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‎d0/da2/number__of__positive__divisors_8cpp.html‎

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<p>C++ Program to calculate the number of positive divisors.
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
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<code>#include &lt;iostream&gt;</code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for number_of_positive_divisors.cpp:</div>
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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> std::cin &gt;&gt; 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> std::cout &lt;&lt; <span class="stringliteral">&quot;All non-zero numbers are divisors of 0 !&quot;</span> &lt;&lt; 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> std::cout &lt;&lt; <span class="stringliteral">&quot;Number of positive divisors is : &quot;</span>;</div>
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<div class="line"><span class="lineno"> 89</span> std::cout &lt;&lt; <a class="code hl_function" href="#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(n) &lt;&lt; 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="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> <a href="../../d0/da2/number__of__positive__divisors_8cpp_source.html#l00070">number_of_positive_divisors.cpp:70</a></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> <a href="../../d0/da2/number__of__positive__divisors_8cpp_source.html#l00033">number_of_positive_divisors.cpp:33</a></div></div>
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<p class="definition">Definition at line <a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp_source.html#l00080">80</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"> 80</span> {</div>
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<div class="line"><span class="lineno"> 81</span> <a class="code hl_function" href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
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<div class="line"><span class="lineno"> 82</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 83</span>}</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> <a href="../../d0/da2/number__of__positive__divisors_8cpp_source.html#l00069">number_of_positive_divisors.cpp:69</a></div></div>
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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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<div class="fragment"><div class="line"><span class="lineno"> 33</span> {</div>
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<div class="line"><span class="lineno"> 34</span> <span class="keywordflow">if</span> (n &lt; 0) {</div>
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<div class="line"><span class="lineno"> 35</span> n = -n; <span class="comment">// take the absolute value of n</span></div>
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<div class="line"><span class="lineno"> 36</span> }</div>
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<div class="line"><span class="lineno"> 37</span> </div>
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<div class="line"><span class="lineno"> 38</span> <span class="keywordtype">int</span> number_of_divisors = 1;</div>
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<div class="line"><span class="lineno"> 39</span> </div>
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<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i * i &lt;= n; i++) {</div>
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<div class="line"><span class="lineno"> 41</span> <span class="comment">// This part is doing the prime factorization.</span></div>
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<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>
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<div class="line"><span class="lineno"> 43</span> <span class="comment">// already previously find the corresponding prime divisor and dvided</span></div>
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<div class="line"><span class="lineno"> 44</span> <span class="comment">// n by that prime. Therefore, all the divisors found here will</span></div>
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<div class="line"><span class="lineno"> 45</span> <span class="comment">// actually be primes.</span></div>
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<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>
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<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>
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<div class="line"><span class="lineno"> 48</span> <span class="comment">// the remaining number is a prime itself.</span></div>
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<div class="line"><span class="lineno"> 49</span> <span class="keywordtype">int</span> prime_exponent = 0;</div>
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<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">while</span> (n % i == 0) {</div>
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<div class="line"><span class="lineno"> 51</span> <span class="comment">// Repeatedly divide n by the prime divisor n to compute</span></div>
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<div class="line"><span class="lineno"> 52</span> <span class="comment">// the exponent (e_i in the algorithm description).</span></div>
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<div class="line"><span class="lineno"> 53</span> prime_exponent++;</div>
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<div class="line"><span class="lineno"> 54</span> n /= i;</div>
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<div class="line"><span class="lineno"> 55</span> }</div>
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<div class="line"><span class="lineno"> 56</span> number_of_divisors *= prime_exponent + 1;</div>
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<div class="line"><span class="lineno"> 57</span> }</div>
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<div class="line"><span class="lineno"> 58</span> <span class="keywordflow">if</span> (n &gt; 1) {</div>
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<div class="line"><span class="lineno"> 59</span> <span class="comment">// In case the remaining number n is a prime number itself</span></div>
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<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>
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<div class="line"><span class="lineno"> 61</span> number_of_divisors *= 2;</div>
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<div class="line"><span class="lineno"> 62</span> }</div>
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<div class="line"><span class="lineno"> 63</span> </div>
