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<div class="title">strongly_connected_components.h</div> </div>
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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 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">// This code computes the strongly connected components of a directed graph,</span></div>
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<div class="line"><a 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 name="l00016"></a><span class="lineno"> 16</span> <span class="comment">//</span></div>
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<div class="line"><a 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 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 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 name="l00020"></a><span class="lineno"> 20</span> <span class="comment">//</span></div>
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<div class="line"><a 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 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 name="l00023"></a><span class="lineno"> 23</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// SIMPLE EXAMPLE:</span></div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">//</span></div>
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<div class="line"><a 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 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 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 name="l00029"></a><span class="lineno"> 29</span> <span class="comment">//</span></div>
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<div class="line"><a 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 name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// FindStronglyConnectedComponents(</span></div>
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<div class="line"><a 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 name="l00033"></a><span class="lineno"> 33</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// The nodes of each strongly connected components will be listed in each</span></div>
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<div class="line"><a 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 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 name="l00037"></a><span class="lineno"> 37</span> <span class="comment">//</span></div>
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<div class="line"><a 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 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 name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// convert it to int or even int32 rather than using size_t which takes 64 bits.</span></div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  </div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="preprocessor">#ifndef UTIL_GRAPH_STRONGLY_CONNECTED_COMPONENTS_H_</span></div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#define UTIL_GRAPH_STRONGLY_CONNECTED_COMPONENTS_H_</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  </div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="preprocessor">#include <limits></span></div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="preprocessor">#include <vector></span></div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  </div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="preprocessor">#include "ortools/base/logging.h"</span></div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="preprocessor">#include "ortools/base/macros.h"</span></div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  </div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</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 name="l00052"></a><span class="lineno"> 52</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 name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// easiest use case.</span></div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// The requirement of the different types are:</span></div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</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 name="l00057"></a><span class="lineno"> 57</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 name="l00058"></a><span class="lineno"> 58</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 name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// iterates over the adjacency list of the given node:</span></div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// for (const NodeIndex head : graph[node]) {}</span></div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// - The type SccOutput must implement the function:</span></div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// emplace_back(NodeIndex const* begin, NodeIndex const* end);</span></div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</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 name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// are found (In the reverse topological order).</span></div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// More practical details on the algorithm:</span></div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// - It deals properly with self-loop and duplicate nodes.</span></div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// - It is really fast! and work in O(nodes + edges).</span></div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</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 name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// uses less than the input graph.</span></div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</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 name="l00072"></a><span class="lineno"> 72</span> <span class="keywordtype">void</span> <a class="code" href="strongly__connected__components_8h.html#aafab5785b250e1013c13511ce478f36b">FindStronglyConnectedComponents</a>(<span class="keyword">const</span> <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>  <span class="keyword">const</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph, SccOutput* components);</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  </div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</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 name="l00076"></a><span class="lineno"> 76</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 name="l00077"></a><span class="lineno"> 77</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</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 name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// an input either. See StaticGraph in ortools/graph/graph.h</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// for an efficient graph data structure compatible with this algorithm.</span></div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="keyword">template</span> <<span class="keyword">typename</span> NodeIndex></div>
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<div class="line"><a name="l00082"></a><span class="lineno"><a class="line" href="struct_scc_counter_output.html"> 82</a></span> <span class="keyword">struct </span><a class="code" href="struct_scc_counter_output.html">SccCounterOutput</a> {</div>
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<div class="line"><a name="l00083"></a><span class="lineno"><a class="line" href="struct_scc_counter_output.html#aa1c5d9076a0daa336ed562752e6fd5a3"> 83</a></span>  <span class="keywordtype">int</span> <a class="code" href="struct_scc_counter_output.html#aa1c5d9076a0daa336ed562752e6fd5a3">number_of_components</a> = 0;</div>
