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<a href="BinPackingProblemSat_8java.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span>&#160;<span class="comment">// Copyright 2010-2018 Google LLC</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span>&#160;<span class="comment">// Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span></div><div class="line"><a name="l00003"></a><span class="lineno"> 3</span>&#160;<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>&#160;<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>&#160;<span class="comment">//</span></div><div class="line"><a name="l00006"></a><span class="lineno"> 6</span>&#160;<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>&#160;<span class="comment">//</span></div><div class="line"><a name="l00008"></a><span class="lineno"> 8</span>&#160;<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>&#160;<span class="comment">// distributed under the License is distributed on an &quot;AS IS&quot; BASIS,</span></div><div class="line"><a name="l00010"></a><span class="lineno"> 10</span>&#160;<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>&#160;<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>&#160;<span class="comment">// limitations under the License.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span>&#160;</div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span>&#160;<span class="keyword">import</span> <a class="code" href="namespacecom.html">com</a>.<a class="code" href="namespacecom_1_1google.html">google</a>.<a class="code" href="namespacecom_1_1google_1_1ortools.html">ortools</a>.<a class="code" href="namespacecom_1_1google_1_1ortools_1_1sat.html">sat</a>.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html">CpModel</a>;</div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span>&#160;<span class="keyword">import</span> <a class="code" href="namespacecom.html">com</a>.<a class="code" href="namespacecom_1_1google.html">google</a>.<a class="code" href="namespacecom_1_1google_1_1ortools.html">ortools</a>.<a class="code" href="namespacecom_1_1google_1_1ortools_1_1sat.html">sat</a>.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html">CpSolver</a>;</div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span>&#160;<span class="keyword">import</span> <a class="code" href="namespacecom.html">com</a>.<a class="code" href="namespacecom_1_1google.html">google</a>.<a class="code" href="namespacecom_1_1google_1_1ortools.html">ortools</a>.<a class="code" href="namespacecom_1_1google_1_1ortools_1_1sat.html">sat</a>.<a class="code" href="enumcom_1_1google_1_1ortools_1_1sat_1_1CpSolverStatus.html">CpSolverStatus</a>;</div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160;<span class="keyword">import</span> <a class="code" href="namespacecom.html">com</a>.<a class="code" href="namespacecom_1_1google.html">google</a>.<a class="code" href="namespacecom_1_1google_1_1ortools.html">ortools</a>.<a class="code" href="namespacecom_1_1google_1_1ortools_1_1sat.html">sat</a>.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1IntVar.html">IntVar</a>;</div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="keyword">import</span> <a class="code" href="namespacecom.html">com</a>.<a class="code" href="namespacecom_1_1google.html">google</a>.<a class="code" href="namespacecom_1_1google_1_1ortools.html">ortools</a>.<a class="code" href="namespacecom_1_1google_1_1ortools_1_1sat.html">sat</a>.<a class="code" href="interfacecom_1_1google_1_1ortools_1_1sat_1_1LinearExpr.html">LinearExpr</a>;</div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160;</div><div class="line"><a name="l00021"></a><span class="lineno"><a class="line" href="classBinPackingProblemSat.html"> 21</a></span>&#160;<span class="keyword">public</span> <span class="keyword">class </span><a class="code" href="classBinPackingProblemSat.html">BinPackingProblemSat</a> {</div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160; <span class="keyword">static</span> {</div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; System.loadLibrary(<span class="stringliteral">&quot;jniortools&quot;</span>);</div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; }</div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160;</div><div class="line"><a name="l00026"></a><span class="lineno"><a class="line" href="classBinPackingProblemSat.html#afa9e5ac747bed45c6c2b421e3c8bcf21"> 26</a></span>&#160; <span class="keyword">public</span> <span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code" href="classBinPackingProblemSat.html#afa9e5ac747bed45c6c2b421e3c8bcf21">main</a>(String[] args) <span class="keywordflow">throws</span> Exception {</div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <span class="comment">// Data.</span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; <span class="keywordtype">int</span> binCapacity = 100;</div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keywordtype">int</span> slackCapacity = 20;</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="keywordtype">int</span> numBins = 5;</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160;</div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <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="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordtype">int</span> numItems = items.length;</div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160;</div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <span class="comment">// Model.