mirror of
https://github.com/TheAlgorithms/C-Plus-Plus.git
synced 2026-05-02 14:31:57 +08:00
Documentation for 53a6c16730
This commit is contained in:
github-actions
@@ -3,7 +3,7 @@
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
|
||||
<meta http-equiv="X-UA-Compatible" content="IE=11"/>
|
||||
<meta name="generator" content="Doxygen 1.9.2"/>
|
||||
<meta name="generator" content="Doxygen 1.9.3"/>
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1"/>
|
||||
<title>Algorithms_in_C++: math/number_of_positive_divisors.cpp File Reference</title>
|
||||
<link href="../../tabs.css" rel="stylesheet" type="text/css"/>
|
||||
@@ -30,8 +30,8 @@ MathJax.Hub.Config({
|
||||
<div id="titlearea">
|
||||
<table cellspacing="0" cellpadding="0">
|
||||
<tbody>
|
||||
<tr style="height: 56px;">
|
||||
<td id="projectalign" style="padding-left: 0.5em;">
|
||||
<tr id="projectrow">
|
||||
<td id="projectalign">
|
||||
<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
|
||||
</div>
|
||||
<div id="projectbrief">Set of algorithms implemented in C++.</div>
|
||||
@@ -41,7 +41,7 @@ MathJax.Hub.Config({
|
||||
</table>
|
||||
</div>
|
||||
<!-- end header part -->
|
||||
<!-- Generated by Doxygen 1.9.2 -->
|
||||
<!-- Generated by Doxygen 1.9.3 -->
|
||||
<script type="text/javascript">
|
||||
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
|
||||
var searchBox = new SearchBox("searchBox", "../../search",'Search','.html');
|
||||
@@ -144,18 +144,18 @@ list of positive divisors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.</p>
|
||||
</table>
|
||||
</div><div class="memdoc">
|
||||
<p >Main function </p>
|
||||
<div class="fragment"><div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> {</div>
|
||||
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
|
||||
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordtype">int</span> n;</div>
|
||||
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> n;</div>
|
||||
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keywordflow">if</span> (n == 0) {</div>
|
||||
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"All non-zero numbers are divisors of 0 !"</span> << <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"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> } <span class="keywordflow">else</span> {</div>
|
||||
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Number of positive divisors is : "</span>;</div>
|
||||
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(n) << <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"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> }</div>
|
||||
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 81</span> {</div>
|
||||
<div class="line"><span class="lineno"> 82</span> <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
|
||||
<div class="line"><span class="lineno"> 83</span> <span class="keywordtype">int</span> n;</div>
|
||||
<div class="line"><span class="lineno"> 84</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> >> n;</div>
|
||||
<div class="line"><span class="lineno"> 85</span> <span class="keywordflow">if</span> (n == 0) {</div>
|
||||
<div class="line"><span class="lineno"> 86</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"All non-zero numbers are divisors of 0 !"</span> << <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"> 87</span> } <span class="keywordflow">else</span> {</div>
|
||||
<div class="line"><span class="lineno"> 88</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Number of positive divisors is : "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 89</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(n) << <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"> 90</span> }</div>
|
||||
<div class="line"><span class="lineno"> 91</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><span class="lineno"> 92</span>}</div>
|
||||
<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></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="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>
|
||||
@@ -192,39 +192,39 @@ Here is the call graph for this function:</div>
|
||||
</dd>
|
||||
</dl>
|
||||
<dl class="section return"><dt>Returns</dt><dd>number of positive divisors of n (or 1 if n = 0) </dd></dl>
|
||||
<div class="fragment"><div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> {</div>
|
||||
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordflow">if</span> (n < 0) {</div>
|
||||
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> n = -n; <span class="comment">// take the absolute value of n</span></div>
|
||||
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> }</div>
|
||||
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
|
||||
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordtype">int</span> number_of_divisors = 1;</div>
|
||||
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
|
||||
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i * i <= n; i++) {</div>
|
||||
