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<div class="title">sieve_of_eratosthenes.cpp File Reference</div> </div>
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<p>Get list of prime numbers using Sieve of Eratosthenes Sieve of Eratosthenes is an algorithm to find the primes that is between 2 to N (as defined in main).
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
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Include dependency graph for sieve_of_eratosthenes.cpp:</div>
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Functions</h2></td></tr>
<tr class="memitem:a1e606c2e5ac180a770ebe0d1706b8ca2"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a1e606c2e5ac180a770ebe0d1706b8ca2">sieve</a> (uint32_t N, bool *<a class="el" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>)</td></tr>
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<tr class="memitem:ae0de20c22cf2304b1cbe70953d57e7b7"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#ae0de20c22cf2304b1cbe70953d57e7b7">print</a> (uint32_t N, const bool *<a class="el" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>)</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Get list of prime numbers using Sieve of Eratosthenes Sieve of Eratosthenes is an algorithm to find the primes that is between 2 to N (as defined in main). </p>
<p>Time Complexity : \(O(N \cdot\log N)\) <br />
Space Complexity : \(O(N)\)</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d4/d9c/primes__up__to__billion_8cpp.html" title="Compute prime numbers upto 1 billion.">primes_up_to_billion.cpp</a> <a class="el" href="../../de/d9b/prime__numbers_8cpp.html" title="Get list of prime numbers.">prime_numbers.cpp</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
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<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; {</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; uint32_t N = 100;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="keywordtype">bool</span> *<a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a> = <span class="keyword">new</span> <span class="keywordtype">bool</span>[N];</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <a class="code" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a1e606c2e5ac180a770ebe0d1706b8ca2">sieve</a>(N, <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>);</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <a class="code" href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#ae0de20c22cf2304b1cbe70953d57e7b7">print</a>(N, <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>);</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <span class="keyword">delete</span>[] <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae0de20c22cf2304b1cbe70953d57e7b7">&#9670;&nbsp;</a></span>print()</h2>
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<td class="memname">void print </td>
<td>(</td>
<td class="paramtype">uint32_t&#160;</td>
<td class="paramname"><em>N</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const bool *&#160;</td>
<td class="paramname"><em>isprime</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>This function prints out the primes to STDOUT </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir"></td><td class="paramname">N</td><td>number of primes to check </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">isprime</td><td>a boolean array of size <code>N</code> identifying if <code>i</code>^th number is prime or not </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; {</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keywordflow">for</span> (uint32_t i = 2; i &lt;= N; i++) {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">if</span> (!<a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>[i]) {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <a class="codeRef" 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"><a name="l00042"></a><span class="lineno"> 42</span>&#160; }</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; }</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a1e606c2e5ac180a770ebe0d1706b8ca2">&#9670;&nbsp;</a></span>sieve()</h2>
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<td class="memname">void sieve </td>
<td>(</td>
<td class="paramtype">uint32_t&#160;</td>
<td class="paramname"><em>N</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">bool *&#160;</td>
<td class="paramname"><em>isprime</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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</div><div class="memdoc">
<p>This is the function that finds the primes and eliminates the multiples. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir"></td><td class="paramname">N</td><td>number of primes to check </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">isprime</td><td>a boolean array of size <code>N</code> identifying if <code>i</code>^th number is prime or not </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160; {</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160; <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>[0] = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>[1] = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; <span class="keywordflow">for</span> (uint32_t i = 2; i * i &lt;= N; i++) {</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; <span class="keywordflow">if</span> (!<a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>[i]) {</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; <span class="keywordflow">for</span> (uint32_t j = (i &lt;&lt; 1); j &lt;= N; j = j + i) {</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; <a class="code" href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>[j] = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; }</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; }</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; }</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160;}</div>
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<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_ae0de20c22cf2304b1cbe70953d57e7b7"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#ae0de20c22cf2304b1cbe70953d57e7b7">print</a></div><div class="ttdeci">void print(uint32_t N, const bool *isprime)</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:38</div></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="asieve__of__eratosthenes_8cpp_html_a1e606c2e5ac180a770ebe0d1706b8ca2"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a1e606c2e5ac180a770ebe0d1706b8ca2">sieve</a></div><div class="ttdeci">void sieve(uint32_t N, bool *isprime)</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:21</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>
<div class="ttc" id="aprime__factorization_8cpp_html_a7fe38b570a51e448430d6a0f072c2f23"><div class="ttname"><a href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a></div><div class="ttdeci">bool isprime[1000006]</div><div class="ttdef"><b>Definition:</b> prime_factorization.cpp:13</div></div>
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