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<p>Implementation of <a href="https://en.wikipedia.org/wiki/Range_minimum_query" target="_blank">Sparse Table</a> data structure.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for sparse_table.cpp:</div>
<div class="dyncontent">
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Namespaces</h2></td></tr>
<tr class="memitem:dd/d69/namespacerange__queries"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d69/namespacerange__queries.html">range_queries</a></td></tr>
<tr class="memdesc:dd/d69/namespacerange__queries"><td class="mdescLeft">&#160;</td><td class="mdescRight">Algorithms and Data Structures that support range queries and updates. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:d9/d55/namespacesparse__table"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d55/namespacesparse__table.html">sparse_table</a></td></tr>
<tr class="memdesc:d9/d55/namespacesparse__table"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a40810d8c0fe3f8cf432ab128b1ae0300"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a40810d8c0fe3f8cf432ab128b1ae0300"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d4/d96/range__queries_2sparse__table_8cpp.html#a40810d8c0fe3f8cf432ab128b1ae0300">range_queries::sparse_table::computeLogs</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;A)</td></tr>
<tr class="separator:a40810d8c0fe3f8cf432ab128b1ae0300"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a803a2451e87021d14ae06f148383e6bc"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a803a2451e87021d14ae06f148383e6bc"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d4/d96/range__queries_2sparse__table_8cpp.html#a803a2451e87021d14ae06f148383e6bc">range_queries::sparse_table::buildTable</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;A, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;logs)</td></tr>
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<tr class="memitem:a932816c3de9e5ad122b180de60978e8f"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a932816c3de9e5ad122b180de60978e8f"><td class="memTemplItemLeft" align="right" valign="top">int&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d4/d96/range__queries_2sparse__table_8cpp.html#a932816c3de9e5ad122b180de60978e8f">range_queries::sparse_table::getMinimum</a> (int beg, int end, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;logs, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &gt; &amp;table)</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/d96/range__queries_2sparse__table_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation of <a href="https://en.wikipedia.org/wiki/Range_minimum_query" target="_blank">Sparse Table</a> data structure. </p>
<p>Sparse Table is a data structure, that allows answering range queries. It can answer most range queries in O(logn), but its true power is answering range minimum queries or equivalent range maximum queries). For those queries it can compute the answer in O(1) time.</p>
<ul>
<li>Running Time Complexity <br />
</li>
<li>Build : O(NlogN) <br />
</li>
<li>Range Query : O(1) <br />
</li>
</ul>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a803a2451e87021d14ae06f148383e6bc" name="a803a2451e87021d14ae06f148383e6bc"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a803a2451e87021d14ae06f148383e6bc">&#9670;&#160;</a></span>buildTable()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename T &gt; </div>
<table class="memname">
<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &gt; range_queries::sparse_table::buildTable </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;&#160;</td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;&#160;</td>
<td class="paramname"><em>logs</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>This functions builds the primary data structure sparse table </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>value of the size of the input array </td></tr>
<tr><td class="paramname">A</td><td>array of the input integers </td></tr>
<tr><td class="paramname">logs</td><td>array of the log table </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>created sparse table data structure </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 57</span> {</div>
<div class="line"><span class="lineno"> 58</span> <span class="keywordtype">int</span> n = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 59</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;T&gt;</a> &gt; table(20, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a>(n + 5, 0));</div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordtype">int</span> curLen = 0;</div>
<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= logs[n]; i++) {</div>
<div class="line"><span class="lineno"> 62</span> curLen = 1 &lt;&lt; i;</div>
<div class="line"><span class="lineno"> 63</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j + curLen &lt; n; j++) {</div>
<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">if</span> (curLen == 1) {</div>
<div class="line"><span class="lineno"> 65</span> table[i][j] = A[j];</div>
<div class="line"><span class="lineno"> 66</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 67</span> table[i][j] =</div>
<div class="line"><span class="lineno"> 68</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(table[i - 1][j], table[i - 1][j + curLen / 2]);</div>
<div class="line"><span class="lineno"> 69</span> }</div>
<div class="line"><span class="lineno"> 70</span> }</div>
<div class="line"><span class="lineno"> 71</span> }</div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordflow">return</span> table;</div>
<div class="line"><span class="lineno"> 73</span>}</div>
<div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a40810d8c0fe3f8cf432ab128b1ae0300">&#9670;&#160;</a></span>computeLogs()</h2>
