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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 2010-2018 Google LLC</span></div><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><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><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><div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div><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><div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div><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><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><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><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><div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> </div><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><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#ifndef UTIL_GRAPH_UTIL_H_</span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#define UTIL_GRAPH_UTIL_H_</span></div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include <algorithm></span></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include <map></span></div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include <memory></span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include <set></span></div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#include <string></span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#include <unordered_map></span></div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#include <vector></span></div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span> </div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include "ortools/base/hash.h"</span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include "ortools/base/map_util.h"</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include "<a class="code" href="connected__components_8h.html">ortools/graph/connected_components.h</a>"</span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#include "<a class="code" href="graph_8h.html">ortools/graph/graph.h</a>"</span></div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#include "<a class="code" href="iterators_8h.html">ortools/graph/iterators.h</a>"</span></div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span> </div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="keyword">namespace </span><a class="code" href="namespaceutil.html">util</a> {</div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span> </div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// Here's a set of simple diagnosis tools. Notes:</span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// - A self-arc is an arc from a node to itself.</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// - We say that an arc A->B is duplicate when there is another arc A->B in the</span></div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// same graph.</span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// - A graph is said "weakly connected" if it is connected when considering all</span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// arcs as undirected edges.</span></div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// - A graph is said "symmetric" iff for all (a, b), the number of arcs a->b</span></div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// is equal to the number of arcs b->a.</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">//</span></div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// All these diagnosis work in O(graph size), since the inverse Ackerman</span></div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// function is <= 5 for all practical instances, and are very fast.</span></div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">//</span></div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// If the graph is a "static" kind, they must be finalized, except for</span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// GraphHasSelfArcs() and GraphIsWeaklyConnected() which also support</span></div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// non-finalized StaticGraph<>.</span></div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#ac4af76993c891ee4ad507783edec2a1c">GraphHasSelfArcs</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>& graph);</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#a6b37593970a26f5c88b3d2ea9acea9d2">GraphHasDuplicateArcs</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>& graph);</div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#a784b483eeae1b49164a8a02fe9c0d3ba">GraphIsSymmetric</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>& graph);</div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#a97311561fd1f01e9f35b2f7ce18b0af3">GraphIsWeaklyConnected</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>& graph);</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span> </div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// Returns a fresh copy of a given graph.</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#a0ed748741b17dad9e6cc485728bb0043">CopyGraph</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>& graph);</div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span> </div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment">// Creates a remapped copy of graph "graph", where node i becomes node</span></div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// new_node_index[i].</span></div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// "new_node_index" must be a valid permutation of [0..num_nodes-1] or the</span></div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// behavior is undefined (it may die).</span></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// Note that you can call IsValidPermutation() to check it yourself.</span></div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#acfecdce43e9933bde2a94fd879f12f5f">RemapGraph</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>& graph,</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">const</span> std::vector<int>& new_node_index);</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span> </div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// Gets the induced subgraph of "graph" restricted to the nodes in "nodes":</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// the resulting graph will have exactly nodes.size() nodes, and its</span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// node #0 will be the former graph's node #nodes[0], etc.</span></div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// See https://en.wikipedia.org/wiki/Induced_subgraph .</span></div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment">// The "nodes" must be a valid subset (no repetitions) of</span></div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// [0..graph.num_nodes()-1], or the behavior is undefined (it may die).</span></div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// Note that you can call IsSubsetOf0N() to check it yourself.</span></div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment">//</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// Current complexity: O(num old nodes + num new arcs). It could easily</span></div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// be done in O(num new nodes + num new arcs) but with a higher constant.</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#ad1df170a504d335462a1104a942e6069">GetSubgraphOfNodes</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>& graph,</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keyword">const</span> std::vector<int>& nodes);</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span> </div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// This can be used to view a directed graph (that supports reverse arcs)</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// from graph.h as un undirected graph: operator[](node) returns a</span></div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// pseudo-container that iterates over all nodes adjacent to "node" (from</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment">// outgoing or incoming arcs).</span></div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// CAVEAT: Self-arcs (aka loops) will appear twice.</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment">//</span></div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// Example:</span></div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment">// ReverseArcsStaticGraph<> dgraph;</span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// ...