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<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 />
<code>#include &lt;cstdint&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
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Include dependency graph for sparse_table.cpp:</div>
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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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Classes</h2></td></tr>
<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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Namespaces</h2></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="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>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><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 <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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<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 <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 />
</li>
<li>Build : O(NlogN) <br />
</li>
<li>Range Query : O(1) <br />
</li>
</ul>
<p class="definition">Definition in file <a class="el" href="../../d8/dab/sparse__table_8cpp_source.html">sparse_table.cpp</a>.</p>
</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="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d8/dab/sparse__table_8cpp_source.html#l00160">160</a> of file <a class="el" href="../../d8/dab/sparse__table_8cpp_source.html">sparse_table.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 160</span> {</div>
<div class="line"><span class="lineno"> 161</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 162</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 163</span>}</div>
<div class="ttc" id="asparse__table_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../d8/dab/sparse__table_8cpp_source.html#l00129">sparse_table.cpp:129</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">void test </td>
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<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p>&lt; array on which RMQ will be performed.</p>
<p>&lt; size of self test's array</p>
<p>&lt; declaring sparse tree</p>
<p>&lt; copying array to the struct</p>
<p>&lt; passing the array's size to the struct</p>
<p>&lt; precomputing sparse tree</p>
<p>&lt; as 1 is smallest from 1..9</p>
<p>&lt; as 2 is smallest from 2..6</p>
<p>&lt; as 3 is smallest from 3..8</p>
<p class="definition">Definition at line <a class="el" href="../../d8/dab/sparse__table_8cpp_source.html#l00129">129</a> of file <a class="el" href="../../d8/dab/sparse__table_8cpp_source.html">sparse_table.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 129</span> {</div>
<div class="line"><span class="lineno"> 130</span> <span class="comment">/* We take an array as an input on which we need to perform the ranged</span></div>
<div class="line"><span class="lineno"> 131</span><span class="comment"> * minimum queries[RMQ](https://en.wikipedia.org/wiki/Range_minimum_query).</span></div>
<div class="line"><span class="lineno"> 132</span><span class="comment"> */</span></div>
<div class="line"><span class="lineno"> 133</span> std::array&lt;int64_t, 10&gt; testcase = {</div>
<div class="line"><span class="lineno"> 134</span> 1, 2, 3, 4, 5,</div>
<div class="line"><span class="lineno"> 135</span> 6, 7, 8, 9, 10}; </div>
<div class="line"><span class="lineno"> 136</span> <span class="keywordtype">size_t</span> testcase_size =</div>
<div class="line"><span class="lineno"> 137</span> <span class="keyword">sizeof</span>(testcase) / <span class="keyword">sizeof</span>(testcase[0]); </div>
<div class="line"><span class="lineno"> 138</span> </div>
<div class="line"><span class="lineno"> 139</span> <a class="code hl_struct" href="../../da/d37/structdata__structures_1_1sparse__table_1_1_sparse__table.html">data_structures::sparse_table::Sparse_table</a></div>
<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 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.<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>
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<a name="doc-var-members" id="doc-var-members"></a><h2 id="header-doc-var-members" class="groupheader">Variable Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#af7db62f21983565c64d5d42d2a49888e">&#9670;&#160;</a></span>M</h2>
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<td class="memname">uint8_t data_structures::sparse_table::M = 14</td>
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<span class="mlabels"><span class="mlabel constexpr">constexpr</span></span> </td>
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<p>ceil(log2(N)). </p>
<p class="definition">Definition at line <a class="el" href="../../d8/dab/sparse__table_8cpp_source.html#l00049">49</a> of file <a class="el" href="../../d8/dab/sparse__table_8cpp_source.html">sparse_table.cpp</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a10f3ffb3f6f7e1b83d556b9c8de89a5d">&#9670;&#160;</a></span>N</h2>
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<td class="memname">uint32_t data_structures::sparse_table::N = 12345</td>
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<span class="mlabels"><span class="mlabel constexpr">constexpr</span></span> </td>
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<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>
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