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<h2>C++ Reference</h2>
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<li><a href="../cpp_algorithms/annotated.html">Algorithms</a></li>
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<h1 style="color: #145A32;">C++ Reference: Graph</h1>
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<div class="title">shortestpaths.h</div> </div>
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<a href="shortestpaths_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2018 Google LLC</span></div>
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<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div>
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<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  </div>
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<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">// This file contains various shortest paths utilities.</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// Keywords: directed graph, cheapest path, shortest path, Dijkstra, spp.</span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>  </div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#ifndef OR_TOOLS_GRAPH_SHORTESTPATHS_H_</span></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#define OR_TOOLS_GRAPH_SHORTESTPATHS_H_</span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  </div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include <functional></span></div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include <memory></span></div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#include <string></span></div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#include <vector></span></div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  </div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include "ortools/base/integral_types.h"</span></div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include "ortools/base/macros.h"</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  </div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  </div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// Dijsktra Shortest path with callback based description of the</span></div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// graph. The callback returns the distance between two nodes, a</span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// distance of 'disconnected_distance' indicates no arcs between these</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// two nodes. Ownership of the callback is taken by the function that</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// will delete it in the end. This function returns true if</span></div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// 'start_node' and 'end_node' are connected, false otherwise.</span></div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#a53e6a83fcbd689abf5b3078b0236f9f1">DijkstraShortestPath</a>(<span class="keywordtype">int</span> node_count, <span class="keywordtype">int</span> start_node, <span class="keywordtype">int</span> end_node,</div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  std::function<int64(<span class="keywordtype">int</span>, <span class="keywordtype">int</span>)> graph,</div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  int64 disconnected_distance, std::vector<int>* nodes);</div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  </div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// Stable version of the Dijsktra Shortest path with callback based description</span></div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// of the graph. The callback returns the distance between two nodes, a</span></div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// distance of 'disconnected_distance' indicates no arcs between these</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// two nodes. Ownership of the callback is taken by the function that</span></div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// will delete it in the end. This function returns true if</span></div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// 'start_node' and 'end_node' are connected, false otherwise.</span></div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#ad56bae19a2298c3163af96ca7f8b89b1">StableDijkstraShortestPath</a>(<span class="keywordtype">int</span> node_count, <span class="keywordtype">int</span> start_node, <span class="keywordtype">int</span> end_node,</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  std::function<int64(<span class="keywordtype">int</span>, <span class="keywordtype">int</span>)> graph,</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  int64 disconnected_distance,</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  std::vector<int>* nodes);</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  </div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// Bellman-Ford Shortest path with callback-based description of the</span></div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// graph. The callback returns the distance between two nodes, a</span></div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// distance of 'disconnected_distance' indicates no arcs between these</span></div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// two nodes. Ownership of the callback is taken by the function that</span></div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// will delete it in the end. This function returns true if</span></div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// 'start_node' and 'end_node' are connected, false otherwise. If</span></div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// true, it will fill the 'nodes' vector with the sequence of nodes on</span></div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// the shortest path between 'start_node' and 'end_node'.</span></div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#ad5bfec6ea714171fbff2d8b791d0d286">BellmanFordShortestPath</a>(<span class="keywordtype">int</span> node_count, <span class="keywordtype">int</span> start_node, <span class="keywordtype">int</span> end_node,</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  std::function<int64(<span class="keywordtype">int</span>, <span class="keywordtype">int</span>)> graph,</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  int64 disconnected_distance,</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  std::vector<int>* nodes);</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  </div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// A* Shortest path with function based description of the</span></div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">// graph. The graph function returns the distance between two nodes, a</span></div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// distance of 'disconnected_distance' indicates no arcs between these</span></div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// two nodes. Additionally, the heuristic callback returns a</span></div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// an approximate distance between the node and the target, which guides</span></div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// the search. If the heuristic is admissible (ie. never overestimates cost),</span></div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// the A* algorithm returns an optimal solution.</span></div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment">// This function returns true if 'start_node' and 'end_node' are</span></div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// connected, false otherwise.</span></div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research.html#acff272be25bcf9641218c05c59ec1a4e">AStarShortestPath</a>(<span class="keywordtype">int</span> node_count, <span class="keywordtype">int</span> start_node, <span class="keywordtype">int</span> end_node,</div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  std::function<int64(<span class="keywordtype">int</span>, <span class="keywordtype">int</span>)> graph,</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  std::function<int64(<span class="keywordtype">int</span>)> heuristic,</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  int64 disconnected_distance, std::vector<int>* nodes);</div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  </div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  </div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="preprocessor">#endif // OR_TOOLS_GRAPH_SHORTESTPATHS_H_</span></div>
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</div><!-- fragment --></div><!-- contents -->
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<div class="ttc" id="anamespaceoperations__research_html_a53e6a83fcbd689abf5b3078b0236f9f1"><div class="ttname"><a href="namespaceoperations__research.html#a53e6a83fcbd689abf5b3078b0236f9f1">operations_research::DijkstraShortestPath</a></div><div class="ttdeci">bool DijkstraShortestPath(int node_count, int start_node, int end_node, std::function< int64(int, int)> graph, int64 disconnected_distance, std::vector< int > *nodes)</div></div>
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<div class="ttc" id="anamespaceoperations__research_html_ad5bfec6ea714171fbff2d8b791d0d286"><div class="ttname"><a href="namespaceoperations__research.html#ad5bfec6ea714171fbff2d8b791d0d286">operations_research::BellmanFordShortestPath</a></div><div class="ttdeci">bool BellmanFordShortestPath(int node_count, int start_node, int end_node, std::function< int64(int, int)> graph, int64 disconnected_distance, std::vector< int > *nodes)</div></div>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdef"><b>Definition:</b> <a href="christofides_8h_source.html#l00033">christofides.h:33</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_ad56bae19a2298c3163af96ca7f8b89b1"><div class="ttname"><a href="namespaceoperations__research.html#ad56bae19a2298c3163af96ca7f8b89b1">operations_research::StableDijkstraShortestPath</a></div><div class="ttdeci">bool StableDijkstraShortestPath(int node_count, int start_node, int end_node, std::function< int64(int, int)> graph, int64 disconnected_distance, std::vector< int > *nodes)</div></div>
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<div class="ttc" id="anamespaceoperations__research_html_acff272be25bcf9641218c05c59ec1a4e"><div class="ttname"><a href="namespaceoperations__research.html#acff272be25bcf9641218c05c59ec1a4e">operations_research::AStarShortestPath</a></div><div class="ttdeci">bool AStarShortestPath(int node_count, int start_node, int end_node, std::function< int64(int, int)> graph, std::function< int64(int)> heuristic, int64 disconnected_distance, std::vector< int > *nodes)</div></div>
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