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295 lines
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<div class="headertitle"><div class="title">range_minimum_query.h</div></div>
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<a href="range__minimum__query_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment">// We use the notation min(arr, i, j) for the minimum arr[x] such that i <= x</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment">// and x < j.</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment">// Range Minimum Query (RMQ) is a data structure preprocessing an array arr so</span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">// that querying min(arr, i, j) takes O(1) time. The preprocessing takes</span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">// O(n*log(n)) time and memory.</span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment">// Note: There exists an O(n) preprocessing algorithm, but it is considerably</span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment">// more involved and the hidden constants behind it are much higher.</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment">//</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment">// The algorithms are well explained in Wikipedia:</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment">// https://en.wikipedia.org/wiki/Range_minimum_query.</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment">//</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">//</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">// Implementation: The idea is to cache every min(arr, i, j) where j - i is a</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">// power of two, i.e. j = i + 2^k for some k. Provided this information, we can</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">// answer all queries in O(1): given a pair (i, j) find the maximum k such that</span></div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">// i + 2^k < j and note that</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">// std::min(min(arr, i, i+2^k), min(arr, j-2^k, j)) = min(arr, i, j).</span></div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> </div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor">#ifndef OR_TOOLS_UTIL_RANGE_MINIMUM_QUERY_H_</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="preprocessor">#define OR_TOOLS_UTIL_RANGE_MINIMUM_QUERY_H_</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> </div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="preprocessor">#include <algorithm></span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="preprocessor">#include <functional></span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="preprocessor">#include <numeric></span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="preprocessor">#include <utility></span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> </div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="preprocessor">#include "<a class="code" href="bitset_8h.html">ortools/util/bitset.h</a>"</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> </div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><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"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="keyword">template</span> <<span class="keyword">typename</span> T, <span class="keyword">typename</span> Compare = std::less<T>></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_range_minimum_query.html"> 46</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1_range_minimum_query.html">RangeMinimumQuery</a> {</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keyword">explicit</span> <a class="code hl_function" href="classoperations__research_1_1_range_minimum_query.html#a763ae33513a652d6233c8a2c78c75ffd">RangeMinimumQuery</a>(std::vector<T> <a class="code hl_function" href="classoperations__research_1_1_range_minimum_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">array</a>);</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <a class="code hl_function" href="classoperations__research_1_1_range_minimum_query.html#a763ae33513a652d6233c8a2c78c75ffd">RangeMinimumQuery</a>(std::vector<T> <a class="code hl_function" href="classoperations__research_1_1_range_minimum_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">array</a>, Compare cmp);</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// Returns the minimum (w.r.t. Compare) arr[x], where x is contained in</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// [from, to).</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> T <a class="code hl_function" href="classoperations__research_1_1_range_minimum_query.html#a20bd6e147a4ff92b8290e3c9bc7e366a">GetMinimumFromRange</a>(<span class="keywordtype">int</span> from, <span class="keywordtype">int</span> to) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keyword">const</span> std::vector<T>& <a class="code hl_function" href="classoperations__research_1_1_range_minimum_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">array</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="comment">// cache_[k][i] = min(arr, i, i+2^k).