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<li><a href="../cpp_algorithms/annotated.html">Algorithms</a></li>
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<li><a href="../cpp_sat/annotated.html">CP-SAT</a></li>
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<h1 style="color: #145A32;">C++ Reference: Graph</h1>
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<a href="util_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 2010-2021 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">// A collections of utilities for the Graph classes in ./graph.h.</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>  </div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#ifndef UTIL_GRAPH_UTIL_H_</span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#define UTIL_GRAPH_UTIL_H_</span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>  </div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include <algorithm></span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include <cstdint></span></div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include <map></span></div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include <memory></span></div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#include <set></span></div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#include <string></span></div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#include <vector></span></div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  </div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include "absl/container/flat_hash_map.h"</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include "absl/container/inlined_vector.h"</span></div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include "ortools/base/hash.h"</span></div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#include "ortools/base/map_util.h"</span></div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#include "<a class="code" href="connected__components_8h.html">ortools/graph/connected_components.h</a>"</span></div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#include "<a class="code" href="graph_8h.html">ortools/graph/graph.h</a>"</span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor">#include "<a class="code" href="iterators_8h.html">ortools/graph/iterators.h</a>"</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  </div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="keyword">namespace </span><a class="code" href="namespaceutil.html">util</a> {</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  </div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// Here's a set of simple diagnosis tools. Notes:</span></div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// - A self-arc is an arc from a node to itself.</span></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// - We say that an arc A->B is duplicate when there is another arc A->B in the</span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// same graph.</span></div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// - A graph is said "weakly connected" if it is connected when considering all</span></div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// arcs as undirected edges.</span></div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// - A graph is said "symmetric" iff for all (a, b), the number of arcs a->b</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// is equal to the number of arcs b->a.</span></div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// All these diagnosis work in O(graph size), since the inverse Ackerman</span></div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// function is <= 5 for all practical instances, and are very fast.</span></div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// If the graph is a "static" kind, they must be finalized, except for</span></div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// GraphHasSelfArcs() and GraphIsWeaklyConnected() which also support</span></div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// non-finalized StaticGraph<>.</span></div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#a9aedc5b3920b0ce89959be43ece7625b">GraphHasSelfArcs</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph);</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#a7cab01cf2313ef202fdb8d1540430c1c">GraphHasDuplicateArcs</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph);</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#aa94a02ae5c14feb50676668f2de166dc">GraphIsSymmetric</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph);</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#ab66702bf387ec38027c1f94444872510">GraphIsWeaklyConnected</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph);</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  </div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// Returns a fresh copy of a given graph.</span></div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#ae5f98804c317dda817bff628d868c4dd">CopyGraph</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph);</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  </div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// Creates a remapped copy of graph "graph", where node i becomes node</span></div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// new_node_index[i].</span></div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// "new_node_index" must be a valid permutation of [0..num_nodes-1] or the</span></div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// behavior is undefined (it may die).</span></div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// Note that you can call IsValidPermutation() to check it yourself.</span></div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#aab5724a929530fa1d28749dc82852388">RemapGraph</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph,</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keyword">const</span> std::vector<int>& new_node_index);</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  </div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// Gets the induced subgraph of "graph" restricted to the nodes in "nodes":</span></div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// the resulting graph will have exactly nodes.size() nodes, and its</span></div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// node #0 will be the former graph's node #nodes[0], etc.</span></div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// See https://en.wikipedia.org/wiki/Induced_subgraph .</span></div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// The "nodes" must be a valid subset (no repetitions) of</span></div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// [0..graph.num_nodes()-1], or the behavior is undefined (it may die).</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// Note that you can call IsSubsetOf0N() to check it yourself.</span></div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment">// Current complexity: O(num old nodes + num new arcs). It could easily</span></div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment">// be done in O(num new nodes + num new arcs) but with a higher constant.</span></div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#a99094e047812eb44a7c2b3b82091f560">GetSubgraphOfNodes</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph,</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keyword">const</span> std::vector<int>& nodes);</div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  </div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// This can be used to view a directed graph (that supports reverse arcs)</span></div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// from graph.h as un undirected graph: operator[](node) returns a</span></div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// pseudo-container that iterates over all nodes adjacent to "node" (from</span></div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// outgoing or incoming arcs).</span></div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// CAVEAT: Self-arcs (aka loops) will appear twice.</span></div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// Example:</span></div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment">// ReverseArcsStaticGraph<> dgraph;</span></div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// ...</span></div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// UndirectedAdjacencyListsOfDirectedGraph<decltype(dgraph)> ugraph(dgraph);</span></div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// for (int neighbor_of_node_42 : ugraph[42]) { ... }</span></div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00100"></a><span class="lineno"><a class="line" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html"> 100</a></span> <span class="keyword">class </span><a class="code" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html">UndirectedAdjacencyListsOfDirectedGraph</a> {</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00102"></a><span class="lineno"><a class="line" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html#a0a6c3259e0f5b11ae67f15beefa1020c"> 102</a></span>  <span class="keyword">explicit</span> <a class="code" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html#a0a6c3259e0f5b11ae67f15beefa1020c">UndirectedAdjacencyListsOfDirectedGraph</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph)</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  : graph_(graph) {}</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  </div>
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<div class="line"><a name="l00105"></a><span class="lineno"><a class="line" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html#a2380f2634e304c2161485c0d395b78eb"> 105</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Graph::OutgoingOrOppositeIncomingArcIterator <a class="code" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html#a2380f2634e304c2161485c0d395b78eb">ArcIterator</a>;</div>
