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<p>Functions for finding Prime Numbers using Sieve of Eratosthenes.
<a href="#details">More...</a></p>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Functions for finding Prime Numbers using Sieve of Eratosthenes. </p>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Compute prime numbers upto 1 billion. </p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/d9b/prime__numbers_8cpp.html" title="Get list of prime numbers.">prime_numbers.cpp</a> <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html" title="Get list of prime numbers using Sieve of Eratosthenes.">sieve_of_eratosthenes.cpp</a> </dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/d9b/prime__numbers_8cpp.html" title="Get list of prime numbers.">prime_numbers.cpp</a> <a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html" title="Prime Numbers using Sieve of Eratosthenes">sieve_of_eratosthenes.cpp</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>

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<div class="header">
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<a href="#namespaces">Namespaces</a> &#124;
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<div class="headertitle"><div class="title">sieve_of_eratosthenes.cpp File Reference</div></div>
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<div class="contents">
<p>Get list of prime numbers using Sieve of Eratosthenes.
<p>Prime Numbers using <a href="https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes" target="_blank">Sieve of Eratosthenes</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
@@ -121,19 +122,32 @@ Include dependency graph for sieve_of_eratosthenes.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html">math</a></td></tr>
<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <br /></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="../../d2/db0/namespacesieve__of__eratosthenes.html">sieve_of_eratosthenes</a></td></tr>
<tr class="memdesc:d2/db0/namespacesieve__of__eratosthenes"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for finding Prime Numbers using Sieve of Eratosthenes. <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:a7eebd5e7686a8db363f937b2f30d3818" id="r_a7eebd5e7686a8db363f937b2f30d3818"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; bool &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a7eebd5e7686a8db363f937b2f30d3818">sieve</a> (uint32_t N)</td></tr>
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<tr class="memdesc:a22be949d160b26361f7e323310f7fa0c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to sieve out the primes. <br /></td></tr>
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<tr class="memitem:a55bc4a221e584d33b79b322432ecc0f3" id="r_a55bc4a221e584d33b79b322432ecc0f3"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a55bc4a221e584d33b79b322432ecc0f3">math::sieve_of_eratosthenes::print</a> (uint32_t N, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; bool &gt; &amp;<a class="el" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>)</td></tr>
<tr class="memdesc:a55bc4a221e584d33b79b322432ecc0f3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to print the prime numbers. <br /></td></tr>
<tr class="separator:a55bc4a221e584d33b79b322432ecc0f3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a483bb8ccf42aaf7375a83e91490eda1e" id="r_a483bb8ccf42aaf7375a83e91490eda1e"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a> ()</td></tr>
<tr class="memdesc:a483bb8ccf42aaf7375a83e91490eda1e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
<tr class="separator:a483bb8ccf42aaf7375a83e91490eda1e"><td class="memSeparator" colspan="2">&#160;</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>
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Get list of prime numbers using Sieve of Eratosthenes. </p>
<div class="textblock"><p>Prime Numbers using <a href="https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes" target="_blank">Sieve of Eratosthenes</a> </p>
<p>Sieve of Eratosthenes is an algorithm that finds all the primes between 2 and N.</p>
<p>Time Complexity : \(O(N \cdot\log \log N)\) <br />
Space Complexity : \(O(N)\)</p>
@@ -153,37 +167,30 @@ Space Complexity : \(O(N)\)</p>
</tr>
</table>
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<p>Main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 65</span> {</div>
<div class="line"><span class="lineno"> 66</span> <a class="code hl_function" href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
<div class="line"><span class="lineno"> 67</span> </div>
<div class="line"><span class="lineno"> 68</span> uint32_t <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 100;</div>
<div class="line"><span class="lineno"> 69</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a> = <a class="code hl_function" href="#a7eebd5e7686a8db363f937b2f30d3818">sieve</a>(N);</div>
