Documentation for c6af943508

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realstealthninja
2024-11-04 12:10:37 +00:00
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commit fb1d00ead7
518 changed files with 13882 additions and 10974 deletions

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@@ -126,7 +126,7 @@ Include dependency graph for gcd_of_n_numbers.cpp:</div>
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
Namespaces</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html">math</a></td></tr>
<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <br /></td></tr>
<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for assert <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/ddb/namespacegcd__of__n__numbers.html">gcd_of_n_numbers</a></td></tr>
<tr class="memdesc:d2/ddb/namespacegcd__of__n__numbers"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute GCD of numbers in an array. <br /></td></tr>
@@ -238,7 +238,7 @@ template&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/
<div class="line"><span class="lineno"> 77</span> }</div>
<div class="line"><span class="lineno"> 78</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
<div class="line"><span class="lineno"> 79</span>}</div>
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition</b> fibonacci_sum.cpp:76</div></div>
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition</b> fibonacci_sum.cpp:77</div></div>
<div class="ttc" id="agcd__of__n__numbers_8cpp_html_a509a35e11ed1e17a9e00dd56320a4181"><div class="ttname"><a href="#a509a35e11ed1e17a9e00dd56320a4181">math::gcd_of_n_numbers::gcd_two</a></div><div class="ttdeci">int gcd_two(int x, int y)</div><div class="ttdoc">Function to compute GCD of 2 numbers x and y.</div><div class="ttdef"><b>Definition</b> gcd_of_n_numbers.cpp:35</div></div>
<div class="ttc" id="agcd__of__n__numbers_8cpp_html_a71b9357c7a722f8208499d9ba573297a"><div class="ttname"><a href="#a71b9357c7a722f8208499d9ba573297a">math::gcd_of_n_numbers::check_all_zeros</a></div><div class="ttdeci">bool check_all_zeros(const std::array&lt; int, n &gt; &amp;a)</div><div class="ttdoc">Function to check if all elements in the array are 0.</div><div class="ttdef"><b>Definition</b> gcd_of_n_numbers.cpp:53</div></div>
<div class="ttc" id="asize_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a></div></div>