</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> std::vector<std::vector<T>> cache_;</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> Compare cmp_;</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> </div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> DISALLOW_COPY_AND_ASSIGN(<a class="code hl_class" href="classoperations__research_1_1_range_minimum_query.html">RangeMinimumQuery</a>);</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span>};</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="comment">// RangeMinimumIndexQuery is similar to RangeMinimumQuery, but</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment">// GetMinimumIndexFromRange returns the index for which the minimum is attained.</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="keyword">template</span> <<span class="keyword">typename</span> T, <span class="keyword">typename</span> Compare = std::less<T>></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_range_minimum_index_query.html"> 68</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1_range_minimum_index_query.html">RangeMinimumIndexQuery</a> {</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keyword">explicit</span> <a class="code hl_function" href="classoperations__research_1_1_range_minimum_index_query.html#a74499390c02d0f270713377a4300999d">RangeMinimumIndexQuery</a>(std::vector<T> <a class="code hl_function" href="classoperations__research_1_1_range_minimum_index_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">array</a>);</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <a class="code hl_function" href="classoperations__research_1_1_range_minimum_index_query.html#a74499390c02d0f270713377a4300999d">RangeMinimumIndexQuery</a>(std::vector<T> <a class="code hl_function" href="classoperations__research_1_1_range_minimum_index_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">array</a>, Compare cmp);</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> </div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// Returns an index idx from [from, to) such that arr[idx] is the minimum</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">// value of arr over the interval [from, to).</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordtype">int</span> <a class="code hl_function" href="classoperations__research_1_1_range_minimum_index_query.html#ac2073ec0893ee9e7d713752213b1fa8a">GetMinimumIndexFromRange</a>(<span class="keywordtype">int</span> from, <span class="keywordtype">int</span> to) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// Returns the original array.</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keyword">const</span> std::vector<T>& <a class="code hl_function" href="classoperations__research_1_1_range_minimum_index_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">array</a>() <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// Returns a vector with values 0, 1, ... n - 1 for a given n.</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keyword">static</span> std::vector<int> CreateIndexVector(<span class="keywordtype">int</span> n);</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keyword">struct </span>IndexComparator {</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordtype">bool</span> operator()(<span class="keywordtype">int</span> lhs_idx, <span class="keywordtype">int</span> rhs_idx) <span class="keyword">const</span>;</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keyword">const</span> std::vector<T> <a class="code hl_function" href="classoperations__research_1_1_range_minimum_index_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">array</a>;</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> Compare cmp;</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> } cmp_;</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1_range_minimum_query.html">RangeMinimumQuery<int, IndexComparator></a> rmq_;</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> DISALLOW_COPY_AND_ASSIGN(<a class="code hl_class" href="classoperations__research_1_1_range_minimum_index_query.html">RangeMinimumIndexQuery</a>);</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span>};</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span><span class="comment">// RangeMinimumQuery implementation</span></div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span><span class="keyword">template</span> <<span class="keyword">typename</span> T, <span class="keyword">typename</span> Compare></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_range_minimum_query.html#a763ae33513a652d6233c8a2c78c75ffd"> 94</a></span><span class="keyword">inline</span> <a class="code hl_function" href="classoperations__research_1_1_range_minimum_query.html#a763ae33513a652d6233c8a2c78c75ffd">RangeMinimumQuery<T, Compare>::RangeMinimumQuery</a>(std::vector<T> array)</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> : <a class="code hl_class" href="classoperations__research_1_1_range_minimum_query.html">RangeMinimumQuery</a>(<a class="code hl_namespace" href="namespacestd.html">std</a>::move(array), Compare()) {}</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> </div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment">// Reminder: The task is to fill cache_ so that</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment">// cache_[k][i] = min(arr, i, i+2^k) for every k <= Log2(n) and i <= n-2^k.