<div class="line"><span class="lineno"> 70</span> <a class="code hl_function" href="#a235843bdf82d2a6cc8596ae8fd3b8df9">print</a>(N, is_prime);</div>
<div class="line"><span class="lineno"> 71</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 72</span>}</div>
<div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition</b> sparse_table.cpp:47</div></div>
<div class="ttc" id="anamespacemath_html_abd8f794b2229b42876169ff841b6e444"><div class="ttname"><a href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">math::is_prime</a></div><div class="ttdeci">bool is_prime(int64_t num)</div><div class="ttdoc">Function to check if the given number is prime or not.</div><div class="ttdef"><b>Definition</b> check_prime.cpp:31</div></div>
<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_a235843bdf82d2a6cc8596ae8fd3b8df9"><div class="ttname"><a href="#a235843bdf82d2a6cc8596ae8fd3b8df9">print</a></div><div class="ttdeci">void print(uint32_t N, const std::vector&lt; bool &gt; &amp;is_prime)</div><div class="ttdef"><b>Definition</b> sieve_of_eratosthenes.cpp:44</div></div>
<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_a7eebd5e7686a8db363f937b2f30d3818"><div class="ttname"><a href="#a7eebd5e7686a8db363f937b2f30d3818">sieve</a></div><div class="ttdeci">std::vector&lt; bool &gt; sieve(uint32_t N)</div><div class="ttdef"><b>Definition</b> sieve_of_eratosthenes.cpp:26</div></div>
<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition</b> sieve_of_eratosthenes.cpp:56</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>
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 119</span> {</div>
<div class="line"><span class="lineno"> 120</span> <a class="code hl_function" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>();</div>
<div class="line"><span class="lineno"> 121</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 122</span>}</div>
<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> sieve_of_eratosthenes.cpp:80</div></div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
<div class="dyncontent">
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<h2 class="memtitle"><span class="permalink"><a href="#a235843bdf82d2a6cc8596ae8fd3b8df9">&#9670;&#160;</a></span>print()</h2>
<a id="a55bc4a221e584d33b79b322432ecc0f3" name="a55bc4a221e584d33b79b322432ecc0f3"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a55bc4a221e584d33b79b322432ecc0f3">&#9670;&#160;</a></span>print()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void print </td>
<td class="memname">void math::sieve_of_eratosthenes::print </td>
<td>(</td>
<td class="paramtype">uint32_t</td> <td class="paramname"><span class="paramname"><em>N</em></span>, </td>
</tr>
@@ -194,93 +201,142 @@ Here is the call graph for this function:</div>
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<p>This function prints out the primes to STDOUT </p><dl class="params"><dt>Parameters</dt><dd>
<p>Function to print the prime numbers. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">N</td><td>number of primes to check </td></tr>
<tr><td class="paramname">N</td><td>number till which primes are to be found </td></tr>
<tr><td class="paramname">is_prime</td><td>a vector of <code>N + 1</code> booleans identifying if <code>i</code>^th number is a prime or not </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 44</span> {</div>
<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">for</span> (uint32_t i = 2; i &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">if</span> (is_prime[i]) {</div>
<div class="line"><span class="lineno"> 47</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="charliteral">&#39; &#39;</span>;</div>
<div class="line"><span class="lineno"> 48</span> }</div>
<div class="line"><span class="lineno"> 49</span> }</div>
<div class="line"><span class="lineno"> 50</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 51</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 64</span> {</div>
<div class="line"><span class="lineno"> 65</span> <span class="keywordflow">for</span> (uint32_t i = 2; i &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">if</span> (is_prime[i]) {</div>
<div class="line"><span class="lineno"> 67</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i &lt;&lt; <span class="charliteral">&#39; &#39;</span>;</div>
<div class="line"><span class="lineno"> 68</span> }</div>
<div class="line"><span class="lineno"> 69</span> }</div>
<div class="line"><span class="lineno"> 70</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 71</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition</b> sparse_table.cpp:47</div></div>
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a7eebd5e7686a8db363f937b2f30d3818">&#9670;&#160;</a></span>sieve()</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a22be949d160b26361f7e323310f7fa0c">&#9670;&#160;</a></span>sieve()</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; bool &gt; sieve </td>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; bool &gt; math::sieve_of_eratosthenes::sieve </td>
<td>(</td>