</span></div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="comment">// UndirectedAdjacencyListsOfDirectedGraph<decltype(dgraph)> ugraph(dgraph);</span></div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment">// for (int neighbor_of_node_42 : ugraph[42]) { ... }</span></div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00098"></a><span class="lineno"><a class="line" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html"> 98</a></span> <span class="keyword">class </span><a class="code" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html">UndirectedAdjacencyListsOfDirectedGraph</a> {</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00100"></a><span class="lineno"><a class="line" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html#aa3254dffa224cf75efab4e3b034b39d8"> 100</a></span>  <span class="keyword">explicit</span> <a class="code" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html#aa3254dffa224cf75efab4e3b034b39d8">UndirectedAdjacencyListsOfDirectedGraph</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& graph)</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  : graph_(graph) {}</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span> </div><div class="line"><a name="l00103"></a><span class="lineno"><a class="line" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html#a6402dd9e7851af22b907c0af3e240dce"> 103</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Graph::OutgoingOrOppositeIncomingArcIterator <a class="code" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html#a6402dd9e7851af22b907c0af3e240dce">ArcIterator</a>;</div><div class="line"><a name="l00104"></a><span class="lineno"><a class="line" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator.html"> 104</a></span>  <span class="keyword">class </span><a class="code" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator.html">AdjacencyListIterator</a> : <span class="keyword">public</span> <a class="code" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html#a6402dd9e7851af22b907c0af3e240dce">ArcIterator</a> {</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keyword">public</span>:</div><div class="line"><a name="l00106"></a><span class="lineno"><a class="line" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator.html#a12996aa34ae37ed7efa6fb2eca4ff54e"> 106</a></span>  <span class="keyword">explicit</span> <a class="code" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator.html#a12996aa34ae37ed7efa6fb2eca4ff54e">AdjacencyListIterator</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& graph, <a class="code" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html#a6402dd9e7851af22b907c0af3e240dce">ArcIterator</a>&& arc_it)</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  : <a class="code" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html#a6402dd9e7851af22b907c0af3e240dce">ArcIterator</a>(arc_it), graph_(graph) {}</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">// Overwrite operator* to return the heads of the arcs.</span></div><div class="line"><a name="l00109"></a><span class="lineno"><a class="line" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator.html#a9c411230b6cd51ca80cb31a1f8387ae8"> 109</a></span>  <span class="keyword">typename</span> <a class="code" href="classutil_1_1BaseGraph.html#adb271cf4bcf2de5b5bbe300d7054af29">Graph::NodeIndex</a> <a class="code" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator.html#a9c411230b6cd51ca80cb31a1f8387ae8">operator*</a>()<span class="keyword"> const </span>{</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordflow">return</span> graph_.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(ArcIterator::operator*());</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  }</div><div class="line"><a name="l00112"></a><span class="lineno"> 112</span> </div><div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& graph_;</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  };</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span> </div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="comment">// Returns a pseudo-container of all the nodes adjacent to "node".</span></div><div class="line"><a name="l00118"></a><span class="lineno"><a class="line" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html#a8d68da65b93ce8e85c66d431858897bb"> 118</a></span>  BeginEndWrapper<AdjacencyListIterator> <a class="code" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html#a8d68da65b93ce8e85c66d431858897bb">operator[]</a>(<span class="keywordtype">int</span> node)<span class="keyword"> const </span>{</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keyword">const</span> <span class="keyword">auto</span>& arc_range = graph_.OutgoingOrOppositeIncomingArcs(node);</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordflow">return</span> {<a class="code" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator.html">AdjacencyListIterator</a>(graph_, arc_range.begin()),</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <a class="code" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator.html">AdjacencyListIterator</a>(graph_, arc_range.end())};</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  }</div><div class="line"><a name="l00123"></a><span class="lineno"> 123</span> </div><div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keyword">private</span>:</div><div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& graph_;</div><div class="line"><a name="l00126"></a><span class="lineno"> 126</span> };</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span> </div><div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment">// Computes the weakly connected components of a directed graph that</span></div><div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="comment">// provides the OutgoingOrOppositeIncomingArcs() API, and returns them</span></div><div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment">// as a mapping from node to component index. See GetConnectedComponens().</span></div><div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00132"></a><span class="lineno"><a class="line" href="namespaceutil.html#ab34783e729bb5fc99042893f6bfcbb2f"> 132</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_1ListGraph.html">Graph</a>& graph) {</div><div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceutil.html#a13f0e8f7e15873600cf8e395958c71e1">GetConnectedComponents</a>(</div><div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  graph.<a class="code" href="classutil_1_1BaseGraph.html#a0f551c921fa0b5aaa334a6e36f61db4a">num_nodes</a>(), <a class="code" href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html">UndirectedAdjacencyListsOfDirectedGraph<Graph></a>(graph));</div><div class="line"><a name="l00135"></a><span class="lineno"> 135</span> }</div><div class="line"><a name="l00136"></a><span class="lineno"> 136</span> </div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment">// Returns true iff the given vector is a subset of [0..n-1], i.e.</span></div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment">// all elements i are such that 0 <= i < n and no two elements are equal.</span></div><div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment">// "n" must be >= 0 or the result is undefined.</span></div><div class="line"><a name="l00140"></a><span class="lineno"> 140</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><div class="line"><a name="l00141"></a><span class="lineno"> 141</span> </div><div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment">// Returns true iff the given vector is a permutation of [0..size()-1].</span></div><div class="line"><a name="l00143"></a><span class="lineno"><a class="line" href="namespaceutil.html#ad7986b01cf61a31c09a27b4a97db6a83"> 143</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><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceutil.html#aa9fb4c9a176acaf72053b11727436e9e">IsSubsetOf0N</a>(v, v.size());</div><div class="line"><a name="l00145"></a><span class="lineno"> 145</span> }</div><div class="line"><a name="l00146"></a><span class="lineno"> 146</span> </div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment">// Returns a copy of "graph", without self-arcs and duplicate arcs.</span></div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#a8a06031908a024a50dbdddc394a22490">RemoveSelfArcsAndDuplicateArcs</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>& graph);</div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span> </div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment">// Given an arc path, changes it to a sub-path with the same source and</span></div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment">// destination but without any cycle. Nothing happen if the path was already</span></div><div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment">// without cycle.</span></div><div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment">//</span></div><div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment">// The graph class should support Tail(arc) and Head(arc). They should both</span></div><div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment">// return an integer representing the corresponding tail/head of the passed arc.</span></div><div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment">//</span></div><div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment">// TODO(user): In some cases, there is more than one possible solution. We could</span></div><div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment">// take some arc costs and return the cheapest path instead. Or return the</span></div><div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment">// shortest path in term of number of arcs.