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@@ -318,6 +318,7 @@ Math</h1>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/check_prime.cpp" target="_blank">Check Prime</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/complex_numbers.cpp" target="_blank">Complex Numbers</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/double_factorial.cpp" target="_blank">Double Factorial</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/eratosthenes.cpp" target="_blank">Eratosthenes</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/eulers_totient_function.cpp" target="_blank">Eulers Totient Function</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/extended_euclid_algorithm.cpp" target="_blank">Extended Euclid Algorithm</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/factorial.cpp" target="_blank">Factorial</a></li>

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<div class="headertitle"><div class="title">eratosthenes.cpp File Reference</div></div>
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<p><a href="https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes" target="_blank">The Sieve of Eratosthenes</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;chrono&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;string&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for eratosthenes.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:dd/d47/namespacemath"><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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Functions</h2></td></tr>
<tr class="memitem:a91366864111e1fac29722ca45e02ea8f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a91366864111e1fac29722ca45e02ea8f">math::sieve</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; bool &gt; *vec)</td></tr>
<tr class="memdesc:a91366864111e1fac29722ca45e02ea8f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Performs the sieve. <br /></td></tr>
<tr class="separator:a91366864111e1fac29722ca45e02ea8f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad09d59850865012a6fd95d89954c82e4"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ad09d59850865012a6fd95d89954c82e4">math::print_primes</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; bool &gt; const &amp;<a class="el" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>)</td></tr>
<tr class="memdesc:ad09d59850865012a6fd95d89954c82e4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Prints all the indexes of true values in the passed <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>. <br /></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/da6/eratosthenes_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-tests the sieve function for major inconsistencies. <br /></td></tr>
<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/da6/eratosthenes_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">main</a> (int argc, char *argv[])</td></tr>
<tr class="memdesc:a0ddf1224851353fc92bfbff6f499fa97"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes" target="_blank">The Sieve of Eratosthenes</a> </p>
<p>Store an array of booleans where a true value indicates that it's index is prime. For all the values in the array starting from 2 which we know is prime, we walk the array in multiples of the current outer value setting them to not prime. If we remove all multiples of a value as we see it, we'll be left with just primes.</p>
<p>Pass "print" as a command line arg to see the generated list of primes </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/thechubbypanda" target="_blank">Keval Kapdee</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a0ddf1224851353fc92bfbff6f499fa97" name="a0ddf1224851353fc92bfbff6f499fa97"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<td class="paramtype">int&#160;</td>
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<p>Main function. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">argc</td><td>commandline argument count </td></tr>
<tr><td class="paramname">argv</td><td>commandline array of arguments </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 87</span> {</div>
<div class="line"><span class="lineno"> 88</span> <a class="code hl_function" href="../../d7/da6/eratosthenes_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 89</span> </div>
<div class="line"><span class="lineno"> 90</span> <span class="comment">// The largest prime we will check for</span></div>
<div class="line"><span class="lineno"> 91</span> <span class="keyword">auto</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">max</a> = 10000;</div>
<div class="line"><span class="lineno"> 92</span> </div>
<div class="line"><span class="lineno"> 93</span> <span class="comment">// Store a boolean for every number which states if that index is prime or</span></div>
<div class="line"><span class="lineno"> 94</span> <span class="comment">// not</span></div>
<div class="line"><span class="lineno"> 95</span> <span class="keyword">auto</span> <a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(max, <span class="keyword">true</span>);</div>
<div class="line"><span class="lineno"> 96</span> </div>
