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<div class="headertitle"><div class="title">sparse_table.cpp File Reference</div></div>
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<div class="contents">
<p>Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> for <code>min()</code> function.
<p>Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> for <span class="tt">min()</span> function.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;array&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
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<p><a href="../../d8/dab/sparse__table_8cpp_source.html">Go to the source code of this file.</a></p>
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<tr class="memitem:data_5Fstructures_3A_3Asparse_5Ftable_3A_3ASparse_5Ftable" id="r_data_5Fstructures_3A_3Asparse_5Ftable_3A_3ASparse_5Ftable"><td class="memItemLeft" align="right" valign="top">struct &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html">data_structures::sparse_table::Sparse_table</a></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d3c/namespacedata__structures.html">data_structures</a></td></tr>
<tr class="memitem:data_5Fstructures" id="r_data_5Fstructures"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d5/d3c/namespacedata__structures.html">data_structures</a></td></tr>
<tr class="memdesc:d5/d3c/namespacedata__structures"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><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="memitem:sparse_5Ftable" id="r_sparse_5Ftable"><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>
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Functions</h2></td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
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<tr class="memdesc:a0ddf1224851353fc92bfbff6f499fa97"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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Variables</h2></td></tr>
<tr class="memitem:a10f3ffb3f6f7e1b83d556b9c8de89a5d" id="r_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><td class="memItemLeft" align="right" valign="top">constexpr uint32_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a> = 12345</td></tr>
<tr class="memdesc:a10f3ffb3f6f7e1b83d556b9c8de89a5d"><td class="mdescLeft">&#160;</td><td class="mdescRight">A struct to represent sparse table for <code>min()</code> as their invariant function, for the given array <code>A</code>. The answer to queries are stored in the array ST. <br /></td></tr>
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<tr class="memdesc:a10f3ffb3f6f7e1b83d556b9c8de89a5d"><td class="mdescLeft">&#160;</td><td class="mdescRight">A struct to represent sparse table for <span class="tt">min()</span> as their invariant function, for the given array <span class="tt">A</span>. The answer to queries are stored in the array ST. <br /></td></tr>
<tr class="memitem:af7db62f21983565c64d5d42d2a49888e" id="r_af7db62f21983565c64d5d42d2a49888e"><td class="memItemLeft" align="right" valign="top">constexpr uint8_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#af7db62f21983565c64d5d42d2a49888e">data_structures::sparse_table::M</a> = 14</td></tr>
<tr class="memdesc:af7db62f21983565c64d5d42d2a49888e"><td class="mdescLeft">&#160;</td><td class="mdescRight">ceil(log2(N)). <br /></td></tr>
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</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> for <code>min()</code> function. </p>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> for <span class="tt">min()</span> function. </p>
<p>Implementation of <a href="https://en.wikipedia.org/wiki/Range_minimum_query" target="_blank">Sparse Table</a> data structure.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/manncodes" target="_blank">Mann Patel</a></dd></dl>
<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. The only drawback of this data structure is, that it can only be used on immutable arrays. This means, that the array cannot be changed between two queries.</p>
<p>If any element in the array changes, the complete data structure has to be recomputed.</p>
<dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000004">Todo</a></b></dt><dd>make stress tests.</dd></dl>
<dl class="section warning"><dt>Warning</dt><dd>This sparse table is made for <code>min(a1,a2,...an)</code> duplicate invariant function. This implementation can be changed to other functions like <code><a class="el" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd()</a></code>, <code><a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm()</a></code>, and <code>max()</code> by changing a few lines of code.</dd></dl>
<dl class="section warning"><dt>Warning</dt><dd>This sparse table is made for <span class="tt">min(a1,a2,...an)</span> duplicate invariant function. This implementation can be changed to other functions like <span class="tt"><a class="el" href="../../d4/da0/gcd__iterative__euclidean_8cpp.html#ae48807fa2b7000afae599e67f327545e">gcd()</a></span>, <span class="tt"><a class="el" href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm()</a></span>, and <span class="tt">max()</span> by changing a few lines of code.</dd></dl>
<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 />
@@ -195,7 +175,7 @@ Variables</h2></td></tr>
</ul>
<p class="definition">Definition in file <a class="el" href="../../d8/dab/sparse__table_8cpp_source.html">sparse_table.cpp</a>.</p>
</div><h2 class="groupheader">Function Documentation</h2>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">static void test </td>