</span></div><div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="keywordtype">void</span> <a class="code" href="namespaceutil.html#a06fa201576c927d92657e090fa86bfdb">RemoveCyclesFromPath</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>& graph, std::vector<int>* arc_path);</div><div class="line"><a name="l00163"></a><span class="lineno"> 163</span> </div><div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="comment">// Returns true iff the given path contains a cycle.</span></div><div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#adbb18bcb2f9d64cbbaeb57c328f57e7b">PathHasCycle</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>& graph, <span class="keyword">const</span> std::vector<int>& arc_path);</div><div class="line"><a name="l00167"></a><span class="lineno"> 167</span> </div><div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="comment">// Returns a vector representing a mapping from arcs to arcs such that each arc</span></div><div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="comment">// is mapped to another arc with its (tail, head) flipped, if such an arc</span></div><div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment">// exists (otherwise it is mapped to -1).</span></div><div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment">// If the graph is symmetric, the returned mapping is bijective and reflexive,</span></div><div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment">// i.e. out[out[arc]] = arc for all "arc", where "out" is the returned vector.</span></div><div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment">// If "die_if_not_symmetric" is true, this function CHECKs() that the graph</span></div><div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="comment">// is symmetric.</span></div><div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment">//</span></div><div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment">// Self-arcs are always mapped to themselves.</span></div><div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment">//</span></div><div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment">// Note that since graphs may have multi-arcs, the mapping isn't necessarily</span></div><div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment">// unique, hence the function name.</span></div><div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00181"></a><span class="lineno"> 181</span> std::vector<int> <a class="code" href="namespaceutil.html#ae469c559688b92f36bae2788c2e6063e">ComputeOnePossibleReverseArcMapping</a>(<span class="keyword">const</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>& graph,</div><div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keywordtype">bool</span> die_if_not_symmetric);</div><div class="line"><a name="l00183"></a><span class="lineno"> 183</span> </div><div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment">// Implementations of the templated methods.</span></div><div class="line"><a name="l00185"></a><span class="lineno"> 185</span> </div><div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00187"></a><span class="lineno"><a class="line" href="namespaceutil.html#ac4af76993c891ee4ad507783edec2a1c"> 187</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#ac4af76993c891ee4ad507783edec2a1c">GraphHasSelfArcs</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& graph) {</div><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> arc : graph.<a class="code" href="classutil_1_1BaseGraph.html#abcfd7c21143e5ed38573c0dd60826dd8">AllForwardArcs</a>()) {</div><div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <span class="keywordflow">if</span> (graph.<a class="code" href="classutil_1_1ListGraph.html#aba03f198f690155bca2ab23b039cea54">Tail</a>(arc) == graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc)) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  }</div><div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00192"></a><span class="lineno"> 192</span> }</div><div class="line"><a name="l00193"></a><span class="lineno"> 193</span> </div><div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00195"></a><span class="lineno"><a class="line" href="namespaceutil.html#a6b37593970a26f5c88b3d2ea9acea9d2"> 195</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#a6b37593970a26f5c88b3d2ea9acea9d2">GraphHasDuplicateArcs</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& graph) {</div><div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1BaseGraph.html#a0eba6e5899924388644dfa2258ae8929">Graph::ArcIndex</a> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a>;</div><div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1BaseGraph.html#adb271cf4bcf2de5b5bbe300d7054af29">Graph::NodeIndex</a> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a>;</div><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  std::vector<bool> tmp_node_mask(graph.<a class="code" href="classutil_1_1BaseGraph.html#a0f551c921fa0b5aaa334a6e36f61db4a">num_nodes</a>(), <span class="keyword">false</span>);</div><div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a> tail : graph.<a class="code" href="classutil_1_1BaseGraph.html#a32ba4a5ca9a4b89f750eb2dc56518b02">AllNodes</a>()) {</div><div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1ListGraph.html#ab63770fa993b9347586d2852b841bdc2">OutgoingArcs</a>(tail)) {</div><div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a> head = graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc);</div><div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keywordflow">if</span> (tmp_node_mask[head]) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  tmp_node_mask[head] = <span class="keyword">true</span>;</div><div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  }</div><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#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1ListGraph.html#ab63770fa993b9347586d2852b841bdc2">OutgoingArcs</a>(tail)) {</div><div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  tmp_node_mask[graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc)] = <span class="keyword">false</span>;</div><div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  }</div><div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  }</div><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00210"></a><span class="lineno"> 210</span> }</div><div class="line"><a name="l00211"></a><span class="lineno"> 211</span> </div><div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00213"></a><span class="lineno"><a class="line" href="namespaceutil.html#a784b483eeae1b49164a8a02fe9c0d3ba"> 213</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#a784b483eeae1b49164a8a02fe9c0d3ba">GraphIsSymmetric</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& graph) {</div><div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1BaseGraph.html#adb271cf4bcf2de5b5bbe300d7054af29">Graph::NodeIndex</a> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a>;</div><div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1BaseGraph.html#a0eba6e5899924388644dfa2258ae8929">Graph::ArcIndex</a> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a>;</div><div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="comment">// Create a reverse copy of the graph.</span></div><div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <a class="code" href="classutil_1_1StaticGraph.html">StaticGraph<NodeIndex, ArcIndex></a> reverse_graph(graph.<a class="code" href="classutil_1_1BaseGraph.html#a0f551c921fa0b5aaa334a6e36f61db4a">num_nodes</a>(),</div><div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  graph.<a class="code" href="classutil_1_1BaseGraph.html#aefb468e4d4a3128c91b3bad9f5b314c8">num_arcs</a>());</div><div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a> node : graph.<a class="code" href="classutil_1_1BaseGraph.html#a32ba4a5ca9a4b89f750eb2dc56518b02">AllNodes</a>()) {</div><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1ListGraph.html#ab63770fa993b9347586d2852b841bdc2">OutgoingArcs</a>(node)) {</div><div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  reverse_graph.<a class="code" href="classutil_1_1StaticGraph.html#a10d877b38553e9d2d0ce6fcfc4427df4">AddArc</a>(graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc), node);</div><div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  }</div><div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  }</div><div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  reverse_graph.Build();</div><div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="comment">// Compare the graph to its reverse, one adjacency list at a time.</span></div><div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  std::vector<ArcIndex> count(graph.<a class="code" href="classutil_1_1BaseGraph.html#a0f551c921fa0b5aaa334a6e36f61db4a">num_nodes</a>(), 0);</div><div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a> node : graph.