<div class="line"><span class="lineno"> 97</span> <span class="comment">// Store the algorithm start time</span></div>
<div class="line"><span class="lineno"> 98</span> <span class="keyword">auto</span> start = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/high_resolution_clock/now.html">std::chrono::high_resolution_clock::now</a>();</div>
<div class="line"><span class="lineno"> 99</span> </div>
<div class="line"><span class="lineno"> 100</span> <span class="comment">// Run the sieve</span></div>
<div class="line"><span class="lineno"> 101</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#a91366864111e1fac29722ca45e02ea8f">math::sieve</a>(&amp;<a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>);</div>
<div class="line"><span class="lineno"> 102</span> </div>
<div class="line"><span class="lineno"> 103</span> <span class="comment">// Time difference calculation</span></div>
<div class="line"><span class="lineno"> 104</span> <span class="keyword">auto</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">time</a> = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/duration/duration_cast.html">std::chrono::duration_cast</a>&lt;</div>
<div class="line"><span class="lineno"> 105</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/duration.html">std::chrono::duration&lt;double, std::ratio&lt;1&gt;</a>&gt;&gt;(</div>
<div class="line"><span class="lineno"> 106</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/high_resolution_clock/now.html">std::chrono::high_resolution_clock::now</a>() - start)</div>
<div class="line"><span class="lineno"> 107</span> .count();</div>
<div class="line"><span class="lineno"> 108</span> </div>
<div class="line"><span class="lineno"> 109</span> <span class="comment">// Print the primes if we see that &quot;print&quot; was passed as an arg</span></div>
<div class="line"><span class="lineno"> 110</span> <span class="keywordflow">if</span> (argc &gt; 1 &amp;&amp; argv[1] == <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(<span class="stringliteral">&quot;print&quot;</span>)) {</div>
<div class="line"><span class="lineno"> 111</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#ad09d59850865012a6fd95d89954c82e4">math::print_primes</a>(<a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>);</div>
<div class="line"><span class="lineno"> 112</span> }</div>
<div class="line"><span class="lineno"> 113</span> </div>
<div class="line"><span class="lineno"> 114</span> <span class="comment">// Print the time taken we found earlier</span></div>
<div class="line"><span class="lineno"> 115</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;Time taken: &quot;</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">time</a> &lt;&lt; <span class="stringliteral">&quot; seconds&quot;</span> &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"> 116</span> </div>
<div class="line"><span class="lineno"> 117</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 118</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>
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<div class="ttc" id="aduration_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/duration.html">std::chrono::duration</a></div></div>
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<div class="ttc" id="aeratosthenes_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d7/da6/eratosthenes_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-tests the sieve function for major inconsistencies.</div><div class="ttdef"><b>Definition:</b> eratosthenes.cpp:64</div></div>
<div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
<div class="ttc" id="anamespacemath_html_a91366864111e1fac29722ca45e02ea8f"><div class="ttname"><a href="../../dd/d47/namespacemath.html#a91366864111e1fac29722ca45e02ea8f">math::sieve</a></div><div class="ttdeci">void sieve(std::vector&lt; bool &gt; *vec)</div><div class="ttdoc">Performs the sieve.</div><div class="ttdef"><b>Definition:</b> eratosthenes.cpp:33</div></div>
<div class="ttc" id="anamespacemath_html_ad09d59850865012a6fd95d89954c82e4"><div class="ttname"><a href="../../dd/d47/namespacemath.html#ad09d59850865012a6fd95d89954c82e4">math::print_primes</a></div><div class="ttdeci">void print_primes(std::vector&lt; bool &gt; const &amp;primes)</div><div class="ttdoc">Prints all the indexes of true values in the passed std::vector.</div><div class="ttdef"><b>Definition:</b> eratosthenes.cpp:51</div></div>
<div class="ttc" id="anow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/high_resolution_clock/now.html">std::chrono::high_resolution_clock::now</a></div><div class="ttdeci">T now(T... args)</div></div>
<div class="ttc" id="aprime__numbers_8cpp_html_a9575f3a51eeb8a57d657b3db6a4b441a"><div class="ttname"><a href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a></div><div class="ttdeci">std::vector&lt; int &gt; primes(size_t max)</div><div class="ttdef"><b>Definition:</b> prime_numbers.cpp:12</div></div>
<div class="ttc" id="atime_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a></div><div class="ttdeci">T time(T... args)</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">static void test </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td></td>