<td class="paramtype">uint32_t</td> <td class="paramname"><span class="paramname"><em>N</em></span></td><td>)</td>
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<p>This is the function that finds the primes and eliminates the multiples. Contains a common optimization to start eliminating multiples of a prime p starting from p * p since all of the lower multiples have been already eliminated. </p><dl class="params"><dt>Parameters</dt><dd>
<p>Function to sieve out the primes. </p>
<p>This function finds all the primes between 2 and N using the Sieve of Eratosthenes algorithm. It starts by assuming all numbers (except zero and one) are prime and then iteratively marks the multiples of each prime as non-prime.</p>
<p>Contains a common optimization to start eliminating multiples of a prime p starting from p * p since all of the lower multiples have been already eliminated. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">N</td><td>number of primes to check </td></tr>
<tr><td class="paramname">N</td><td>number till which primes are to be found </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>is_prime a vector of <code>N + 1</code> booleans identifying if <code>i</code>^th number is a prime or not </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 26</span> {</div>
<div class="line"><span class="lineno"> 27</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>(N + 1, <span class="keyword">true</span>);</div>
<div class="line"><span class="lineno"> 28</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[0] = <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[1] = <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 29</span> <span class="keywordflow">for</span> (uint32_t i = 2; i * i &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><span class="lineno"> 30</span> <span class="keywordflow">if</span> (is_prime[i]) {</div>
<div class="line"><span class="lineno"> 31</span> <span class="keywordflow">for</span> (uint32_t j = i * i; j &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; j += i) {</div>
<div class="line"><span class="lineno"> 32</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[j] = <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 33</span> }</div>
<div class="line"><span class="lineno"> 34</span> }</div>
<div class="line"><span class="lineno"> 35</span> }</div>
<div class="line"><span class="lineno"> 36</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>;</div>
<div class="line"><span class="lineno"> 37</span>}</div>
</div><!-- fragment -->
<div class="fragment"><div class="line"><span class="lineno"> 44</span> {</div>
<div class="line"><span class="lineno"> 45</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>(N + 1, <span class="keyword">true</span>); <span class="comment">// Initialize all as prime numbers</span></div>
<div class="line"><span class="lineno"> 46</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[0] = <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[1] = <span class="keyword">false</span>; <span class="comment">// 0 and 1 are not prime numbers</span></div>
<div class="line"><span class="lineno"> 47</span> </div>
<div class="line"><span class="lineno"> 48</span> <span class="keywordflow">for</span> (uint32_t i = 2; i * i &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">if</span> (is_prime[i]) {</div>
<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">for</span> (uint32_t j = i * i; j &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; j += i) {</div>
<div class="line"><span class="lineno"> 51</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>[j] = <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 52</span> }</div>
<div class="line"><span class="lineno"> 53</span> }</div>
<div class="line"><span class="lineno"> 54</span> }</div>
<div class="line"><span class="lineno"> 55</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">is_prime</a>;</div>
<div class="line"><span class="lineno"> 56</span>}</div>
<div class="ttc" id="anamespacemath_html_abd8f794b2229b42876169ff841b6e444"><div class="ttname"><a href="../../dd/d47/namespacemath.html#abd8f794b2229b42876169ff841b6e444">math::is_prime</a></div><div class="ttdeci">bool is_prime(int64_t num)</div><div class="ttdoc">Function to check if the given number is prime or not.</div><div class="ttdef"><b>Definition</b> check_prime.cpp:31</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="#a88ec9ad42717780d6caaff9d3d6977f9">&#9670;&#160;</a></span>tests()</h2>
<a id="a483bb8ccf42aaf7375a83e91490eda1e" name="a483bb8ccf42aaf7375a83e91490eda1e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">&#9670;&#160;</a></span>tests()</h2>
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<td class="memname">void tests </td>
<td class="memname">static void tests </td>
<td>(</td>
<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
</tr>
</table>
</td>
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<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<p>Test implementations </p>