<a class="code" href="classutil_1_1BaseGraph.html#a32ba4a5ca9a4b89f750eb2dc56518b02">AllNodes</a>()) {</div><div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1ListGraph.html#ab63770fa993b9347586d2852b841bdc2">OutgoingArcs</a>(node)) {</div><div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  ++count[graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc)];</div><div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  }</div><div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a> arc : reverse_graph.OutgoingArcs(node)) {</div><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keywordflow">if</span> (--count[reverse_graph.Head(arc)] < 0) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  }</div><div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1ListGraph.html#ab63770fa993b9347586d2852b841bdc2">OutgoingArcs</a>(node)) {</div><div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordflow">if</span> (count[graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc)] != 0) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  }</div><div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  }</div><div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00239"></a><span class="lineno"> 239</span> }</div><div class="line"><a name="l00240"></a><span class="lineno"> 240</span> </div><div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00242"></a><span class="lineno"><a class="line" href="namespaceutil.html#a97311561fd1f01e9f35b2f7ce18b0af3"> 242</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#a97311561fd1f01e9f35b2f7ce18b0af3">GraphIsWeaklyConnected</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& graph) {</div><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1BaseGraph.html#adb271cf4bcf2de5b5bbe300d7054af29">Graph::NodeIndex</a> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a>;</div><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  static_assert(std::numeric_limits<NodeIndex>::max() <= INT_MAX,</div><div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="stringliteral">"GraphIsWeaklyConnected() isn't yet implemented for graphs"</span></div><div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="stringliteral">" that support more than INT_MAX nodes. Reach out to"</span></div><div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="stringliteral">" or-core-team@ if you need this."</span>);</div><div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="keywordflow">if</span> (graph.<a class="code" href="classutil_1_1BaseGraph.html#a0f551c921fa0b5aaa334a6e36f61db4a">num_nodes</a>() == 0) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <a class="code" href="classDenseConnectedComponentsFinder.html">DenseConnectedComponentsFinder</a> union_find;</div><div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  union_find.<a class="code" href="classDenseConnectedComponentsFinder.html#a46780e194c525fa9853fa899d69b4340">SetNumberOfNodes</a>(graph.<a class="code" href="classutil_1_1BaseGraph.html#a0f551c921fa0b5aaa334a6e36f61db4a">num_nodes</a>());</div><div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> <a class="code" href="classutil_1_1BaseGraph.html#a0eba6e5899924388644dfa2258ae8929">Graph::ArcIndex</a> arc = 0; arc < graph.<a class="code" href="classutil_1_1BaseGraph.html#aefb468e4d4a3128c91b3bad9f5b314c8">num_arcs</a>(); ++arc) {</div><div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  union_find.<a class="code" href="classDenseConnectedComponentsFinder.html#aba450cf3f16d9386d043c4354a19a4aa">AddEdge</a>(graph.<a class="code" href="classutil_1_1ListGraph.html#aba03f198f690155bca2ab23b039cea54">Tail</a>(arc), graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc));</div><div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  }</div><div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordflow">return</span> union_find.<a class="code" href="classDenseConnectedComponentsFinder.html#a5090a0bdc205d23778d2b8a742f5c5fd">GetNumberOfComponents</a>() == 1;</div><div class="line"><a name="l00255"></a><span class="lineno"> 255</span> }</div><div class="line"><a name="l00256"></a><span class="lineno"> 256</span> </div><div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00258"></a><span class="lineno"><a class="line" href="namespaceutil.html#a0ed748741b17dad9e6cc485728bb0043"> 258</a></span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#a0ed748741b17dad9e6cc485728bb0043">CopyGraph</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& graph) {</div><div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  std::unique_ptr<Graph> new_graph(</div><div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="keyword">new</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>(graph.<a class="code" href="classutil_1_1BaseGraph.html#a0f551c921fa0b5aaa334a6e36f61db4a">num_nodes</a>(), graph.<a class="code" href="classutil_1_1BaseGraph.html#aefb468e4d4a3128c91b3bad9f5b314c8">num_arcs</a>()));</div><div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> node : graph.<a class="code" href="classutil_1_1BaseGraph.html#a32ba4a5ca9a4b89f750eb2dc56518b02">AllNodes</a>()) {</div><div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> arc : graph.<a class="code" href="classutil_1_1ListGraph.html#ab63770fa993b9347586d2852b841bdc2">OutgoingArcs</a>(node)) {</div><div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  new_graph->AddArc(node, graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc));</div><div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  }</div><div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  }</div><div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  new_graph->Build();</div><div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keywordflow">return</span> new_graph;</div><div class="line"><a name="l00268"></a><span class="lineno"> 268</span> }</div><div class="line"><a name="l00269"></a><span class="lineno"> 269</span> </div><div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00271"></a><span class="lineno"><a class="line" href="namespaceutil.html#acfecdce43e9933bde2a94fd879f12f5f"> 271</a></span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#acfecdce43e9933bde2a94fd879f12f5f">RemapGraph</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& old_graph,</div><div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keyword">const</span> std::vector<int>& new_node_index) {</div><div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  DCHECK(<a class="code" href="namespaceutil.html#ad7986b01cf61a31c09a27b4a97db6a83">IsValidPermutation</a>(new_node_index)) << <span class="stringliteral">"Invalid permutation"</span>;</div><div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> num_nodes = old_graph.<a class="code" href="classutil_1_1BaseGraph.html#a0f551c921fa0b5aaa334a6e36f61db4a">num_nodes</a>();</div><div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  CHECK_EQ(new_node_index.size(), num_nodes);</div><div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  std::unique_ptr<Graph> new_graph(<span class="keyword">new</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>(num_nodes, old_graph.<a class="code" href="classutil_1_1BaseGraph.html#aefb468e4d4a3128c91b3bad9f5b314c8">num_arcs</a>()));</div><div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1BaseGraph.html#adb271cf4bcf2de5b5bbe300d7054af29">Graph::NodeIndex</a> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a>;</div><div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1BaseGraph.html#a0eba6e5899924388644dfa2258ae8929">Graph::ArcIndex</a> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a>;</div><div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a> node : old_graph.<a class="code" href="classutil_1_1BaseGraph.html#a32ba4a5ca9a4b89f750eb2dc56518b02">AllNodes</a>()) {</div><div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a> arc : old_graph.<a class="code" href="classutil_1_1ListGraph.html#ab63770fa993b9347586d2852b841bdc2">OutgoingArcs</a>(node)) {</div><div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  new_graph->AddArc(new_node_index[node],</div><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  new_node_index[old_graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc)]);</div><div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  }</div><div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  }</div><div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  new_graph->Build();</div><div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="keywordflow">return</span> new_graph;</div><div class="line"><a name="l00287"></a><span class="lineno"> 287</span> }</div><div class="line"><a name="l00288"></a><span class="lineno"> 288</span> </div><div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00290"></a><span class="lineno"><a class="line" href="namespaceutil.html#ad1df170a504d335462a1104a942e6069"> 290</a></span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#ad1df170a504d335462a1104a942e6069">GetSubgraphOfNodes</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& old_graph,</div><div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="keyword">const</span> std::vector<int>& nodes) {</div><div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1BaseGraph.html#adb271cf4bcf2de5b5bbe300d7054af29">Graph::NodeIndex</a> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a>;</div><div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1BaseGraph.html#a0eba6e5899924388644dfa2258ae8929">Graph::ArcIndex</a> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a>;</div><div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  DCHECK(<a class="code" href="namespaceutil.html#aa9fb4c9a176acaf72053b11727436e9e">IsSubsetOf0N</a>(nodes, old_graph.