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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;cassert&gt;</code><br />
<code>#include &lt;cstdint&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
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Include dependency graph for largest_power.cpp:</div>
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<p><a href="../../d5/d7a/largest__power_8cpp_source.html">Go to the source code of this file.</a></p>
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Namespaces</h2></td></tr>
<tr class="memitem:math" id="r_math"><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 assert <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:afa39ec943a4836c878e1614fd89b146f" id="r_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. <br /></td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#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. <br /></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>
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<a name="details" id="details"></a><h2 id="header-details" 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)]</p><ul>
<li>\ldots + 1 <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" target="_blank">uday6670</a> </dd></dl>
</li>
</ul>
<p class="definition">Definition in file <a class="el" href="../../d5/d7a/largest__power_8cpp_source.html">largest_power.cpp</a>.</p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" 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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<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>
<p class="definition">Definition at line <a class="el" href="../../d5/d7a/largest__power_8cpp_source.html#l00074">74</a> of file <a class="el" href="../../d5/d7a/largest__power_8cpp_source.html">largest_power.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 74</span> {</div>
<div class="line"><span class="lineno"> 75</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// execute the tests</span></div>
<div class="line"><span class="lineno"> 76</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 77</span>}</div>
<div class="ttc" id="alargest__power_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#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> <a href="../../d5/d7a/largest__power_8cpp_source.html#l00048">largest_power.cpp:48</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">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><span class="tt">void</span> </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d5/d7a/largest__power_8cpp_source.html#l00048">48</a> of file <a class="el" href="../../d5/d7a/largest__power_8cpp_source.html">largest_power.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 48</span> {</div>
<div class="line"><span class="lineno"> 49</span> uint8_t test_case_1 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">math::largestPower</a>(5, 2);</div>
<div class="line"><span class="lineno"> 50</span> assert(test_case_1 == 3);</div>
<div class="line"><span class="lineno"> 51</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 52</span> </div>
<div class="line"><span class="lineno"> 53</span> uint16_t test_case_2 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">math::largestPower</a>(10, 3);</div>
<div class="line"><span class="lineno"> 54</span> assert(test_case_2 == 4);</div>
<div class="line"><span class="lineno"> 55</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 2 Passed!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 56</span> </div>
<div class="line"><span class="lineno"> 57</span> uint32_t test_case_3 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">math::largestPower</a>(25, 5);</div>
<div class="line"><span class="lineno"> 58</span> assert(test_case_3 == 6);</div>
<div class="line"><span class="lineno"> 59</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 3 Passed!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 60</span> </div>
<div class="line"><span class="lineno"> 61</span> uint32_t test_case_4 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">math::largestPower</a>(27, 2);</div>
<div class="line"><span class="lineno"> 62</span> assert(test_case_4 == 23);</div>
<div class="line"><span class="lineno"> 63</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 4 Passed!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 64</span> </div>
<div class="line"><span class="lineno"> 65</span> uint16_t test_case_5 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">math::largestPower</a>(7, 3);</div>
<div class="line"><span class="lineno"> 66</span> assert(test_case_5 == 2);</div>
<div class="line"><span class="lineno"> 67</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 5 Passed!&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 68</span>}</div>
<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> <a href="../../d5/d7a/largest__power_8cpp_source.html#l00029">largest_power.cpp:29</a></div></div>
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