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<li class="navelem"><a class="el" href="dir_a7cc1eeded8f693d0da6c729bc88c45a.html">ortools</a></li><li class="navelem"><a class="el" href="dir_dddac007a45022d9da6ea1dee012c3b9.html">sat</a></li><li class="navelem"><a class="el" href="dir_8005d2da67a7154daa1c0c8b69782d62.html">samples</a></li> </ul>
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<div class="title">BinPackingProblemSat.cs</div> </div>
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<a href="BinPackingProblemSat_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><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="keyword">using</span> System;</div><div class="line"><a name="l00015"></a><span class="lineno"> 15</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_1Sat.html">Sat</a>;</div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div><div class="line"><a name="l00017"></a><span class="lineno"><a class="line" href="classBinPackingProblemSat.html"> 17</a></span> <span class="keyword">public</span> <span class="keyword">class </span><a class="code" href="classBinPackingProblemSat.html">BinPackingProblemSat</a></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="keyword">static</span> <span class="keywordtype">void</span> Main()</div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  {</div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  <span class="comment">// Data.</span></div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  <span class="keywordtype">int</span> bin_capacity = 100;</div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  <span class="keywordtype">int</span> slack_capacity = 20;</div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  <span class="keywordtype">int</span> num_bins = 5;</div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span> </div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="keywordtype">int</span>[,] items = <span class="keyword">new</span> <span class="keywordtype">int</span>[,] { { 20, 6 }, { 15, 6 }, { 30, 4 }, { 45, 3 } };</div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="keywordtype">int</span> num_items = items.GetLength(0);</div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span> </div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="comment">// Model.</span></div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html">CpModel</a> model = <span class="keyword">new</span> <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html">CpModel</a>();</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span> </div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="comment">// Main variables.</span></div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1IntVar.html">IntVar</a>[,] x = <span class="keyword">new</span> <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1IntVar.html">IntVar</a>[num_items, num_bins];</div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_items; ++i)</div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  {</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordtype">int</span> num_copies = items[i, 1];</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b < num_bins; ++b)</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  {</div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  x[i, b] = model.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html#a0e96e31fd021191475ec9008b1b8022f">NewIntVar</a>(0, num_copies, String.Format(<span class="stringliteral">"x_{0}_{1}"</span>, i, b));</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  }</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  }</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span> </div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="comment">// Load variables.</span></div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1IntVar.html">IntVar</a>[] load = <span class="keyword">new</span> <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1IntVar.html">IntVar</a>[num_bins];</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b < num_bins; ++b)</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  {</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  load[b] = model.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html#a0e96e31fd021191475ec9008b1b8022f">NewIntVar</a>(0, bin_capacity, String.Format(<span class="stringliteral">"load_{0}"</span>, b));</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  }</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> </div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="comment">// Slack variables.</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1IntVar.html">IntVar</a>[] slacks = <span class="keyword">new</span> <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1IntVar.html">IntVar</a>[num_bins];</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b < num_bins; ++b)</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  {</div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  slacks[b] = model.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html#aabc77d1b1ef5eed086a385d05b334b15">NewBoolVar</a>(String.Format(<span class="stringliteral">"slack_{0}"</span>, b));</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  }</div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span> </div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="comment">// Links load and x.</span></div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keywordtype">int</span>[] sizes = <span class="keyword">new</span> <span class="keywordtype">int</span>[num_items];</div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_items; ++i)</div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  {</div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  sizes[i] = items[i, 0];</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="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b < num_bins; ++b)</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  {</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1IntVar.html">IntVar</a>[] tmp = <span class="keyword">new</span> <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1IntVar.html">IntVar</a>[num_items];</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_items; ++i)</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  {</div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  tmp[i] = x[i, b];</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  }</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  model.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html#ae9082049e3e606979b1f76cabce037ec">Add</a>(load[b] == tmp.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1LinearExpr.html#afac2f2ce8e925932a09fb21bcafb0f7b">ScalProd</a>(sizes));</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> </div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="comment">// Place all items.