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<div class="line"><a name="l00106"></a><span class="lineno"><a class="line" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator.html"> 106</a></span>  <span class="keyword">class </span><a class="code" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator.html">AdjacencyListIterator</a> : <span class="keyword">public</span> <a class="code" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html#a2380f2634e304c2161485c0d395b78eb">ArcIterator</a> {</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00108"></a><span class="lineno"><a class="line" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator.html#a544dc5fdf254f2bcd1b7dfa67ef41b7a"> 108</a></span>  <span class="keyword">explicit</span> <a class="code" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator.html#a544dc5fdf254f2bcd1b7dfa67ef41b7a">AdjacencyListIterator</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph, <a class="code" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html#a2380f2634e304c2161485c0d395b78eb">ArcIterator</a>&& arc_it)</div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  : <a class="code" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html#a2380f2634e304c2161485c0d395b78eb">ArcIterator</a>(arc_it), graph_(graph) {}</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="comment">// Overwrite operator* to return the heads of the arcs.</span></div>
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<div class="line"><a name="l00111"></a><span class="lineno"><a class="line" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator.html#a1ce6d58586efadff072fb5b4591f5ea3"> 111</a></span>  <span class="keyword">typename</span> <a class="code" href="classutil_1_1_base_graph.html#aec05ff3d270a5f888e1623c2a99ff2aa">Graph::NodeIndex</a> <a class="code" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator.html#a1ce6d58586efadff072fb5b4591f5ea3">operator*</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">return</span> graph_.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(ArcIterator::operator*());</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>  </div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph_;</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>  </div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="comment">// Returns a pseudo-container of all the nodes adjacent to "node".</span></div>
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<div class="line"><a name="l00120"></a><span class="lineno"><a class="line" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html#acb3986c66a9d18524b947fd391f68240"> 120</a></span>  <a class="code" href="classutil_1_1_begin_end_wrapper.html">BeginEndWrapper<AdjacencyListIterator></a> <a class="code" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html#acb3986c66a9d18524b947fd391f68240">operator[]</a>(<span class="keywordtype">int</span> node)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keyword">const</span> <span class="keyword">auto</span>& arc_range = graph_.OutgoingOrOppositeIncomingArcs(node);</div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keywordflow">return</span> {<a class="code" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator.html">AdjacencyListIterator</a>(graph_, arc_range.begin()),</div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <a class="code" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator.html">AdjacencyListIterator</a>(graph_, arc_range.end())};</div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  }</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  </div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph_;</div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> };</div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  </div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment">// Computes the weakly connected components of a directed graph that</span></div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment">// provides the OutgoingOrOppositeIncomingArcs() API, and returns them</span></div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment">// as a mapping from node to component index. See GetConnectedComponens().</span></div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00134"></a><span class="lineno"><a class="line" href="namespaceutil.html#ab34783e729bb5fc99042893f6bfcbb2f"> 134</a></span> std::vector<int> <a class="code" href="namespaceutil.html#ab34783e729bb5fc99042893f6bfcbb2f">GetWeaklyConnectedComponents</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph) {</div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceutil.html#a366d433bd2afb387ea527c581447dffc">GetConnectedComponents</a>(</div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  graph.<a class="code" href="classutil_1_1_base_graph.html#a6a2df5042167b234f6dc3aed4acfa6c9">num_nodes</a>(), <a class="code" href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html">UndirectedAdjacencyListsOfDirectedGraph<Graph></a>(graph));</div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> }</div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  </div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment">// Returns true iff the given vector is a subset of [0..n-1], i.e.</span></div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="comment">// all elements i are such that 0 <= i < n and no two elements are equal.</span></div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment">// "n" must be >= 0 or the result is undefined.</span></div>
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<div class="line"><a name="l00142"></a><span class="lineno"><a class="line" href="namespaceutil.html#aa9fb4c9a176acaf72053b11727436e9e"> 142</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#aa9fb4c9a176acaf72053b11727436e9e">IsSubsetOf0N</a>(<span class="keyword">const</span> std::vector<int>& v, <span class="keywordtype">int</span> n);</div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  </div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment">// Returns true iff the given vector is a permutation of [0..size()-1].</span></div>
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<div class="line"><a name="l00145"></a><span class="lineno"><a class="line" href="namespaceutil.html#ad7986b01cf61a31c09a27b4a97db6a83"> 145</a></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#ad7986b01cf61a31c09a27b4a97db6a83">IsValidPermutation</a>(<span class="keyword">const</span> std::vector<int>& v) {</div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceutil.html#aa9fb4c9a176acaf72053b11727436e9e">IsSubsetOf0N</a>(v, v.size());</div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> }</div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  </div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment">// Returns a copy of "graph", without self-arcs and duplicate arcs.</span></div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#a95c44a2c444a459f0866bd5607537314">RemoveSelfArcsAndDuplicateArcs</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph);</div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  </div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment">// Given an arc path, changes it to a sub-path with the same source and</span></div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment">// destination but without any cycle. Nothing happen if the path was already</span></div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment">// without cycle.</span></div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment">// The graph class should support Tail(arc) and Head(arc). They should both</span></div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment">// return an integer representing the corresponding tail/head of the passed arc.</span></div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment">// TODO(user): In some cases, there is more than one possible solution. We could</span></div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="comment">// take some arc costs and return the cheapest path instead. Or return the</span></div>
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment">// shortest path in term of number of arcs.</span></div>
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<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="keywordtype">void</span> <a class="code" href="namespaceutil.html#a77ac83968fcb358183853127d83d595a">RemoveCyclesFromPath</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph, std::vector<int>* arc_path);</div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  </div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="comment">// Returns true iff the given path contains a cycle.</span></div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#a3215b610ebe65cde55008dc1367c434e">PathHasCycle</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph, <span class="keyword">const</span> std::vector<int>& arc_path);</div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  </div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment">// Returns a vector representing a mapping from arcs to arcs such that each arc</span></div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment">// is mapped to another arc with its (tail, head) flipped, if such an arc</span></div>
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<div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment">// exists (otherwise it is mapped to -1).</span></div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment">// If the graph is symmetric, the returned mapping is bijective and reflexive,</span></div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="comment">// i.e. out[out[arc]] = arc for all "arc", where "out" is the returned vector.</span></div>
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<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment">// If "die_if_not_symmetric" is true, this function CHECKs() that the graph</span></div>
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<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment">// is symmetric.</span></div>
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<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment">// Self-arcs are always mapped to themselves.</span></div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="comment">// Note that since graphs may have multi-arcs, the mapping isn't necessarily</span></div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment">// unique, hence the function name.</span></div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment">// PERFORMANCE: If you see this function taking too much memory and/or too much</span></div>
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment">// time, reach out to viger@: one could halve the memory usage and speed it up.</span></div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span> std::vector<int> <a class="code" href="namespaceutil.html#a00a901881f9035f66a4204da4c0ea3e5">ComputeOnePossibleReverseArcMapping</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>& graph,</div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keywordtype">bool</span> die_if_not_symmetric);</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">// Implementations of the templated methods.</span></div>