<a class="code" href="classutil_1_1BaseGraph.html#a0f551c921fa0b5aaa334a6e36f61db4a">num_nodes</a>())) << <span class="stringliteral">"Invalid subset"</span>;</div><div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  std::vector<NodeIndex> new_node_index(old_graph.<a class="code" href="classutil_1_1BaseGraph.html#a0f551c921fa0b5aaa334a6e36f61db4a">num_nodes</a>(), -1);</div><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a> new_index = 0; new_index < nodes.size(); ++new_index) {</div><div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  new_node_index[nodes[new_index]] = new_index;</div><div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  }</div><div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="comment">// Do a first pass to count the arcs, so that we don't allocate more memory</span></div><div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="comment">// than needed.</span></div><div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a> num_arcs = 0;</div><div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a> node : nodes) {</div><div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a> arc : old_graph.<a class="code" href="classutil_1_1ListGraph.html#ab63770fa993b9347586d2852b841bdc2">OutgoingArcs</a>(node)) {</div><div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keywordflow">if</span> (new_node_index[old_graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc)] != -1) ++num_arcs;</div><div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  }</div><div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  }</div><div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="comment">// A second pass where we actually copy the subgraph.</span></div><div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="comment">// NOTE(user): there might seem to be a bit of duplication with RemapGraph(),</span></div><div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="comment">// but there is a key difference: the loop below only iterates on "nodes",</span></div><div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="comment">// which could be much smaller than all the graph's nodes.</span></div><div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  std::unique_ptr<Graph> new_graph(<span class="keyword">new</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>(nodes.size(), num_arcs));</div><div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a> new_tail = 0; new_tail < nodes.size(); ++new_tail) {</div><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a> old_tail = nodes[new_tail];</div><div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a> arc : old_graph.<a class="code" href="classutil_1_1ListGraph.html#ab63770fa993b9347586d2852b841bdc2">OutgoingArcs</a>(old_tail)) {</div><div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a> new_head = new_node_index[old_graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc)];</div><div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="keywordflow">if</span> (new_head != -1) new_graph->AddArc(new_tail, new_head);</div><div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  }</div><div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  }</div><div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  new_graph->Build();</div><div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="keywordflow">return</span> new_graph;</div><div class="line"><a name="l00321"></a><span class="lineno"> 321</span> }</div><div class="line"><a name="l00322"></a><span class="lineno"> 322</span> </div><div class="line"><a name="l00323"></a><span class="lineno"> 323</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00324"></a><span class="lineno"><a class="line" href="namespaceutil.html#a8a06031908a024a50dbdddc394a22490"> 324</a></span> std::unique_ptr<Graph> <a class="code" href="namespaceutil.html#a8a06031908a024a50dbdddc394a22490">RemoveSelfArcsAndDuplicateArcs</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& graph) {</div><div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  std::unique_ptr<Graph> g(<span class="keyword">new</span> <a class="code" href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">Graph</a>(graph.<a class="code" href="classutil_1_1BaseGraph.html#a0f551c921fa0b5aaa334a6e36f61db4a">num_nodes</a>(), graph.<a class="code" href="classutil_1_1BaseGraph.html#aefb468e4d4a3128c91b3bad9f5b314c8">num_arcs</a>()));</div><div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1BaseGraph.html#a0eba6e5899924388644dfa2258ae8929">Graph::ArcIndex</a> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a>;</div><div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classutil_1_1BaseGraph.html#adb271cf4bcf2de5b5bbe300d7054af29">Graph::NodeIndex</a> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a>;</div><div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  std::vector<bool> tmp_node_mask(graph.<a class="code" href="classutil_1_1BaseGraph.html#a0f551c921fa0b5aaa334a6e36f61db4a">num_nodes</a>(), <span class="keyword">false</span>);</div><div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a> tail : graph.<a class="code" href="classutil_1_1BaseGraph.html#a32ba4a5ca9a4b89f750eb2dc56518b02">AllNodes</a>()) {</div><div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1ListGraph.html#ab63770fa993b9347586d2852b841bdc2">OutgoingArcs</a>(tail)) {</div><div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">NodeIndex</a> head = graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc);</div><div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <span class="keywordflow">if</span> (head != tail && !tmp_node_mask[head]) {</div><div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  tmp_node_mask[head] = <span class="keyword">true</span>;</div><div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  g->AddArc(tail, head);</div><div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  }</div><div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  }</div><div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code" href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">ArcIndex</a> arc : graph.<a class="code" href="classutil_1_1ListGraph.html#ab63770fa993b9347586d2852b841bdc2">OutgoingArcs</a>(tail)) {</div><div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  tmp_node_mask[graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc)] = <span class="keyword">false</span>;</div><div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  }</div><div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  }</div><div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  g->Build();</div><div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="keywordflow">return</span> g;</div><div class="line"><a name="l00343"></a><span class="lineno"> 343</span> }</div><div class="line"><a name="l00344"></a><span class="lineno"> 344</span> </div><div class="line"><a name="l00345"></a><span class="lineno"> 345</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00346"></a><span class="lineno"><a class="line" href="namespaceutil.html#a06fa201576c927d92657e090fa86bfdb"> 346</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceutil.html#a06fa201576c927d92657e090fa86bfdb">RemoveCyclesFromPath</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& graph, std::vector<int>* arc_path) {</div><div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="keywordflow">if</span> (arc_path->empty()) <span class="keywordflow">return</span>;</div><div class="line"><a name="l00348"></a><span class="lineno"> 348</span> </div><div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="comment">// This maps each node to the latest arc in the given path that leaves it.</span></div><div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  std::map<int, int> last_arc_leaving_node;</div><div class="line"><a name="l00351"></a><span class="lineno"> 351</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_1ListGraph.html#aba03f198f690155bca2ab23b039cea54">Tail</a>(arc)] = arc;</div><div class="line"><a name="l00352"></a><span class="lineno"> 352</span> </div><div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="comment">// Special case for the destination.</span></div><div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="comment">// Note that this requires that -1 is not a valid arc of Graph.