIndex>::max();</div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> </div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="comment">// Each node expanded by the DFS will be pushed on this stack. A node is only</span></div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="comment">// popped back when its strongly connected component has been explored and</span></div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="comment">// outputted.</span></div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> std::vector<NodeIndex> scc_stack_;</div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> </div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="comment">// This is equivalent to the "low link" of a node in Tarjan's algorithm.</span></div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="comment">// Basically, scc_start_index_.back() represent the 1-based index in</span></div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="comment">// scc_stack_ of the beginning of the current strongly connected component.</span></div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="comment">// All the nodes after this index will be on the same component.</span></div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> std::vector<NodeIndex> scc_start_index_;</div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> </div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="comment">// Each node is assigned an index which changes 2 times in the algorithm:</span></div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <span class="comment">// - Everyone starts with an index of 0 which means unexplored.</span></div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="comment">// - The first time they are explored by the DFS and pushed on scc_stack_,</span></div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="comment">// they get their 1-based index on this stack.</span></div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="comment">// - Once they have been processed and outputted to components, they are said</span></div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="comment">// to be settled, and their index become kSettledIndex.</span></div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> std::vector<NodeIndex> node_index_;</div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> </div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="comment">// This is a well known way to do an efficient iterative DFS. Each time a node</span></div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="comment">// is explored, all its adjacent nodes are pushed on this stack. The iterative</span></div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <span class="comment">// dfs processes the nodes one by one by popping them back from here.</span></div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> std::vector<NodeIndex> node_to_process_;</div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span>};</div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> </div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span><span class="comment">// Simple wrapper function for most usage.</span></div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span><span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex, <span class="keyword">typename</span> Graph, <span class="keyword">typename</span> SccOutput></div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"><a class="line" href="strongly__connected__components_8h.html#aafab5785b250e1013c13511ce478f36b"> 212</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="strongly__connected__components_8h.html#aafab5785b250e1013c13511ce478f36b">FindStronglyConnectedComponents</a>(<span class="keyword">const</span> <a class="code hl_typedef" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> num_nodes,</div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph,</div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> SccOutput* components) {</div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <a class="code hl_class" href="class_strongly_connected_components_finder.html">StronglyConnectedComponentsFinder<NodeIndex, Graph, SccOutput></a> helper;</div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keywordflow">return</span> helper.<a class="code hl_function" href="class_strongly_connected_components_finder.html#ae578e6662172f4c25bb8ad068a597ba5">FindStronglyConnectedComponents</a>(num_nodes, graph, components);</div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span>}</div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> </div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span><span class="preprocessor">#endif </span><span class="comment">// UTIL_GRAPH_STRONGLY_CONNECTED_COMPONENTS_H_</span></div>
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<div class="ttc" id="aclass_strongly_connected_components_finder_html"><div class="ttname"><a href="class_strongly_connected_components_finder.html">StronglyConnectedComponentsFinder</a></div><div class="ttdef"><b>Definition:</b> <a href="strongly__connected__components_8h_source.html#l00104">strongly_connected_components.h:104</a></div></div>
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<div class="ttc" id="aclass_strongly_connected_components_finder_html_a4db5c4e5c0437428c74f692ac4601af7"><div class="ttname"><a href="class_strongly_connected_components_finder.html#a4db5c4e5c0437428c74f692ac4601af7">StronglyConnectedComponentsFinder::NodeIsInCurrentDfsPath</a></div><div class="ttdeci">bool NodeIsInCurrentDfsPath(NodeIndex node) const</div><div class="ttdef"><b>Definition:</b> <a href="strongly__connected__components_8h_source.html#l00177">strongly_connected_components.h:177</a></div></div>
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<div class="ttc" id="aclass_strongly_connected_components_finder_html_ae578e6662172f4c25bb8ad068a597ba5"><div class="ttname"><a href="class_strongly_connected_components_finder.html#ae578e6662172f4c25bb8ad068a597ba5">StronglyConnectedComponentsFinder::FindStronglyConnectedComponents</a></div><div class="ttdeci">void FindStronglyConnectedComponents(const NodeIndex num_nodes, const Graph &graph, SccOutput *components)</div><div class="ttdef"><b>Definition:</b> <a href="strongly__connected__components_8h_source.html#l00106">strongly_connected_components.h:106</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a7ffcae041a5d746371436101400cdb6b"><div class="ttname"><a href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">operations_research::NodeIndex</a></div><div class="ttdeci">int32_t NodeIndex</div><div class="ttdef"><b>Definition:</b> <a href="ebert__graph_8h_source.html#l00201">ebert_graph.h:193</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#l02362">graph.h:2362</a></div></div>
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<div class="ttc" id="astrongly__connected__components_8h_html_aafab5785b250e1013c13511ce478f36b"><div class="ttname"><a href="strongly__connected__components_8h.html#aafab5785b250e1013c13511ce478f36b">FindStronglyConnectedComponents</a></div><div class="ttdeci">void FindStronglyConnectedComponents(const NodeIndex num_nodes, const Graph &graph, SccOutput *components)</div><div class="ttdef"><b>Definition:</b> <a href="strongly__connected__components_8h_source.html#l00212">strongly_connected_components.h:212</a></div></div>
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<div class="ttc" id="astruct_scc_counter_output_html"><div class="ttname"><a href="struct_scc_counter_output.html">SccCounterOutput</a></div><div class="ttdef"><b>Definition:</b> <a href="strongly__connected__components_8h_source.html#l00083">strongly_connected_components.h:83</a></div></div>
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<div class="ttc" id="astruct_scc_counter_output_html_aa1c5d9076a0daa336ed562752e6fd5a3"><div class="ttname"><a href="struct_scc_counter_output.html#aa1c5d9076a0daa336ed562752e6fd5a3">SccCounterOutput::number_of_components</a></div><div class="ttdeci">int number_of_components</div><div class="ttdef"><b>Definition:</b> <a href="strongly__connected__components_8h_source.html#l00084">strongly_connected_components.h:84</a></div></div>
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<div class="ttc" id="astruct_scc_counter_output_html_ac706b4714b4a833d82f355d3c06c18af"><div class="ttname"><a href="struct_scc_counter_output.html#ac706b4714b4a833d82f355d3c06c18af">SccCounterOutput::emplace_back</a></div><div class="ttdeci">void emplace_back(NodeIndex const *b, NodeIndex const *e)</div><div class="ttdef"><b>Definition:</b> <a href="strongly__connected__components_8h_source.html#l00085">strongly_connected_components.h:85</a></div></div>
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<div class="ttc" id="astruct_scc_counter_output_html_af9593d4a5ff4274efaf429cb4f9e57cc"><div class="ttname"><a href="struct_scc_counter_output.html#af9593d4a5ff4274efaf429cb4f9e57cc">SccCounterOutput::size</a></div><div class="ttdeci">int size() const</div><div class="ttdef"><b>Definition:</b> <a href="strongly__connected__components_8h_source.html#l00090">strongly_connected_components.h:90</a></div></div>
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