326 lines
29 KiB
HTML
326 lines
29 KiB
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<div class="headertitle"><div class="title">nurses_cp.cc</div></div>
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<div class="contents">
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<p >List of constraint solver samples:</p>
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<div class="fragment"><div class="line"><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><span class="comment">//</span></div>
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<div class="line"><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><span class="comment">//</span></div>
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<div class="line"><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><span class="comment">// limitations under the License.</span></div>
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<div class="line"> </div>
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<div class="line"><span class="preprocessor">#include <numeric></span> <span class="comment">// std::iota</span></div>
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<div class="line"> </div>
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<div class="line"><span class="preprocessor">#include "absl/flags/flag.h"</span></div>
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<div class="line"><span class="preprocessor">#include "<a class="code" href="init__google_8h.html">ortools/base/init_google.h</a>"</span></div>
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<div class="line"><span class="preprocessor">#include "<a class="code" href="base_2logging_8h.html">ortools/base/logging.h</a>"</span></div>
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<div class="line"><span class="preprocessor">#include "<a class="code" href="logging__flags_8h.html">ortools/base/logging_flags.h</a>"</span></div>
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<div class="line"><span class="preprocessor">#include "<a class="code" href="constraint__solver_8h.html">ortools/constraint_solver/constraint_solver.h</a>"</span></div>
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<div class="line"> </div>
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<div class="line"><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><span class="keywordtype">void</span> SolveNursesExample() {</div>
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<div class="line"> <span class="comment">// Instantiate the solver.</span></div>
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<div class="line"> Solver solver(<span class="stringliteral">"NursesExample"</span>);</div>
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<div class="line"> std::array<int, 4> nurses;</div>
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<div class="line"> std::iota(std::begin(nurses), <a id="a0" name="a0"></a><a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">std::end</a>(nurses), 0);</div>
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<div class="line"> {</div>
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<div class="line"> std::ostringstream oss;</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : nurses) oss << <span class="charliteral">' '</span> << i;</div>
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<div class="line"> <a id="a1" name="a1"></a><a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a id="a2" name="a2"></a><a class="code hl_variable" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) << <span class="stringliteral">"Nurses:"</span> << oss.str();</div>
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<div class="line"> }</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// Nurse assigned to shift 0 means not working that day.</span></div>
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<div class="line"> std::array<int, 4> shifts;</div>
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<div class="line"> std::iota(std::begin(shifts), <a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">std::end</a>(shifts), 0);</div>
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<div class="line"> {</div>
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<div class="line"> std::ostringstream oss;</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : shifts) oss << <span class="charliteral">' '</span> << i;</div>
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<div class="line"> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) << <span class="stringliteral">"Shifts:"</span> << oss.str();</div>
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<div class="line"> }</div>
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<div class="line"> </div>
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<div class="line"> std::array<int, 7> days;</div>
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<div class="line"> std::iota(std::begin(days), <a class="code hl_variable" href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">std::end</a>(days), 0);</div>
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<div class="line"> {</div>
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<div class="line"> std::ostringstream oss;</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">auto</span> i : days) oss << <span class="charliteral">' '</span> << i;</div>
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<div class="line"> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) << <span class="stringliteral">"Days:"</span> << oss.str();</div>
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<div class="line"> }</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// Create shift variables.</span></div>
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<div class="line"> std::vector<std::vector<IntVar*>> shifts_matrix(nurses.size());</div>
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<div class="line"> std::vector<IntVar*> shifts_flat;</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> nurse : nurses) {</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> day : days) {</div>
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<div class="line"> std::ostringstream oss;</div>
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<div class="line"> oss << <span class="stringliteral">"shifts(nurse: "</span> << nurse << <span class="stringliteral">", day: "</span> << day << <span class="stringliteral">")"</span>;</div>
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<div class="line"> IntVar* <a id="a3" name="a3"></a><a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a> = solver.MakeIntVar(shifts.front(), shifts.back(), oss.str());</div>
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<div class="line"> shifts_matrix[nurse].push_back(<a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>);</div>