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<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<p>Self-tests the sieve function for major inconsistencies. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 64</span> {</div>
<div class="line"><span class="lineno"> 65</span> <span class="keyword">auto</span> <a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a> = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;bool&gt;</a>(10, <span class="keyword">true</span>);</div>
<div class="line"><span class="lineno"> 66</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#a91366864111e1fac29722ca45e02ea8f">math::sieve</a>(&amp;<a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>);</div>
<div class="line"><span class="lineno"> 67</span> assert(<a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>[0] == <span class="keyword">false</span>);</div>
<div class="line"><span class="lineno"> 68</span> assert(<a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>[1] == <span class="keyword">false</span>);</div>
<div class="line"><span class="lineno"> 69</span> assert(<a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>[2] == <span class="keyword">true</span>);</div>
<div class="line"><span class="lineno"> 70</span> assert(<a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>[3] == <span class="keyword">true</span>);</div>
<div class="line"><span class="lineno"> 71</span> assert(<a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>[4] == <span class="keyword">false</span>);</div>
<div class="line"><span class="lineno"> 72</span> assert(<a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>[5] == <span class="keyword">true</span>);</div>
<div class="line"><span class="lineno"> 73</span> assert(<a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>[6] == <span class="keyword">false</span>);</div>
<div class="line"><span class="lineno"> 74</span> assert(<a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>[7] == <span class="keyword">true</span>);</div>
<div class="line"><span class="lineno"> 75</span> assert(<a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>[8] == <span class="keyword">false</span>);</div>
<div class="line"><span class="lineno"> 76</span> assert(<a class="code hl_function" href="../../de/d9b/prime__numbers_8cpp.html#a9575f3a51eeb8a57d657b3db6a4b441a">primes</a>[9] == <span class="keyword">false</span>);</div>
<div class="line"><span class="lineno"> 77</span> </div>
<div class="line"><span class="lineno"> 78</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 successfully passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 79</span>}</div>
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<tr class="memdesc:a91366864111e1fac29722ca45e02ea8f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Performs the sieve. <br /></td></tr>
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<p>Prints all the indexes of true values in the passed <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>. </p>
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<div class="fragment"><div class="line"><span class="lineno"> 51</span> {</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a91366864111e1fac29722ca45e02ea8f">&#9670;&#160;</a></span>sieve()</h2>
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<p>Performs the sieve. </p>
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<div class="fragment"><div class="line"><span class="lineno"> 33</span> {</div>
<div class="line"><span class="lineno"> 34</span> (*vec)[0] = <span class="keyword">false</span>;</div>
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<div class="line"><span class="lineno"> 36</span> </div>
<div class="line"><span class="lineno"> 37</span> <span class="comment">// The sieve sets values to false as they are found not prime</span></div>
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<tr id="row_13_25_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d40/integral__approximation2_8cpp.html" target="_self">integral_approximation2.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Monte_Carlo_integration" target="_blank">Monte Carlo Integration</a> </td></tr>
<tr id="row_13_26_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/db8/inv__sqrt_8cpp.html" target="_self">inv_sqrt.cpp</a></td><td class="desc">Implementation of <a href="https://medium.com/hard-mode/the-legendary-fast-inverse-square-root-e51fee3b49d9" target="_blank">the inverse square root Root</a> </td></tr>
<tr id="row_13_27_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/d9d/large__factorial_8cpp.html" target="_self">large_factorial.cpp</a></td><td class="desc">Compute factorial of any arbitratily large number/ </td></tr>
<tr id="row_13_28_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><a href="d4/d86/large__number_8h_source.html"><span class="icondoc"></span></a><a class="el" href="d4/d86/large__number_8h.html" target="_self">large_number.h</a></td><td class="desc">Library to perform arithmatic operations on arbitrarily large numbers </td></tr>
