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<div class="headertitle"><div class="title">number_of_positive_divisors.cpp</div></div>
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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="l00024" name="l00024"></a><span class="lineno"> 24</span> </div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include &lt;cassert&gt;</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include &lt;iostream&gt;</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 &lt; 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 &lt;= 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 &gt; 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 &gt;&gt; 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 &lt;&lt; <span class="stringliteral">&quot;All non-zero numbers are divisors of 0 !&quot;</span> &lt;&lt; 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 &lt;&lt; <span class="stringliteral">&quot;Number of positive divisors is : &quot;</span>;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> std::cout &lt;&lt; <a class="code hl_function" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(n) &lt;&lt; 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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