</span></div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html">CpModel</a> model = <span class="keyword">new</span> <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html">CpModel</a>();</div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160;</div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; <span class="comment">// Main variables.</span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1IntVar.html">IntVar</a>[][] x = <span class="keyword">new</span> <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1IntVar.html">IntVar</a>[numItems][numBins];</div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; numItems; ++i) {</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="keywordtype">int</span> numCopies = items[i][1];</div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b &lt; numBins; ++b) {</div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; x[i][b] = model.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#a78e6aa0bcdec9be8fc0d39c46b94d851">newIntVar</a>(0, numCopies, <span class="stringliteral">&quot;x_&quot;</span> + i + <span class="stringliteral">&quot;_&quot;</span> + b);</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; }</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; }</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160;</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="comment">// Load variables.</span></div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1IntVar.html">IntVar</a>[] load = <span class="keyword">new</span> <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1IntVar.html">IntVar</a>[numBins];</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b &lt; numBins; ++b) {</div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; load[b] = model.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#a78e6aa0bcdec9be8fc0d39c46b94d851">newIntVar</a>(0, binCapacity, <span class="stringliteral">&quot;load_&quot;</span> + b);</div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; }</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160;</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <span class="comment">// Slack variables.</span></div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1IntVar.html">IntVar</a>[] slacks = <span class="keyword">new</span> <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1IntVar.html">IntVar</a>[numBins];</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b &lt; numBins; ++b) {</div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; slacks[b] = model.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#a08ef439d15caa1e1a1a713d20edaa8a6">newBoolVar</a>(<span class="stringliteral">&quot;slack_&quot;</span> + b);</div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; }</div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;</div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="comment">// Links load and x.</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordtype">int</span>[] sizes = <span class="keyword">new</span> <span class="keywordtype">int</span>[numItems];</div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; numItems; ++i) {</div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; sizes[i] = items[i][0];</div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; }</div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b &lt; numBins; ++b) {</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1IntVar.html">IntVar</a>[] vars = <span class="keyword">new</span> <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1IntVar.html">IntVar</a>[numItems];</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; numItems; ++i) {</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; vars[i] = x[i][b];</div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; }</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; model.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#a0868f8bc35ae63fb326d569e50df1dea">addEquality</a>(<a class="code" href="interfacecom_1_1google_1_1ortools_1_1sat_1_1LinearExpr.html">LinearExpr</a>.<a class="code" href="interfacecom_1_1google_1_1ortools_1_1sat_1_1LinearExpr.html#a3d9212f8954f9eab6a2c29fd7d5155cc">scalProd</a>(vars, sizes), load[b]);</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; }</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160;</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="comment">// Place all items.</span></div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; numItems; ++i) {</div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1IntVar.html">IntVar</a>[] vars = <span class="keyword">new</span> <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1IntVar.html">IntVar</a>[numBins];</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b &lt; numBins; ++b) {</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; vars[b] = x[i][b];</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; }</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; model.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#a0868f8bc35ae63fb326d569e50df1dea">addEquality</a>(<a class="code" href="interfacecom_1_1google_1_1ortools_1_1sat_1_1LinearExpr.html">LinearExpr</a>.<a class="code" href="interfacecom_1_1google_1_1ortools_1_1sat_1_1LinearExpr.html#a91bf9e3c160333c55934d430c4b6a763">sum</a>(vars), items[i][1]);</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; }</div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160;</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <span class="comment">// Links load and slack.