<tr id="row_13_29_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d5/d7a/largest__power_8cpp.html" target="_self">largest_power.cpp</a></td><td class="desc">Algorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula </td></tr>
<tr id="row_13_30_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d5/d83/lcm__sum_8cpp.html" target="_self">lcm_sum.cpp</a></td><td class="desc">An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) +
<tr id="row_13_21_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/d46/finding__number__of__digits__in__a__number_8cpp.html" target="_self">finding_number_of_digits_in_a_number.cpp</a></td><td class="desc">[Program to count digits in an integer](<a href="https://www.geeksforgeeks.org/program-count-digits-integer-3-different-methods">https://www.geeksforgeeks.org/program-count-digits-integer-3-different-methods</a>) </td></tr>
<tr id="row_13_22_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/da0/gcd__iterative__euclidean_8cpp.html" target="_self">gcd_iterative_euclidean.cpp</a></td><td class="desc">Compute the greatest common denominator of two integers using <em>iterative form</em> of <a href="https://en.wikipedia.org/wiki/Euclidean_algorithm" target="_blank">Euclidean algorithm</a> </td></tr>
<tr id="row_13_23_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/d11/gcd__of__n__numbers_8cpp.html" target="_self">gcd_of_n_numbers.cpp</a></td><td class="desc">This program aims at calculating the GCD of n numbers by division method </td></tr>
<tr id="row_13_24_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d45/gcd__recursive__euclidean_8cpp.html" target="_self">gcd_recursive_euclidean.cpp</a></td><td class="desc">Compute the greatest common denominator of two integers using <em>recursive form</em> of <a href="https://en.wikipedia.org/wiki/Euclidean_algorithm" target="_blank">Euclidean algorithm</a> </td></tr>
<tr id="row_13_25_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/de9/integral__approximation_8cpp.html" target="_self">integral_approximation.cpp</a></td><td class="desc">Compute integral approximation of the function using <a href="https://en.wikipedia.org/wiki/Riemann_sum" target="_blank">Riemann sum</a> </td></tr>
<tr id="row_13_26_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d40/integral__approximation2_8cpp.html" target="_self">integral_approximation2.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Monte_Carlo_integration" target="_blank">Monte Carlo Integration</a> </td></tr>
<tr id="row_13_27_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/db8/inv__sqrt_8cpp.html" target="_self">inv_sqrt.cpp</a></td><td class="desc">Implementation of <a href="https://medium.com/hard-mode/the-legendary-fast-inverse-square-root-e51fee3b49d9" target="_blank">the inverse square root Root</a> </td></tr>
<tr id="row_13_28_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/d9d/large__factorial_8cpp.html" target="_self">large_factorial.cpp</a></td><td class="desc">Compute factorial of any arbitratily large number/ </td></tr>
<tr id="row_13_29_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><a href="d4/d86/large__number_8h_source.html"><span class="icondoc"></span></a><a class="el" href="d4/d86/large__number_8h.html" target="_self">large_number.h</a></td><td class="desc">Library to perform arithmatic operations on arbitrarily large numbers </td></tr>
<tr id="row_13_30_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d5/d7a/largest__power_8cpp.html" target="_self">largest_power.cpp</a></td><td class="desc">Algorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula </td></tr>
<tr id="row_13_31_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d5/d83/lcm__sum_8cpp.html" target="_self">lcm_sum.cpp</a></td><td class="desc">An algorithm to calculate the sum of LCM: \(\mathrm{LCM}(1,n) +
\mathrm{LCM}(2,n) + \ldots + \mathrm{LCM}(n,n)\) </td></tr>
<tr id="row_13_31_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d21/least__common__multiple_8cpp.html" target="_self">least_common_multiple.cpp</a></td><td class="desc"></td></tr>
<tr id="row_13_32_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d9/d44/magic__number_8cpp.html" target="_self">magic_number.cpp</a></td><td class="desc">A simple program to check if the given number is a magic number or not. A number is said to be a magic number, if the sum of its digits are calculated till a single digit recursively by adding the sum of the digits after every addition. If the single digit comes out to be 1,then the number is a magic number </td></tr>
<tr id="row_13_33_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/d42/miller__rabin_8cpp.html" target="_self">miller_rabin.cpp</a></td><td class="desc"></td></tr>
<tr id="row_13_34_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="df/d72/modular__division_8cpp.html" target="_self">modular_division.cpp</a></td><td class="desc">An algorithm to divide two numbers under modulo p <a href="https://www.geeksforgeeks.org/modular-division" target="_blank">Modular Division</a> </td></tr>
<tr id="row_13_35_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/d6d/modular__exponentiation_8cpp.html" target="_self">modular_exponentiation.cpp</a></td><td class="desc">C++ Program for Modular Exponentiation Iteratively </td></tr>
