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<div class="title">SimpleMaxFlowProgram.cs</div> </div>
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<a href="SimpleMaxFlowProgram_8cs.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">// [START program]</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="keyword">using</span> System;</div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="keyword">using</span> <a class="code" href="namespaceGoogle.html">Google</a>.<a class="code" href="namespaceGoogle_1_1OrTools.html">OrTools</a>.<a class="code" href="namespaceGoogle_1_1OrTools_1_1Graph.html">Graph</a>;</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"><a class="line" href="classSimpleMaxFlowProgram.html"> 18</a></span> <span class="keyword">public</span> <span class="keyword">class </span><a class="code" href="classSimpleMaxFlowProgram.html">SimpleMaxFlowProgram</a></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> {</div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> Main()</div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  {</div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  <span class="comment">// [START data]</span></div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  <span class="comment">// Define three parallel arrays: start_nodes, end_nodes, and the capacities</span></div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  <span class="comment">// between each pair. For instance, the arc from node 0 to node 1 has a</span></div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  <span class="comment">// capacity of 20.</span></div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="comment">// From Taha's 'Introduction to Operations Research',</span></div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="comment">// example 6.4-2.</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  <span class="keywordtype">int</span>[] startNodes = {0, 0, 0, 1, 1, 2, 2, 3, 3};</div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keywordtype">int</span>[] endNodes = {1, 2, 3, 2, 4, 3, 4, 2, 4};</div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keywordtype">int</span>[] capacities = {20, 30, 10, 40, 30, 10, 20, 5, 20};</div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="comment">// [END data]</span></div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  </div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="comment">// [START constraints]</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="comment">// Instantiate a SimpleMaxFlow solver.</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html">MaxFlow</a> maxFlow = <span class="keyword">new</span> <a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html">MaxFlow</a>();</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  </div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="comment">// Add each arc.</span></div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < startNodes.Length; ++i)</div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  {</div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordtype">int</span> arc = maxFlow.<a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a66eac4815c71eebe1806433677f0254f">AddArcWithCapacity</a>(startNodes[i], endNodes[i],</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  capacities[i]);</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keywordflow">if</span> (arc != i) <span class="keywordflow">throw</span> <span class="keyword">new</span> Exception(<span class="stringliteral">"Internal error"</span>);</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  }</div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="comment">// [END constraints]</span></div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  </div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="comment">// [START solve]</span></div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="comment">// Find the maximum flow between node 0 and node 4.</span></div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html">MaxFlow</a>.<a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a67a0db04d321a74b7e7fcfd3f1a3f70b">Status</a> solveStatus = maxFlow.<a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a5e78274982ba66a0e1d32059b14f4f9b">Solve</a>(0, 4);</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="comment">// [END solve]</span></div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  </div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="comment">// [START print_solution]</span></div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordflow">if</span> (solveStatus == <a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html">MaxFlow</a>.<a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a67a0db04d321a74b7e7fcfd3f1a3f70b">Status</a>.OPTIMAL)</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  {</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  Console.WriteLine(<span class="stringliteral">"Max. flow: "</span> + maxFlow.<a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#aed1e8fa4267c0a2360847a2f8fd1ee95">OptimalFlow</a>());</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  Console.WriteLine(<span class="stringliteral">""</span>);</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  Console.WriteLine(<span class="stringliteral">" Arc Flow / Capacity"</span>);</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < maxFlow.<a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a84633dc5be4b4ebf2bde7f60e664ed52">NumArcs</a>(); ++i)</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>  Console.WriteLine(maxFlow.<a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#af78c832e5a9d686751aff0d21ac8f3e4">Tail</a>(i) + <span class="stringliteral">" -> "</span> +</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  maxFlow.<a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#ad6ab95970447703dcf73d01dda07a3d2">Head</a>(i) + <span class="stringliteral">" "</span> +</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keywordtype">string</span>.Format(<span class="stringliteral">"{0,3}"</span>, maxFlow.<a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a4db64727a4ade79cd3e10b10966a88a9">Flow</a>(i)) + <span class="stringliteral">" / "</span> +</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordtype">string</span>.Format(<span class="stringliteral">"{0,3}"</span>, maxFlow.<a class="code" href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a6812340dd92c7eaf5c34080fce687db6">Capacity</a>(i)));</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  }</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="keywordflow">else</span></div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  {</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  Console.WriteLine(<span class="stringliteral">"Solving the max flow problem failed. Solver status: "</span> +</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  solveStatus);</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  }</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">// [END print_solution]</span></div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  }</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> }</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// [END program]</span></div>
