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<p>Algorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
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Include dependency graph for largest_power.cpp:</div>
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Functions</h2></td></tr>
<tr class="memitem:afa39ec943a4836c878e1614fd89b146f"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">math::largestPower</a> (uint32_t n, const uint16_t &amp;p)</td></tr>
<tr class="memdesc:afa39ec943a4836c878e1614fd89b146f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to calculate largest power. <a href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">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="../../d5/d7a/largest__power_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function for testing largestPower function. test cases and assert statement. <a href="../../d5/d7a/largest__power_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="../../d5/d7a/largest__power_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d5/d7a/largest__power_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>Algorithm to find largest x such that p^x divides n! (factorial) using Legendre's Formula. </p>
<p>Given an integer n and a prime number p, the task is to find the largest x such that p^x (p raised to power x) divides n! (factorial). This will be done using Legendre's formula: x = [n/(p^1)] + [n/(p^2)] + [n/(p^3)] + \ldots + 1 </p><dl class="section see"><dt>See also</dt><dd>more on <a href="https://math.stackexchange.com/questions/141196/highest-power-of-a-prime-p-dividing-n">https://math.stackexchange.com/questions/141196/highest-power-of-a-prime-p-dividing-n</a> </dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/uday6670">uday6670</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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<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="l00075"></a><span class="lineno"> 75</span>&#160;{ </div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <a class="code" href="../../d5/d7a/largest__power_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160;} </div>
<div class="ttc" id="alargest__power_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d5/d7a/largest__power_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Function for testing largestPower function. test cases and assert statement.</div><div class="ttdef"><b>Definition:</b> largest_power.cpp:47</div></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>Function for testing largestPower function. test cases and assert statement. </p>
<dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
<div class="fragment"><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; uint8_t test_case_1 = <a class="code" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">math::largestPower</a>(5,2);</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; assert(test_case_1==3);</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</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;Test 1 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="l00052"></a><span class="lineno"> 52</span>&#160; </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; uint16_t test_case_2 = <a class="code" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">math::largestPower</a>(10,3);</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; assert(test_case_2==4);</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</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;Test 2 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="l00056"></a><span class="lineno"> 56</span>&#160; </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; uint32_t test_case_3 = <a class="code" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">math::largestPower</a>(25,5);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; assert(test_case_3==6);</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</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;Test 3 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="l00060"></a><span class="lineno"> 60</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; uint32_t test_case_4 = <a class="code" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">math::largestPower</a>(27,2);</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; assert(test_case_4==23);</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</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;Test 4 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="l00064"></a><span class="lineno"> 64</span>&#160; </div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; uint16_t test_case_5 = <a class="code" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">math::largestPower</a>(7,3);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; assert(test_case_5==2);</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;Test 5 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="l00068"></a><span class="lineno"> 68</span>&#160;} </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="anamespacemath_html_afa39ec943a4836c878e1614fd89b146f"><div class="ttname"><a href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">math::largestPower</a></div><div class="ttdeci">uint64_t largestPower(uint32_t n, const uint16_t &amp;p)</div><div class="ttdoc">Function to calculate largest power.</div><div class="ttdef"><b>Definition:</b> largest_power.cpp:26</div></div>
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