<div class="fragment"><div class="line"><span class="lineno"> 56</span> {</div>
<div class="line"><span class="lineno"> 57</span> <span class="comment">// 0 1 2 3 4 5 6 7 8 9 10</span></div>
<div class="line"><span class="lineno"> 58</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> ans{<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>};</div>
<div class="line"><span class="lineno"> 59</span> assert(<a class="code hl_function" href="#a7eebd5e7686a8db363f937b2f30d3818">sieve</a>(10) == ans);</div>
<div class="line"><span class="lineno"> 60</span>}</div>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 80</span> {</div>
<div class="line"><span class="lineno"> 81</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> is_prime_1 =</div>
<div class="line"><span class="lineno"> 82</span> <a class="code hl_function" href="#a22be949d160b26361f7e323310f7fa0c">math::sieve_of_eratosthenes::sieve</a>(<span class="keyword">static_cast&lt;</span>uint32_t<span class="keyword">&gt;</span>(10));</div>
<div class="line"><span class="lineno"> 83</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> is_prime_2 =</div>
<div class="line"><span class="lineno"> 84</span> <a class="code hl_function" href="#a22be949d160b26361f7e323310f7fa0c">math::sieve_of_eratosthenes::sieve</a>(<span class="keyword">static_cast&lt;</span>uint32_t<span class="keyword">&gt;</span>(20));</div>
<div class="line"><span class="lineno"> 85</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> is_prime_3 =</div>
<div class="line"><span class="lineno"> 86</span> <a class="code hl_function" href="#a22be949d160b26361f7e323310f7fa0c">math::sieve_of_eratosthenes::sieve</a>(<span class="keyword">static_cast&lt;</span>uint32_t<span class="keyword">&gt;</span>(100));</div>
<div class="line"><span class="lineno"> 87</span> </div>
<div class="line"><span class="lineno"> 88</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> expected_1{<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
<div class="line"><span class="lineno"> 89</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>};</div>
<div class="line"><span class="lineno"> 90</span> assert(is_prime_1 == expected_1);</div>
<div class="line"><span class="lineno"> 91</span> </div>
<div class="line"><span class="lineno"> 92</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a> expected_2{<span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
<div class="line"><span class="lineno"> 93</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
<div class="line"><span class="lineno"> 94</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
<div class="line"><span class="lineno"> 95</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>};</div>
<div class="line"><span class="lineno"> 96</span> assert(is_prime_2 == expected_2);</div>
<div class="line"><span class="lineno"> 97</span> </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;bool&gt;</a> expected_3{</div>
<div class="line"><span class="lineno"> 99</span> <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>,</div>
<div class="line"><span class="lineno"> 100</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
<div class="line"><span class="lineno"> 101</span> <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
<div class="line"><span class="lineno"> 102</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>,</div>
<div class="line"><span class="lineno"> 103</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>,</div>
<div class="line"><span class="lineno"> 104</span> <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
<div class="line"><span class="lineno"> 105</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>,</div>
<div class="line"><span class="lineno"> 106</span> <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
<div class="line"><span class="lineno"> 107</span> <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>,</div>
<div class="line"><span class="lineno"> 108</span> <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">false</span>, <span class="keyword">true</span>, <span class="keyword">false</span>, <span class="keyword">false</span>,</div>
<div class="line"><span class="lineno"> 109</span> <span class="keyword">false</span>};</div>
<div class="line"><span class="lineno"> 110</span> assert(is_prime_3 == expected_3);</div>
<div class="line"><span class="lineno"> 111</span> </div>
<div class="line"><span class="lineno"> 112</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All tests have passed successfully!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 113</span>}</div>
<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_a22be949d160b26361f7e323310f7fa0c"><div class="ttname"><a href="#a22be949d160b26361f7e323310f7fa0c">math::sieve_of_eratosthenes::sieve</a></div><div class="ttdeci">std::vector&lt; bool &gt; sieve(uint32_t N)</div><div class="ttdoc">Function to sieve out the primes.</div><div class="ttdef"><b>Definition</b> sieve_of_eratosthenes.cpp:44</div></div>