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<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  </div>
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<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00192"></a><span class="lineno"><a class="line" href="namespaceutil.html#a9aedc5b3920b0ce89959be43ece7625b"> 192</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#a9aedc5b3920b0ce89959be43ece7625b">GraphHasSelfArcs</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph) {</div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> arc : graph.<a class="code" href="classutil_1_1_base_graph.html#a10ee27e856003f599bc0a2265a3ab11d">AllForwardArcs</a>()) {</div>
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keywordflow">if</span> (graph.<a class="code" href="classutil_1_1_list_graph.html#a2eeae3a8497dc3942e3db3128a10d41c">Tail</a>(arc) == graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc)) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  }</div>
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<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> }</div>
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<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  </div>
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<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00200"></a><span class="lineno"><a class="line" href="namespaceutil.html#a7cab01cf2313ef202fdb8d1540430c1c"> 200</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#a7cab01cf2313ef202fdb8d1540430c1c">GraphHasDuplicateArcs</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph) {</div>
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<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1_base_graph.html#a92531459eff09455cfa63976f5024906">Graph::ArcIndex</a> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a>;</div>
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<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1_base_graph.html#aec05ff3d270a5f888e1623c2a99ff2aa">Graph::NodeIndex</a> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a>;</div>
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<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  std::vector<bool> tmp_node_mask(graph.<a class="code" href="classutil_1_1_base_graph.html#a6a2df5042167b234f6dc3aed4acfa6c9">num_nodes</a>(), <span class="keyword">false</span>);</div>
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<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> tail : graph.<a class="code" href="classutil_1_1_base_graph.html#a8a40f2c75615a26ba71e94dd7d42f481">AllNodes</a>()) {</div>
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<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1_list_graph.html#ad7db584fc1fe14ce9296131fda625994">OutgoingArcs</a>(tail)) {</div>
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<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> head = graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc);</div>
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<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keywordflow">if</span> (tmp_node_mask[head]) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  tmp_node_mask[head] = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  }</div>
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<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1_list_graph.html#ad7db584fc1fe14ce9296131fda625994">OutgoingArcs</a>(tail)) {</div>
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<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  tmp_node_mask[graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc)] = <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  }</div>
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<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  }</div>
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<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> }</div>
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<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  </div>
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<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00218"></a><span class="lineno"><a class="line" href="namespaceutil.html#aa94a02ae5c14feb50676668f2de166dc"> 218</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#aa94a02ae5c14feb50676668f2de166dc">GraphIsSymmetric</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph) {</div>
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<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1_base_graph.html#aec05ff3d270a5f888e1623c2a99ff2aa">Graph::NodeIndex</a> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a>;</div>
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<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1_base_graph.html#a92531459eff09455cfa63976f5024906">Graph::ArcIndex</a> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a>;</div>
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<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="comment">// Create a reverse copy of the graph.</span></div>
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<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <a class="code" href="classutil_1_1_static_graph.html">StaticGraph<NodeIndex, ArcIndex></a> reverse_graph(graph.<a class="code" href="classutil_1_1_base_graph.html#a6a2df5042167b234f6dc3aed4acfa6c9">num_nodes</a>(),</div>
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<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  graph.<a class="code" href="classutil_1_1_base_graph.html#a4d3fc55a2fe209a908470199437cec9a">num_arcs</a>());</div>
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<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node : graph.<a class="code" href="classutil_1_1_base_graph.html#a8a40f2c75615a26ba71e94dd7d42f481">AllNodes</a>()) {</div>
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<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1_list_graph.html#ad7db584fc1fe14ce9296131fda625994">OutgoingArcs</a>(node)) {</div>
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<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  reverse_graph.<a class="code" href="classutil_1_1_static_graph.html#a7b505ba4a01bce342d049f5a8674da72">AddArc</a>(graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc), node);</div>
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<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  }</div>
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<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  }</div>
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<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  reverse_graph.<a class="code" href="classutil_1_1_static_graph.html#a6a4d37693b809140b0dde7abd463d04e">Build</a>();</div>
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<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="comment">// Compare the graph to its reverse, one adjacency list at a time.</span></div>
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<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  std::vector<ArcIndex> count(graph.<a class="code" href="classutil_1_1_base_graph.html#a6a2df5042167b234f6dc3aed4acfa6c9">num_nodes</a>(), 0);</div>
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<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node : graph.<a class="code" href="classutil_1_1_base_graph.html#a8a40f2c75615a26ba71e94dd7d42f481">AllNodes</a>()) {</div>
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<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1_list_graph.html#ad7db584fc1fe14ce9296131fda625994">OutgoingArcs</a>(node)) {</div>
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<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  ++count[graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc)];</div>
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<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  }</div>
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<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc : reverse_graph.<a class="code" href="classutil_1_1_static_graph.html#ad7db584fc1fe14ce9296131fda625994">OutgoingArcs</a>(node)) {</div>
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<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="keywordflow">if</span> (--count[reverse_graph.<a class="code" href="classutil_1_1_static_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc)] < 0) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  }</div>
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<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1_list_graph.html#ad7db584fc1fe14ce9296131fda625994">OutgoingArcs</a>(node)) {</div>
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<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keywordflow">if</span> (count[graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc)] != 0) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  }</div>
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<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  }</div>
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<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00244"></a><span class="lineno"> 244</span> }</div>
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<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  </div>
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<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00247"></a><span class="lineno"><a class="line" href="namespaceutil.html#ab66702bf387ec38027c1f94444872510"> 247</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#ab66702bf387ec38027c1f94444872510">GraphIsWeaklyConnected</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph) {</div>
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<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1_base_graph.html#aec05ff3d270a5f888e1623c2a99ff2aa">Graph::NodeIndex</a> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a>;</div>
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<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  static_assert(std::numeric_limits<NodeIndex>::max() <= INT_MAX,</div>
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<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="stringliteral">"GraphIsWeaklyConnected() isn't yet implemented for graphs"</span></div>
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<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="stringliteral">" that support more than INT_MAX nodes. Reach out to"</span></div>