</span></div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="keywordtype">int</span> safeCapacity = binCapacity - slackCapacity;</div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b &lt; numBins; ++b) {</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="comment">// slack[b] =&gt; load[b] &lt;= safeCapacity.</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; model.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#aa6ca2dd3953a03ee98a2e9d3a21b128d">addLessOrEqual</a>(load[b], safeCapacity).<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1Constraint.html#ac86aa1f6eb0c1e93c11162475c1b39f8">onlyEnforceIf</a>(slacks[b]);</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <span class="comment">// not(slack[b]) =&gt; load[b] &gt; safeCapacity.</span></div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; model.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#aa1b6332d3c8a47f50381b356717c0ddc">addGreaterOrEqual</a>(load[b], safeCapacity + 1).<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1Constraint.html#ac86aa1f6eb0c1e93c11162475c1b39f8">onlyEnforceIf</a>(slacks[b].not());</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; }</div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160;</div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; <span class="comment">// Maximize sum of slacks.</span></div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; model.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#acb34d552ea6355d29e95f087cf0da722">maximize</a>(<a class="code" href="interfacecom_1_1google_1_1ortools_1_1sat_1_1LinearExpr.html">LinearExpr</a>.<a class="code" href="interfacecom_1_1google_1_1ortools_1_1sat_1_1LinearExpr.html#a91bf9e3c160333c55934d430c4b6a763">sum</a>(slacks));</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160;</div><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="comment">// Solves and prints out the solution.</span></div><div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html">CpSolver</a> solver = <span class="keyword">new</span> <a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html">CpSolver</a>();</div><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <a class="code" href="enumcom_1_1google_1_1ortools_1_1sat_1_1CpSolverStatus.html">CpSolverStatus</a> status = solver.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html#aad90759e27de74339bfb97c3f31bc509">solve</a>(model);</div><div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; System.out.println(<span class="stringliteral">&quot;Solve status: &quot;</span> + status);</div><div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="keywordflow">if</span> (status == <a class="code" href="enumcom_1_1google_1_1ortools_1_1sat_1_1CpSolverStatus.html">CpSolverStatus</a>.<a class="code" href="enumcom_1_1google_1_1ortools_1_1sat_1_1CpSolverStatus.html#af0c586bfb4b5c079c8f94fde2c878337">OPTIMAL</a>) {</div><div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; System.out.printf(<span class="stringliteral">&quot;Optimal objective value: %f%n&quot;</span>, solver.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html#a9b7c07281602ed5206bf5eb7f57bd063">objectiveValue</a>());</div><div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> b = 0; b &lt; numBins; ++b) {</div><div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; System.out.printf(<span class="stringliteral">&quot;load_%d = %d%n&quot;</span>, b, solver.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html#afec653ca08cdff3ec58642c199bbdb55">value</a>(load[b]));</div><div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; numItems; ++i) {</div><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; System.out.printf(<span class="stringliteral">&quot; item_%d_%d = %d%n&quot;</span>, i, b, solver.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html#afec653ca08cdff3ec58642c199bbdb55">value</a>(x[i][b]));</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; }</div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; }</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; }</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; System.out.println(<span class="stringliteral">&quot;Statistics&quot;</span>);</div><div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; System.out.println(<span class="stringliteral">&quot; - conflicts : &quot;</span> + solver.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html#a529ec05c15cfb3ecdb30f3331e32fd4b">numConflicts</a>());</div><div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; System.out.println(<span class="stringliteral">&quot; - branches : &quot;</span> + solver.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html#a3d6654a7d7606fe5f81ab3be7a3f8cfa">numBranches</a>());</div><div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; System.out.println(<span class="stringliteral">&quot; - wall time : &quot;</span> + solver.<a class="code" href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html#a25f9fb12f1b0d0cd22a71763b470b4d9">wallTime</a>() + <span class="stringliteral">&quot; s&quot;</span>);</div><div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; }</div><div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160;}</div><div class="ttc" id="namespacecom_1_1google_1_1ortools_1_1sat_html"><div class="ttname"><a href="namespacecom_1_1google_1_1ortools_1_1sat.html">com.google.ortools.sat</a></div><div class="ttdef"><b>Definition:</b> <a href="AllDifferentConstraintProto_8java_source.html#l00004">AllDifferentConstraintProto.java:4</a></div></div>
