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<div id="projectname">TheAlgorithms/C++<span id="projectnumber"> 1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../d4/da4/number__of__positive__divisors_8cpp__incl.svg" width="179" height="126"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:ad89ccced8504b5116046cfa03066ffeb" id="r_ad89ccced8504b5116046cfa03066ffeb"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a> (int n)</td></tr>
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@@ -140,6 +159,8 @@ Finally, there are \((e_1+1) \times (e_2+1)\times\cdots\times (e_k+1)\) positive
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\(\mbox{number_of_positive_divisors}(36) = (2+1) \cdot (2+1) = 9\). <br />
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list of positive divisors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.</p>
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<p>Similarly, for N = -36 the number of positive divisors remain same. </p>
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<p class="definition">Definition in file <a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp_source.html">number_of_positive_divisors.cpp</a>.</p>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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@@ -156,29 +177,23 @@ list of positive divisors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.</p>
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</table>
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</div><div class="memdoc">
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<p>Main function </p>
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<p class="definition">Definition at line <a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp_source.html#l00081">81</a> of file <a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp_source.html">number_of_positive_divisors.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 81</span> {</div>
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<div class="line"><span class="lineno"> 82</span> <a class="code hl_function" href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
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<div class="line"><span class="lineno"> 83</span> <span class="keywordtype">int</span> n;</div>
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<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>
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<div class="line"><span class="lineno"> 84</span> std::cin >> n;</div>
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<div class="line"><span class="lineno"> 85</span> <span class="keywordflow">if</span> (n == 0) {</div>
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<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>
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<div class="line"><span class="lineno"> 86</span> std::cout << <span class="stringliteral">"All non-zero numbers are divisors of 0 !"</span> << std::endl;</div>
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<div class="line"><span class="lineno"> 87</span> } <span class="keywordflow">else</span> {</div>
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<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>
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<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="#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>
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<div class="line"><span class="lineno"> 88</span> std::cout << <span class="stringliteral">"Number of positive divisors is : "</span>;</div>
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<div class="line"><span class="lineno"> 89</span> std::cout << <a class="code hl_function" href="#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(n) << std::endl;</div>
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<div class="line"><span class="lineno"> 90</span> }</div>
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<div class="line"><span class="lineno"> 91</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 92</span>}</div>
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<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>
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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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<div class="ttc" id="anumber__of__positive__divisors_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition</b> number_of_positive_divisors.cpp:70</div></div>
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<div class="ttc" id="anumber__of__positive__divisors_8cpp_html_ad89ccced8504b5116046cfa03066ffeb"><div class="ttname"><a href="#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a></div><div class="ttdeci">int number_of_positive_divisors(int n)</div><div class="ttdef"><b>Definition</b> number_of_positive_divisors.cpp:33</div></div>
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>number of positive divisors of n (or 1 if n = 0) </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp_source.html#l00033">33</a> of file <a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp_source.html">number_of_positive_divisors.cpp</a>.</p>
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<p class="definition">Definition at line <a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp_source.html#l00070">70</a> of file <a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp_source.html">number_of_positive_divisors.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 70</span> {</div>
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<div class="line"><span class="lineno"> 71</span> assert(<a class="code hl_function" href="#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(36) == 9);</div>
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<div class="line"><span class="lineno"> 72</span> assert(<a class="code hl_function" href="#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(-36) == 9);</div>
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<div class="line"><span class="lineno"> 74</span> assert(<a class="code hl_function" href="#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(2011) == 2); <span class="comment">// 2011 is a prime</span></div>
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<div class="line"><span class="lineno"> 75</span> assert(<a class="code hl_function" href="#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(756) == 24); <span class="comment">// 756 = 2^2 * 3^3 * 7</span></div>
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<div class="headertitle"><div class="title">number_of_positive_divisors.cpp</div></div>
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<div class="contents">
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<a href="../../d0/da2/number__of__positive__divisors_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
|
||||
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include <cassert></span></div>
|
||||
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include <iostream></span></div>
|
||||
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> </div>
|
||||
<div class="foldopen" id="foldopen00033" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"><a class="line" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb"> 33</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(<span class="keywordtype">int</span> n) {</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>
|
||||
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> </div>
|
||||
<div class="foldopen" id="foldopen00070" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"><a class="line" href="../../d0/da2/number__of__positive__divisors_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9"> 70</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>() {</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>
|
||||
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> </div>
|
||||
<div class="foldopen" id="foldopen00081" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"><a class="line" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 81</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</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> std::cin >> 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> std::cout << <span class="stringliteral">"All non-zero numbers are divisors of 0 !"</span> << std::endl;</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> std::cout << <span class="stringliteral">"Number of positive divisors is : "</span>;</div>
|
||||
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> std::cout << <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(n) << std::endl;</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>
|
||||
<div class="ttc" id="anumber__of__positive__divisors_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="../../d0/da2/number__of__positive__divisors_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition</b> <a href="#l00070">number_of_positive_divisors.cpp:70</a></div></div>
|
||||
<div class="ttc" id="anumber__of__positive__divisors_8cpp_html_ad89ccced8504b5116046cfa03066ffeb"><div class="ttname"><a href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a></div><div class="ttdeci">int number_of_positive_divisors(int n)</div><div class="ttdef"><b>Definition</b> <a href="#l00033">number_of_positive_divisors.cpp:33</a></div></div>
|
||||
<div class="ttc" id="anumber__of__positive__divisors_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d0/da2/number__of__positive__divisors_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition</b> <a href="#l00081">number_of_positive_divisors.cpp:81</a></div></div>
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