</span></div><div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  last_arc_leaving_node[graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc_path->back())] = -1;</div><div class="line"><a name="l00356"></a><span class="lineno"> 356</span> </div><div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <span class="comment">// Reconstruct the path by starting at the source and then following the</span></div><div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  <span class="comment">// "next" arcs. We override the given arc_path at the same time.</span></div><div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="keywordtype">int</span> node = graph.<a class="code" href="classutil_1_1ListGraph.html#aba03f198f690155bca2ab23b039cea54">Tail</a>(arc_path->front());</div><div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="keywordtype">int</span> new_size = 0;</div><div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="keywordflow">while</span> (new_size < arc_path->size()) { <span class="comment">// To prevent cycle on bad input.</span></div><div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> arc = gtl::FindOrDie(last_arc_leaving_node, node);</div><div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  <span class="keywordflow">if</span> (arc == -1) <span class="keywordflow">break</span>;</div><div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  (*arc_path)[new_size++] = arc;</div><div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  node = graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc);</div><div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  }</div><div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  arc_path->resize(new_size);</div><div class="line"><a name="l00368"></a><span class="lineno"> 368</span> }</div><div class="line"><a name="l00369"></a><span class="lineno"> 369</span> </div><div class="line"><a name="l00370"></a><span class="lineno"> 370</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00371"></a><span class="lineno"><a class="line" href="namespaceutil.html#adbb18bcb2f9d64cbbaeb57c328f57e7b"> 371</a></span> <span class="keywordtype">bool</span> <a class="code" href="namespaceutil.html#adbb18bcb2f9d64cbbaeb57c328f57e7b">PathHasCycle</a>(<span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& graph, <span class="keyword">const</span> std::vector<int>& arc_path) {</div><div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <span class="keywordflow">if</span> (arc_path.empty()) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  std::set<int> seen;</div><div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  seen.insert(graph.<a class="code" href="classutil_1_1ListGraph.html#aba03f198f690155bca2ab23b039cea54">Tail</a>(arc_path.front()));</div><div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> arc : arc_path) {</div><div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  <span class="keywordflow">if</span> (!gtl::InsertIfNotPresent(&seen, graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc))) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div><div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  }</div><div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div><div class="line"><a name="l00379"></a><span class="lineno"> 379</span> }</div><div class="line"><a name="l00380"></a><span class="lineno"> 380</span> </div><div class="line"><a name="l00381"></a><span class="lineno"> 381</span> <span class="keyword">template</span> <<span class="keyword">class</span> Graph></div><div class="line"><a name="l00382"></a><span class="lineno"><a class="line" href="namespaceutil.html#ae469c559688b92f36bae2788c2e6063e"> 382</a></span> std::vector<int> <a class="code" href="namespaceutil.html#ae469c559688b92f36bae2788c2e6063e">ComputeOnePossibleReverseArcMapping</a>(</div><div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="keyword">const</span> <a class="code" href="classutil_1_1ListGraph.html">Graph</a>& graph, <span class="keywordtype">bool</span> die_if_not_symmetric) {</div><div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  std::vector<int> reverse_arc(graph.<a class="code" href="classutil_1_1BaseGraph.html#aefb468e4d4a3128c91b3bad9f5b314c8">num_arcs</a>(), -1);</div><div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  std::unordered_multimap<std::pair<<span class="comment">/*tail*/</span> int, <span class="comment">/*head*/</span> <span class="keywordtype">int</span>>,</div><div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  <span class="comment">/*arc index*/</span> <span class="keywordtype">int</span>></div><div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  arc_map;</div><div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> arc = 0; arc < graph.<a class="code" href="classutil_1_1BaseGraph.html#aefb468e4d4a3128c91b3bad9f5b314c8">num_arcs</a>(); ++arc) {</div><div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> tail = graph.<a class="code" href="classutil_1_1ListGraph.html#aba03f198f690155bca2ab23b039cea54">Tail</a>(arc);</div><div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> head = graph.<a class="code" href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">Head</a>(arc);</div><div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  <span class="keywordflow">if</span> (tail == head) {</div><div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="comment">// Special case: directly map any self-arc to itself.</span></div><div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  reverse_arc[arc] = arc;</div><div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  <span class="keywordflow">continue</span>;</div><div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  }</div><div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  <span class="comment">// Lookup for the reverse arc of the current one...</span></div><div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <span class="keyword">auto</span> it = arc_map.find({head, tail});</div><div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  <span class="keywordflow">if</span> (it != arc_map.end()) {</div><div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  <span class="comment">// Found a reverse arc! Store the mapping and remove the</span></div><div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  <span class="comment">// reverse arc from the map.</span></div><div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  reverse_arc[arc] = it->second;</div><div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  reverse_arc[it->second] = arc;</div><div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  arc_map.erase(it);</div><div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <span class="comment">// Reverse arc not in the map. Add the current arc to the map.</span></div><div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  arc_map.insert({{tail, head}, arc});</div><div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  }</div><div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  }</div><div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <span class="comment">// Algorithm check, for debugging.</span></div><div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  DCHECK_EQ(std::count(reverse_arc.begin(), reverse_arc.end(), -1),</div><div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  arc_map.size());</div><div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  <span class="keywordflow">if</span> (die_if_not_symmetric) {</div><div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  CHECK_EQ(arc_map.size(), 0)</div><div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  << <span class="stringliteral">"The graph is not symmetric: "</span> << arc_map.size() << <span class="stringliteral">" of "</span></div><div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  << graph.<a class="code" href="classutil_1_1BaseGraph.html#aefb468e4d4a3128c91b3bad9f5b314c8">num_arcs</a>() << <span class="stringliteral">" arcs did not have a reverse."</span>;</div><div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  }</div><div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <span class="keywordflow">return</span> reverse_arc;</div><div class="line"><a name="l00418"></a><span class="lineno"> 418</span> }</div><div class="line"><a name="l00419"></a><span class="lineno"> 419</span> </div><div class="line"><a name="l00420"></a><span class="lineno"> 420</span> } <span class="comment">// namespace util</span></div><div class="line"><a name="l00421"></a><span class="lineno"> 421</span> </div><div class="line"><a name="l00422"></a><span class="lineno"> 422</span> <span class="preprocessor">#endif // UTIL_GRAPH_UTIL_H_</span></div><div class="ttc" id="classutil_1_1BaseGraph_html_abcfd7c21143e5ed38573c0dd60826dd8"><div class="ttname"><a href="classutil_1_1BaseGraph.html#abcfd7c21143e5ed38573c0dd60826dd8">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#l00935">graph.h:935</a></div></div>