</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="comment">// Note that cache_[k+1][i] = min(cache_[k][i], cache_[k][i+2^k]), hence every</span></div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span><span class="comment">// row can be efficiently computed from the previous.</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span><span class="keyword">template</span> <<span class="keyword">typename</span> T, <span class="keyword">typename</span> Compare></div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_range_minimum_query.html#a465072ee13cc92eb72c9201039672065"> 102</a></span><a class="code hl_function" href="classoperations__research_1_1_range_minimum_query.html#a763ae33513a652d6233c8a2c78c75ffd">RangeMinimumQuery<T, Compare>::RangeMinimumQuery</a>(std::vector<T> array,</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> Compare cmp)</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> : cache_(<a class="code hl_function" href="namespaceoperations__research.html#ac2dd49087312b4acbda94f5c6cb668f7">MostSignificantBitPosition32</a>(array.size()) + 1),</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> cmp_(<a class="code hl_namespace" href="namespacestd.html">std</a>::move(cmp)) {</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keyword">const</span> <span class="keywordtype">int</span> array_size = <a class="code hl_function" href="classoperations__research_1_1_range_minimum_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">array</a>.size();</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> cache_[0] = std::move(<a class="code hl_function" href="classoperations__research_1_1_range_minimum_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">array</a>);</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> row_idx = 1; row_idx < cache_.size(); ++row_idx) {</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keyword">const</span> <span class="keywordtype">int</span> row_length = array_size - (1 << row_idx) + 1;</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keyword">const</span> <span class="keywordtype">int</span> window = 1 << (row_idx - 1);</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> cache_[row_idx].resize(row_length);</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> col_idx = 0; col_idx < row_length; ++col_idx) {</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> cache_[row_idx][col_idx] =</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(cache_[row_idx - 1][col_idx],</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> cache_[row_idx - 1][col_idx + window], cmp_);</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> }</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> }</div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span>}</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> </div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="keyword">template</span> <<span class="keyword">typename</span> T, <span class="keyword">typename</span> Compare></div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_range_minimum_query.html#a20bd6e147a4ff92b8290e3c9bc7e366a"> 121</a></span><span class="keyword">inline</span> T <a class="code hl_function" href="classoperations__research_1_1_range_minimum_query.html#a20bd6e147a4ff92b8290e3c9bc7e366a">RangeMinimumQuery<T, Compare>::GetMinimumFromRange</a>(<span class="keywordtype">int</span> from,</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordtype">int</span> to)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <a class="code hl_define" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(0, from);</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <a class="code hl_define" href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a>(from, to);</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <a class="code hl_define" href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a>(to, array().size());</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keyword">const</span> <span class="keywordtype">int</span> log_diff = <a class="code hl_function" href="namespaceoperations__research.html#ac2dd49087312b4acbda94f5c6cb668f7">MostSignificantBitPosition32</a>(to - from);</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keyword">const</span> <span class="keywordtype">int</span> window = 1 << log_diff;</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keyword">const</span> std::vector<T>& <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a> = cache_[log_diff];</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(<a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>[from], <a class="code hl_variable" href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a>[to - window], cmp_);</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span>}</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> </div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span><span class="keyword">template</span> <<span class="keyword">typename</span> T, <span class="keyword">typename</span> Compare></div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_range_minimum_query.html#a19e84487ac8cfb253b5ee8ae83a24d59"> 133</a></span><span class="keyword">inline</span> <span class="keyword">const</span> std::vector<T>& <a class="code hl_function" href="classoperations__research_1_1_range_minimum_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">RangeMinimumQuery<T, Compare>::array</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keywordflow">return</span> cache_[0];</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span>}</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> </div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span><span