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<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="stringliteral">" or-core-team@ if you need this."</span>);</div>
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<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keywordflow">if</span> (graph.<a class="code" href="classutil_1_1_base_graph.html#a6a2df5042167b234f6dc3aed4acfa6c9">num_nodes</a>() == 0) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <a class="code" href="class_dense_connected_components_finder.html">DenseConnectedComponentsFinder</a> union_find;</div>
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<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  union_find.<a class="code" href="class_dense_connected_components_finder.html#ad8e718920ab9683d39af650d714cffe1">SetNumberOfNodes</a>(graph.<a class="code" href="classutil_1_1_base_graph.html#a6a2df5042167b234f6dc3aed4acfa6c9">num_nodes</a>());</div>
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<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> <a class="code" href="classutil_1_1_base_graph.html#a92531459eff09455cfa63976f5024906">Graph::ArcIndex</a> arc = 0; arc < graph.<a class="code" href="classutil_1_1_base_graph.html#a4d3fc55a2fe209a908470199437cec9a">num_arcs</a>(); ++arc) {</div>
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<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  union_find.<a class="code" href="class_dense_connected_components_finder.html#a428ab6b7c944afe33bd86a6a1ae7e668">AddEdge</a>(graph.<a class="code" href="classutil_1_1_list_graph.html#a2eeae3a8497dc3942e3db3128a10d41c">Tail</a>(arc), graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc));</div>
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<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  }</div>
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<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keywordflow">return</span> union_find.<a class="code" href="class_dense_connected_components_finder.html#af1a300e659dbc3041b1485f12855bd31">GetNumberOfComponents</a>() == 1;</div>
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<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> }</div>
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<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  </div>
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<div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00263"></a><span class="lineno"><a class="line" href="namespaceutil.html#ae5f98804c317dda817bff628d868c4dd"> 263</a></span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#ae5f98804c317dda817bff628d868c4dd">CopyGraph</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph) {</div>
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<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  std::unique_ptr<Graph> new_graph(</div>
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<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keyword">new</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>(graph.<a class="code" href="classutil_1_1_base_graph.html#a6a2df5042167b234f6dc3aed4acfa6c9">num_nodes</a>(), graph.<a class="code" href="classutil_1_1_base_graph.html#a4d3fc55a2fe209a908470199437cec9a">num_arcs</a>()));</div>
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<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> node : graph.<a class="code" href="classutil_1_1_base_graph.html#a8a40f2c75615a26ba71e94dd7d42f481">AllNodes</a>()) {</div>
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<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> arc : graph.<a class="code" href="classutil_1_1_list_graph.html#ad7db584fc1fe14ce9296131fda625994">OutgoingArcs</a>(node)) {</div>
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<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  new_graph->AddArc(node, graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc));</div>
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<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  }</div>
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<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  }</div>
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<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  new_graph->Build();</div>
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<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">return</span> new_graph;</div>
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<div class="line"><a name="l00273"></a><span class="lineno"> 273</span> }</div>
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<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  </div>
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<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00276"></a><span class="lineno"><a class="line" href="namespaceutil.html#aab5724a929530fa1d28749dc82852388"> 276</a></span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#aab5724a929530fa1d28749dc82852388">RemapGraph</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& old_graph,</div>
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<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keyword">const</span> std::vector<int>& new_node_index) {</div>
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<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  DCHECK(<a class="code" href="namespaceutil.html#ad7986b01cf61a31c09a27b4a97db6a83">IsValidPermutation</a>(new_node_index)) << <span class="stringliteral">"Invalid permutation"</span>;</div>
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<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> num_nodes = old_graph.<a class="code" href="classutil_1_1_base_graph.html#a6a2df5042167b234f6dc3aed4acfa6c9">num_nodes</a>();</div>
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<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  CHECK_EQ(new_node_index.size(), num_nodes);</div>
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<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  std::unique_ptr<Graph> new_graph(<span class="keyword">new</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>(num_nodes, old_graph.<a class="code" href="classutil_1_1_base_graph.html#a4d3fc55a2fe209a908470199437cec9a">num_arcs</a>()));</div>
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<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1_base_graph.html#aec05ff3d270a5f888e1623c2a99ff2aa">Graph::NodeIndex</a> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a>;</div>
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<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1_base_graph.html#a92531459eff09455cfa63976f5024906">Graph::ArcIndex</a> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a>;</div>
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<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node : old_graph.<a class="code" href="classutil_1_1_base_graph.html#a8a40f2c75615a26ba71e94dd7d42f481">AllNodes</a>()) {</div>
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<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc : old_graph.<a class="code" href="classutil_1_1_list_graph.html#ad7db584fc1fe14ce9296131fda625994">OutgoingArcs</a>(node)) {</div>
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<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  new_graph->AddArc(new_node_index[node],</div>
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<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  new_node_index[old_graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc)]);</div>
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<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  }</div>
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<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  }</div>
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<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  new_graph->Build();</div>
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<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="keywordflow">return</span> new_graph;</div>
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<div class="line"><a name="l00292"></a><span class="lineno"> 292</span> }</div>
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<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  </div>
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<div class="line"><a name="l00294"></a><span class="lineno"> 294</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00295"></a><span class="lineno"><a class="line" href="namespaceutil.html#a99094e047812eb44a7c2b3b82091f560"> 295</a></span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#a99094e047812eb44a7c2b3b82091f560">GetSubgraphOfNodes</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& old_graph,</div>
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<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="keyword">const</span> std::vector<int>& nodes) {</div>
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<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1_base_graph.html#aec05ff3d270a5f888e1623c2a99ff2aa">Graph::NodeIndex</a> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a>;</div>
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<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1_base_graph.html#a92531459eff09455cfa63976f5024906">Graph::ArcIndex</a> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a>;</div>
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<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  DCHECK(<a class="code" href="namespaceutil.html#aa9fb4c9a176acaf72053b11727436e9e">IsSubsetOf0N</a>(nodes, old_graph.<a class="code" href="classutil_1_1_base_graph.html#a6a2df5042167b234f6dc3aed4acfa6c9">num_nodes</a>())) << <span class="stringliteral">"Invalid subset"</span>;</div>
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<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  std::vector<NodeIndex> new_node_index(old_graph.<a class="code" href="classutil_1_1_base_graph.html#a6a2df5042167b234f6dc3aed4acfa6c9">num_nodes</a>(), -1);</div>
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<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> new_index = 0; new_index < nodes.size(); ++new_index) {</div>
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<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  new_node_index[nodes[new_index]] = new_index;</div>
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<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  }</div>