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<div class="line"><a name="l00084"></a><span class="lineno"><a class="line" href="struct_scc_counter_output.html#ac706b4714b4a833d82f355d3c06c18af"> 84</a></span>  <span class="keywordtype">void</span> <a class="code" href="struct_scc_counter_output.html#ac706b4714b4a833d82f355d3c06c18af">emplace_back</a>(<a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> <span class="keyword">const</span>* b, <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> <span class="keyword">const</span>* e) {</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  ++<a class="code" href="struct_scc_counter_output.html#aa1c5d9076a0daa336ed562752e6fd5a3">number_of_components</a>;</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  }</div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <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 name="l00088"></a><span class="lineno"> 88</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 name="l00089"></a><span class="lineno"><a class="line" href="struct_scc_counter_output.html#af9593d4a5ff4274efaf429cb4f9e57cc"> 89</a></span>  <span class="keywordtype">int</span> <a class="code" href="struct_scc_counter_output.html#af9593d4a5ff4274efaf429cb4f9e57cc">size</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="struct_scc_counter_output.html#aa1c5d9076a0daa336ed562752e6fd5a3">number_of_components</a>; }</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>  </div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// This implementation is slightly different than a classical iterative version</span></div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</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 name="l00094"></a><span class="lineno"> 94</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 name="l00095"></a><span class="lineno"> 95</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 name="l00096"></a><span class="lineno"> 96</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 name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// algorithm.</span></div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment">// TODO(user): Possible optimizations:</span></div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</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 name="l00101"></a><span class="lineno"> 101</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 name="l00102"></a><span class="lineno"> 102</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 name="l00103"></a><span class="lineno"><a class="line" href="class_strongly_connected_components_finder.html"> 103</a></span> <span class="keyword">class </span><a class="code" href="class_strongly_connected_components_finder.html">StronglyConnectedComponentsFinder</a> {</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00105"></a><span class="lineno"><a class="line" href="class_strongly_connected_components_finder.html#ae578e6662172f4c25bb8ad068a597ba5"> 105</a></span>  <span class="keywordtype">void</span> <a class="code" href="class_strongly_connected_components_finder.html#ae578e6662172f4c25bb8ad068a597ba5">FindStronglyConnectedComponents</a>(<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> num_nodes,</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <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="l00107"></a><span class="lineno"> 107</span>  SccOutput* components) {</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">// Reset the class fields.</span></div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  scc_stack_.clear();</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  scc_start_index_.clear();</div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  node_index_.assign(num_nodes, 0);</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  node_to_process_.clear();</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="comment">// Optimization. This will always be equal to scc_start_index_.back() except</span></div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</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 name="l00116"></a><span class="lineno"> 116</span>  <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> current_scc_start = 0;</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  </div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</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 name="l00119"></a><span class="lineno"> 119</span>  <span class="comment">// them.</span></div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> base_node = 0; base_node < num_nodes; ++base_node) {</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</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 name="l00122"></a><span class="lineno"> 122</span>  DCHECK_EQ(0, node_to_process_.size());</div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  node_to_process_.push_back(base_node);</div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keywordflow">do</span> {</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> node = node_to_process_.back();</div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> index = node_index_[node];</div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordflow">if</span> (index == 0) {</div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</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 name="l00129"></a><span class="lineno"> 129</span>  scc_stack_.push_back(node);</div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  current_scc_start = scc_stack_.size();</div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  node_index_[node] = current_scc_start;</div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  scc_start_index_.push_back(current_scc_start);</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="comment">// Enqueue all its adjacent nodes.</span></div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> min_head_index = kSettledIndex;</div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> head : graph[node]) {</div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> head_index = node_index_[head];</div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keywordflow">if</span> (head_index == 0) {</div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  node_to_process_.push_back(head);</div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="comment">// Note that if head_index == kSettledIndex, nothing happens.</span></div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  min_head_index = std::min(min_head_index, head_index);</div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  }</div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  }</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>  <span class="comment">// Update the start of this strongly connected component.</span></div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</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 name="l00148"></a><span class="lineno"> 148</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 name="l00149"></a><span class="lineno"> 149</span>  <span class="comment">// be 0.</span></div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordflow">while</span> (current_scc_start > min_head_index) {</div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  scc_start_index_.pop_back();</div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  current_scc_start = scc_start_index_.back();</div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  }</div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  node_to_process_.pop_back();</div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordflow">if</span> (current_scc_start == index) {</div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="comment">// We found a strongly connected component.</span></div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  components->emplace_back(&scc_stack_[current_scc_start - 1],</div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  &scc_stack_[0] + scc_stack_.size());</div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</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 name="l00161"></a><span class="lineno"> 161</span>  node_index_[scc_stack_[i]] = kSettledIndex;</div>
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  }</div>
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<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  scc_stack_.resize(current_scc_start - 1);</div>