<div class="ttc" id="interfacecom_1_1google_1_1ortools_1_1sat_1_1LinearExpr_html"><div class="ttname"><a href="interfacecom_1_1google_1_1ortools_1_1sat_1_1LinearExpr.html">com.google.ortools.sat.LinearExpr</a></div><div class="ttdoc">A linear expression interface that can be parsed.</div><div class="ttdef"><b>Definition:</b> <a href="LinearExpr_8java_source.html#l00017">LinearExpr.java:17</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1Constraint_html_ac86aa1f6eb0c1e93c11162475c1b39f8"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1Constraint.html#ac86aa1f6eb0c1e93c11162475c1b39f8">com.google.ortools.sat.Constraint.onlyEnforceIf</a></div><div class="ttdeci">void onlyEnforceIf(Literal lit)</div><div class="ttdoc">Adds a literal to the constraint.</div><div class="ttdef"><b>Definition:</b> <a href="com_2google_2ortools_2sat_2Constraint_8java_source.html#l00032">com/google/ortools/sat/Constraint.java:32</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel_html_a0868f8bc35ae63fb326d569e50df1dea"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#a0868f8bc35ae63fb326d569e50df1dea">com.google.ortools.sat.CpModel.addEquality</a></div><div class="ttdeci">Constraint addEquality(LinearExpr expr, long value)</div><div class="ttdoc">Adds.</div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8java_source.html#l00153">CpModel.java:153</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver_html"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html">com.google.ortools.sat.CpSolver</a></div><div class="ttdoc">Wrapper around the SAT solver.</div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8java_source.html#l00026">CpSolver.java:26</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel_html_a78e6aa0bcdec9be8fc0d39c46b94d851"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#a78e6aa0bcdec9be8fc0d39c46b94d851">com.google.ortools.sat.CpModel.newIntVar</a></div><div class="ttdeci">IntVar newIntVar(long lb, long ub, String name)</div><div class="ttdoc">Creates an integer variable with domain [lb, ub].</div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8java_source.html#l00069">CpModel.java:69</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver_html_a9b7c07281602ed5206bf5eb7f57bd063"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html#a9b7c07281602ed5206bf5eb7f57bd063">com.google.ortools.sat.CpSolver.objectiveValue</a></div><div class="ttdeci">double objectiveValue()</div><div class="ttdoc">Returns the best objective value found during search.</div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8java_source.html#l00066">CpSolver.java:66</a></div></div>
<div class="ttc" id="namespacecom_html"><div class="ttname"><a href="namespacecom.html">com</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel_html_a08ef439d15caa1e1a1a713d20edaa8a6"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#a08ef439d15caa1e1a1a713d20edaa8a6">com.google.ortools.sat.CpModel.newBoolVar</a></div><div class="ttdeci">IntVar newBoolVar(String name)</div><div class="ttdoc">Creates a Boolean variable with the given name.</div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8java_source.html#l00085">CpModel.java:85</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver_html_afec653ca08cdff3ec58642c199bbdb55"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html#afec653ca08cdff3ec58642c199bbdb55">com.google.ortools.sat.CpSolver.value</a></div><div class="ttdeci">long value(IntVar var)</div><div class="ttdoc">Returns the value of a variable in the last solution found.</div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8java_source.html#l00079">CpSolver.java:79</a></div></div>
<div class="ttc" id="enumcom_1_1google_1_1ortools_1_1sat_1_1CpSolverStatus_html"><div class="ttname"><a href="enumcom_1_1google_1_1ortools_1_1sat_1_1CpSolverStatus.html">com.google.ortools.sat.CpSolverStatus</a></div><div class="ttdef"><b>Definition:</b> <a href="CpSolverStatus_8java_source.html#l00013">CpSolverStatus.java:13</a></div></div>
<div class="ttc" id="namespacecom_1_1google_1_1ortools_html"><div class="ttname"><a href="namespacecom_1_1google_1_1ortools.html">com.google.ortools</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver_html_a529ec05c15cfb3ecdb30f3331e32fd4b"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html#a529ec05c15cfb3ecdb30f3331e32fd4b">com.google.ortools.sat.CpSolver.numConflicts</a></div><div class="ttdeci">long numConflicts()</div><div class="ttdoc">Returns the number of conflicts created during search.</div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8java_source.html#l00104">CpSolver.java:104</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel_html_aa1b6332d3c8a47f50381b356717c0ddc"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#aa1b6332d3c8a47f50381b356717c0ddc">com.google.ortools.sat.CpModel.addGreaterOrEqual</a></div><div class="ttdeci">Constraint addGreaterOrEqual(LinearExpr expr, long value)</div><div class="ttdoc">Adds.</div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8java_source.html#l00194">CpModel.java:194</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1IntVar_html"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1IntVar.html">com.google.ortools.sat.IntVar</a></div><div class="ttdoc">An integer variable.</div><div class="ttdef"><b>Definition:</b> <a href="com_2google_2ortools_2sat_2IntVar_8java_source.html#l00021">com/google/ortools/sat/IntVar.java:21</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel_html"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html">com.google.ortools.sat.CpModel</a></div><div class="ttdoc">Main modeling class.</div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8java_source.html#l00040">CpModel.java:40</a></div></div>