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<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">return</span> number_of_divisors;</div>
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<div class="line"><span class="lineno"> 65</span>}</div>
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<p class="definition">Definition at line <a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp_source.html#l00032">32</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"> 32</span> {</div>
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<div class="line"><span class="lineno"> 33</span> <span class="keywordflow">if</span> (n &lt; 0) {</div>
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<div class="line"><span class="lineno"> 34</span> n = -n; <span class="comment">// take the absolute value of n</span></div>
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<div class="line"><span class="lineno"> 35</span> }</div>
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<div class="line"><span class="lineno"> 36</span> </div>
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<div class="line"><span class="lineno"> 37</span> <span class="keywordtype">int</span> number_of_divisors = 1;</div>
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<div class="line"><span class="lineno"> 38</span> </div>
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<div class="line"><span class="lineno"> 39</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i * i &lt;= n; i++) {</div>
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<div class="line"><span class="lineno"> 40</span> <span class="comment">// This part is doing the prime factorization.</span></div>
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<div class="line"><span class="lineno"> 41</span> <span class="comment">// Note that we cannot find a composite divisor of n unless we would</span></div>
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<div class="line"><span class="lineno"> 42</span> <span class="comment">// already previously find the corresponding prime divisor and dvided</span></div>
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<div class="line"><span class="lineno"> 43</span> <span class="comment">// n by that prime. Therefore, all the divisors found here will</span></div>
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<div class="line"><span class="lineno"> 44</span> <span class="comment">// actually be primes.</span></div>
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<div class="line"><span class="lineno"> 45</span> <span class="comment">// The loop terminates early when it is left with a number n which</span></div>
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<div class="line"><span class="lineno"> 46</span> <span class="comment">// does not have a divisor smaller or equal to sqrt(n) - that means</span></div>
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<div class="line"><span class="lineno"> 47</span> <span class="comment">// the remaining number is a prime itself.</span></div>
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<div class="line"><span class="lineno"> 48</span> <span class="keywordtype">int</span> prime_exponent = 0;</div>
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<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">while</span> (n % i == 0) {</div>
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<div class="line"><span class="lineno"> 50</span> <span class="comment">// Repeatedly divide n by the prime divisor n to compute</span></div>
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<div class="line"><span class="lineno"> 51</span> <span class="comment">// the exponent (e_i in the algorithm description).</span></div>
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<div class="line"><span class="lineno"> 52</span> prime_exponent++;</div>
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<div class="line"><span class="lineno"> 53</span> n /= i;</div>
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<div class="line"><span class="lineno"> 54</span> }</div>
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<div class="line"><span class="lineno"> 55</span> number_of_divisors *= prime_exponent + 1;</div>
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<div class="line"><span class="lineno"> 56</span> }</div>
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<div class="line"><span class="lineno"> 57</span> <span class="keywordflow">if</span> (n &gt; 1) {</div>
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<div class="line"><span class="lineno"> 58</span> <span class="comment">// In case the remaining number n is a prime number itself</span></div>
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<div class="line"><span class="lineno"> 59</span> <span class="comment">// (essentially p_k^1) the final answer is also multiplied by (e_k+1).</span></div>
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<div class="line"><span class="lineno"> 60</span> number_of_divisors *= 2;</div>
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<div class="line"><span class="lineno"> 61</span> }</div>
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<div class="line"><span class="lineno"> 62</span> </div>
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<div class="line"><span class="lineno"> 63</span> <span class="keywordflow">return</span> number_of_divisors;</div>
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<div class="line"><span class="lineno"> 64</span>}</div>
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<p>Test implementations </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"> 73</span> assert(<a class="code hl_function" href="#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(1) == 1);</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="line"><span class="lineno"> 76</span>}</div>
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<p class="definition">Definition at line <a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp_source.html#l00069">69</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"> 69</span> {</div>
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<div class="line"><span class="lineno"> 70</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"> 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>(1) == 1);</div>
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<div class="line"><span class="lineno"> 73</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"> 74</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="line"><span class="lineno"> 75</span>}</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> <a href="../../d0/da2/number__of__positive__divisors_8cpp_source.html#l00032">number_of_positive_divisors.cpp:32</a></div></div>
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