<ahref="range__minimum__query_8h.html">Go to the documentation of this file.</a><divclass="fragment"><divclass="line"><aname="l00001"></a><spanclass="lineno"> 1</span> <spanclass="comment">// Copyright 2010-2021 Google LLC</span></div><divclass="line"><aname="l00002"></a><spanclass="lineno"> 2</span> <spanclass="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div><divclass="line"><aname="l00003"></a><spanclass="lineno"> 3</span> <spanclass="comment">// you may not use this file except in compliance with the License.</span></div><divclass="line"><aname="l00004"></a><spanclass="lineno"> 4</span> <spanclass="comment">// You may obtain a copy of the License at</span></div><divclass="line"><aname="l00005"></a><spanclass="lineno"> 5</span> <spanclass="comment">//</span></div><divclass="line"><aname="l00006"></a><spanclass="lineno"> 6</span> <spanclass="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div><divclass="line"><aname="l00007"></a><spanclass="lineno"> 7</span> <spanclass="comment">//</span></div><divclass="line"><aname="l00008"></a><spanclass="lineno"> 8</span> <spanclass="comment">// Unless required by applicable law or agreed to in writing, software</span></div><divclass="line"><aname="l00009"></a><spanclass="lineno"> 9</span> <spanclass="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div><divclass="line"><aname="l00010"></a><spanclass="lineno"> 10</span> <spanclass="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div><divclass="line"><aname="l00011"></a><spanclass="lineno"> 11</span> <spanclass="comment">// See the License for the specific language governing permissions and</span></div><divclass="line"><aname="l00012"></a><spanclass="lineno"> 12</span> <spanclass="comment">// limitations under the License.</span></div><divclass="line"><aname="l00013"></a><spanclass="lineno"> 13</span> </div><divclass="line"><aname="l00014"></a><spanclass="lineno"> 14</span> <spanclass="comment">// We use the notation min(arr, i, j) for the minimum arr[x] such that i <= x</span></div><divclass="line"><aname="l00015"></a><spanclass="lineno"> 15</span> <spanclass="comment">// and x < j.</span></div><divclass="line"><aname="l00016"></a><spanclass="lineno"> 16</span> <spanclass="comment">// Range Minimum Query (RMQ) is a data structure preprocessing an array arr so</span></div><divclass="line"><aname="l00017"></a><spanclass="lineno"> 17</span> <spanclass="comment">// that querying min(arr, i, j) takes O(1) time. The preprocessing takes</span></div><divclass="line"><aname="l00018"></a><spanclass="lineno"> 18</span> <spanclass="comment">// O(n*log(n)) time and memory.</span></div><divclass="line"><aname="l00019"></a><spanclass="lineno"> 19</span> </div><divclass="line"><aname="l00020"></a><spanclass="lineno"> 20</span> <spanclass="comment">// Note: There exists an O(n) preprocessing algorithm, but it is considerably</span></div><divclass="line"><aname="l00021"></a><spanclass="lineno"> 21</span> <spanclass="comment">// more involved and the hidden constants behind it are much higher.</span></div><divclass="line"><aname="l00022"></a><spanclass="lineno"> 22</span> <spanclass="comment">//</span></div><divclass="line"><aname="l00023"></a><spanclass="lineno"> 23</span> <spanclass="comment">// The algorithms are well explained in Wikipedia:</span></div><divclass="line"><aname="l00024"></a><spanclass="lineno"> 24</span> <spanclass="comment">// https://en.wikipedia.org/wiki/Range_minimum_query.</span></div><divclass="line"><aname="l00025"></a><spanclass="lineno"> 25</span> <spanclass="comment">//</span></div><divclass="line"><aname="l00026"></a><spanclass="lineno"> 26</span> <spanclass="comment"
<divclass="ttc"id="classoperations__research_1_1_range_minimum_index_query_html_a19e84487ac8cfb253b5ee8ae83a24d59"><divclass="ttname"><ahref="classoperations__research_1_1_range_minimum_index_query.html#a19e84487ac8cfb253b5ee8ae83a24d59">operations_research::RangeMinimumIndexQuery::array</a></div><divclass="ttdeci">const std::vector< T >& array() const</div><divclass="ttdef"><b>Definition:</b><ahref="range__minimum__query_8h_source.html#l00169">range_minimum_query.h:169</a></div></div>
<divclass="ttc"id="classoperations__research_1_1_range_minimum_query_html_a763ae33513a652d6233c8a2c78c75ffd"><divclass="ttname"><ahref="classoperations__research_1_1_range_minimum_query.html#a763ae33513a652d6233c8a2c78c75ffd">operations_research::RangeMinimumQuery::RangeMinimumQuery</a></div><divclass="ttdeci">RangeMinimumQuery(std::vector< T > array)</div><divclass="ttdef"><b>Definition:</b><ahref="range__minimum__query_8h_source.html#l00094">range_minimum_query.h:94</a></div></div>
<divclass="ttc"id="namespaceoperations__research_html"><divclass="ttname"><ahref="namespaceoperations__research.html">operations_research</a></div><divclass="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><divclass="ttdef"><b>Definition:</b><ahref="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
<divclass="ttc"id="classoperations__research_1_1_range_minimum_index_query_html_ac2073ec0893ee9e7d713752213b1fa8a"><divclass="ttname"><ahref="classoperations__research_1_1_range_minimum_index_query.html#ac2073ec0893ee9e7d713752213b1fa8a">operations_research::RangeMinimumIndexQuery::GetMinimumIndexFromRange</a></div><divclass="ttdeci">int GetMinimumIndexFromRange(int from, int to) const</div><divclass="ttdef"><b>Definition:</b><ahref="range__minimum__query_8h_source.html#l00150">range_minimum_query.h:150</a></div></div>