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<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="comment">// Do a first pass to count the arcs, so that we don't allocate more memory</span></div>
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<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="comment">// than needed.</span></div>
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<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> num_arcs = 0;</div>
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<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> node : nodes) {</div>
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<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc : old_graph.<a class="code" href="classutil_1_1_list_graph.html#ad7db584fc1fe14ce9296131fda625994">OutgoingArcs</a>(node)) {</div>
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<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="keywordflow">if</span> (new_node_index[old_graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc)] != -1) ++num_arcs;</div>
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<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  }</div>
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<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  }</div>
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<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="comment">// A second pass where we actually copy the subgraph.</span></div>
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<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="comment">// NOTE(user): there might seem to be a bit of duplication with RemapGraph(),</span></div>
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<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="comment">// but there is a key difference: the loop below only iterates on "nodes",</span></div>
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<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="comment">// which could be much smaller than all the graph's nodes.</span></div>
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<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  std::unique_ptr<Graph> new_graph(<span class="keyword">new</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>(nodes.size(), num_arcs));</div>
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<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> new_tail = 0; new_tail < nodes.size(); ++new_tail) {</div>
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<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> old_tail = nodes[new_tail];</div>
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<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc : old_graph.<a class="code" href="classutil_1_1_list_graph.html#ad7db584fc1fe14ce9296131fda625994">OutgoingArcs</a>(old_tail)) {</div>
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<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> new_head = new_node_index[old_graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc)];</div>
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<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keywordflow">if</span> (new_head != -1) new_graph->AddArc(new_tail, new_head);</div>
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<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  }</div>
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<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  }</div>
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<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  new_graph->Build();</div>
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<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keywordflow">return</span> new_graph;</div>
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<div class="line"><a name="l00326"></a><span class="lineno"> 326</span> }</div>
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<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  </div>
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<div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00329"></a><span class="lineno"><a class="line" href="namespaceutil.html#a95c44a2c444a459f0866bd5607537314"> 329</a></span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#a95c44a2c444a459f0866bd5607537314">RemoveSelfArcsAndDuplicateArcs</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph) {</div>
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<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  std::unique_ptr<Graph> g(<span class="keyword">new</span> <a class="code" href="namespaceutil.html#a2f76166dbe0c4055a1f256235ad00478">Graph</a>(graph.<a class="code" href="classutil_1_1_base_graph.html#a6a2df5042167b234f6dc3aed4acfa6c9">num_nodes</a>(), graph.<a class="code" href="classutil_1_1_base_graph.html#a4d3fc55a2fe209a908470199437cec9a">num_arcs</a>()));</div>
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<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1_base_graph.html#a92531459eff09455cfa63976f5024906">Graph::ArcIndex</a> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a>;</div>
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<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1_base_graph.html#aec05ff3d270a5f888e1623c2a99ff2aa">Graph::NodeIndex</a> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a>;</div>
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<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  std::vector<bool> tmp_node_mask(graph.<a class="code" href="classutil_1_1_base_graph.html#a6a2df5042167b234f6dc3aed4acfa6c9">num_nodes</a>(), <span class="keyword">false</span>);</div>
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<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> tail : graph.<a class="code" href="classutil_1_1_base_graph.html#a8a40f2c75615a26ba71e94dd7d42f481">AllNodes</a>()) {</div>
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<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1_list_graph.html#ad7db584fc1fe14ce9296131fda625994">OutgoingArcs</a>(tail)) {</div>
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<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a7ffcae041a5d746371436101400cdb6b">NodeIndex</a> head = graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc);</div>
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<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="keywordflow">if</span> (head != tail && !tmp_node_mask[head]) {</div>
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<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  tmp_node_mask[head] = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  g->AddArc(tail, head);</div>
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<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  }</div>
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<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  }</div>
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<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1_list_graph.html#ad7db584fc1fe14ce9296131fda625994">OutgoingArcs</a>(tail)) {</div>
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<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  tmp_node_mask[graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc)] = <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  }</div>
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<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  }</div>
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<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  g->Build();</div>
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<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="keywordflow">return</span> g;</div>
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<div class="line"><a name="l00348"></a><span class="lineno"> 348</span> }</div>
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<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  </div>
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<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00351"></a><span class="lineno"><a class="line" href="namespaceutil.html#a77ac83968fcb358183853127d83d595a"> 351</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceutil.html#a77ac83968fcb358183853127d83d595a">RemoveCyclesFromPath</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph, std::vector<int>* arc_path) {</div>
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<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <span class="keywordflow">if</span> (arc_path->empty()) <span class="keywordflow">return</span>;</div>
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<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  </div>
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<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="comment">// This maps each node to the latest arc in the given path that leaves it.</span></div>
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<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  std::map<int, int> last_arc_leaving_node;</div>
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<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> arc : *arc_path) last_arc_leaving_node[graph.<a class="code" href="classutil_1_1_list_graph.html#a2eeae3a8497dc3942e3db3128a10d41c">Tail</a>(arc)] = arc;</div>
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<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  </div>
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<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  <span class="comment">// Special case for the destination.</span></div>
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<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="comment">// Note that this requires that -1 is not a valid arc of Graph.</span></div>
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<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  last_arc_leaving_node[graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc_path->back())] = -1;</div>
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<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  </div>
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<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="comment">// Reconstruct the path by starting at the source and then following the</span></div>
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<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  <span class="comment">// "next" arcs. We override the given arc_path at the same time.</span></div>