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@@ -1,7 +1,7 @@
var sieve__of__eratosthenes_8cpp =
[
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<li>problem()&#160;:&#160;<a class="el" href="db/dd3/ode__forward__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">ode_forward_euler.cpp</a>, <a class="el" href="d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">ode_midpoint_euler.cpp</a>, <a class="el" href="d3/d06/ode__semi__implicit__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">ode_semi_implicit_euler.cpp</a></li>
<li>push()&#160;:&#160;<a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#aae41c72130114bf31204cde6873b6095">paranthesis_matching.cpp</a></li>

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@@ -119,7 +119,6 @@ $(function(){initNavTree('globals_s.html',''); initResizable(true); });
<li>show_data()&#160;:&#160;<a class="el" href="d4/d7a/shell__sort2_8cpp.html#a951127aea9d7e1e53ea9ae0868633246">shell_sort2.cpp</a></li>
<li>show_pascal()&#160;:&#160;<a class="el" href="dc/d1a/pascal__triangle_8cpp.html#ad7a31d9cb2818d21b1ba12aead7f4c5c">pascal_triangle.cpp</a></li>
<li>Sieve()&#160;:&#160;<a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html#a031cada84819ed6426f58e4f7e81261c">primes_up_to_billion.cpp</a></li>
<li>sieve()&#160;:&#160;<a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a7eebd5e7686a8db363f937b2f30d3818">sieve_of_eratosthenes.cpp</a></li>
<li>SieveOfEratosthenes()&#160;:&#160;<a class="el" href="db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099">prime_factorization.cpp</a></li>
<li>SLEEP()&#160;:&#160;<a class="el" href="dd/d92/memory__game_8cpp.html#a5bdc30951221eae9c33413ff9eb574f6">memory_game.cpp</a></li>
<li>sortcol()&#160;:&#160;<a class="el" href="df/d47/fcfs__scheduling_8cpp.html#a18920aa331faf4476b251c8cdb2c2bec">fcfs_scheduling.cpp</a></li>

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<tr id="row_108_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d88/namespaceset_kth_bit.html" target="_self">setKthBit</a></td><td class="desc">Functions for the [From the right, set the Kth bit in the binary representation of N] (<a href="https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/">https://practice.geeksforgeeks.org/problems/set-kth-bit3724/1/</a>) implementation </td></tr>
<tr id="row_109_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/dd3/namespace_s_h_a.html" target="_self">SHA</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/SHA-1" target="_blank">SHA-1</a> algorithm implementation </td></tr>
<tr id="row_110_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/deb/namespaceshortest__common__supersequence.html" target="_self">shortest_common_supersequence</a></td><td class="desc">Shortest Common Super Sequence algorithm </td></tr>
<tr id="row_111_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d6d/namespacesimpson__method.html" target="_self">simpson_method</a></td><td class="desc">Contains the Simpson's method implementation </td></tr>
<tr id="row_112_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d5/d91/namespacesorting.html" target="_self">sorting</a></td><td class="desc">For working with vectors </td></tr>
<tr id="row_113_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d55/namespacesparse__table.html" target="_self">sparse_table</a></td><td class="desc">Functions for Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> </td></tr>
<tr id="row_114_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="da/dd3/namespacespirograph.html" target="_self">spirograph</a></td><td class="desc"></td></tr>
<tr id="row_115_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d1c/namespacestack__using__queue.html" target="_self">stack_using_queue</a></td><td class="desc">Functions for the <a href="https://www.studytonight.com/data-structures/stack-using-queue" target="_blank">Stack Using Queue</a> implementation </td></tr>
<tr id="row_116_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d2/dcf/namespacestatistics.html" target="_self">statistics</a></td><td class="desc">Statistical algorithms </td></tr>
<tr id="row_117_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/dcc/namespacestd.html" target="_self">std</a></td><td class="desc">STL namespace </td></tr>
<tr id="row_118_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d1d/namespacestrand.html" target="_self">strand</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Strand_sort" target="_blank">Strand Sort</a> algorithm </td></tr>
<tr id="row_119_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d91/namespacestrassens__multiplication.html" target="_self">strassens_multiplication</a></td><td class="desc">Namespace for performing strassen's multiplication </td></tr>
<tr id="row_120_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/dd6/namespacestring.html" target="_self">string</a></td><td class="desc">String manipulation algorithms </td></tr>