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<div class="ttc" id="namespaceutil_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="ttdoc">Returns true iff the given vector is a permutation of [0..size()-1].</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00143">util.h:143</a></div></div>
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<div class="ttc" id="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_html"><div class="ttname"><a href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html">util::UndirectedAdjacencyListsOfDirectedGraph</a></div><div class="ttdoc">This can be used to view a directed graph (that supports reverse arcs) from graph....</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00098">util.h:98</a></div></div>
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<div class="ttc" id="namespaceutil_html"><div class="ttname"><a href="namespaceutil.html">util</a></div><div class="ttdoc">Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in c...</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="classDenseConnectedComponentsFinder_html_a46780e194c525fa9853fa899d69b4340"><div class="ttname"><a href="classDenseConnectedComponentsFinder.html#a46780e194c525fa9853fa899d69b4340">DenseConnectedComponentsFinder::SetNumberOfNodes</a></div><div class="ttdeci">void SetNumberOfNodes(int num_nodes)</div><div class="ttdoc">Sets the number of nodes in the graph.</div></div>
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<div class="ttc" id="namespaceutil_html_a8a06031908a024a50dbdddc394a22490"><div class="ttname"><a href="namespaceutil.html#a8a06031908a024a50dbdddc394a22490">util::RemoveSelfArcsAndDuplicateArcs</a></div><div class="ttdeci">std::unique_ptr< Graph > RemoveSelfArcsAndDuplicateArcs(const Graph &graph)</div><div class="ttdoc">Returns a copy of "graph", without self-arcs and duplicate arcs.</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00324">util.h:324</a></div></div>
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<div class="ttc" id="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator_html_a9c411230b6cd51ca80cb31a1f8387ae8"><div class="ttname"><a href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator.html#a9c411230b6cd51ca80cb31a1f8387ae8">util::UndirectedAdjacencyListsOfDirectedGraph::AdjacencyListIterator::operator *</a></div><div class="ttdeci">Graph::NodeIndex operator *() const</div><div class="ttdoc">Overwrite operator* to return the heads of the arcs.</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00109">util.h:109</a></div></div>
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<div class="ttc" id="namespaceutil_html_ae76339cb2dcd3bc05ad762146f91fdda"><div class="ttname"><a href="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">util::Graph</a></div><div class="ttdeci">ListGraph Graph</div><div class="ttdoc">Defining the simplest Graph interface as Graph for convenience.</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l02358">graph.h:2358</a></div></div>
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<div class="ttc" id="namespaceutil_html_ae469c559688b92f36bae2788c2e6063e"><div class="ttname"><a href="namespaceutil.html#ae469c559688b92f36bae2788c2e6063e">util::ComputeOnePossibleReverseArcMapping</a></div><div class="ttdeci">std::vector< int > ComputeOnePossibleReverseArcMapping(const Graph &graph, bool die_if_not_symmetric)</div><div class="ttdoc">Returns a vector representing a mapping from arcs to arcs such that each arc is mapped to another arc...</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00382">util.h:382</a></div></div>
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<div class="ttc" id="classutil_1_1BaseGraph_html_a0f551c921fa0b5aaa334a6e36f61db4a"><div class="ttname"><a href="classutil_1_1BaseGraph.html#a0f551c921fa0b5aaa334a6e36f61db4a">util::BaseGraph::num_nodes</a></div><div class="ttdeci">NodeIndexType num_nodes() const</div><div class="ttdoc">Returns the number of valid nodes in the graph.</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00201">graph.h:201</a></div></div>
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<div class="ttc" id="classDenseConnectedComponentsFinder_html"><div class="ttname"><a href="classDenseConnectedComponentsFinder.html">DenseConnectedComponentsFinder</a></div><div class="ttdoc">NOTE(user): The rest of the functions below should also be in namespace util, but for historical reas...</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="namespaceutil_html_a6b37593970a26f5c88b3d2ea9acea9d2"><div class="ttname"><a href="namespaceutil.html#a6b37593970a26f5c88b3d2ea9acea9d2">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#l00195">util.h:195</a></div></div>
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<div class="ttc" id="classutil_1_1ListGraph_html_aba03f198f690155bca2ab23b039cea54"><div class="ttname"><a href="classutil_1_1ListGraph.html#aba03f198f690155bca2ab23b039cea54">util::ListGraph::Tail</a></div><div class="ttdeci">NodeIndexType Tail(ArcIndexType arc) const</div><div class="ttdoc">Returns the tail/head of a valid arc.</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l01107">graph.h:1107</a></div></div>
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<div class="ttc" id="namespaceutil_html_a13f0e8f7e15873600cf8e395958c71e1"><div class="ttname"><a href="namespaceutil.html#a13f0e8f7e15873600cf8e395958c71e1">util::GetConnectedComponents</a></div><div class="ttdeci">std::vector< int > GetConnectedComponents(int num_nodes, const UndirectedGraph &graph)</div><div class="ttdoc">Finds the connected components of the graph, using BFS internally.</div><div class="ttdef"><b>Definition:</b> <a href="connected__components_8h_source.html#l00289">connected_components.h:289</a></div></div>
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<div class="ttc" id="namespaceutil_html_a97311561fd1f01e9f35b2f7ce18b0af3"><div class="ttname"><a href="namespaceutil.html#a97311561fd1f01e9f35b2f7ce18b0af3">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#l00242">util.h:242</a></div></div>
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<div class="ttc" id="connected__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="iterators_8h_html"><div class="ttname"><a href="iterators_8h.html">iterators.h</a></div></div>
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<div class="ttc" id="namespaceutil_html_ac4af76993c891ee4ad507783edec2a1c"><div class="ttname"><a href="namespaceutil.html#ac4af76993c891ee4ad507783edec2a1c">util::GraphHasSelfArcs</a></div><div class="ttdeci">bool GraphHasSelfArcs(const Graph &graph)</div><div class="ttdoc">Here's a set of simple diagnosis tools.</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00187">util.h:187</a></div></div>
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<div class="ttc" id="namespaceutil_html_acfecdce43e9933bde2a94fd879f12f5f"><div class="ttname"><a href="namespaceutil.html#acfecdce43e9933bde2a94fd879f12f5f">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="ttdoc">Creates a remapped copy of graph "graph", where node i becomes node new_node_index[i].</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00271">util.h:271</a></div></div>
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<div class="ttc" id="namespaceutil_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 class="ttdoc">Returns true iff the given vector is a subset of [0..n-1], i.e.</div></div>
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<div class="ttc" id="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator_html"><div class="ttname"><a href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator.html">util::UndirectedAdjacencyListsOfDirectedGraph::AdjacencyListIterator</a></div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00104">util.h:104</a></div></div>
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<div class="ttc" id="namespaceutil_html_ad1df170a504d335462a1104a942e6069"><div class="ttname"><a href="namespaceutil.html#ad1df170a504d335462a1104a942e6069">util::GetSubgraphOfNodes</a></div><div class="ttdeci">std::unique_ptr< Graph > GetSubgraphOfNodes(const Graph &graph, const std::vector< int > &nodes)</div><div class="ttdoc">Gets the induced subgraph of "graph" restricted to the nodes in "nodes": the resulting graph will hav...</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00290">util.h:290</a></div></div>
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<div class="ttc" id="classutil_1_1StaticGraph_html"><div class="ttname"><a href="classutil_1_1StaticGraph.html">util::StaticGraph</a></div><div class="ttdoc">Most efficient implementation of a graph without reverse arcs:</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00396">graph.h:396</a></div></div>
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<div class="ttc" id="namespaceutil_html_a784b483eeae1b49164a8a02fe9c0d3ba"><div class="ttname"><a href="namespaceutil.html#a784b483eeae1b49164a8a02fe9c0d3ba">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#l00213">util.h:213</a></div></div>
