<ahref="eulerian__path_8h.html">Go to the documentation of this file.</a><divclass="fragment"><divclass="line"><aname="l00001"></a><spanclass="lineno"> 1</span> <spanclass="comment">// Copyright 2010-2018 Google LLC</span></div><divclass="line"><aname="l00002"></a><spanclass="lineno"> 2</span> <spanclass="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div><divclass="line"><aname="l00003"></a><spanclass="lineno"> 3</span> <spanclass="comment">// you may not use this file except in compliance with the License.</span></div><divclass="line"><aname="l00004"></a><spanclass="lineno"> 4</span> <spanclass="comment">// You may obtain a copy of the License at</span></div><divclass="line"><aname="l00005"></a><spanclass="lineno"> 5</span> <spanclass="comment">//</span></div><divclass="line"><aname="l00006"></a><spanclass="lineno"> 6</span> <spanclass="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div><divclass="line"><aname="l00007"></a><spanclass="lineno"> 7</span> <spanclass="comment">//</span></div><divclass="line"><aname="l00008"></a><spanclass="lineno"> 8</span> <spanclass="comment">// Unless required by applicable law or agreed to in writing, software</span></div><divclass="line"><aname="l00009"></a><spanclass="lineno"> 9</span> <spanclass="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div><divclass="line"><aname="l00010"></a><spanclass="lineno"> 10</span> <spanclass="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div><divclass="line"><aname="l00011"></a><spanclass="lineno"> 11</span> <spanclass="comment">// See the License for the specific language governing permissions and</span></div><divclass="line"><aname="l00012"></a><spanclass="lineno"> 12</span> <spanclass="comment">// limitations under the License.</span></div><divclass="line"><aname="l00013"></a><spanclass="lineno"> 13</span> </div><divclass="line"><aname="l00014"></a><spanclass="lineno"> 14</span> <spanclass="comment">// Utility to build Eulerian paths and tours on a graph. For more information,</span></div><divclass="line"><aname="l00015"></a><spanclass="lineno"> 15</span> <spanclass="comment">// see https://en.wikipedia.org/wiki/Eulerian_path.</span></div><divclass="line"><aname="l00016"></a><spanclass="lineno"> 16</span> <spanclass="comment">// As of 10/2015, only undirected graphs are supported.</span></div><divclass="line"><aname="l00017"></a><spanclass="lineno"> 17</span> <spanclass="comment">//</span></div><divclass="line"><aname="l00018"></a><spanclass="lineno"> 18</span> <spanclass="comment">// Usage:</span></div><divclass="line"><aname="l00019"></a><spanclass="lineno"> 19</span> <spanclass="comment">// - Building an Eulerian tour on a ReverseArcListGraph:</span></div><divclass="line"><aname="l00020"></a><spanclass="lineno"> 20</span> <spanclass="comment">// ReverseArcListGraph<int, int> graph;</span></div><divclass="line"><aname="l00021"></a><spanclass="lineno"> 21</span> <spanclass="comment">// // Fill graph</span></div><divclass="line"><aname="l00022"></a><spanclass="lineno"> 22</span> <spanclass="comment">// std::vector<int> tour = BuildEulerianTour(graph);</span></div><divclass="line"><aname="l00023"></a><spanclass="lineno"> 23</span> <spanclass="comment">//</span></div><divclass="line"><aname="l00024"></a><spanclass="lineno"> 24</span> <spanclass="comment">// - Building an Eulerian path on a ReverseArcListGraph:</span></div><divclass="line"><aname="l00025"></a><spanclass="lineno"> 25</span> <spanclass="comment">// ReverseArcListGraph<int, int> graph;</span></div><divclass="line"><aname="l00026"></a><spanclass="lineno"> 26</span> <spanclass="comment">// // Fill graph</span>
<divclass="ttc"id="namespaceutil_html_ae76339cb2dcd3bc05ad762146f91fdda"><divclass="ttname"><ahref="namespaceutil.html#ae76339cb2dcd3bc05ad762146f91fdda">util::Graph</a></div><divclass="ttdeci">ListGraph Graph</div><divclass="ttdoc">Defining the simplest Graph interface as Graph for convenience.</div><divclass="ttdef"><b>Definition:</b><ahref="graph_8h_source.html#l02358">graph.h:2358</a></div></div>