<tr id="row_13_36_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/d53/modular__inverse__fermat__little__theorem_8cpp.html" target="_self">modular_inverse_fermat_little_theorem.cpp</a></td><td class="desc">C++ Program to find the modular inverse using <a href="https://en.wikipedia.org/wiki/Fermat%27s_little_theorem" target="_blank">Fermat's Little Theorem</a> </td></tr>
<tr id="row_13_37_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/d2d/modular__inverse__simple_8cpp.html" target="_self">modular_inverse_simple.cpp</a></td><td class="desc">Simple implementation of <a href="https://en.wikipedia.org/wiki/Modular_multiplicative_inverse" target="_blank">modular multiplicative inverse</a> </td></tr>
<tr id="row_13_38_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d27/n__bonacci_8cpp.html" target="_self">n_bonacci.cpp</a></td><td class="desc">Implementation of the <a href="http://oeis.org/wiki/N-bonacci_numbers" target="_blank">N-bonacci</a> series </td></tr>
<tr id="row_13_39_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/dbb/n__choose__r_8cpp.html" target="_self">n_choose_r.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Combination" target="_blank">Combinations</a> n choose r function implementation </td></tr>
<tr id="row_13_40_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/dab/ncr__modulo__p_8cpp.html" target="_self">ncr_modulo_p.cpp</a></td><td class="desc">This program aims at calculating <a href="https://cp-algorithms.com/combinatorics/binomial-coefficients.html" target="_blank">nCr modulo p</a> </td></tr>
<tr id="row_13_41_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/da2/number__of__positive__divisors_8cpp.html" target="_self">number_of_positive_divisors.cpp</a></td><td class="desc">C++ Program to calculate the number of positive divisors </td></tr>
<tr id="row_13_42_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d3/dfe/perimeter_8cpp.html" target="_self">perimeter.cpp</a></td><td class="desc">Implementations for the <a href="https://en.wikipedia.org/wiki/Perimeter" target="_blank">perimeter</a> of various shapes </td></tr>
<tr id="row_13_43_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="df/def/power__for__huge__numbers_8cpp.html" target="_self">power_for_huge_numbers.cpp</a></td><td class="desc">Compute powers of large numbers </td></tr>
<tr id="row_13_44_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d38/power__of__two_8cpp.html" target="_self">power_of_two.cpp</a></td><td class="desc">Implementation to check whether a number is a power of 2 or not </td></tr>
<tr id="row_13_45_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d0d/prime__factorization_8cpp.html" target="_self">prime_factorization.cpp</a></td><td class="desc">Prime factorization of positive integers </td></tr>
<tr id="row_13_46_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/d9b/prime__numbers_8cpp.html" target="_self">prime_numbers.cpp</a></td><td class="desc">Get list of prime numbers </td></tr>
<tr id="row_13_47_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html" target="_self">primes_up_to_billion.cpp</a></td><td class="desc">Compute prime numbers upto 1 billion </td></tr>
<tr id="row_13_48_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/d08/realtime__stats_8cpp.html" target="_self">realtime_stats.cpp</a></td><td class="desc">Compute statistics for data entered in rreal-time </td></tr>
<tr id="row_13_49_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html" target="_self">sieve_of_eratosthenes.cpp</a></td><td class="desc">Get list of prime numbers using Sieve of Eratosthenes </td></tr>
<tr id="row_13_50_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="da/d24/sqrt__double_8cpp.html" target="_self">sqrt_double.cpp</a></td><td class="desc">Calculate the square root of any positive real number in \(O(\log
<tr id="row_13_32_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d21/least__common__multiple_8cpp.html" target="_self">least_common_multiple.cpp</a></td><td class="desc"></td></tr>
<tr id="row_13_33_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d9/d44/magic__number_8cpp.html" target="_self">magic_number.cpp</a></td><td class="desc">A simple program to check if the given number is a magic number or not. A number is said to be a magic number, if the sum of its digits are calculated till a single digit recursively by adding the sum of the digits after every addition. If the single digit comes out to be 1,then the number is a magic number </td></tr>
<tr id="row_13_34_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/d42/miller__rabin_8cpp.html" target="_self">miller_rabin.cpp</a></td><td class="desc"></td></tr>
<tr id="row_13_35_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="df/d72/modular__division_8cpp.html" target="_self">modular_division.cpp</a></td><td class="desc">An algorithm to divide two numbers under modulo p <a href="https://www.geeksforgeeks.org/modular-division" target="_blank">Modular Division</a> </td></tr>
<tr id="row_13_36_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/d6d/modular__exponentiation_8cpp.html" target="_self">modular_exponentiation.cpp</a></td><td class="desc">C++ Program for Modular Exponentiation Iteratively </td></tr>