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<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  <span class="keywordtype">int</span> node = graph.<a class="code" href="classutil_1_1_list_graph.html#a2eeae3a8497dc3942e3db3128a10d41c">Tail</a>(arc_path->front());</div>
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<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <span class="keywordtype">int</span> new_size = 0;</div>
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<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="keywordflow">while</span> (new_size < arc_path->size()) { <span class="comment">// To prevent cycle on bad input.</span></div>
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<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> arc = gtl::FindOrDie(last_arc_leaving_node, node);</div>
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<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="keywordflow">if</span> (arc == -1) <span class="keywordflow">break</span>;</div>
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<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  (*arc_path)[new_size++] = arc;</div>
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<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  node = graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc);</div>
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<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  }</div>
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<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  arc_path->resize(new_size);</div>
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<div class="line"><a name="l00373"></a><span class="lineno"> 373</span> }</div>
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<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  </div>
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<div class="line"><a name="l00375"></a><span class="lineno"> 375</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00376"></a><span class="lineno"><a class="line" href="namespaceutil.html#a3215b610ebe65cde55008dc1367c434e"> 376</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#a3215b610ebe65cde55008dc1367c434e">PathHasCycle</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph, <span class="keyword">const</span> std::vector<int>& arc_path) {</div>
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<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <span class="keywordflow">if</span> (arc_path.empty()) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  std::set<int> seen;</div>
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<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  seen.insert(graph.<a class="code" href="classutil_1_1_list_graph.html#a2eeae3a8497dc3942e3db3128a10d41c">Tail</a>(arc_path.front()));</div>
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<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> arc : arc_path) {</div>
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<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <span class="keywordflow">if</span> (!gtl::InsertIfNotPresent(&seen, graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc))) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  }</div>
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<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00384"></a><span class="lineno"> 384</span> }</div>
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<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  </div>
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<div class="line"><a name="l00386"></a><span class="lineno"> 386</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div>
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<div class="line"><a name="l00387"></a><span class="lineno"><a class="line" href="namespaceutil.html#a00a901881f9035f66a4204da4c0ea3e5"> 387</a></span> std::vector<int> <a class="code" href="namespaceutil.html#a00a901881f9035f66a4204da4c0ea3e5">ComputeOnePossibleReverseArcMapping</a>(</div>
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<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <span class="keyword">const</span> <a class="code" href="classutil_1_1_list_graph.html">Graph</a>& graph, <span class="keywordtype">bool</span> die_if_not_symmetric) {</div>
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<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  std::vector<int> reverse_arc(graph.<a class="code" href="classutil_1_1_base_graph.html#a4d3fc55a2fe209a908470199437cec9a">num_arcs</a>(), -1);</div>
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<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <span class="comment">// We need a multi-map since a given (tail,head) may appear several times.</span></div>
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<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  <span class="comment">// NOTE(user): It's free, in terms of space, to use InlinedVector<int, 4></span></div>
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<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="comment">// rather than std::vector<int>. See go/inlined-vector-size.</span></div>
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<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  absl::flat_hash_map<std::pair<<span class="comment">/*tail*/</span> int, <span class="comment">/*head*/</span> <span class="keywordtype">int</span>>,</div>
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<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  absl::InlinedVector<int, 4>></div>
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<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  arc_map;</div>
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<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  </div>
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<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> arc = 0; arc < graph.<a class="code" href="classutil_1_1_base_graph.html#a4d3fc55a2fe209a908470199437cec9a">num_arcs</a>(); ++arc) {</div>
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<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> tail = graph.<a class="code" href="classutil_1_1_list_graph.html#a2eeae3a8497dc3942e3db3128a10d41c">Tail</a>(arc);</div>
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<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> head = graph.<a class="code" href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">Head</a>(arc);</div>
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<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  <span class="keywordflow">if</span> (tail == head) {</div>
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<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  <span class="comment">// Special case: directly map any self-arc to itself.</span></div>
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<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  reverse_arc[arc] = arc;</div>
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<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  <span class="keywordflow">continue</span>;</div>
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<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  }</div>
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<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <span class="comment">// Lookup for the reverse arc of the current one...</span></div>
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<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  <span class="keyword">auto</span> it = arc_map.find({head, tail});</div>
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<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  <span class="keywordflow">if</span> (it != arc_map.end()) {</div>
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<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  <span class="comment">// Found a reverse arc! Store the mapping and remove the</span></div>
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<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <span class="comment">// reverse arc from the map.</span></div>
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<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  reverse_arc[arc] = it->second.back();</div>
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<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  reverse_arc[it->second.back()] = arc;</div>
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<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  <span class="keywordflow">if</span> (it->second.size() > 1) {</div>
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<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  it->second.pop_back();</div>
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<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  arc_map.erase(it);</div>
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<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  }</div>
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<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  } <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  <span class="comment">// Reverse arc not in the map. Add the current arc to the map.</span></div>
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<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  arc_map[{tail, head}].push_back(arc);</div>
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<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  }</div>
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<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  }</div>
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<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  <span class="comment">// Algorithm check, for debugging.</span></div>
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<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  <span class="keywordflow">if</span> (DEBUG_MODE) {</div>
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<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  int64_t num_unmapped_arcs = 0;</div>
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<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& p : arc_map) {</div>
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<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  num_unmapped_arcs += p.second.size();</div>
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<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  }</div>