<td class="memname">void test </td>
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<td></td>
@@ -284,23 +264,26 @@ Variables</h2></td></tr>
<div class="line"><span class="lineno"> 140</span> st{}; </div>
<div class="line"><span class="lineno"> 141</span> </div>
<div class="line"><span class="lineno"> 142</span> std::copy(std::begin(testcase), std::end(testcase),</div>
<div class="line"><span class="lineno"> 143</span> std::begin(st.A)); </div>
<div class="line"><span class="lineno"> 144</span> st.n = testcase_size; </div>
<div class="line"><span class="lineno"> 143</span> std::begin(st.<a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ab78620742305a35ff2f8d61179f47d3e">A</a>)); </div>
<div class="line"><span class="lineno"> 144</span> st.<a class="code hl_variable" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ad71ecd43d0af1127df5f4006258f9635">n</a> = testcase_size; </div>
<div class="line"><span class="lineno"> 145</span> </div>
<div class="line"><span class="lineno"> 146</span> st.buildST(); </div>
<div class="line"><span class="lineno"> 147</span> </div>
<div class="line"><span class="lineno"> 148</span> <span class="comment">// pass queries of the form: [l,r]</span></div>
<div class="line"><span class="lineno"> 149</span> assert(st.query(1, 9) == 1); </div>
<div class="line"><span class="lineno"> 150</span> assert(st.query(2, 6) == 2); </div>
<div class="line"><span class="lineno"> 151</span> assert(st.query(3, 8) == 3); </div>
<div class="line"><span class="lineno"> 149</span> assert(st.<a class="code hl_function" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#a0c8cbe7239232863f104793c08273039">query</a>(1, 9) == 1); </div>
<div class="line"><span class="lineno"> 150</span> assert(st.<a class="code hl_function" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#a0c8cbe7239232863f104793c08273039">query</a>(2, 6) == 2); </div>
<div class="line"><span class="lineno"> 151</span> assert(st.<a class="code hl_function" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#a0c8cbe7239232863f104793c08273039">query</a>(3, 8) == 3); </div>
<div class="line"><span class="lineno"> 152</span> </div>
<div class="line"><span class="lineno"> 153</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Self-test implementations passed!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 154</span>}</div>
<div class="ttc" id="astructdata__structures_1_1sparse__table_1_1_sparse__table_html"><div class="ttname"><a href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html">data_structures::sparse_table::Sparse_table</a></div><div class="ttdef"><b>Definition</b> <a href="../../d8/dab/sparse__table_8cpp_source.html#l00051">sparse_table.cpp:51</a></div></div>
<div class="ttc" id="astructdata__structures_1_1sparse__table_1_1_sparse__table_html_a0c8cbe7239232863f104793c08273039"><div class="ttname"><a href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#a0c8cbe7239232863f104793c08273039">data_structures::sparse_table::Sparse_table::query</a></div><div class="ttdeci">int64_t query(int64_t l, int64_t r)</div><div class="ttdoc">Queries the sparse table for the value of the interval [l, r] (i.e. from l to r inclusive).</div><div class="ttdef"><b>Definition</b> <a href="../../d8/dab/sparse__table_8cpp_source.html#l00110">sparse_table.cpp:110</a></div></div>
<div class="ttc" id="astructdata__structures_1_1sparse__table_1_1_sparse__table_html_ab78620742305a35ff2f8d61179f47d3e"><div class="ttname"><a href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ab78620742305a35ff2f8d61179f47d3e">data_structures::sparse_table::Sparse_table::A</a></div><div class="ttdeci">std::array&lt; int64_t, N &gt; A</div><div class="ttdoc">input array to perform RMQ.</div><div class="ttdef"><b>Definition</b> <a href="../../d8/dab/sparse__table_8cpp_source.html#l00057">sparse_table.cpp:57</a></div></div>
<div class="ttc" id="astructdata__structures_1_1sparse__table_1_1_sparse__table_html_ad71ecd43d0af1127df5f4006258f9635"><div class="ttname"><a href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html#ad71ecd43d0af1127df5f4006258f9635">data_structures::sparse_table::Sparse_table::n</a></div><div class="ttdeci">size_t n</div><div class="ttdoc">size of input array.</div><div class="ttdef"><b>Definition</b> <a href="../../d8/dab/sparse__table_8cpp_source.html#l00052">sparse_table.cpp:52</a></div></div>
</div><!-- fragment -->
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<h2 class="groupheader">Variable Documentation</h2>
<a name="doc-var-members" id="doc-var-members"></a><h2 id="header-doc-var-members" class="groupheader">Variable Documentation</h2>
<a id="af7db62f21983565c64d5d42d2a49888e" name="af7db62f21983565c64d5d42d2a49888e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af7db62f21983565c64d5d42d2a49888e">&#9670;&#160;</a></span>M</h2>
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<p>A struct to represent sparse table for <code>min()</code> as their invariant function, for the given array <code>A</code>. The answer to queries are stored in the array ST. </p>
<p>A struct to represent sparse table for <span class="tt">min()</span> as their invariant function, for the given array <span class="tt">A</span>. The answer to queries are stored in the array ST. </p>
<p>the maximum size of the array. </p>
<p class="definition">Definition at line <a class="el" href="../../d8/dab/sparse__table_8cpp_source.html#l00048">48</a> of file <a class="el" href="../../d8/dab/sparse__table_8cpp_source.html">sparse_table.cpp</a>.</p>
@@ -356,11 +339,19 @@ Variables</h2></td></tr>
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