class="comment">// RangeMinimumIndexQuery implementation</span></div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span><span class="keyword">template</span> <<span class="keyword">typename</span> T, <span class="keyword">typename</span> Compare></div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_range_minimum_index_query.html#a74499390c02d0f270713377a4300999d"> 139</a></span><span class="keyword">inline</span> <a class="code hl_function" href="classoperations__research_1_1_range_minimum_index_query.html#a74499390c02d0f270713377a4300999d">RangeMinimumIndexQuery<T, Compare>::RangeMinimumIndexQuery</a>(</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> std::vector<T> array)</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> : <a class="code hl_class" href="classoperations__research_1_1_range_minimum_index_query.html">RangeMinimumIndexQuery</a>(<a class="code hl_namespace" href="namespacestd.html">std</a>::move(array), Compare()) {}</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> </div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="keyword">template</span> <<span class="keyword">typename</span> T, <span class="keyword">typename</span> Compare></div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_range_minimum_index_query.html#af6a1139c873366ba6d987a051312ab3f"> 144</a></span><a class="code hl_function" href="classoperations__research_1_1_range_minimum_index_query.html#a74499390c02d0f270713377a4300999d">RangeMinimumIndexQuery<T, Compare>::RangeMinimumIndexQuery</a>(std::vector<T> array,</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> Compare cmp)</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> : cmp_({std::move(<a class="code hl_function" href="classoperations__research_1_1_range_minimum_index_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">array</a>), std::move(cmp)}),</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> rmq_(CreateIndexVector(cmp_.array.size()), cmp_) {}</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> </div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span><span class="keyword">template</span> <<span class="keyword">typename</span> T, <span class="keyword">typename</span> Compare></div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_range_minimum_index_query.html#ac2073ec0893ee9e7d713752213b1fa8a"> 150</a></span><span class="keyword">inline</span> <span class="keywordtype">int</span> <a class="code hl_function" href="classoperations__research_1_1_range_minimum_index_query.html#ac2073ec0893ee9e7d713752213b1fa8a">RangeMinimumIndexQuery<T, Compare>::GetMinimumIndexFromRange</a>(</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keywordtype">int</span> from, <span class="keywordtype">int</span> to)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordflow">return</span> rmq_.GetMinimumFromRange(from, to);</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span>}</div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> </div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span><span class="keyword">template</span> <<span class="keyword">typename</span> T, <span class="keyword">typename</span> Compare></div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span><span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code hl_class" href="classoperations__research_1_1_range_minimum_index_query.html">RangeMinimumIndexQuery<T, Compare>::IndexComparator::operator()</a>(</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keywordtype">int</span> lhs_idx, <span class="keywordtype">int</span> rhs_idx)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="keywordflow">return</span> cmp(array[lhs_idx], array[rhs_idx]);</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span>}</div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> </div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span><span class="keyword">template</span> <<span class="keyword">typename</span> T, <span class="keyword">typename</span> Compare></div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span>std::vector<int> RangeMinimumIndexQuery<T, Compare>::CreateIndexVector(<span class="keywordtype">int</span> n) {</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> std::vector<int> result(n, 0);</div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> std::iota(result.begin(), result.end(), 0);</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <span class="keywordflow">return</span> result;</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span>}</div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> </div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span><span class="keyword">template</span> <<span class="keyword">typename</span> T, <span class="keyword">typename</span> Compare></div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"><a class="line" href="classoperations__research_1_1_range_minimum_index_query.html#a19e84487ac8cfb253b5ee8ae83a24d59"> 169</a></span><span class="keyword">inline</span> <span class="keyword">const</span> std::vector<T>& <a class="code