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<div class="line"> shifts_flat.push_back(<a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>);</div>
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<div class="line"> }</div>
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<div class="line"> }</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// Create nurse variables.</span></div>
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<div class="line"> std::vector<std::vector<IntVar*>> nurses_matrix(shifts.size());</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> shift : shifts) {</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> day : days) {</div>
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<div class="line"> std::ostringstream oss;</div>
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<div class="line"> oss << <span class="stringliteral">"nurses(shift: "</span> << shift << <span class="stringliteral">", day: "</span> << day << <span class="stringliteral">")"</span>;</div>
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<div class="line"> IntVar* <a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a> = solver.MakeIntVar(nurses.front(), nurses.back(), oss.str());</div>
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<div class="line"> nurses_matrix[shift].push_back(<a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>);</div>
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<div class="line"> }</div>
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<div class="line"> }</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// Set relationships between shifts and nurses.</span></div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> day : days) {</div>
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<div class="line"> std::vector<IntVar*> nurses_for_day(shifts.size());</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> shift : shifts) {</div>
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<div class="line"> nurses_for_day[shift] = nurses_matrix[shift][day];</div>
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<div class="line"> }</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> nurse : nurses) {</div>
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<div class="line"> IntVar* s = shifts_matrix[nurse][day];</div>
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<div class="line"> solver.AddConstraint(</div>
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<div class="line"> solver.MakeEquality(solver.MakeElement(nurses_for_day, s), nurse));</div>
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<div class="line"> }</div>
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<div class="line"> }</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// Make assignments different on each day i.e.</span></div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> day : days) {</div>
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<div class="line"> <span class="comment">// no shift can have two nurses</span></div>
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<div class="line"> std::vector<IntVar*> shifts_for_day(nurses.size());</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> nurse : nurses) {</div>
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<div class="line"> shifts_for_day[nurse] = shifts_matrix[nurse][day];</div>
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<div class="line"> }</div>
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<div class="line"> solver.AddConstraint(solver.MakeAllDifferent(shifts_for_day));</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// no nurses can have more than one shifts a day</span></div>
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<div class="line"> std::vector<IntVar*> nurses_for_day(shifts.size());</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> shift : shifts) {</div>
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<div class="line"> nurses_for_day[shift] = nurses_matrix[shift][day];</div>
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<div class="line"> }</div>
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<div class="line"> solver.AddConstraint(solver.MakeAllDifferent(nurses_for_day));</div>
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<div class="line"> }</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// Each nurse works 5 or 6 days in a week.</span></div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> nurse : nurses) {</div>
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<div class="line"> std::vector<IntVar*> nurse_is_working;</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> day : days) {</div>
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<div class="line"> nurse_is_working.push_back(</div>
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<div class="line"> solver.MakeIsGreaterOrEqualCstVar(shifts_matrix[nurse][day], 1));</div>
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<div class="line"> }</div>
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<div class="line"> solver.AddConstraint(solver.MakeSumGreaterOrEqual(nurse_is_working, 5));</div>
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<div class="line"> solver.AddConstraint(solver.MakeSumLessOrEqual(nurse_is_working, 6));</div>
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<div class="line"> }</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// Create works_shift variables.</span></div>
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<div class="line"> <span class="comment">// works_shift_matrix[n][s] is True if</span></div>
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<div class="line"> <span class="comment">// nurse n works shift s at least once during the week.</span></div>
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<div class="line"> std::vector<std::vector<IntVar*>> works_shift_matrix(nurses.size());</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> nurse : nurses) {</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> shift : shifts) {</div>
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<div class="line"> std::ostringstream oss;</div>
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<div class="line"> oss << <span class="stringliteral">"work_shift(nurse: "</span> << nurse << <span class="stringliteral">", shift: "</span> << shift << <span class="stringliteral">")"</span>;</div>
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<div class="line"> works_shift_matrix[nurse].push_back(solver.MakeBoolVar(oss.str()));</div>
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<div class="line"> }</div>
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<div class="line"> }</div>