</span></div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_items; ++i)</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  {</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1IntVar.html">IntVar</a>[] tmp = <span class="keyword">new</span> <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1IntVar.html">IntVar</a>[num_bins];</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b < num_bins; ++b)</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  {</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  tmp[b] = x[i, b];</div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  }</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  model.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html#ae9082049e3e606979b1f76cabce037ec">Add</a>(<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1LinearExpr.html">LinearExpr</a>.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1LinearExpr.html#ad96e88c200476e5c6ee55b5266219abe">Sum</a>(tmp) == items[i, 1]);</div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  }</div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span> </div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="comment">// Links load and slack.</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordtype">int</span> safe_capacity = bin_capacity - slack_capacity;</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b < num_bins; ++b)</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  {</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="comment">// slack[b] => load[b] <= safe_capacity.</span></div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  model.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html#ae9082049e3e606979b1f76cabce037ec">Add</a>(load[b] <= safe_capacity).<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1Constraint.html#ad1b0d13e53d3d3ffcb5d52176d5b7da1">OnlyEnforceIf</a>(slacks[b]);</div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="comment">// not(slack[b]) => load[b] > safe_capacity.</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  model.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html#ae9082049e3e606979b1f76cabce037ec">Add</a>(load[b] > safe_capacity).<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1Constraint.html#ad1b0d13e53d3d3ffcb5d52176d5b7da1">OnlyEnforceIf</a>(slacks[b].Not());</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  }</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span> </div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="comment">// Maximize sum of slacks.</span></div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  model.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html#ad95f4beaa7861fabb203a54c9744a406">Maximize</a>(<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1LinearExpr.html">LinearExpr</a>.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1LinearExpr.html#ad96e88c200476e5c6ee55b5266219abe">Sum</a>(slacks));</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span> </div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="comment">// Solves and prints out the solution.</span></div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html">CpSolver</a> solver = <span class="keyword">new</span> <a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html">CpSolver</a>();</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <a class="code" href="namespaceGoogle_1_1OrTools_1_1Sat.html#aa595d3031f0d84a540d17c50a43ad040">CpSolverStatus</a> status = solver.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html#a839735ac35ab3931bc63f220ff8fca40">Solve</a>(model);</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  Console.WriteLine(String.Format(<span class="stringliteral">"Solve status: {0}"</span>, status));</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keywordflow">if</span> (status == <a class="code" href="namespaceGoogle_1_1OrTools_1_1Sat.html#aa595d3031f0d84a540d17c50a43ad040">CpSolverStatus</a>.Optimal) {</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  Console.WriteLine(String.Format(<span class="stringliteral">"Optimal objective value: {0}"</span>,</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  solver.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html#a39a3749a67eb8cc805ae70bac32dcd2f">ObjectiveValue</a>));</div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b < num_bins; ++b)</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  {</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  Console.WriteLine(String.Format(<span class="stringliteral">"load_{0} = {1}"</span>,</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  b, solver.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html#adf7a9fa17e43afbf7fcc4470038e09a3">Value</a>(load[b])));</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_items; ++i)</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  {</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  Console.WriteLine(<span class="keywordtype">string</span>.Format(<span class="stringliteral">" item_{0}_{1} = {2}"</span>,</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  i, b, solver.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html#adf7a9fa17e43afbf7fcc4470038e09a3">Value</a>(x[i, b])));</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>  }</div><div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  }</div><div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  Console.WriteLine(<span class="stringliteral">"Statistics"</span>);</div><div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  Console.WriteLine(String.Format(<span class="stringliteral">" - conflicts : {0}"</span>,</div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  solver.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html#a7693b6f79a632169e6013a684e571ca1">NumConflicts</a>()));</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  Console.WriteLine(String.Format(<span class="stringliteral">" - branches : {0}"</span>,</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  solver.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html#a5c344afdabaea460cab201cd9170a9a0">NumBranches</a>()));</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  Console.WriteLine(String.Format(<span class="stringliteral">" - wall time : {0} s"</span>,</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  solver.<a class="code" href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html#a7dd451e39ae41daf2dc9832ef93cf485">WallTime</a>()));</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="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1CpModel_html_ad95f4beaa7861fabb203a54c9744a406"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html#ad95f4beaa7861fabb203a54c9744a406">Google.OrTools.Sat.CpModel.Maximize</a></div><div class="ttdeci">void Maximize(LinearExpr obj)</div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8cs_source.html#l00588">CpModel.cs:588</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver_html_adf7a9fa17e43afbf7fcc4470038e09a3"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html#adf7a9fa17e43afbf7fcc4470038e09a3">Google.OrTools.Sat.CpSolver.Value</a></div><div class="ttdeci">long Value(LinearExpr e)</div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8cs_source.html#l00096">CpSolver.cs:96</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1IntVar_html"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1IntVar.html">Google.OrTools.Sat.IntVar</a></div><div class="ttdef"><b>Definition:</b> <a href="IntegerExpressions_8cs_source.html#l00495">IntegerExpressions.cs:495</a></div></div>
