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<div class="title">count_of_trailing_ciphers_in_factorial_n.cpp File Reference</div> </div>
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<p><a href="https://www.tutorialspoint.com/count-trailing-zeros-in-factorial-of-a-number-in-cplusplus">Count the number of ciphers</a> in <code>n!</code> implementation
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
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Include dependency graph for count_of_trailing_ciphers_in_factorial_n.cpp:</div>
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<tr class="memdesc:d7/d81/namespacebit__manipulation"><td class="mdescLeft">&#160;</td><td class="mdescRight">for <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="memdesc:dc/d2f/namespacecount__of__trailing__ciphers__in__factorial__n"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the <a href="https://www.tutorialspoint.com/count-trailing-zeros-in-factorial-of-a-number-in-cplusplus">Count the number of ciphers</a> in <code>n!</code> implementation. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a0d5e1d651d0d30bd682f176d8f2b83d0"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#a0d5e1d651d0d30bd682f176d8f2b83d0">bit_manipulation::count_of_trailing_ciphers_in_factorial_n::numberOfCiphersInFactorialN</a> (uint64_t n)</td></tr>
<tr class="memdesc:a0d5e1d651d0d30bd682f176d8f2b83d0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to count the number of the trailing ciphers. <a href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#a0d5e1d651d0d30bd682f176d8f2b83d0">More...</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="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></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="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><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://www.tutorialspoint.com/count-trailing-zeros-in-factorial-of-a-number-in-cplusplus">Count the number of ciphers</a> in <code>n!</code> implementation </p>
<p>Given an integer number as input. The goal is to find the number of trailing zeroes in the factorial calculated for that number. A factorial of a number N is a product of all numbers in the range [1, N].</p>
<p>We know that we get a trailing zero only if the number is multiple of 10 or has a factor pair (2,5). In all factorials of any number greater than 5, we have many 2s more than 5s in the prime factorization of that number. Dividing a number by powers of 5 will give us the count of 5s in its factors. So, the number of 5s will tell us the number of trailing zeroes. </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Swastyy">Swastika Gupta</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>
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<td class="paramtype">void&#160;</td>
<td class="paramname"></td><td>)</td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; {</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <a class="code" href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160;}</div>
<div class="ttc" id="acount__of__trailing__ciphers__in__factorial__n_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition:</b> count_of_trailing_ciphers_in_factorial_n.cpp:59</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0d5e1d651d0d30bd682f176d8f2b83d0">&#9670;&nbsp;</a></span>numberOfCiphersInFactorialN()</h2>
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<td class="memname">uint64_t bit_manipulation::count_of_trailing_ciphers_in_factorial_n::numberOfCiphersInFactorialN </td>
<td>(</td>
<td class="paramtype">uint64_t&#160;</td>
<td class="paramname"><em>n</em></td><td>)</td>
<td></td>
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<p>Function to count the number of the trailing ciphers. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>number for which <code>n!</code> ciphers are returned </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>count, Number of ciphers in <code>n!</code>. </dd></dl>
<div class="fragment"><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="comment">// count is to store the number of 5&#39;s in factorial(n)</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; uint64_t count = 0;</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; <span class="comment">// Keep dividing n by powers of</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="comment">// 5 and update count</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="keywordflow">for</span> (uint64_t i = 5; n / i &gt;= 1; i *= 5) {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; count += <span class="keyword">static_cast&lt;</span>uint64_t<span class="keyword">&gt;</span>(n) / i;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; }</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; </div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <span class="keywordflow">return</span> count;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&nbsp;</a></span>test()</h2>
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<td class="memname">static void test </td>
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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"><a name="l00059"></a><span class="lineno"> 59</span>&#160; {</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="comment">// 1st test</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;1st test &quot;</span>;</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <a class="code" href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#a0d5e1d651d0d30bd682f176d8f2b83d0">numberOfCiphersInFactorialN</a>(395) == 97);</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &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="l00065"></a><span class="lineno"> 65</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="comment">// 2nd test</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;2nd test &quot;</span>;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <a class="code" href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#a0d5e1d651d0d30bd682f176d8f2b83d0">numberOfCiphersInFactorialN</a>(977) == 242);</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &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="l00071"></a><span class="lineno"> 71</span>&#160; </div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="comment">// 3rd test</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;3rd test &quot;</span>;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <a class="code" href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#a0d5e1d651d0d30bd682f176d8f2b83d0">numberOfCiphersInFactorialN</a>(871) == 215);</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &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="l00077"></a><span class="lineno"> 77</span>&#160; </div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="comment">// 4th test</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;4th test &quot;</span>;</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <a class="code" href="../../da/d50/count__of__trailing__ciphers__in__factorial__n_8cpp.html#a0d5e1d651d0d30bd682f176d8f2b83d0">numberOfCiphersInFactorialN</a>(239) == 57);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed&quot;</span> &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="l00083"></a><span class="lineno"> 83</span>&#160; </div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="comment">// 5th test</span></div>
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<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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