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<div class="line"> </div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> nurse : nurses) {</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> shift : shifts) {</div>
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<div class="line"> std::vector<IntVar*> shift_s_for_nurse;</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> day : days) {</div>
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<div class="line"> shift_s_for_nurse.push_back(</div>
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<div class="line"> solver.MakeIsEqualCstVar(shifts_matrix[nurse][day], shift));</div>
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<div class="line"> }</div>
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<div class="line"> solver.AddConstraint(</div>
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<div class="line"> solver.MakeEquality(works_shift_matrix[nurse][shift],</div>
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<div class="line"> solver.MakeMax(shift_s_for_nurse)->Var()));</div>
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<div class="line"> }</div>
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<div class="line"> }</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// For each shift(other than 0), at most 2 nurses are assigned to that shift</span></div>
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<div class="line"> <span class="comment">// during the week.</span></div>
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<div class="line"> <span class="keywordflow">for</span> (std::size_t shift = 1; shift < shifts.size(); ++shift) {</div>
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<div class="line"> std::vector<IntVar*> nurses_for_shift;</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> nurse : nurses) {</div>
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<div class="line"> nurses_for_shift.push_back(works_shift_matrix[nurse][shift]);</div>
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<div class="line"> }</div>
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<div class="line"> solver.AddConstraint(solver.MakeSumLessOrEqual(nurses_for_shift, 2));</div>
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<div class="line"> }</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// If a nurse works shifts 2 or 3 on,</span></div>
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<div class="line"> <span class="comment">// he must also work that shift the previous day or the following day.</span></div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> shift : {2, 3}) {</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> day : days) {</div>
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<div class="line"> IntVar* v0 = solver.MakeIsEqualVar(nurses_matrix[shift][day],</div>
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<div class="line"> nurses_matrix[shift][(day + 1) % 7]);</div>
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<div class="line"> IntVar* v1 = solver.MakeIsEqualVar(nurses_matrix[shift][(day + 1) % 7],</div>
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<div class="line"> nurses_matrix[shift][(day + 2) % 7]);</div>
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<div class="line"> solver.AddConstraint(solver.MakeEquality(solver.MakeMax(v0, v1), 1));</div>
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<div class="line"> }</div>
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<div class="line"> }</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// ----- Search monitors and decision builder -----</span></div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// Create the decision builder.</span></div>
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<div class="line"> DecisionBuilder* <span class="keyword">const</span> main_phase = solver.MakePhase(</div>
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<div class="line"> shifts_flat, <a id="a4" name="a4"></a><a class="code hl_enumvalue" href="classoperations__research_1_1_solver.html#ab7ab23bc58ea40dc03a5418ddbce7601a1a148a0aaaad7f56eea42df9876e7ae9">Solver::CHOOSE_FIRST_UNBOUND</a>, <a id="a5" name="a5"></a><a class="code hl_enumvalue" href="classoperations__research_1_1_solver.html#a45c5a2dd0d47110ef5b00408854d8d84a26ee6f4132972f3880a16bf01faf5886">Solver::ASSIGN_MIN_VALUE</a>);</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// Search log.</span></div>
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<div class="line"> SearchMonitor* <span class="keyword">const</span> search_log = <span class="keyword">nullptr</span>;</div>
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<div class="line"> </div>
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<div class="line"> SearchLimit* limit = <span class="keyword">nullptr</span>;</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// Create the solution collector.</span></div>
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<div class="line"> SolutionCollector* <span class="keyword">const</span> collector = solver.MakeAllSolutionCollector();</div>
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<div class="line"> collector->Add(shifts_flat);</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// Solve</span></div>
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<div class="line"> solver.Solve(main_phase, search_log, <span class="keyword">nullptr</span>, limit, collector);</div>
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<div class="line"> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) << <span class="stringliteral">"Number of solutions: "</span> << collector->solution_count();</div>
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<div class="line"> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) << <span class="stringliteral">""</span>;</div>
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<div class="line"> </div>
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<div class="line"> <span class="comment">// Display a few solutions picked at random.</span></div>
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<div class="line"> std::array<int, 4> a_few_solutions = {859, 2034, 5091, 7003};</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> solution : a_few_solutions) {</div>
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<div class="line"> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) << <span class="stringliteral">"Solution "</span> << solution << <span class="stringliteral">":"</span>;</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> day : days) {</div>
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<div class="line"> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) << <span class="stringliteral">"Day "</span> << day << <span class="stringliteral">":"</span>;</div>
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<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span> nurse : nurses) {</div>