<tr id="row_121_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d03/namespacestring__search.html" target="_self">string_search</a></td><td class="desc">String search algorithms </td></tr>
<tr id="row_122_" class="even"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_122_" class="arrow" onclick="dynsection.toggleFolder('122_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/dcb/namespacestrings.html" target="_self">strings</a></td><td class="desc">String algorithms </td></tr>
<tr id="row_122_0_" class="odd" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/dbc/namespacestrings_1_1boyer__moore.html" target="_self">boyer_moore</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Boyer%E2%80%93Moore_string-search_algorithm" target="_blank">Boyer Moore</a> algorithm implementation </td></tr>
<tr id="row_123_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d74/namespacesubarray__sum.html" target="_self">subarray_sum</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" target="_blank">Subset sum</a> implementation </td></tr>
<tr id="row_124_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/def/namespacesublist__search.html" target="_self">sublist_search</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/sublist-search-search-a-linked-list-in-another-list" target="_blank">Sublist Search</a> implementation </td></tr>
<tr id="row_125_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dc/d3a/namespacesubset__sum.html" target="_self">subset_sum</a></td><td class="desc">Functions for [Sub-set sum problem] (<a href="https://en.wikipedia.org/wiki/Subset_sum_problem">https://en.wikipedia.org/wiki/Subset_sum_problem</a>) algorithm </td></tr>
<tr id="row_126_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/d95/namespace_subsets.html" target="_self">Subsets</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" target="_blank">Subset Sum</a> problem </td></tr>
<tr id="row_127_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d9f/namespacesudoku__solver.html" target="_self">sudoku_solver</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Sudoku" target="_blank">Sudoku Solver</a> implementation </td></tr>
<tr id="row_128_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/df4/namespacetests.html" target="_self">tests</a></td><td class="desc">Testcases to check Union of Two Arrays </td></tr>
<tr id="row_129_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d3f/namespacetravelling_salesman__bitmanipulation.html" target="_self">travellingSalesman_bitmanipulation</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/travelling-salesman-problem-set-1/" target="_blank">Travelling Salesman Bitmask</a> implementation </td></tr>
<tr id="row_130_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/dab/namespacetree__234.html" target="_self">tree_234</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/2%E2%80%933%E2%80%934_tree" target="_blank">234 tree</a> </td></tr>
<tr id="row_131_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d8e/namespacetrie__operations.html" target="_self">trie_operations</a></td><td class="desc">Functions for <a href="https://iq.opengenus.org/autocomplete-using-trie-data-structure/" target="_blank">Trie datastructure</a> implementation </td></tr>
<tr id="row_132_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d0a/namespacetrie__using__hashmap.html" target="_self">trie_using_hashmap</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Trie" target="_blank">Trie</a> data structure using hashmap implementation </td></tr>
<tr id="row_133_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d17/namespaceutil__functions.html" target="_self">util_functions</a></td><td class="desc">Various utility functions used in Neural network </td></tr>
<tr id="row_134_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/d84/namespaceutils.html" target="_self">utils</a></td><td class="desc">This namespace contains the definitions of the functions called from the class <a class="el" href="d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html" title="Class which contains all methods required for calculating nCr mod p.">math::ncr_modulo_p::NCRModuloP</a> </td></tr>
<tr id="row_135_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/d91/namespacevector__cross.html" target="_self">vector_cross</a></td><td class="desc">Functions for Vector Cross Product algorithms </td></tr>
<tr id="row_136_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/da2/namespacevigenere.html" target="_self">vigenere</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher" target="_blank">vigenère cipher</a> algorithm </td></tr>
<tr id="row_137_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d21/namespacewave__sort.html" target="_self">wave_sort</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/sort-array-wave-form-2/" target="_blank">Wave sort</a> implementation </td></tr>
<tr id="row_138_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/d52/namespacewiggle__sort.html" target="_self">wiggle_sort</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/wiggle-sort-ii/" target="_blank">Wiggle Sort</a> algorithm </td></tr>