<div class="ttc" id="interfacecom_1_1google_1_1ortools_1_1sat_1_1LinearExpr_html_a3d9212f8954f9eab6a2c29fd7d5155cc"><div class="ttname"><a href="interfacecom_1_1google_1_1ortools_1_1sat_1_1LinearExpr.html#a3d9212f8954f9eab6a2c29fd7d5155cc">com.google.ortools.sat.LinearExpr.scalProd</a></div><div class="ttdeci">static LinearExpr scalProd(IntVar[] variables, long[] coefficients)</div><div class="ttdoc">Creates a scalar product.</div><div class="ttdef"><b>Definition:</b> <a href="LinearExpr_8java_source.html#l00033">LinearExpr.java:33</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel_html_aa6ca2dd3953a03ee98a2e9d3a21b128d"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#aa6ca2dd3953a03ee98a2e9d3a21b128d">com.google.ortools.sat.CpModel.addLessOrEqual</a></div><div class="ttdeci">Constraint addLessOrEqual(LinearExpr expr, long value)</div><div class="ttdoc">Adds.</div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8java_source.html#l00168">CpModel.java:168</a></div></div>
<div class="ttc" id="namespacecom_1_1google_html"><div class="ttname"><a href="namespacecom_1_1google.html">com.google</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel_html_acb34d552ea6355d29e95f087cf0da722"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpModel.html#acb34d552ea6355d29e95f087cf0da722">com.google.ortools.sat.CpModel.maximize</a></div><div class="ttdeci">void maximize(LinearExpr expr)</div><div class="ttdoc">Adds a maximization objective of a linear expression.</div><div class="ttdef"><b>Definition:</b> <a href="CpModel_8java_source.html#l00967">CpModel.java:967</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver_html_a3d6654a7d7606fe5f81ab3be7a3f8cfa"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html#a3d6654a7d7606fe5f81ab3be7a3f8cfa">com.google.ortools.sat.CpSolver.numBranches</a></div><div class="ttdeci">long numBranches()</div><div class="ttdoc">Returns the number of branches explored during search.</div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8java_source.html#l00099">CpSolver.java:99</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver_html_a25f9fb12f1b0d0cd22a71763b470b4d9"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html#a25f9fb12f1b0d0cd22a71763b470b4d9">com.google.ortools.sat.CpSolver.wallTime</a></div><div class="ttdeci">double wallTime()</div><div class="ttdoc">Returns the wall time of the search.</div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8java_source.html#l00109">CpSolver.java:109</a></div></div>
<div class="ttc" id="classBinPackingProblemSat_html"><div class="ttname"><a href="classBinPackingProblemSat.html">BinPackingProblemSat</a></div><div class="ttdoc">Solves a bin packing problem with the CP-SAT solver.</div><div class="ttdef"><b>Definition:</b> <a href="BinPackingProblemSat_8java_source.html#l00021">BinPackingProblemSat.java:21</a></div></div>
<div class="ttc" id="interfacecom_1_1google_1_1ortools_1_1sat_1_1LinearExpr_html_a91bf9e3c160333c55934d430c4b6a763"><div class="ttname"><a href="interfacecom_1_1google_1_1ortools_1_1sat_1_1LinearExpr.html#a91bf9e3c160333c55934d430c4b6a763">com.google.ortools.sat.LinearExpr.sum</a></div><div class="ttdeci">static LinearExpr sum(IntVar[] variables)</div><div class="ttdoc">Creates a sum expression.</div><div class="ttdef"><b>Definition:</b> <a href="LinearExpr_8java_source.html#l00028">LinearExpr.java:28</a></div></div>
<div class="ttc" id="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver_html_aad90759e27de74339bfb97c3f31bc509"><div class="ttname"><a href="classcom_1_1google_1_1ortools_1_1sat_1_1CpSolver.html#aad90759e27de74339bfb97c3f31bc509">com.google.ortools.sat.CpSolver.solve</a></div><div class="ttdeci">CpSolverStatus solve(CpModel model)</div><div class="ttdoc">Solves the given module, and returns the solve status.</div><div class="ttdef"><b>Definition:</b> <a href="CpSolver_8java_source.html#l00033">CpSolver.java:33</a></div></div>
<div class="ttc" id="enumcom_1_1google_1_1ortools_1_1sat_1_1CpSolverStatus_html_af0c586bfb4b5c079c8f94fde2c878337"><div class="ttname"><a href="enumcom_1_1google_1_1ortools_1_1sat_1_1CpSolverStatus.html#af0c586bfb4b5c079c8f94fde2c878337">com.google.ortools.sat.CpSolverStatus.OPTIMAL</a></div><div class="ttdeci">OPTIMAL</div><div class="ttdef"><b>Definition:</b> <a href="CpSolverStatus_8java_source.html#l00059">CpSolverStatus.java:59</a></div></div>
<div class="ttc" id="classBinPackingProblemSat_html_afa9e5ac747bed45c6c2b421e3c8bcf21"><div class="ttname"><a href="classBinPackingProblemSat.html#afa9e5ac747bed45c6c2b421e3c8bcf21">BinPackingProblemSat.main</a></div><div class="ttdeci">static void main(String[] args)</div><div class="ttdef"><b>Definition:</b> <a href="BinPackingProblemSat_8java_source.html#l00026">BinPackingProblemSat.java:26</a></div></div>
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