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<div class="line"> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) << <span class="stringliteral">"Nurse "</span> << nurse << <span class="stringliteral">" assigned to "</span></div>
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<div class="line"> << <span class="stringliteral">"Task "</span></div>
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<div class="line"> << collector->Value(solution,</div>
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<div class="line"> shifts_flat[nurse * days.size() + day]);</div>
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<div class="line"> }</div>
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<div class="line"> }</div>
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<div class="line"> }</div>
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<div class="line"> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) << <span class="stringliteral">"Advanced usage:"</span>;</div>
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<div class="line"> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) << <span class="stringliteral">"Time: "</span> << solver.wall_time() << <span class="stringliteral">"ms"</span>;</div>
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<div class="line">}</div>
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<div class="line">} <span class="comment">// namespace operations_research</span></div>
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<div class="line"> </div>
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<div class="line"><span class="keywordtype">int</span> <a id="a6" name="a6"></a><a class="code hl_function" href="fz_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a>(<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span>** argv) {</div>
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<div class="line"> <a id="a7" name="a7"></a><a class="code hl_function" href="init__google_8h.html#a16af2bccb0196e1a9bb628559c95b7cb">InitGoogle</a>(argv[0], &argc, &argv, <span class="keyword">true</span>);</div>
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<div class="line"> absl::SetFlag(&FLAGS_logtostderr, <span class="keyword">true</span>);</div>
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<div class="line"> operations_research::SolveNursesExample();</div>
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<div class="line"> <span class="keywordflow">return</span> EXIT_SUCCESS;</div>
|
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<div class="line">}</div>
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<div class="ttc" id="abase_2logging_8h_html"><div class="ttname"><a href="base_2logging_8h.html">logging.h</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_accad43a85d781d53381cd53a9894b6ae"><div class="ttname"><a href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a></div><div class="ttdeci">#define LOG(severity)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00420">base/logging.h:420</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_solver_html_a45c5a2dd0d47110ef5b00408854d8d84a26ee6f4132972f3880a16bf01faf5886"><div class="ttname"><a href="classoperations__research_1_1_solver.html#a45c5a2dd0d47110ef5b00408854d8d84a26ee6f4132972f3880a16bf01faf5886">operations_research::Solver::ASSIGN_MIN_VALUE</a></div><div class="ttdeci">@ ASSIGN_MIN_VALUE</div><div class="ttdoc">Selects the min value of the selected variable.</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_8h_source.html#l00355">constraint_solver.h:355</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_solver_html_ab7ab23bc58ea40dc03a5418ddbce7601a1a148a0aaaad7f56eea42df9876e7ae9"><div class="ttname"><a href="classoperations__research_1_1_solver.html#ab7ab23bc58ea40dc03a5418ddbce7601a1a148a0aaaad7f56eea42df9876e7ae9">operations_research::Solver::CHOOSE_FIRST_UNBOUND</a></div><div class="ttdeci">@ CHOOSE_FIRST_UNBOUND</div><div class="ttdoc">Select the first unbound variable.</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_8h_source.html#l00276">constraint_solver.h:276</a></div></div>
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<div class="ttc" id="aconstraint__solver_8h_html"><div class="ttname"><a href="constraint__solver_8h.html">constraint_solver.h</a></div></div>
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<div class="ttc" id="aexpr__array_8cc_html_a472a99923cbe11ae7b5a5d157d9ad465"><div class="ttname"><a href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a></div><div class="ttdeci">IntVar * var</div><div class="ttdef"><b>Definition:</b> <a href="expr__array_8cc_source.html#l01874">expr_array.cc:1874</a></div></div>
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<div class="ttc" id="afz_8cc_html_a3c04138a5bfe5d72780bb7e82a18e627"><div class="ttname"><a href="fz_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a></div><div class="ttdeci">int main(int argc, char **argv)</div><div class="ttdef"><b>Definition:</b> <a href="fz_8cc_source.html#l00179">fz.cc:179</a></div></div>
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<div class="ttc" id="ainit__google_8h_html"><div class="ttname"><a href="init__google_8h.html">init_google.h</a></div></div>
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<div class="ttc" id="ainit__google_8h_html_a16af2bccb0196e1a9bb628559c95b7cb"><div class="ttname"><a href="init__google_8h.html#a16af2bccb0196e1a9bb628559c95b7cb">InitGoogle</a></div><div class="ttdeci">void InitGoogle(const char *usage, int *argc, char ***argv, bool deprecated)</div><div class="ttdef"><b>Definition:</b> <a href="init__google_8h_source.html#l00032">init_google.h:32</a></div></div>
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<div class="ttc" id="alog__severity_8h_html_ab4a2cbab234914b320b7fae11b6e8cb9"><div class="ttname"><a href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a></div><div class="ttdeci">const int INFO</div><div class="ttdef"><b>Definition:</b> <a href="log__severity_8h_source.html#l00031">log_severity.h:31</a></div></div>
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<div class="ttc" id="alogging__flags_8h_html"><div class="ttname"><a href="logging__flags_8h.html">logging_flags.h</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</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="asparse__submatrix_8cc_html_a4d53eac2ef2732c28fa9fb663e0c19a7"><div class="ttname"><a href="sparse__submatrix_8cc.html#a4d53eac2ef2732c28fa9fb663e0c19a7">end</a></div><div class="ttdeci">std::optional< int64_t > end</div><div class="ttdef"><b>Definition:</b> <a href="sparse__submatrix_8cc_source.html#l00036">sparse_submatrix.cc:36</a></div></div>
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</div><!-- fragment --> </div><!-- contents -->
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