<tr id="row_13_37_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/d53/modular__inverse__fermat__little__theorem_8cpp.html" target="_self">modular_inverse_fermat_little_theorem.cpp</a></td><td class="desc">C++ Program to find the modular inverse using <a href="https://en.wikipedia.org/wiki/Fermat%27s_little_theorem" target="_blank">Fermat's Little Theorem</a> </td></tr>
<tr id="row_13_38_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d6/d2d/modular__inverse__simple_8cpp.html" target="_self">modular_inverse_simple.cpp</a></td><td class="desc">Simple implementation of <a href="https://en.wikipedia.org/wiki/Modular_multiplicative_inverse" target="_blank">modular multiplicative inverse</a> </td></tr>
<tr id="row_13_39_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d27/n__bonacci_8cpp.html" target="_self">n_bonacci.cpp</a></td><td class="desc">Implementation of the <a href="http://oeis.org/wiki/N-bonacci_numbers" target="_blank">N-bonacci</a> series </td></tr>
<tr id="row_13_40_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d1/dbb/n__choose__r_8cpp.html" target="_self">n_choose_r.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Combination" target="_blank">Combinations</a> n choose r function implementation </td></tr>
<tr id="row_13_41_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/dab/ncr__modulo__p_8cpp.html" target="_self">ncr_modulo_p.cpp</a></td><td class="desc">This program aims at calculating <a href="https://cp-algorithms.com/combinatorics/binomial-coefficients.html" target="_blank">nCr modulo p</a> </td></tr>
<tr id="row_13_42_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/da2/number__of__positive__divisors_8cpp.html" target="_self">number_of_positive_divisors.cpp</a></td><td class="desc">C++ Program to calculate the number of positive divisors </td></tr>
<tr id="row_13_43_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d3/dfe/perimeter_8cpp.html" target="_self">perimeter.cpp</a></td><td class="desc">Implementations for the <a href="https://en.wikipedia.org/wiki/Perimeter" target="_blank">perimeter</a> of various shapes </td></tr>
<tr id="row_13_44_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="df/def/power__for__huge__numbers_8cpp.html" target="_self">power_for_huge_numbers.cpp</a></td><td class="desc">Compute powers of large numbers </td></tr>
<tr id="row_13_45_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d38/power__of__two_8cpp.html" target="_self">power_of_two.cpp</a></td><td class="desc">Implementation to check whether a number is a power of 2 or not </td></tr>
<tr id="row_13_46_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="db/d0d/prime__factorization_8cpp.html" target="_self">prime_factorization.cpp</a></td><td class="desc">Prime factorization of positive integers </td></tr>
<tr id="row_13_47_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/d9b/prime__numbers_8cpp.html" target="_self">prime_numbers.cpp</a></td><td class="desc">Get list of prime numbers </td></tr>
<tr id="row_13_48_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d9c/primes__up__to__billion_8cpp.html" target="_self">primes_up_to_billion.cpp</a></td><td class="desc">Compute prime numbers upto 1 billion </td></tr>
<tr id="row_13_49_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d0/d08/realtime__stats_8cpp.html" target="_self">realtime_stats.cpp</a></td><td class="desc">Compute statistics for data entered in rreal-time </td></tr>
<tr id="row_13_50_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html" target="_self">sieve_of_eratosthenes.cpp</a></td><td class="desc">Get list of prime numbers using Sieve of Eratosthenes </td></tr>
<tr id="row_13_51_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="da/d24/sqrt__double_8cpp.html" target="_self">sqrt_double.cpp</a></td><td class="desc">Calculate the square root of any positive real number in \(O(\log
N)\) time, with precision fixed using <a href="https://en.wikipedia.org/wiki/Bisection_method" target="_blank">bisection method</a> of root-finding </td></tr>
<tr id="row_13_51_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="de/d47/string__fibonacci_8cpp.html" target="_self">string_fibonacci.cpp</a></td><td class="desc">This Programme returns the Nth fibonacci as a string </td></tr>
<tr id="row_13_52_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="d4/d9d/sum__of__binomial__coefficient_8cpp.html" target="_self">sum_of_binomial_coefficient.cpp</a></td><td class="desc">Algorithm to find sum of binomial coefficients of a given positive integer </td></tr>
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<tr id="row_13_54_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;">&#160;</span><span class="icondoc"></span><a class="el" href="df/d66/vector__cross__product_8cpp.html" target="_self">vector_cross_product.cpp</a></td><td class="desc">Calculates the <a href="https://en.wikipedia.org/wiki/Cross_product" target="_blank">Cross Product</a> and the magnitude of two mathematical 3D vectors </td></tr>
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