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<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  scc_start_index_.pop_back();</div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  current_scc_start =</div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  scc_start_index_.empty() ? 0 : scc_start_index_.back();</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>  }</div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  } <span class="keywordflow">while</span> (!node_to_process_.empty());</div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  }</div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  }</div>
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<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  </div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</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 name="l00174"></a><span class="lineno"> 174</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 name="l00175"></a><span class="lineno"> 175</span>  <span class="comment">// complex variant based on the core DFS algo.</span></div>
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<div class="line"><a name="l00176"></a><span class="lineno"><a class="line" href="class_strongly_connected_components_finder.html#a4db5c4e5c0437428c74f692ac4601af7"> 176</a></span>  <span class="keywordtype">bool</span> <a class="code" href="class_strongly_connected_components_finder.html#a4db5c4e5c0437428c74f692ac4601af7">NodeIsInCurrentDfsPath</a>(<a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> node)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordflow">return</span> node_index_[node] > 0 && node_index_[node] < kSettledIndex;</div>
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<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  }</div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  </div>
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<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keyword">static</span> constexpr <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> kSettledIndex =</div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  std::numeric_limits<NodeIndex>::max();</div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  </div>
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</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 name="l00185"></a><span class="lineno"> 185</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 name="l00186"></a><span class="lineno"> 186</span>  <span class="comment">// outputted.</span></div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  std::vector<NodeIndex> scc_stack_;</div>
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<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  </div>
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<div class="line"><a name="l00189"></a><span class="lineno"> 189</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 name="l00190"></a><span class="lineno"> 190</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 name="l00191"></a><span class="lineno"> 191</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 name="l00192"></a><span class="lineno"> 192</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 name="l00193"></a><span class="lineno"> 193</span>  std::vector<NodeIndex> scc_start_index_;</div>
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  </div>
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<div class="line"><a name="l00195"></a><span class="lineno"> 195</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 name="l00196"></a><span class="lineno"> 196</span>  <span class="comment">// - Everyone starts with an index of 0 which means unexplored.</span></div>
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</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 name="l00198"></a><span class="lineno"> 198</span>  <span class="comment">// they get their 1-based index on this stack.</span></div>
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<div class="line"><a name="l00199"></a><span class="lineno"> 199</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 name="l00200"></a><span class="lineno"> 200</span>  <span class="comment">// to be settled, and their index become kSettledIndex.</span></div>
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<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  std::vector<NodeIndex> node_index_;</div>
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<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  </div>
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<div class="line"><a name="l00203"></a><span class="lineno"> 203</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 name="l00204"></a><span class="lineno"> 204</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 name="l00205"></a><span class="lineno"> 205</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 name="l00206"></a><span class="lineno"> 206</span>  std::vector<NodeIndex> node_to_process_;</div>
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<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> };</div>
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<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  </div>
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<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment">// Simple wrapper function for most usage.</span></div>
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<div class="line"><a name="l00210"></a><span class="lineno"> 210</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 name="l00211"></a><span class="lineno"><a class="line" href="strongly__connected__components_8h.html#aafab5785b250e1013c13511ce478f36b"> 211</a></span> <span class="keywordtype">void</span> <a class="code" href="strongly__connected__components_8h.html#aafab5785b250e1013c13511ce478f36b">FindStronglyConnectedComponents</a>(<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a272bcc4d6ee0e87a7fc430a5cb13c582">NodeIndex</a> num_nodes,</div>
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<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <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="l00213"></a><span class="lineno"> 213</span>  SccOutput* components) {</div>
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<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <a class="code" href="class_strongly_connected_components_finder.html">StronglyConnectedComponentsFinder<NodeIndex, Graph, SccOutput></a> helper;</div>
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<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keywordflow">return</span> helper.<a class="code" href="class_strongly_connected_components_finder.html#ae578e6662172f4c25bb8ad068a597ba5">FindStronglyConnectedComponents</a>(num_nodes, graph, components);</div>
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<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> }</div>
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<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  </div>
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<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="preprocessor">#endif </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#l00103">strongly_connected_components.h:103</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#l00176">strongly_connected_components.h:176</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#l00105">strongly_connected_components.h:105</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="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#l02360">graph.h:2360</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#l00211">strongly_connected_components.h:211</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#l00082">strongly_connected_components.h:82</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#l00083">strongly_connected_components.h:83</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#l00084">strongly_connected_components.h:84</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#l00089">strongly_connected_components.h:89</a></div></div>
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