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<span id="sfml">Google OR-Tools 8.2</span>
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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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<li><a href="../cpp_sat/annotated.html">CP-SAT</a></li>
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<h1 style="color: #145A32;">C++ Reference: Algorithms</h1>
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<div class="title">hungarian.h</div> </div>
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<a href="hungarian_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">//</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// IMPORTANT NOTE: we advise using the code in</span></div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// graph/linear_assignment.h whose complexity is</span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">// usually much smaller.</span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">// TODO(user): base this code on LinearSumAssignment.</span></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">// For each of the four functions declared in this file, in case the input</span></div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">// parameter 'cost' contains NaN, the function will return without invoking the</span></div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">// Hungarian algorithm, and the output parameters 'direct_assignment' and</span></div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">// 'reverse_assignment' will be left unchanged.</span></div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">//</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="comment">// An O(n^4) implementation of the Kuhn-Munkres algorithm (a.k.a. the</span></div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// Hungarian algorithm) for solving the assignment problem.</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// The assignment problem takes a set of agents, a set of tasks and a</span></div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">// cost associated with assigning each agent to each task and produces</span></div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">// an optimal (i.e., least cost) assignment of agents to tasks.</span></div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// The code also enables computing a maximum assignment by changing the</span></div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// input matrix.</span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// This code is based on (read: translated from) the Java version</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// (read: translated from) the Python version at</span></div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// http://www.clapper.org/software/python/munkres/.</span></div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  </div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="preprocessor">#ifndef OR_TOOLS_ALGORITHMS_HUNGARIAN_H_</span></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="preprocessor">#define OR_TOOLS_ALGORITHMS_HUNGARIAN_H_</span></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="preprocessor">#include <vector></span></div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  </div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#include "absl/container/flat_hash_map.h"</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  </div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  </div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// See IMPORTANT NOTE at the top of the file.</span></div>
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<div class="line"><a name="l00048"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#a9c61bb2d6de0894f19675e2110458877"> 48</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research.html#a9c61bb2d6de0894f19675e2110458877">MinimizeLinearAssignment</a>(</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keyword">const</span> std::vector<std::vector<double> >& cost,</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  absl::flat_hash_map<int, int>* direct_assignment,</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  absl::flat_hash_map<int, int>* reverse_assignment);</div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  </div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// See IMPORTANT NOTE at the top of the file.</span></div>
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<div class="line"><a name="l00054"></a><span class="lineno"><a class="line" href="namespaceoperations__research.html#ada8ccc36ef736b10ce389fbd347c4282"> 54</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research.html#ada8ccc36ef736b10ce389fbd347c4282">MaximizeLinearAssignment</a>(</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keyword">const</span> std::vector<std::vector<double> >& cost,</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  absl::flat_hash_map<int, int>* direct_assignment,</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  absl::flat_hash_map<int, int>* reverse_assignment);</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  </div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> } <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  </div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_ALGORITHMS_HUNGARIAN_H_</span></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="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html_a9c61bb2d6de0894f19675e2110458877"><div class="ttname"><a href="namespaceoperations__research.html#a9c61bb2d6de0894f19675e2110458877">operations_research::MinimizeLinearAssignment</a></div><div class="ttdeci">void MinimizeLinearAssignment(const std::vector< std::vector< double > > &cost, absl::flat_hash_map< int, int > *direct_assignment, absl::flat_hash_map< int, int > *reverse_assignment)</div></div>
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<div class="ttc" id="anamespaceoperations__research_html_ada8ccc36ef736b10ce389fbd347c4282"><div class="ttname"><a href="namespaceoperations__research.html#ada8ccc36ef736b10ce389fbd347c4282">operations_research::MaximizeLinearAssignment</a></div><div class="ttdeci">void MaximizeLinearAssignment(const std::vector< std::vector< double > > &cost, absl::flat_hash_map< int, int > *direct_assignment, absl::flat_hash_map< int, int > *reverse_assignment)</div></div>
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