<tr id="row_139_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="db/d03/namespacewildcard__matching.html" target="_self">wildcard_matching</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/wildcard-pattern-matching/" target="_blank">Wildcard Matching</a> problem </td></tr>
<tr id="row_140_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d21/namespacewindowed__median.html" target="_self">windowed_median</a></td><td class="desc">Functions for the Windowed Median algorithm implementation </td></tr>
<tr id="row_141_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/d53/namespaceword__break.html" target="_self">word_break</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/word-break/" target="_blank">Word Break</a> problem </td></tr>
<tr id="row_142_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d47/namespace_x_o_r.html" target="_self">XOR</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/XOR_cipher" target="_blank">XOR cipher</a> algorithm </td></tr>
<tr id="row_111_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d2/db0/namespacesieve__of__eratosthenes.html" target="_self">sieve_of_eratosthenes</a></td><td class="desc">Functions for finding Prime Numbers using Sieve of Eratosthenes </td></tr>
<tr id="row_112_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d6d/namespacesimpson__method.html" target="_self">simpson_method</a></td><td class="desc">Contains the Simpson's method implementation </td></tr>
<tr id="row_113_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d5/d91/namespacesorting.html" target="_self">sorting</a></td><td class="desc">For working with vectors </td></tr>
<tr id="row_114_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d55/namespacesparse__table.html" target="_self">sparse_table</a></td><td class="desc">Functions for Implementation of <a href="https://brilliant.org/wiki/sparse-table/" target="_blank">Sparse Table</a> </td></tr>
<tr id="row_115_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="da/dd3/namespacespirograph.html" target="_self">spirograph</a></td><td class="desc"></td></tr>
<tr id="row_116_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d1c/namespacestack__using__queue.html" target="_self">stack_using_queue</a></td><td class="desc">Functions for the <a href="https://www.studytonight.com/data-structures/stack-using-queue" target="_blank">Stack Using Queue</a> implementation </td></tr>
<tr id="row_117_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d2/dcf/namespacestatistics.html" target="_self">statistics</a></td><td class="desc">Statistical algorithms </td></tr>
<tr id="row_118_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/dcc/namespacestd.html" target="_self">std</a></td><td class="desc">STL namespace </td></tr>
<tr id="row_119_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d1d/namespacestrand.html" target="_self">strand</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Strand_sort" target="_blank">Strand Sort</a> algorithm </td></tr>
<tr id="row_120_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d91/namespacestrassens__multiplication.html" target="_self">strassens_multiplication</a></td><td class="desc">Namespace for performing strassen's multiplication </td></tr>
<tr id="row_121_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/dd6/namespacestring.html" target="_self">string</a></td><td class="desc">String manipulation algorithms </td></tr>
<tr id="row_122_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d03/namespacestring__search.html" target="_self">string_search</a></td><td class="desc">String search algorithms </td></tr>
<tr id="row_123_" class="odd"><td class="entry"><span style="width:0px;display:inline-block;">&#160;</span><span id="arr_123_" class="arrow" onclick="dynsection.toggleFolder('123_')">&#9658;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/dcb/namespacestrings.html" target="_self">strings</a></td><td class="desc">String algorithms </td></tr>
<tr id="row_123_0_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/dbc/namespacestrings_1_1boyer__moore.html" target="_self">boyer_moore</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Boyer%E2%80%93Moore_string-search_algorithm" target="_blank">Boyer Moore</a> algorithm implementation </td></tr>
<tr id="row_124_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d74/namespacesubarray__sum.html" target="_self">subarray_sum</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" target="_blank">Subset sum</a> implementation </td></tr>
<tr id="row_125_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/def/namespacesublist__search.html" target="_self">sublist_search</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/sublist-search-search-a-linked-list-in-another-list" target="_blank">Sublist Search</a> implementation </td></tr>
