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<p>C++ Program to calculate number of divisors.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for number_of_positive_divisors.cpp:</div>
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Functions</h2></td></tr>
<tr class="memitem:ad89ccced8504b5116046cfa03066ffeb"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a> (int n)</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>C++ Program to calculate number of divisors. </p>
<p>This algorithm use the prime factorization approach. Any number can be written in multiplication of its prime factors. <br />
Let N = P1^E1 * P2^E2 ... Pk^Ek <br />
Therefore. number-of-divisors(N) = (E1+1) * (E2+1) ... (Ek+1). <br />
Where P1, P2 ... Pk are prime factors and E1, E2 ... Ek are exponents respectively.</p>
<p>Example:- <br />
N = 36 <br />
36 = (3^2 * 2^2) <br />
number_of_positive_divisors(36) = (2+1) * (2+1) = 9. <br />
list of positive divisors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.</p>
<p>Similarly if N is -36 at that time number of positive divisors remain same.</p>
<p>Example:- <br />
N = -36 <br />
-36 = -1 * (3^2 * 2^2) <br />
number_of_positive_divisors(-36) = (2+1) * (2+1) = 9. <br />
list of positive divisors of -36 = 1, 2, 3, 4, 6, 9, 12, 18, 36. </p>
</div><h2 class="groupheader">Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; {</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordtype">int</span> n;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; n;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; <span class="keywordflow">if</span> (n &lt; 0) {</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; n = -n;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; }</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordflow">if</span> (n == 0) {</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;All non-zero numbers are divisors of 0 !&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Number of positive divisors is : &quot;</span>;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code" href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a>(n) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; }</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ad89ccced8504b5116046cfa03066ffeb">&#9670;&nbsp;</a></span>number_of_positive_divisors()</h2>
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<td class="memname">int number_of_positive_divisors </td>
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<td class="paramname"><em>n</em></td><td>)</td>
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<p>Algorithm </p>
<div class="fragment"><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; {</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int&gt;</a> prime_exponent_count;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i * i &lt;= n; i++) {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordtype">int</span> prime_count = 0;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; <span class="keywordflow">while</span> (n % i == 0) {</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; prime_count += 1;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; n /= i;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; }</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordflow">if</span> (prime_count != 0) {</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; prime_exponent_count.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(prime_count);</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; }</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; }</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="keywordflow">if</span> (n &gt; 1) {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; prime_exponent_count.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(1);</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; }</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; </div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <span class="keywordtype">int</span> divisors_count = 1;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; prime_exponent_count.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; divisors_count = divisors_count * (prime_exponent_count[i] + 1);</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; }</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keywordflow">return</span> divisors_count;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160;}</div>
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<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt; int &gt;</a></div></div>
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