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<p>Prime factorization of positive integers.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;cstring&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for prime_factorization.cpp:</div>
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Functions</h2></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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Variables</h2></td></tr>
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<tr class="memitem:af097796783684712b8326e5b82bfd4fe" id="r_af097796783684712b8326e5b82bfd4fe"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#af097796783684712b8326e5b82bfd4fe">prime_numbers</a></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Prime factorization of positive integers. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>Main program </p>
<div class="fragment"><div class="line"><span class="lineno"> 62</span> {</div>
<div class="line"><span class="lineno"> 63</span> <span class="keywordtype">int</span> num;</div>
<div class="line"><span class="lineno"> 64</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\t\tComputes the prime factorization\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 65</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Type in a number: &quot;</span>;</div>
<div class="line"><span class="lineno"> 66</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; num;</div>
<div class="line"><span class="lineno"> 67</span> </div>
<div class="line"><span class="lineno"> 68</span> <a class="code hl_function" href="#affe577b9bce8f604f5e2f861c63c7099">SieveOfEratosthenes</a>(num);</div>
<div class="line"><span class="lineno"> 69</span> </div>
<div class="line"><span class="lineno"> 70</span> <a class="code hl_function" href="#a0ece0145fb29a5cf48378c23dde2da46">prime_factorization</a>(num);</div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</span> <span class="comment">// Prime factors with their powers in the given number in new line</span></div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordflow">for</span> (<span class="keyword">auto</span> it : <a class="code hl_variable" href="#acfb0df439a4beae5a34ef131ce737c1b">factors</a>) {</div>
<div class="line"><span class="lineno"> 74</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; it.first &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; it.second &lt;&lt; <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"> 75</span> }</div>
<div class="line"><span class="lineno"> 76</span> </div>
<div class="line"><span class="lineno"> 77</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 78</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>
<div class="ttc" id="aprime__factorization_8cpp_html_a0ece0145fb29a5cf48378c23dde2da46"><div class="ttname"><a href="#a0ece0145fb29a5cf48378c23dde2da46">prime_factorization</a></div><div class="ttdeci">void prime_factorization(int num)</div><div class="ttdef"><b>Definition</b> prime_factorization.cpp:40</div></div>
<div class="ttc" id="aprime__factorization_8cpp_html_acfb0df439a4beae5a34ef131ce737c1b"><div class="ttname"><a href="#acfb0df439a4beae5a34ef131ce737c1b">factors</a></div><div class="ttdeci">std::vector&lt; std::pair&lt; int, int &gt; &gt; factors</div><div class="ttdef"><b>Definition</b> prime_factorization.cpp:19</div></div>
<div class="ttc" id="aprime__factorization_8cpp_html_affe577b9bce8f604f5e2f861c63c7099"><div class="ttname"><a href="#affe577b9bce8f604f5e2f861c63c7099">SieveOfEratosthenes</a></div><div class="ttdeci">void SieveOfEratosthenes(int N)</div><div class="ttdef"><b>Definition</b> prime_factorization.cpp:23</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0ece0145fb29a5cf48378c23dde2da46">&#9670;&#160;</a></span>prime_factorization()</h2>
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<td class="memname">void prime_factorization </td>
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<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>num</em></span></td><td>)</td>
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<p>Prime factorization of a number </p>
<div class="fragment"><div class="line"><span class="lineno"> 40</span> {</div>
<div class="line"><span class="lineno"> 41</span> <span class="keywordtype">int</span> number = num;</div>
<div class="line"><span class="lineno"> 42</span> </div>
<div class="line"><span class="lineno"> 43</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; <a class="code hl_variable" href="#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i] &lt;= num; i++) {</div>
<div class="line"><span class="lineno"> 44</span> <span class="keywordtype">int</span> count = 0;</div>
<div class="line"><span class="lineno"> 45</span> </div>
<div class="line"><span class="lineno"> 46</span> <span class="comment">// termination condition</span></div>
<div class="line"><span class="lineno"> 47</span> <span class="keywordflow">if</span> (number == 1) {</div>
<div class="line"><span class="lineno"> 48</span> <span class="keywordflow">break</span>;</div>
<div class="line"><span class="lineno"> 49</span> }</div>
<div class="line"><span class="lineno"> 50</span> </div>
<div class="line"><span class="lineno"> 51</span> <span class="keywordflow">while</span> (number % <a class="code hl_variable" href="#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i] == 0) {</div>
<div class="line"><span class="lineno"> 52</span> count++;</div>