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</div><!-- fragment --></div><!-- contents -->
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<div class="ttc" id="aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_a5e78274982ba66a0e1d32059b14f4f9b"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a5e78274982ba66a0e1d32059b14f4f9b">Google.OrTools.Graph.MaxFlow.Solve</a></div><div class="ttdeci">MaxFlow.Status Solve(int source, int sink)</div><div class="ttdef"><b>Definition:</b> <a href="MaxFlow_8cs_source.html#l00080">MaxFlow.cs:80</a></div></div>
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<div class="ttc" id="anamespaceGoogle_1_1OrTools_1_1Graph_html"><div class="ttname"><a href="namespaceGoogle_1_1OrTools_1_1Graph.html">Google.OrTools.Graph</a></div><div class="ttdef"><b>Definition:</b> <a href="LinearSumAssignment_8cs_source.html#l00011">LinearSumAssignment.cs:11</a></div></div>
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<div class="ttc" id="aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_a66eac4815c71eebe1806433677f0254f"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a66eac4815c71eebe1806433677f0254f">Google.OrTools.Graph.MaxFlow.AddArcWithCapacity</a></div><div class="ttdeci">int AddArcWithCapacity(int tail, int head, long capacity)</div><div class="ttdef"><b>Definition:</b> <a href="MaxFlow_8cs_source.html#l00050">MaxFlow.cs:50</a></div></div>
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<div class="ttc" id="aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_a4db64727a4ade79cd3e10b10966a88a9"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a4db64727a4ade79cd3e10b10966a88a9">Google.OrTools.Graph.MaxFlow.Flow</a></div><div class="ttdeci">long Flow(int arc)</div><div class="ttdef"><b>Definition:</b> <a href="MaxFlow_8cs_source.html#l00090">MaxFlow.cs:90</a></div></div>
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<div class="ttc" id="anamespaceGoogle_html"><div class="ttname"><a href="namespaceGoogle.html">Google</a></div><div class="ttdef"><b>Definition:</b> <a href="KInt64Vector_8cs_source.html#l00011">KInt64Vector.cs:11</a></div></div>
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<div class="ttc" id="aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html">Google.OrTools.Graph.MaxFlow</a></div><div class="ttdef"><b>Definition:</b> <a href="MaxFlow_8cs_source.html#l00013">MaxFlow.cs:13</a></div></div>
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<div class="ttc" id="aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_a84633dc5be4b4ebf2bde7f60e664ed52"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a84633dc5be4b4ebf2bde7f60e664ed52">Google.OrTools.Graph.MaxFlow.NumArcs</a></div><div class="ttdeci">int NumArcs()</div><div class="ttdef"><b>Definition:</b> <a href="MaxFlow_8cs_source.html#l00060">MaxFlow.cs:60</a></div></div>
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<div class="ttc" id="aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_a67a0db04d321a74b7e7fcfd3f1a3f70b"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a67a0db04d321a74b7e7fcfd3f1a3f70b">Google.OrTools.Graph.MaxFlow.Status</a></div><div class="ttdeci">Status</div><div class="ttdef"><b>Definition:</b> <a href="MaxFlow_8cs_source.html#l00095">MaxFlow.cs:95</a></div></div>
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<div class="ttc" id="aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_ad6ab95970447703dcf73d01dda07a3d2"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#ad6ab95970447703dcf73d01dda07a3d2">Google.OrTools.Graph.MaxFlow.Head</a></div><div class="ttdeci">int Head(int arc)</div><div class="ttdef"><b>Definition:</b> <a href="MaxFlow_8cs_source.html#l00070">MaxFlow.cs:70</a></div></div>
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<div class="ttc" id="aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_aed1e8fa4267c0a2360847a2f8fd1ee95"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#aed1e8fa4267c0a2360847a2f8fd1ee95">Google.OrTools.Graph.MaxFlow.OptimalFlow</a></div><div class="ttdeci">long OptimalFlow()</div><div class="ttdef"><b>Definition:</b> <a href="MaxFlow_8cs_source.html#l00085">MaxFlow.cs:85</a></div></div>
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<div class="ttc" id="aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_a6812340dd92c7eaf5c34080fce687db6"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#a6812340dd92c7eaf5c34080fce687db6">Google.OrTools.Graph.MaxFlow.Capacity</a></div><div class="ttdeci">long Capacity(int arc)</div><div class="ttdef"><b>Definition:</b> <a href="MaxFlow_8cs_source.html#l00075">MaxFlow.cs:75</a></div></div>
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<div class="ttc" id="aclassSimpleMaxFlowProgram_html"><div class="ttname"><a href="classSimpleMaxFlowProgram.html">SimpleMaxFlowProgram</a></div><div class="ttdef"><b>Definition:</b> <a href="SimpleMaxFlowProgram_8cs_source.html#l00018">SimpleMaxFlowProgram.cs:18</a></div></div>
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<div class="ttc" id="anamespaceGoogle_1_1OrTools_html"><div class="ttname"><a href="namespaceGoogle_1_1OrTools.html">Google.OrTools</a></div><div class="ttdef"><b>Definition:</b> <a href="KInt64Vector_8cs_source.html#l00011">KInt64Vector.cs:11</a></div></div>
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<div class="ttc" id="aclassGoogle_1_1OrTools_1_1Graph_1_1MaxFlow_html_af78c832e5a9d686751aff0d21ac8f3e4"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Graph_1_1MaxFlow.html#af78c832e5a9d686751aff0d21ac8f3e4">Google.OrTools.Graph.MaxFlow.Tail</a></div><div class="ttdeci">int Tail(int arc)</div><div class="ttdef"><b>Definition:</b> <a href="MaxFlow_8cs_source.html#l00065">MaxFlow.cs:65</a></div></div>
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</div>
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</div>
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<div id="footer-container">
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<div id="footer">
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</div>
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</div>
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</body>
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</html>
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