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<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  DCHECK_EQ(std::count(reverse_arc.begin(), reverse_arc.end(), -1),</div>
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<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  num_unmapped_arcs);</div>
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<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  }</div>
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<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  <span class="keywordflow">if</span> (die_if_not_symmetric) {</div>
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<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  CHECK_EQ(arc_map.size(), 0)</div>
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<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  << <span class="stringliteral">"The graph is not symmetric: "</span> << arc_map.size() << <span class="stringliteral">" of "</span></div>
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<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  << graph.<a class="code" href="classutil_1_1_base_graph.html#a4d3fc55a2fe209a908470199437cec9a">num_arcs</a>() << <span class="stringliteral">" arcs did not have a reverse."</span>;</div>
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<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  }</div>
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<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="keywordflow">return</span> reverse_arc;</div>
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<div class="line"><a name="l00437"></a><span class="lineno"> 437</span> }</div>
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<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  </div>
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<div class="line"><a name="l00439"></a><span class="lineno"> 439</span> } <span class="comment">// namespace util</span></div>
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<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  </div>
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<div class="line"><a name="l00441"></a><span class="lineno"> 441</span> <span class="preprocessor">#endif </span><span class="comment">// UTIL_GRAPH_UTIL_H_</span></div>
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<div class="ttc" id="aclass_dense_connected_components_finder_html"><div class="ttname"><a href="class_dense_connected_components_finder.html">DenseConnectedComponentsFinder</a></div><div class="ttdef"><b>Definition:</b> <a href="connected__components_8h_source.html#l00081">connected_components.h:81</a></div></div>
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<div class="ttc" id="aclass_dense_connected_components_finder_html_a428ab6b7c944afe33bd86a6a1ae7e668"><div class="ttname"><a href="class_dense_connected_components_finder.html#a428ab6b7c944afe33bd86a6a1ae7e668">DenseConnectedComponentsFinder::AddEdge</a></div><div class="ttdeci">bool AddEdge(int node1, int node2)</div></div>
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<div class="ttc" id="aclass_dense_connected_components_finder_html_ad8e718920ab9683d39af650d714cffe1"><div class="ttname"><a href="class_dense_connected_components_finder.html#ad8e718920ab9683d39af650d714cffe1">DenseConnectedComponentsFinder::SetNumberOfNodes</a></div><div class="ttdeci">void SetNumberOfNodes(int num_nodes)</div></div>
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<div class="ttc" id="aclass_dense_connected_components_finder_html_af1a300e659dbc3041b1485f12855bd31"><div class="ttname"><a href="class_dense_connected_components_finder.html#af1a300e659dbc3041b1485f12855bd31">DenseConnectedComponentsFinder::GetNumberOfComponents</a></div><div class="ttdeci">int GetNumberOfComponents() const</div><div class="ttdef"><b>Definition:</b> <a href="connected__components_8h_source.html#l00099">connected_components.h:99</a></div></div>
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<div class="ttc" id="aclassutil_1_1_base_graph_html_a10ee27e856003f599bc0a2265a3ab11d"><div class="ttname"><a href="classutil_1_1_base_graph.html#a10ee27e856003f599bc0a2265a3ab11d">util::BaseGraph::AllForwardArcs</a></div><div class="ttdeci">IntegerRange< ArcIndex > AllForwardArcs() const</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00942">graph.h:942</a></div></div>
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<div class="ttc" id="aclassutil_1_1_base_graph_html_a4d3fc55a2fe209a908470199437cec9a"><div class="ttname"><a href="classutil_1_1_base_graph.html#a4d3fc55a2fe209a908470199437cec9a">util::BaseGraph::num_arcs</a></div><div class="ttdeci">ArcIndexType num_arcs() const</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00206">graph.h:206</a></div></div>
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<div class="ttc" id="aclassutil_1_1_base_graph_html_a6a2df5042167b234f6dc3aed4acfa6c9"><div class="ttname"><a href="classutil_1_1_base_graph.html#a6a2df5042167b234f6dc3aed4acfa6c9">util::BaseGraph::num_nodes</a></div><div class="ttdeci">NodeIndexType num_nodes() const</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00203">graph.h:203</a></div></div>
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<div class="ttc" id="aclassutil_1_1_base_graph_html_a8a40f2c75615a26ba71e94dd7d42f481"><div class="ttname"><a href="classutil_1_1_base_graph.html#a8a40f2c75615a26ba71e94dd7d42f481">util::BaseGraph::AllNodes</a></div><div class="ttdeci">IntegerRange< NodeIndex > AllNodes() const</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00936">graph.h:936</a></div></div>
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<div class="ttc" id="aclassutil_1_1_base_graph_html_a92531459eff09455cfa63976f5024906"><div class="ttname"><a href="classutil_1_1_base_graph.html#a92531459eff09455cfa63976f5024906">util::BaseGraph< int32_t, int32_t, false >::ArcIndex</a></div><div class="ttdeci">int32_t ArcIndex</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00192">graph.h:192</a></div></div>
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<div class="ttc" id="aclassutil_1_1_base_graph_html_aec05ff3d270a5f888e1623c2a99ff2aa"><div class="ttname"><a href="classutil_1_1_base_graph.html#aec05ff3d270a5f888e1623c2a99ff2aa">util::BaseGraph< int32_t, int32_t, false >::NodeIndex</a></div><div class="ttdeci">int32_t NodeIndex</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00191">graph.h:191</a></div></div>
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<div class="ttc" id="aclassutil_1_1_begin_end_wrapper_html"><div class="ttname"><a href="classutil_1_1_begin_end_wrapper.html">util::BeginEndWrapper</a></div><div class="ttdef"><b>Definition:</b> <a href="iterators_8h_source.html#l00038">iterators.h:38</a></div></div>
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<div class="ttc" id="aclassutil_1_1_list_graph_html"><div class="ttname"><a href="classutil_1_1_list_graph.html">util::ListGraph</a></div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00299">graph.h:299</a></div></div>
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<div class="ttc" id="aclassutil_1_1_list_graph_html_a2eeae3a8497dc3942e3db3128a10d41c"><div class="ttname"><a href="classutil_1_1_list_graph.html#a2eeae3a8497dc3942e3db3128a10d41c">util::ListGraph::Tail</a></div><div class="ttdeci">NodeIndexType Tail(ArcIndexType arc) const</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l01111">graph.h:1111</a></div></div>
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<div class="ttc" id="aclassutil_1_1_list_graph_html_aceb0938bcb2e8e5f37986d4cf8e3a955"><div class="ttname"><a href="classutil_1_1_list_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">util::ListGraph::Head</a></div><div class="ttdeci">NodeIndexType Head(ArcIndexType arc) const</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l01118">graph.h:1118</a></div></div>
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<div class="ttc" id="aclassutil_1_1_list_graph_html_ad7db584fc1fe14ce9296131fda625994"><div class="ttname"><a href="classutil_1_1_list_graph.html#ad7db584fc1fe14ce9296131fda625994">util::ListGraph::OutgoingArcs</a></div><div class="ttdeci">BeginEndWrapper< OutgoingArcIterator > OutgoingArcs(NodeIndexType node) const</div></div>
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<div class="ttc" id="aclassutil_1_1_static_graph_html"><div class="ttname"><a href="classutil_1_1_static_graph.html">util::StaticGraph</a></div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00398">graph.h:398</a></div></div>
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<div class="ttc" id="aclassutil_1_1_static_graph_html_a6a4d37693b809140b0dde7abd463d04e"><div class="ttname"><a href="classutil_1_1_static_graph.html#a6a4d37693b809140b0dde7abd463d04e">util::StaticGraph::Build</a></div><div class="ttdeci">void Build()</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00436">graph.h:436</a></div></div>
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<div class="ttc" id="aclassutil_1_1_static_graph_html_a7b505ba4a01bce342d049f5a8674da72"><div class="ttname"><a href="classutil_1_1_static_graph.html#a7b505ba4a01bce342d049f5a8674da72">util::StaticGraph::AddArc</a></div><div class="ttdeci">ArcIndexType AddArc(NodeIndexType tail, NodeIndexType head)</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l01286">graph.h:1286</a></div></div>
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<div class="ttc" id="aclassutil_1_1_static_graph_html_aceb0938bcb2e8e5f37986d4cf8e3a955"><div class="ttname"><a href="classutil_1_1_static_graph.html#aceb0938bcb2e8e5f37986d4cf8e3a955">util::StaticGraph::Head</a></div><div class="ttdeci">NodeIndexType Head(ArcIndexType arc) const</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l01314">graph.h:1314</a></div></div>
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<div class="ttc" id="aclassutil_1_1_static_graph_html_ad7db584fc1fe14ce9296131fda625994"><div class="ttname"><a href="classutil_1_1_static_graph.html#ad7db584fc1fe14ce9296131fda625994">util::StaticGraph::OutgoingArcs</a></div><div class="ttdeci">BeginEndWrapper< OutgoingArcIterator > OutgoingArcs(NodeIndexType node) const</div></div>
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<div class="ttc" id="aclassutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator_html"><div class="ttname"><a href="classutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator.html">util::UndirectedAdjacencyListsOfDirectedGraph::AdjacencyListIterator</a></div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00106">util.h:106</a></div></div>