hl_function" href="classoperations__research_1_1_range_minimum_index_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">RangeMinimumIndexQuery<T, Compare>::array</a>()<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> <span class="keywordflow">return</span> cmp_.array;</div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span>}</div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_UTIL_RANGE_MINIMUM_QUERY_H_</span></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_ad10edae0a852d72fb76afb1c77735045"><div class="ttname"><a href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a></div><div class="ttdeci">int64_t min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_a4395e95bab44e222cb2e77251017a0e2"><div class="ttname"><a href="base_2logging_8h.html#a4395e95bab44e222cb2e77251017a0e2">DCHECK_LE</a></div><div class="ttdeci">#define DCHECK_LE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00888">base/logging.h:888</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_ab62f5ed8f2d48e29802be0cbbcd1359a"><div class="ttname"><a href="base_2logging_8h.html#ab62f5ed8f2d48e29802be0cbbcd1359a">DCHECK_LT</a></div><div class="ttdeci">#define DCHECK_LT(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00889">base/logging.h:889</a></div></div>
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<div class="ttc" id="abitset_8h_html"><div class="ttname"><a href="bitset_8h.html">bitset.h</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_range_minimum_index_query_html"><div class="ttname"><a href="classoperations__research_1_1_range_minimum_index_query.html">operations_research::RangeMinimumIndexQuery</a></div><div class="ttdef"><b>Definition:</b> <a href="range__minimum__query_8h_source.html#l00068">range_minimum_query.h:68</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_range_minimum_index_query_html_a19e84487ac8cfb253b5ee8ae83a24d59"><div class="ttname"><a href="classoperations__research_1_1_range_minimum_index_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">operations_research::RangeMinimumIndexQuery::array</a></div><div class="ttdeci">const std::vector< T > & array() const</div><div class="ttdef"><b>Definition:</b> <a href="range__minimum__query_8h_source.html#l00169">range_minimum_query.h:169</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_range_minimum_index_query_html_a74499390c02d0f270713377a4300999d"><div class="ttname"><a href="classoperations__research_1_1_range_minimum_index_query.html#a74499390c02d0f270713377a4300999d">operations_research::RangeMinimumIndexQuery::RangeMinimumIndexQuery</a></div><div class="ttdeci">RangeMinimumIndexQuery(std::vector< T > array)</div><div class="ttdef"><b>Definition:</b> <a href="range__minimum__query_8h_source.html#l00139">range_minimum_query.h:139</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_range_minimum_index_query_html_ac2073ec0893ee9e7d713752213b1fa8a"><div class="ttname"><a href="classoperations__research_1_1_range_minimum_index_query.html#ac2073ec0893ee9e7d713752213b1fa8a">operations_research::RangeMinimumIndexQuery::GetMinimumIndexFromRange</a></div><div class="ttdeci">int GetMinimumIndexFromRange(int from, int to) const</div><div class="ttdef"><b>Definition:</b> <a href="range__minimum__query_8h_source.html#l00150">range_minimum_query.h:150</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_range_minimum_query_html"><div class="ttname"><a href="classoperations__research_1_1_range_minimum_query.html">operations_research::RangeMinimumQuery</a></div><div class="ttdef"><b>Definition:</b> <a href="range__minimum__query_8h_source.html#l00046">range_minimum_query.h:46</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_range_minimum_query_html_a19e84487ac8cfb253b5ee8ae83a24d59"><div class="ttname"><a href="classoperations__research_1_1_range_minimum_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">operations_research::RangeMinimumQuery::array</a></div><div class="ttdeci">const std::vector< T > & array() const</div><div class="ttdef"><b>Definition:</b> <a href="range__minimum__query_8h_source.html#l00133">range_minimum_query.h:133</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_range_minimum_query_html_a763ae33513a652d6233c8a2c78c75ffd"><div class="ttname"><a href="classoperations__research_1_1_range_minimum_query.html#a763ae33513a652d6233c8a2c78c75ffd">operations_research::RangeMinimumQuery::RangeMinimumQuery</a></div><div class="ttdeci">RangeMinimumQuery(std::vector< T > array)</div><div class="ttdef"><b>Definition:</b> <a href="range__minimum__query_8h_source.html#l00094">range_minimum_query.h:94</a></div></div>
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<div class="ttc" id="amarkowitz_8cc_html_aea35f36ba98d5bbd8d033382f50c9e52"><div class="ttname"><a href="markowitz_8cc.html#aea35f36ba98d5bbd8d033382f50c9e52">row</a></div><div class="ttdeci">RowIndex row</div><div class="ttdef"><b>Definition:</b> <a href="markowitz_8cc_source.html#l00182">markowitz.cc:182</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="anamespaceoperations__research_html_ac2dd49087312b4acbda94f5c6cb668f7"><div class="ttname"><a href="namespaceoperations__research.html#ac2dd49087312b4acbda94f5c6cb668f7">operations_research::MostSignificantBitPosition32</a></div><div class="ttdeci">int MostSignificantBitPosition32(uint32_t n)</div><div class="ttdef"><b>Definition:</b> <a href="bitset_8h_source.html#l00273">bitset.h:273</a></div></div>
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