<div class="memitem">
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template&lt;typename T &gt; </div>
<table class="memname">
<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; range_queries::sparse_table::computeLogs </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;&#160;</td>
<td class="paramname"><em>A</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>This function precomputes intial log table for further use. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>value of the size of the input array </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>corresponding vector of the log table </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 38</span> {</div>
<div class="line"><span class="lineno"> 39</span> <span class="keywordtype">int</span> n = A.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><span class="lineno"> 40</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;T&gt;</a> logs(n);</div>
<div class="line"><span class="lineno"> 41</span> logs[1] = 0;</div>
<div class="line"><span class="lineno"> 42</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i &lt; n; i++) {</div>
<div class="line"><span class="lineno"> 43</span> logs[i] = logs[i / 2] + 1;</div>
<div class="line"><span class="lineno"> 44</span> }</div>
<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">return</span> logs;</div>
<div class="line"><span class="lineno"> 46</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a932816c3de9e5ad122b180de60978e8f">&#9670;&#160;</a></span>getMinimum()</h2>
<div class="memitem">
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template&lt;typename T &gt; </div>
<table class="memname">
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<td class="memname">int range_queries::sparse_table::getMinimum </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>beg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>end</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &amp;&#160;</td>
<td class="paramname"><em>logs</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; T &gt; &gt; &amp;&#160;</td>
<td class="paramname"><em>table</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>This function is the query function to get the range minimum value </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">beg</td><td>beginning index of the query range </td></tr>
<tr><td class="paramname">end</td><td>ending index of the query range </td></tr>
<tr><td class="paramname">logs</td><td>array of the log table </td></tr>
<tr><td class="paramname">table</td><td>sparse table data structure for the input array </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>minimum value for the [beg, end] range for the input array </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 85</span> {</div>
<div class="line"><span class="lineno"> 86</span> <span class="keywordtype">int</span> p = logs[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> - beg + 1];</div>
<div class="line"><span class="lineno"> 87</span> <span class="keywordtype">int</span> pLen = 1 &lt;&lt; p;</div>
<div class="line"><span class="lineno"> 88</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(table[p][beg], table[p][end - pLen + 1]);</div>
<div class="line"><span class="lineno"> 89</span>}</div>
<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a></div><div class="ttdeci">T end(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<p>Main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 96</span> {</div>
<div class="line"><span class="lineno"> 97</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> A{1, 2, 0, 3, 9};</div>
<div class="line"><span class="lineno"> 98</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> logs = <a class="code hl_function" href="../../d4/d96/range__queries_2sparse__table_8cpp.html#a40810d8c0fe3f8cf432ab128b1ae0300">range_queries::sparse_table::computeLogs</a>(A);</div>
<div class="line"><span class="lineno"> 99</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;int&gt;</a> &gt; table =</div>
<div class="line"><span class="lineno"> 100</span> <a class="code hl_function" href="../../d4/d96/range__queries_2sparse__table_8cpp.html#a803a2451e87021d14ae06f148383e6bc">range_queries::sparse_table::buildTable</a>(A, logs);</div>
<div class="line"><span class="lineno"> 101</span> assert(range_queries::sparse_table::getMinimum(0, 0, logs, table) == 1);</div>
<div class="line"><span class="lineno"> 102</span> assert(range_queries::sparse_table::getMinimum(0, 4, logs, table) == 0);</div>
<div class="line"><span class="lineno"> 103</span> assert(range_queries::sparse_table::getMinimum(2, 4, logs, table) == 0);</div>
<div class="line"><span class="lineno"> 104</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 105</span>}</div>
<div class="ttc" id="arange__queries_2sparse__table_8cpp_html_a40810d8c0fe3f8cf432ab128b1ae0300"><div class="ttname"><a href="../../d4/d96/range__queries_2sparse__table_8cpp.html#a40810d8c0fe3f8cf432ab128b1ae0300">range_queries::sparse_table::computeLogs</a></div><div class="ttdeci">std::vector&lt; T &gt; computeLogs(const std::vector&lt; T &gt; &amp;A)</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:38</div></div>
<div class="ttc" id="arange__queries_2sparse__table_8cpp_html_a803a2451e87021d14ae06f148383e6bc"><div class="ttname"><a href="../../d4/d96/range__queries_2sparse__table_8cpp.html#a803a2451e87021d14ae06f148383e6bc">range_queries::sparse_table::buildTable</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; T &gt; &gt; buildTable(const std::vector&lt; T &gt; &amp;A, const std::vector&lt; T &gt; &amp;logs)</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:56</div></div>
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