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<div class="ttc" id="namespaceGoogle_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="classGoogle_1_1OrTools_1_1Sat_1_1CpModel_html_ae9082049e3e606979b1f76cabce037ec"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html#ae9082049e3e606979b1f76cabce037ec">Google.OrTools.Sat.CpModel.Add</a></div><div class="ttdeci">Constraint Add(BoundedLinearExpression lin)</div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8cs_source.html#l00104">CpModel.cs:104</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver_html_a39a3749a67eb8cc805ae70bac32dcd2f"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html#a39a3749a67eb8cc805ae70bac32dcd2f">Google.OrTools.Sat.CpSolver.ObjectiveValue</a></div><div class="ttdeci">double ObjectiveValue</div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8cs_source.html#l00076">CpSolver.cs:76</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1LinearExpr_html_ad96e88c200476e5c6ee55b5266219abe"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1LinearExpr.html#ad96e88c200476e5c6ee55b5266219abe">Google.OrTools.Sat.LinearExpr.Sum</a></div><div class="ttdeci">static LinearExpr Sum(IEnumerable< IntVar > vars)</div><div class="ttdef"><b>Definition:</b> <a href="IntegerExpressions_8cs_source.html#l00052">IntegerExpressions.cs:52</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver_html_a5c344afdabaea460cab201cd9170a9a0"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html#a5c344afdabaea460cab201cd9170a9a0">Google.OrTools.Sat.CpSolver.NumBranches</a></div><div class="ttdeci">long NumBranches()</div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8cs_source.html#l00173">CpSolver.cs:173</a></div></div>
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<div class="ttc" id="namespaceGoogle_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="classGoogle_1_1OrTools_1_1Sat_1_1CpModel_html"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html">Google.OrTools.Sat.CpModel</a></div><div class="ttdoc">Wrapper class around the cp_model proto.</div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8cs_source.html#l00023">CpModel.cs:23</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver_html_a7dd451e39ae41daf2dc9832ef93cf485"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html#a7dd451e39ae41daf2dc9832ef93cf485">Google.OrTools.Sat.CpSolver.WallTime</a></div><div class="ttdeci">double WallTime()</div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8cs_source.html#l00183">CpSolver.cs:183</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1LinearExpr_html_afac2f2ce8e925932a09fb21bcafb0f7b"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1LinearExpr.html#afac2f2ce8e925932a09fb21bcafb0f7b">Google.OrTools.Sat.LinearExpr.ScalProd</a></div><div class="ttdeci">static LinearExpr ScalProd(IEnumerable< IntVar > vars, IEnumerable< int > coeffs)</div><div class="ttdef"><b>Definition:</b> <a href="IntegerExpressions_8cs_source.html#l00062">IntegerExpressions.cs:62</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver_html_a7693b6f79a632169e6013a684e571ca1"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html#a7693b6f79a632169e6013a684e571ca1">Google.OrTools.Sat.CpSolver.NumConflicts</a></div><div class="ttdeci">long NumConflicts()</div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8cs_source.html#l00178">CpSolver.cs:178</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver_html_a839735ac35ab3931bc63f220ff8fca40"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html#a839735ac35ab3931bc63f220ff8fca40">Google.OrTools.Sat.CpSolver.Solve</a></div><div class="ttdeci">CpSolverStatus Solve(CpModel model)</div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8cs_source.html#l00022">CpSolver.cs:22</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1CpModel_html_aabc77d1b1ef5eed086a385d05b334b15"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html#aabc77d1b1ef5eed086a385d05b334b15">Google.OrTools.Sat.CpModel.NewBoolVar</a></div><div class="ttdeci">IntVar NewBoolVar(string name)</div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8cs_source.html#l00067">CpModel.cs:67</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1LinearExpr_html"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1LinearExpr.html">Google.OrTools.Sat.LinearExpr</a></div><div class="ttdef"><b>Definition:</b> <a href="IntegerExpressions_8cs_source.html#l00049">IntegerExpressions.cs:49</a></div></div>
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<div class="ttc" id="namespaceGoogle_1_1OrTools_1_1Sat_html_aa595d3031f0d84a540d17c50a43ad040"><div class="ttname"><a href="namespaceGoogle_1_1OrTools_1_1Sat.html#aa595d3031f0d84a540d17c50a43ad040">Google.OrTools.Sat.CpSolverStatus</a></div><div class="ttdeci">CpSolverStatus</div><div class="ttdoc">The status returned by a solver trying to solve a CpModelProto.</div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8pb_8cs_source.html#l00172">CpModel.pb.cs:172</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1CpModel_html_a0e96e31fd021191475ec9008b1b8022f"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1CpModel.html#a0e96e31fd021191475ec9008b1b8022f">Google.OrTools.Sat.CpModel.NewIntVar</a></div><div class="ttdeci">IntVar NewIntVar(long lb, long ub, string name)</div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8cs_source.html#l00045">CpModel.cs:45</a></div></div>
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<div class="ttc" id="namespaceGoogle_1_1OrTools_1_1Sat_html"><div class="ttname"><a href="namespaceGoogle_1_1OrTools_1_1Sat.html">Google.OrTools.Sat</a></div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8pb_8cs_source.html#l00012">CpModel.pb.cs:12</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver_html"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1CpSolver.html">Google.OrTools.Sat.CpSolver</a></div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8cs_source.html#l00019">CpSolver.cs:19</a></div></div>
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<div class="ttc" id="classBinPackingProblemSat_html"><div class="ttname"><a href="classBinPackingProblemSat.html">BinPackingProblemSat</a></div><div class="ttdef"><b>Definition:</b> <a href="BinPackingProblemSat_8cs_source.html#l00017">BinPackingProblemSat.cs:17</a></div></div>
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<div class="ttc" id="classGoogle_1_1OrTools_1_1Sat_1_1Constraint_html_ad1b0d13e53d3d3ffcb5d52176d5b7da1"><div class="ttname"><a href="classGoogle_1_1OrTools_1_1Sat_1_1Constraint.html#ad1b0d13e53d3d3ffcb5d52176d5b7da1">Google.OrTools.Sat.Constraint.OnlyEnforceIf</a></div><div class="ttdeci">void OnlyEnforceIf(ILiteral lit)</div><div class="ttdef"><b>Definition:</b> <a href="Constraints_8cs_source.html#l00028">Constraints.cs:28</a></div></div>
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