<div class="line"><span class="lineno"> 53</span> number = number / <a class="code hl_variable" href="#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i];</div>
<div class="line"><span class="lineno"> 54</span> }</div>
<div class="line"><span class="lineno"> 55</span> </div>
<div class="line"><span class="lineno"> 56</span> <span class="keywordflow">if</span> (count)</div>
<div class="line"><span class="lineno"> 57</span> <a class="code hl_variable" href="#acfb0df439a4beae5a34ef131ce737c1b">factors</a>.push_back(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(<a class="code hl_variable" href="#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>[i], count));</div>
<div class="line"><span class="lineno"> 58</span> }</div>
<div class="line"><span class="lineno"> 59</span>}</div>
<div class="ttc" id="amake_pair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a></div><div class="ttdeci">T make_pair(T... args)</div></div>
<div class="ttc" id="aprime__factorization_8cpp_html_af097796783684712b8326e5b82bfd4fe"><div class="ttname"><a href="#af097796783684712b8326e5b82bfd4fe">prime_numbers</a></div><div class="ttdeci">std::vector&lt; int &gt; prime_numbers</div><div class="ttdef"><b>Definition</b> prime_factorization.cpp:16</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#affe577b9bce8f604f5e2f861c63c7099">&#9670;&#160;</a></span>SieveOfEratosthenes()</h2>
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<td class="memname">void SieveOfEratosthenes </td>
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<td class="paramtype">int</td> <td class="paramname"><span class="paramname"><em>N</em></span></td><td>)</td>
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<p>Calculating prime number upto a given range </p>
<div class="fragment"><div class="line"><span class="lineno"> 23</span> {</div>
<div class="line"><span class="lineno"> 24</span> <span class="comment">// initializes the array isprime</span></div>
<div class="line"><span class="lineno"> 25</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/memset.html">memset</a>(<a class="code hl_variable" href="#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>, <span class="keyword">true</span>, <span class="keyword">sizeof</span> <a class="code hl_variable" href="#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>);</div>
<div class="line"><span class="lineno"> 26</span> </div>
<div class="line"><span class="lineno"> 27</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><span class="lineno"> 28</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>[i]) {</div>
<div class="line"><span class="lineno"> 29</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 2 * i; j &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; j += i) <a class="code hl_variable" href="#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>[j] = <span class="keyword">false</span>;</div>
<div class="line"><span class="lineno"> 30</span> }</div>
<div class="line"><span class="lineno"> 31</span> }</div>
<div class="line"><span class="lineno"> 32</span> </div>
<div class="line"><span class="lineno"> 33</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 2; i &lt;= <a class="code hl_variable" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
<div class="line"><span class="lineno"> 34</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="#a7fe38b570a51e448430d6a0f072c2f23">isprime</a>[i])</div>
<div class="line"><span class="lineno"> 35</span> <a class="code hl_variable" href="#af097796783684712b8326e5b82bfd4fe">prime_numbers</a>.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(i);</div>
<div class="line"><span class="lineno"> 36</span> }</div>
<div class="line"><span class="lineno"> 37</span>}</div>
<div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition</b> sparse_table.cpp:47</div></div>
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<div class="ttc" id="aprime__factorization_8cpp_html_a7fe38b570a51e448430d6a0f072c2f23"><div class="ttname"><a href="#a7fe38b570a51e448430d6a0f072c2f23">isprime</a></div><div class="ttdeci">bool isprime[1000006]</div><div class="ttdef"><b>Definition</b> prime_factorization.cpp:13</div></div>
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<h2 class="groupheader">Variable Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#acfb0df439a4beae5a34ef131ce737c1b">&#9670;&#160;</a></span>factors</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt;int, int&gt; &gt; factors</td>
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<p>list of prime factor-pairs </p>
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<h2 class="memtitle"><span class="permalink"><a href="#a7fe38b570a51e448430d6a0f072c2f23">&#9670;&#160;</a></span>isprime</h2>
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<td class="memname">bool isprime[1000006]</td>
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<p>Declaring variables for maintaing prime numbers and to check whether a number is prime or not </p>
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<h2 class="memtitle"><span class="permalink"><a href="#af097796783684712b8326e5b82bfd4fe">&#9670;&#160;</a></span>prime_numbers</h2>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;int&gt; prime_numbers</td>
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<p>list of prime numbers </p>
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