<divclass="ttc"id="namespaceoperations__research_html_a034666fe63ca105b735272974006362a"><divclass="ttname"><ahref="namespaceoperations__research.html#a034666fe63ca105b735272974006362a">operations_research::BuildEulerianTour</a></div><divclass="ttdeci">std::vector< typename Graph::NodeIndex > BuildEulerianTour(const Graph &graph)</div><divclass="ttdoc">Same as above but without specifying a start/end root node (node 0 is taken as default root).</div><divclass="ttdef"><b>Definition:</b><ahref="eulerian__path_8h_source.html#l00128">eulerian_path.h:128</a></div></div>
<divclass="ttc"id="namespaceoperations__research_html_aa63055860fc53f8eed56d23d2571c180"><divclass="ttname"><ahref="namespaceoperations__research.html#aa63055860fc53f8eed56d23d2571c180">operations_research::BuildEulerianTourFromNode</a></div><divclass="ttdeci">std::vector< NodeIndex > BuildEulerianTourFromNode(const Graph &graph, NodeIndex root)</div><divclass="ttdoc">Builds an Eulerian tour/circuit/cycle starting and ending at node root on an undirected graph.</div><divclass="ttdef"><b>Definition:</b><ahref="eulerian__path_8h_source.html#l00116">eulerian_path.h:116</a></div></div>
<divclass="ttc"id="namespaceoperations__research_html_a49b170b2d03863c465331e67b21f0c33"><divclass="ttname"><ahref="namespaceoperations__research.html#a49b170b2d03863c465331e67b21f0c33">operations_research::BuildEulerianPath</a></div><divclass="ttdeci">std::vector< typename Graph::NodeIndex > BuildEulerianPath(const Graph &graph)</div><divclass="ttdoc">Builds an Eulerian path/trail on an undirected graph.</div><divclass="ttdef"><b>Definition:</b><ahref="eulerian__path_8h_source.html#l00138">eulerian_path.h:138</a></div></div>
<divclass="ttc"id="namespaceoperations__research_html"><divclass="ttname"><ahref="namespaceoperations__research.html">operations_research</a></div><divclass="ttdoc">Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in c...</div><divclass="ttdef"><b>Definition:</b><ahref="christofides_8h_source.html#l00033">christofides.h:33</a></div></div>
<divclass="ttc"id="namespaceoperations__research_html_a743d8c9d6f64531bdeb7bbf18023e9d4"><divclass="ttname"><ahref="namespaceoperations__research.html#a743d8c9d6f64531bdeb7bbf18023e9d4">operations_research::BuildEulerianPathFromNode</a></div><divclass="ttdeci">std::vector< NodeIndex > BuildEulerianPathFromNode(const Graph &graph, NodeIndex root)</div><divclass="ttdoc">Builds an Eulerian path/trail on an undirected graph starting from node root.</div><divclass="ttdef"><b>Definition:</b><ahref="eulerian__path_8h_source.html#l00074">eulerian_path.h:74</a></div></div>
<divclass="ttc"id="namespaceoperations__research_html_a6b312dd19c90b2af099e6f159869f7ee"><divclass="ttname"><ahref="namespaceoperations__research.html#a6b312dd19c90b2af099e6f159869f7ee">operations_research::IsSemiEulerianGraph</a></div><divclass="ttdeci">bool IsSemiEulerianGraph(const Graph &graph, std::vector< NodeIndex > *odd_nodes)</div><divclass="ttdoc">Returns true if a graph is Semi-Eulerian, aka at most two of its nodes are of odd degree.</div><divclass="ttdef"><b>Definition:</b><ahref="eulerian__path_8h_source.html#l00055">eulerian_path.h:55</a></div></div>
<divclass="ttc"id="namespaceoperations__research_html_ab1cf773de0cae72d0c44efe5b8f4bb89"><divclass="ttname"><ahref="namespaceoperations__research.html#ab1cf773de0cae72d0c44efe5b8f4bb89">operations_research::IsEulerianGraph</a></div><divclass="ttdeci">bool IsEulerianGraph(const Graph &graph)</div><divclass="ttdoc">Returns true if a graph is Eulerian, aka all its nodes are of even degree.</div><divclass="ttdef"><b>Definition:</b><ahref="eulerian__path_8h_source.html#l00040">eulerian_path.h:40</a></div></div>
<divclass="ttc"id="namespaceoperations__research_html_a0e629e35bfa311b31dd7f5065eb834bb"><divclass="ttname"><ahref="namespaceoperations__research.html#a0e629e35bfa311b31dd7f5065eb834bb">operations_research::NodeIndex</a></div><divclass="ttdeci">int32 NodeIndex</div><divclass="ttdoc">Standard instantiation of ForwardEbertGraph (named 'ForwardStarGraph') of EbertGraph (named 'StarGrap...</div><divclass="ttdef"><b>Definition:</b><ahref="ebert__graph_8h_source.html#l00192">ebert_graph.h:192</a></div></div>