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// This part is doing the prime factorization.</span></div>
|
||||
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// Note that we cannot find a composite divisor of n unless we would</span></div>
|
||||
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// already previously find the corresponding prime divisor and dvided</span></div>
|
||||
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// n by that prime. Therefore, all the divisors found here will</span></div>
|
||||
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="comment">// actually be primes.</span></div>
|
||||
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// The loop terminates early when it is left with a number n which</span></div>
|
||||
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// does not have a divisor smaller or equal to sqrt(n) - that means</span></div>
|
||||
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// the remaining number is a prime itself.</span></div>
|
||||
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordtype">int</span> prime_exponent = 0;</div>
|
||||
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <span class="keywordflow">while</span> (n % i == 0) {</div>
|
||||
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// Repeatedly divide n by the prime divisor n to compute</span></div>
|
||||
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// the exponent (e_i in the algorithm description).</span></div>
|
||||
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> prime_exponent++;</div>
|
||||
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> n /= i;</div>
|
||||
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> }</div>
|
||||
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> number_of_divisors *= prime_exponent + 1;</div>
|
||||
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> }</div>
|
||||
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordflow">if</span> (n > 1) {</div>
|
||||
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// In case the remaining number n is a prime number itself</span></div>
|
||||
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// (essentially p_k^1) the final answer is also multiplied by (e_k+1).</span></div>
|
||||
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> number_of_divisors *= 2;</div>
|
||||
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> }</div>
|
||||
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
|
||||
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">return</span> number_of_divisors;</div>
|
||||
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 33</span> {</div>
|
||||
<div class="line"><span class="lineno"> 34</span> <span class="keywordflow">if</span> (n < 0) {</div>
|
||||
<div class="line"><span class="lineno"> 35</span> n = -n; <span class="comment">// take the absolute value of n</span></div>
|
||||
<div class="line"><span class="lineno"> 36</span> }</div>
|
||||
<div class="line"><span class="lineno"> 37</span> </div>
|
||||
<div class="line"><span class="lineno"> 38</span> <span class="keywordtype">int</span> number_of_divisors = 1;</div>
|
||||
<div class="line"><span class="lineno"> 39</span> </div>
|
||||
<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i * i <= n; i++) {</div>
|
||||
<div class="line"><span class="lineno"> 41</span> <span class="comment">// This part is doing the prime factorization.</span></div>
|
||||
<div class="line"><span class="lineno"> 42</span> <span class="comment">// Note that we cannot find a composite divisor of n unless we would</span></div>
|
||||
<div class="line"><span class="lineno"> 43</span> <span class="comment">// already previously find the corresponding prime divisor and dvided</span></div>
|
||||
<div class="line"><span class="lineno"> 44</span> <span class="comment">// n by that prime. Therefore, all the divisors found here will</span></div>
|
||||
<div class="line"><span class="lineno"> 45</span> <span class="comment">// actually be primes.</span></div>
|
||||
<div class="line"><span class="lineno"> 46</span> <span class="comment">// The loop terminates early when it is left with a number n which</span></div>
|
||||
<div class="line"><span class="lineno"> 47</span> <span class="comment">// does not have a divisor smaller or equal to sqrt(n) - that means</span></div>
|
||||
<div class="line"><span class="lineno"> 48</span> <span class="comment">// the remaining number is a prime itself.</span></div>
|
||||
<div class="line"><span class="lineno"> 49</span> <span class="keywordtype">int</span> prime_exponent = 0;</div>
|
||||
<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">while</span> (n % i == 0) {</div>
|
||||
<div class="line"><span class="lineno"> 51</span> <span class="comment">// Repeatedly divide n by the prime divisor n to compute</span></div>
|
||||
<div class="line"><span class="lineno"> 52</span> <span class="comment">// the exponent (e_i in the algorithm description).</span></div>