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<div class="ttc" id="classutil_1_1BaseGraph_html_a0eba6e5899924388644dfa2258ae8929"><div class="ttname"><a href="classutil_1_1BaseGraph.html#a0eba6e5899924388644dfa2258ae8929">util::BaseGraph< NodeIndexType, ArcIndexType, false >::ArcIndex</a></div><div class="ttdeci">ArcIndexType ArcIndex</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00190">graph.h:190</a></div></div>
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<div class="ttc" id="classutil_1_1ListGraph_html_ad7d3d076d3c154d89f1eda855a34b487"><div class="ttname"><a href="classutil_1_1ListGraph.html#ad7d3d076d3c154d89f1eda855a34b487">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#l01114">graph.h:1114</a></div></div>
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<div class="ttc" id="classutil_1_1ListGraph_html_ab63770fa993b9347586d2852b841bdc2"><div class="ttname"><a href="classutil_1_1ListGraph.html#ab63770fa993b9347586d2852b841bdc2">util::ListGraph::OutgoingArcs</a></div><div class="ttdeci">BeginEndWrapper< OutgoingArcIterator > OutgoingArcs(NodeIndexType node) const</div><div class="ttdoc">Allows to iterate over the forward arcs that verify Tail(arc) == node.</div></div>
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<div class="ttc" id="classDenseConnectedComponentsFinder_html_a5090a0bdc205d23778d2b8a742f5c5fd"><div class="ttname"><a href="classDenseConnectedComponentsFinder.html#a5090a0bdc205d23778d2b8a742f5c5fd">DenseConnectedComponentsFinder::GetNumberOfComponents</a></div><div class="ttdeci">int GetNumberOfComponents() const</div><div class="ttdef"><b>Definition:</b> <a href="connected__components_8h_source.html#l00095">connected_components.h:95</a></div></div>
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<div class="ttc" id="namespaceutil_html_adbb18bcb2f9d64cbbaeb57c328f57e7b"><div class="ttname"><a href="namespaceutil.html#adbb18bcb2f9d64cbbaeb57c328f57e7b">util::PathHasCycle</a></div><div class="ttdeci">bool PathHasCycle(const Graph &graph, const std::vector< int > &arc_path)</div><div class="ttdoc">Returns true iff the given path contains a cycle.</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00371">util.h:371</a></div></div>
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<div class="ttc" id="graph_8h_html"><div class="ttname"><a href="graph_8h.html">graph.h</a></div></div>
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<div class="ttc" id="classutil_1_1BaseGraph_html_a32ba4a5ca9a4b89f750eb2dc56518b02"><div class="ttname"><a href="classutil_1_1BaseGraph.html#a32ba4a5ca9a4b89f750eb2dc56518b02">util::BaseGraph::AllNodes</a></div><div class="ttdeci">IntegerRange< NodeIndex > AllNodes() const</div><div class="ttdoc">Allows nice range-based for loop: for (const NodeIndex node : graph.AllNodes()) { ....</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00929">graph.h:929</a></div></div>
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<div class="ttc" id="classutil_1_1BaseGraph_html_aefb468e4d4a3128c91b3bad9f5b314c8"><div class="ttname"><a href="classutil_1_1BaseGraph.html#aefb468e4d4a3128c91b3bad9f5b314c8">util::BaseGraph::num_arcs</a></div><div class="ttdeci">ArcIndexType num_arcs() const</div><div class="ttdoc">Returns the number of valid arcs in the graph.</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00204">graph.h:204</a></div></div>
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<div class="ttc" id="namespaceutil_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="ttdoc">Computes the weakly connected components of a directed graph that provides the OutgoingOrOppositeInco...</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00132">util.h:132</a></div></div>
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<div class="ttc" id="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator_html_a12996aa34ae37ed7efa6fb2eca4ff54e"><div class="ttname"><a href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_1_1AdjacencyListIterator.html#a12996aa34ae37ed7efa6fb2eca4ff54e">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#l00106">util.h:106</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_a31d858394c5eed1fa21edc3da47047c1"><div class="ttname"><a href="namespaceoperations__research.html#a31d858394c5eed1fa21edc3da47047c1">operations_research::ArcIndex</a></div><div class="ttdeci">int32 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="classutil_1_1BaseGraph_html_adb271cf4bcf2de5b5bbe300d7054af29"><div class="ttname"><a href="classutil_1_1BaseGraph.html#adb271cf4bcf2de5b5bbe300d7054af29">util::BaseGraph< NodeIndexType, ArcIndexType, false >::NodeIndex</a></div><div class="ttdeci">NodeIndexType NodeIndex</div><div class="ttdoc">Typedef so you can use Graph::NodeIndex and Graph::ArcIndex to be generic but also to improve the rea...</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00189">graph.h:189</a></div></div>
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<div class="ttc" id="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_html_aa3254dffa224cf75efab4e3b034b39d8"><div class="ttname"><a href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html#aa3254dffa224cf75efab4e3b034b39d8">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#l00100">util.h:100</a></div></div>
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<div class="ttc" id="classDenseConnectedComponentsFinder_html_aba450cf3f16d9386d043c4354a19a4aa"><div class="ttname"><a href="classDenseConnectedComponentsFinder.html#aba450cf3f16d9386d043c4354a19a4aa">DenseConnectedComponentsFinder::AddEdge</a></div><div class="ttdeci">void AddEdge(int node1, int node2)</div><div class="ttdoc">The main API is the same as ConnectedComponentsFinder (below): see the homonymous functions there.</div></div>
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<div class="ttc" id="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_html_a6402dd9e7851af22b907c0af3e240dce"><div class="ttname"><a href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html#a6402dd9e7851af22b907c0af3e240dce">util::UndirectedAdjacencyListsOfDirectedGraph::ArcIterator</a></div><div class="ttdeci">Graph::OutgoingOrOppositeIncomingArcIterator ArcIterator</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00103">util.h:103</a></div></div>
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<div class="ttc" id="namespaceutil_html_a06fa201576c927d92657e090fa86bfdb"><div class="ttname"><a href="namespaceutil.html#a06fa201576c927d92657e090fa86bfdb">util::RemoveCyclesFromPath</a></div><div class="ttdeci">void RemoveCyclesFromPath(const Graph &graph, std::vector< int > *arc_path)</div><div class="ttdoc">Given an arc path, changes it to a sub-path with the same source and destination but without any cycl...</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00346">util.h:346</a></div></div>
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<div class="ttc" id="namespaceutil_html_a0ed748741b17dad9e6cc485728bb0043"><div class="ttname"><a href="namespaceutil.html#a0ed748741b17dad9e6cc485728bb0043">util::CopyGraph</a></div><div class="ttdeci">std::unique_ptr< Graph > CopyGraph(const Graph &graph)</div><div class="ttdoc">Returns a fresh copy of a given graph.</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00258">util.h:258</a></div></div>
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<div class="ttc" id="namespaceoperations__research_html_a0e629e35bfa311b31dd7f5065eb834bb"><div class="ttname"><a href="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">operations_research::NodeIndex</a></div><div class="ttdeci">int32 NodeIndex</div><div class="ttdoc">Standard instantiation of ForwardEbertGraph (named 'ForwardStarGraph') of EbertGraph (named 'StarGrap...</div><div class="ttdef"><b>Definition:</b> <a href="ebert__graph_8h_source.html#l00192">ebert_graph.h:192</a></div></div>
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<div class="ttc" id="classutil_1_1ListGraph_html"><div class="ttname"><a href="classutil_1_1ListGraph.html">util::ListGraph</a></div><div class="ttdoc">Basic graph implementation without reverse arc.</div><div class="ttdef"><b>Definition:</b> <a href="graph_8h_source.html#l00297">graph.h:297</a></div></div>
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<div class="ttc" id="classutil_1_1StaticGraph_html_a10d877b38553e9d2d0ce6fcfc4427df4"><div class="ttname"><a href="classutil_1_1StaticGraph.html#a10d877b38553e9d2d0ce6fcfc4427df4">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#l01283">graph.h:1283</a></div></div>
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<div class="ttc" id="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph_html_a8d68da65b93ce8e85c66d431858897bb"><div class="ttname"><a href="classutil_1_1UndirectedAdjacencyListsOfDirectedGraph.html#a8d68da65b93ce8e85c66d431858897bb">util::UndirectedAdjacencyListsOfDirectedGraph::operator[]</a></div><div class="ttdeci">BeginEndWrapper< AdjacencyListIterator > operator[](int node) const</div><div class="ttdoc">Returns a pseudo-container of all the nodes adjacent to "node".</div><div class="ttdef"><b>Definition:</b> <a href="util_8h_source.html#l00118">util.h:118</a></div></div>
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