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<div class="ttc" id="aclassutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator_html_a1ce6d58586efadff072fb5b4591f5ea3"><div class="ttname"><a href="classutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator.html#a1ce6d58586efadff072fb5b4591f5ea3">util::UndirectedAdjacencyListsOfDirectedGraph::AdjacencyListIterator::operator*</a></div><div class="ttdeci">Graph::NodeIndex operator*() const</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00111">util.h:111</a></div></div>
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<div class="ttc" id="aclassutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator_html_a544dc5fdf254f2bcd1b7dfa67ef41b7a"><div class="ttname"><a href="classutil_1_1_undirected_adjacency_lists_of_directed_graph_1_1_adjacency_list_iterator.html#a544dc5fdf254f2bcd1b7dfa67ef41b7a">util::UndirectedAdjacencyListsOfDirectedGraph::AdjacencyListIterator::AdjacencyListIterator</a></div><div class="ttdeci">AdjacencyListIterator(const Graph &graph, ArcIterator &&arc_it)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00108">util.h:108</a></div></div>
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<div class="ttc" id="aclassutil_1_1_undirected_adjacency_lists_of_directed_graph_html"><div class="ttname"><a href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html">util::UndirectedAdjacencyListsOfDirectedGraph</a></div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00100">util.h:100</a></div></div>
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<div class="ttc" id="aclassutil_1_1_undirected_adjacency_lists_of_directed_graph_html_a0a6c3259e0f5b11ae67f15beefa1020c"><div class="ttname"><a href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html#a0a6c3259e0f5b11ae67f15beefa1020c">util::UndirectedAdjacencyListsOfDirectedGraph::UndirectedAdjacencyListsOfDirectedGraph</a></div><div class="ttdeci">UndirectedAdjacencyListsOfDirectedGraph(const Graph &graph)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00102">util.h:102</a></div></div>
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<div class="ttc" id="aclassutil_1_1_undirected_adjacency_lists_of_directed_graph_html_a2380f2634e304c2161485c0d395b78eb"><div class="ttname"><a href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html#a2380f2634e304c2161485c0d395b78eb">util::UndirectedAdjacencyListsOfDirectedGraph::ArcIterator</a></div><div class="ttdeci">Graph::OutgoingOrOppositeIncomingArcIterator ArcIterator</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00105">util.h:105</a></div></div>
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<div class="ttc" id="aclassutil_1_1_undirected_adjacency_lists_of_directed_graph_html_acb3986c66a9d18524b947fd391f68240"><div class="ttname"><a href="classutil_1_1_undirected_adjacency_lists_of_directed_graph.html#acb3986c66a9d18524b947fd391f68240">util::UndirectedAdjacencyListsOfDirectedGraph::operator[]</a></div><div class="ttdeci">BeginEndWrapper< AdjacencyListIterator > operator[](int node) const</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00120">util.h:120</a></div></div>
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<div class="ttc" id="aconnected__components_8h_html"><div class="ttname"><a href="connected__components_8h.html">connected_components.h</a></div></div>
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<div class="ttc" id="agraph_8h_html"><div class="ttname"><a href="graph_8h.html">graph.h</a></div></div>
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<div class="ttc" id="aiterators_8h_html"><div class="ttname"><a href="iterators_8h.html">iterators.h</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#l00200">ebert_graph.h:192</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_aecf320bda6e95d1edaf3a546673e3e6b"><div class="ttname"><a href="namespaceoperations__research.html#aecf320bda6e95d1edaf3a546673e3e6b">operations_research::ArcIndex</a></div><div class="ttdeci">int32_t ArcIndex</div><div class="ttdef"><b>Definition:</b> <a href="ebert__graph_8h_source.html#l00201">ebert_graph.h:201</a></div></div>
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<div class="ttc" id="anamespaceutil_html"><div class="ttname"><a href="namespaceutil.html">util</a></div><div class="ttdef"><b>Definition:</b> <a href="connected__components_8h_source.html#l00056">connected_components.h:56</a></div></div>
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<div class="ttc" id="anamespaceutil_html_a00a901881f9035f66a4204da4c0ea3e5"><div class="ttname"><a href="namespaceutil.html#a00a901881f9035f66a4204da4c0ea3e5">util::ComputeOnePossibleReverseArcMapping</a></div><div class="ttdeci">std::vector< int > ComputeOnePossibleReverseArcMapping(const Graph &graph, bool die_if_not_symmetric)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00387">util.h:387</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#l02361">graph.h:2361</a></div></div>
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<div class="ttc" id="anamespaceutil_html_a3215b610ebe65cde55008dc1367c434e"><div class="ttname"><a href="namespaceutil.html#a3215b610ebe65cde55008dc1367c434e">util::PathHasCycle</a></div><div class="ttdeci">bool PathHasCycle(const Graph &graph, const std::vector< int > &arc_path)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00376">util.h:376</a></div></div>
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<div class="ttc" id="anamespaceutil_html_a366d433bd2afb387ea527c581447dffc"><div class="ttname"><a href="namespaceutil.html#a366d433bd2afb387ea527c581447dffc">util::GetConnectedComponents</a></div><div class="ttdeci">std::vector< int > GetConnectedComponents(int num_nodes, const UndirectedGraph &graph)</div><div class="ttdef"><b>Definition:</b> <a href="connected__components_8h_source.html#l00302">connected_components.h:302</a></div></div>
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<div class="ttc" id="anamespaceutil_html_a77ac83968fcb358183853127d83d595a"><div class="ttname"><a href="namespaceutil.html#a77ac83968fcb358183853127d83d595a">util::RemoveCyclesFromPath</a></div><div class="ttdeci">void RemoveCyclesFromPath(const Graph &graph, std::vector< int > *arc_path)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00351">util.h:351</a></div></div>
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<div class="ttc" id="anamespaceutil_html_a7cab01cf2313ef202fdb8d1540430c1c"><div class="ttname"><a href="namespaceutil.html#a7cab01cf2313ef202fdb8d1540430c1c">util::GraphHasDuplicateArcs</a></div><div class="ttdeci">bool GraphHasDuplicateArcs(const Graph &graph)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00200">util.h:200</a></div></div>
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<div class="ttc" id="anamespaceutil_html_a95c44a2c444a459f0866bd5607537314"><div class="ttname"><a href="namespaceutil.html#a95c44a2c444a459f0866bd5607537314">util::RemoveSelfArcsAndDuplicateArcs</a></div><div class="ttdeci">std::unique_ptr< Graph > RemoveSelfArcsAndDuplicateArcs(const Graph &graph)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00329">util.h:329</a></div></div>
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<div class="ttc" id="anamespaceutil_html_a99094e047812eb44a7c2b3b82091f560"><div class="ttname"><a href="namespaceutil.html#a99094e047812eb44a7c2b3b82091f560">util::GetSubgraphOfNodes</a></div><div class="ttdeci">std::unique_ptr< Graph > GetSubgraphOfNodes(const Graph &graph, const std::vector< int > &nodes)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00295">util.h:295</a></div></div>
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<div class="ttc" id="anamespaceutil_html_a9aedc5b3920b0ce89959be43ece7625b"><div class="ttname"><a href="namespaceutil.html#a9aedc5b3920b0ce89959be43ece7625b">util::GraphHasSelfArcs</a></div><div class="ttdeci">bool GraphHasSelfArcs(const Graph &graph)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00192">util.h:192</a></div></div>
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<div class="ttc" id="anamespaceutil_html_aa94a02ae5c14feb50676668f2de166dc"><div class="ttname"><a href="namespaceutil.html#aa94a02ae5c14feb50676668f2de166dc">util::GraphIsSymmetric</a></div><div class="ttdeci">bool GraphIsSymmetric(const Graph &graph)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00218">util.h:218</a></div></div>
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<div class="ttc" id="anamespaceutil_html_aa9fb4c9a176acaf72053b11727436e9e"><div class="ttname"><a href="namespaceutil.html#aa9fb4c9a176acaf72053b11727436e9e">util::IsSubsetOf0N</a></div><div class="ttdeci">bool IsSubsetOf0N(const std::vector< int > &v, int n)</div></div>
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<div class="ttc" id="anamespaceutil_html_aab5724a929530fa1d28749dc82852388"><div class="ttname"><a href="namespaceutil.html#aab5724a929530fa1d28749dc82852388">util::RemapGraph</a></div><div class="ttdeci">std::unique_ptr< Graph > RemapGraph(const Graph &graph, const std::vector< int > &new_node_index)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00276">util.h:276</a></div></div>
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<div class="ttc" id="anamespaceutil_html_ab34783e729bb5fc99042893f6bfcbb2f"><div class="ttname"><a href="namespaceutil.html#ab34783e729bb5fc99042893f6bfcbb2f">util::GetWeaklyConnectedComponents</a></div><div class="ttdeci">std::vector< int > GetWeaklyConnectedComponents(const Graph &graph)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00134">util.h:134</a></div></div>
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<div class="ttc" id="anamespaceutil_html_ab66702bf387ec38027c1f94444872510"><div class="ttname"><a href="namespaceutil.html#ab66702bf387ec38027c1f94444872510">util::GraphIsWeaklyConnected</a></div><div class="ttdeci">bool GraphIsWeaklyConnected(const Graph &graph)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00247">util.h:247</a></div></div>
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<div class="ttc" id="anamespaceutil_html_ad7986b01cf61a31c09a27b4a97db6a83"><div class="ttname"><a href="namespaceutil.html#ad7986b01cf61a31c09a27b4a97db6a83">util::IsValidPermutation</a></div><div class="ttdeci">bool IsValidPermutation(const std::vector< int > &v)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00145">util.h:145</a></div></div>
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<div class="ttc" id="anamespaceutil_html_ae5f98804c317dda817bff628d868c4dd"><div class="ttname"><a href="namespaceutil.html#ae5f98804c317dda817bff628d868c4dd">util::CopyGraph</a></div><div class="ttdeci">std::unique_ptr< Graph > CopyGraph(const Graph &graph)</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00263">util.h:263</a></div></div>
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