|
||||
<div class="line"><span class="lineno"> 53</span> prime_exponent++;</div>
|
||||
<div class="line"><span class="lineno"> 54</span> n /= i;</div>
|
||||
<div class="line"><span class="lineno"> 55</span> }</div>
|
||||
<div class="line"><span class="lineno"> 56</span> number_of_divisors *= prime_exponent + 1;</div>
|
||||
<div class="line"><span class="lineno"> 57</span> }</div>
|
||||
<div class="line"><span class="lineno"> 58</span> <span class="keywordflow">if</span> (n > 1) {</div>
|
||||
<div class="line"><span class="lineno"> 59</span> <span class="comment">// In case the remaining number n is a prime number itself</span></div>
|
||||
<div class="line"><span class="lineno"> 60</span> <span class="comment">// (essentially p_k^1) the final answer is also multiplied by (e_k+1).</span></div>
|
||||
<div class="line"><span class="lineno"> 61</span> number_of_divisors *= 2;</div>
|
||||
<div class="line"><span class="lineno"> 62</span> }</div>
|
||||
<div class="line"><span class="lineno"> 63</span> </div>
|
||||
<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">return</span> number_of_divisors;</div>
|
||||
<div class="line"><span class="lineno"> 65</span>}</div>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
</div>
|
||||
@@ -243,13 +243,13 @@ Here is the call graph for this function:</div>
|
||||
</table>
|
||||
</div><div class="memdoc">
|
||||
<p >Test implementations </p>
|
||||
<div class="fragment"><div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> {</div>
|
||||
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(36) == 9);</div>
|
||||
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(-36) == 9);</div>
|
||||
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(1) == 1);</div>
|
||||
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(2011) == 2); <span class="comment">// 2011 is a prime</span></div>
|
||||
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(756) == 24); <span class="comment">// 756 = 2^2 * 3^3 * 7</span></div>
|
||||
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 70</span> {</div>
|
||||
<div class="line"><span class="lineno"> 71</span> assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(36) == 9);</div>
|
||||
<div class="line"><span class="lineno"> 72</span> assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(-36) == 9);</div>
|
||||
<div class="line"><span class="lineno"> 73</span> assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(1) == 1);</div>
|
||||
<div class="line"><span class="lineno"> 74</span> assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(2011) == 2); <span class="comment">// 2011 is a prime</span></div>
|
||||
<div class="line"><span class="lineno"> 75</span> assert(<a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(756) == 24); <span class="comment">// 756 = 2^2 * 3^3 * 7</span></div>
|
||||
<div class="line"><span class="lineno"> 76</span>}</div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
|
||||
<div class="dyncontent">
|
||||
@@ -265,7 +265,7 @@ Here is the call graph for this function:</div>
|
||||
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
|
||||
<ul>
|
||||
<li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp.html">number_of_positive_divisors.cpp</a></li>
|
||||
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.2 </li>
|
||||
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
|
||||
</ul>
|
||||
</div>
|
||||
</body>
|
||||
|
||||
@@ -1,6 +1,6 @@
|
||||
<map id="main" name="main">
|
||||
<area shape="rect" id="node1" title=" " alt="" coords="5,56,56,83"/>
|
||||
<area shape="rect" id="node2" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/io/manip/endl.html#" title=" " alt="" coords="104,5,176,32"/>
|
||||
<area shape="rect" id="node2" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/io/manip/endl#" title=" " alt="" coords="104,5,176,32"/>
|
||||
<area shape="rect" id="node3" href="$d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb" title=" " alt="" coords="224,74,359,115"/>
|
||||
<area shape="rect" id="node4" href="$d0/da2/number__of__positive__divisors_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9" title=" " alt="" coords="115,107,165,133"/>
|
||||
</map>
|
||||
|
||||
@@ -1 +1 @@
|
||||
1ddf60f3953d9f51e8f82d6aa527fc28
|
||||
de6156481e1a01c0cae481cd575fa63b
|
||||
@@ -21,7 +21,7 @@
|
||||
<!-- Node2 -->
|
||||
<g id="node2" class="node">
|
||||
<title>Node2</title>
|
||||
<g id="a_node2"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/io/manip/endl.html#" xlink:title=" ">
|
||||
<g id="a_node2"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/io/manip/endl#" xlink:title=" ">
|
||||
<polygon fill="white" stroke="black" points="74,-76.5 74,-95.5 128,-95.5 128,-76.5 74,-76.5"/>
|
||||
<text text-anchor="middle" x="101" y="-83.5" font-family="Helvetica,sans-Serif" font-size="10.00">std::endl</text>
|
||||
</a>
|
||||
|
||||
|
Before Width: | Height: | Size: 3.5 KiB After Width: | Height: | Size: 3.5 KiB |
Reference in New Issue
Block a user