<tr id="row_126_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dc/d3a/namespacesubset__sum.html" target="_self">subset_sum</a></td><td class="desc">Functions for [Sub-set sum problem] (<a href="https://en.wikipedia.org/wiki/Subset_sum_problem">https://en.wikipedia.org/wiki/Subset_sum_problem</a>) algorithm </td></tr>
<tr id="row_127_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="de/d95/namespace_subsets.html" target="_self">Subsets</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Subset_sum_problem" target="_blank">Subset Sum</a> problem </td></tr>
<tr id="row_128_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d8/d9f/namespacesudoku__solver.html" target="_self">sudoku_solver</a></td><td class="desc">Functions for the <a href="https://en.wikipedia.org/wiki/Sudoku" target="_blank">Sudoku Solver</a> implementation </td></tr>
<tr id="row_129_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/df4/namespacetests.html" target="_self">tests</a></td><td class="desc">Testcases to check Union of Two Arrays </td></tr>
<tr id="row_130_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d3f/namespacetravelling_salesman__bitmanipulation.html" target="_self">travellingSalesman_bitmanipulation</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/travelling-salesman-problem-set-1/" target="_blank">Travelling Salesman Bitmask</a> implementation </td></tr>
<tr id="row_131_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/dab/namespacetree__234.html" target="_self">tree_234</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/2%E2%80%933%E2%80%934_tree" target="_blank">234 tree</a> </td></tr>
<tr id="row_132_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="df/d8e/namespacetrie__operations.html" target="_self">trie_operations</a></td><td class="desc">Functions for <a href="https://iq.opengenus.org/autocomplete-using-trie-data-structure/" target="_blank">Trie datastructure</a> implementation </td></tr>
<tr id="row_133_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d0a/namespacetrie__using__hashmap.html" target="_self">trie_using_hashmap</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Trie" target="_blank">Trie</a> data structure using hashmap implementation </td></tr>
<tr id="row_134_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d3/d17/namespaceutil__functions.html" target="_self">util_functions</a></td><td class="desc">Various utility functions used in Neural network </td></tr>
<tr id="row_135_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/d84/namespaceutils.html" target="_self">utils</a></td><td class="desc">This namespace contains the definitions of the functions called from the class <a class="el" href="d6/dc1/classmath_1_1ncr__modulo__p_1_1_n_c_r_modulo_p.html" title="Class which contains all methods required for calculating nCr mod p.">math::ncr_modulo_p::NCRModuloP</a> </td></tr>
<tr id="row_136_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d4/d91/namespacevector__cross.html" target="_self">vector_cross</a></td><td class="desc">Functions for Vector Cross Product algorithms </td></tr>
<tr id="row_137_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/da2/namespacevigenere.html" target="_self">vigenere</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher" target="_blank">vigenère cipher</a> algorithm </td></tr>
<tr id="row_138_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d9/d21/namespacewave__sort.html" target="_self">wave_sort</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/sort-array-wave-form-2/" target="_blank">Wave sort</a> implementation </td></tr>
<tr id="row_139_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d0/d52/namespacewiggle__sort.html" target="_self">wiggle_sort</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/wiggle-sort-ii/" target="_blank">Wiggle Sort</a> algorithm </td></tr>
<tr id="row_140_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="db/d03/namespacewildcard__matching.html" target="_self">wildcard_matching</a></td><td class="desc">Functions for the <a href="https://www.geeksforgeeks.org/wildcard-pattern-matching/" target="_blank">Wildcard Matching</a> problem </td></tr>
<tr id="row_141_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="dd/d21/namespacewindowed__median.html" target="_self">windowed_median</a></td><td class="desc">Functions for the Windowed Median algorithm implementation </td></tr>
<tr id="row_142_" class="even"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d6/d53/namespaceword__break.html" target="_self">word_break</a></td><td class="desc">Functions for <a href="https://leetcode.com/problems/word-break/" target="_blank">Word Break</a> problem </td></tr>
<tr id="row_143_" class="odd"><td class="entry"><span style="width:16px;display:inline-block;">&#160;</span><span class="icona"><span class="icon">N</span></span><a class="el" href="d7/d47/namespace_x_o_r.html" target="_self">XOR</a></td><td class="desc">Functions for <a href="https://en.wikipedia.org/wiki/XOR_cipher" target="_blank">XOR cipher</a> algorithm </td></tr>
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