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@@ -115,13 +115,14 @@ $(function(){initNavTree('d1/d21/quick__sort_8cpp.html','../../'); initResizable
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cstdint&gt;</code><br />
<code>#include &lt;ctime&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for quick_sort.cpp:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/db2/quick__sort_8cpp__incl.svg" width="427" height="111"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/db2/quick__sort_8cpp__incl.svg" width="512" height="111"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
</div>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
@@ -191,49 +192,49 @@ Functions</h2></td></tr>
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 201</span> {</div>
<div class="line"><span class="lineno"> 202</span> <span class="keywordtype">int</span> choice = 0;</div>
<div class="line"><span class="lineno"> 203</span> </div>
<div class="line"><span class="lineno"> 204</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;\tAvailable modes\t\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 205</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;1. Self-tests mode\n2. Interactive mode&quot;</span>;</div>
<div class="line"><span class="lineno"> 206</span> </div>
<div class="line"><span class="lineno"> 207</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;\nChoose a mode: &quot;</span>;</div>
<div class="line"><span class="lineno"> 208</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; choice;</div>
<div class="line"><span class="lineno"> 209</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;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 210</span> </div>
<div class="line"><span class="lineno"> 211</span> <span class="keywordflow">while</span> ((choice != 1) &amp;&amp; (choice != 2)) {</div>
<div class="line"><span class="lineno"> 212</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;Invalid option. Choose between the valid modes: &quot;</span>;</div>
<div class="line"><span class="lineno"> 213</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; choice;</div>
<div class="line"><span class="lineno"> 214</span> }</div>
<div class="line"><span class="lineno"> 215</span> </div>
<div class="line"><span class="lineno"> 216</span> <span class="keywordflow">if</span> (choice == 1) {</div>
<div class="line"><span class="lineno"> 217</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
<div class="line"><span class="lineno"> 218</span> <a class="code hl_function" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 219</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (choice == 2) {</div>
<div class="line"><span class="lineno"> 220</span> <span class="keywordtype">int</span> size = 0;</div>
<div class="line"><span class="lineno"> 221</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;\nEnter the number of elements: &quot;</span>;</div>
<div class="line"><span class="lineno"> 222</span> </div>
<div class="line"><span class="lineno"> 223</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; size;</div>
<div class="line"><span class="lineno"> 224</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> arr(size);</div>
<div class="line"><span class="lineno"> 225</span> </div>
<div class="line"><span class="lineno"> 226</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
<div class="line"><span class="lineno"> 227</span> &lt;&lt; <span class="stringliteral">&quot;\nEnter the unsorted elements (can be negative/decimal): &quot;</span>;</div>
<div class="line"><span class="lineno"> 228</span> </div>
<div class="line"><span class="lineno"> 229</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; size; ++i) {</div>
<div class="line"><span class="lineno"> 230</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;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 231</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; arr[i];</div>
<div class="line"><span class="lineno"> 232</span> }</div>
<div class="line"><span class="lineno"> 233</span> <a class="code hl_function" href="#a5e6213e8008356ac6eda9427f3f4b394">sorting::quick_sort::quick_sort</a>(&amp;arr, 0, size - 1);</div>
<div class="line"><span class="lineno"> 234</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;\nSorted array: \n&quot;</span>;</div>
<div class="line"><span class="lineno"> 235</span> <a class="code hl_function" href="#aeccefcf6fcca62c54939c5ec9a93109b">sorting::quick_sort::show</a>(arr, size);</div>
<div class="line"><span class="lineno"> 236</span> }</div>
<div class="line"><span class="lineno"> 237</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 238</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 202</span> {</div>
<div class="line"><span class="lineno"> 203</span> <span class="keywordtype">int</span> choice = 0;</div>
<div class="line"><span class="lineno"> 204</span> </div>
<div class="line"><span class="lineno"> 205</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;\tAvailable modes\t\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 206</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;1. Self-tests mode\n2. Interactive mode&quot;</span>;</div>
<div class="line"><span class="lineno"> 207</span> </div>
<div class="line"><span class="lineno"> 208</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;\nChoose a mode: &quot;</span>;</div>
<div class="line"><span class="lineno"> 209</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; choice;</div>
<div class="line"><span class="lineno"> 210</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;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 211</span> </div>
<div class="line"><span class="lineno"> 212</span> <span class="keywordflow">while</span> ((choice != 1) &amp;&amp; (choice != 2)) {</div>
<div class="line"><span class="lineno"> 213</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;Invalid option. Choose between the valid modes: &quot;</span>;</div>
<div class="line"><span class="lineno"> 214</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; choice;</div>
<div class="line"><span class="lineno"> 215</span> }</div>
<div class="line"><span class="lineno"> 216</span> </div>
<div class="line"><span class="lineno"> 217</span> <span class="keywordflow">if</span> (choice == 1) {</div>
<div class="line"><span class="lineno"> 218</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
<div class="line"><span class="lineno"> 219</span> <a class="code hl_function" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 220</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (choice == 2) {</div>
<div class="line"><span class="lineno"> 221</span> <span class="keywordtype">int</span> size = 0;</div>
<div class="line"><span class="lineno"> 222</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;\nEnter the number of elements: &quot;</span>;</div>
<div class="line"><span class="lineno"> 223</span> </div>
<div class="line"><span class="lineno"> 224</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; size;</div>
<div class="line"><span class="lineno"> 225</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> arr(size);</div>
<div class="line"><span class="lineno"> 226</span> </div>
<div class="line"><span class="lineno"> 227</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
<div class="line"><span class="lineno"> 228</span> &lt;&lt; <span class="stringliteral">&quot;\nEnter the unsorted elements (can be negative/decimal): &quot;</span>;</div>
<div class="line"><span class="lineno"> 229</span> </div>
<div class="line"><span class="lineno"> 230</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; size; ++i) {</div>
<div class="line"><span class="lineno"> 231</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;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 232</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; arr[i];</div>
<div class="line"><span class="lineno"> 233</span> }</div>
<div class="line"><span class="lineno"> 234</span> <a class="code hl_function" href="#a5e6213e8008356ac6eda9427f3f4b394">sorting::quick_sort::quick_sort</a>(&amp;arr, 0, size - 1);</div>
<div class="line"><span class="lineno"> 235</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;\nSorted array: \n&quot;</span>;</div>
<div class="line"><span class="lineno"> 236</span> <a class="code hl_function" href="#aeccefcf6fcca62c54939c5ec9a93109b">sorting::quick_sort::show</a>(arr, size);</div>
<div class="line"><span class="lineno"> 237</span> }</div>
<div class="line"><span class="lineno"> 238</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 239</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="aquick__sort_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> quick_sort.cpp:135</div></div>
<div class="ttc" id="aquick__sort_8cpp_html_a5e6213e8008356ac6eda9427f3f4b394"><div class="ttname"><a href="#a5e6213e8008356ac6eda9427f3f4b394">sorting::quick_sort::quick_sort</a></div><div class="ttdeci">void quick_sort(std::vector&lt; T &gt; *arr, const int &amp;low, const int &amp;high)</div><div class="ttdoc">the main function that implements Quick Sort.</div><div class="ttdef"><b>Definition</b> quick_sort.cpp:86</div></div>
<div class="ttc" id="aquick__sort_8cpp_html_aeccefcf6fcca62c54939c5ec9a93109b"><div class="ttname"><a href="#aeccefcf6fcca62c54939c5ec9a93109b">sorting::quick_sort::show</a></div><div class="ttdeci">void show(const std::vector&lt; T &gt; &amp;arr, const int &amp;size)</div><div class="ttdoc">Utility function to print the array contents.</div><div class="ttdef"><b>Definition</b> quick_sort.cpp:123</div></div>
<div class="ttc" id="aquick__sort_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> quick_sort.cpp:136</div></div>
<div class="ttc" id="aquick__sort_8cpp_html_a5e6213e8008356ac6eda9427f3f4b394"><div class="ttname"><a href="#a5e6213e8008356ac6eda9427f3f4b394">sorting::quick_sort::quick_sort</a></div><div class="ttdeci">void quick_sort(std::vector&lt; T &gt; *arr, const int &amp;low, const int &amp;high)</div><div class="ttdoc">the main function that implements Quick Sort.</div><div class="ttdef"><b>Definition</b> quick_sort.cpp:87</div></div>
<div class="ttc" id="aquick__sort_8cpp_html_aeccefcf6fcca62c54939c5ec9a93109b"><div class="ttname"><a href="#aeccefcf6fcca62c54939c5ec9a93109b">sorting::quick_sort::show</a></div><div class="ttdeci">void show(const std::vector&lt; T &gt; &amp;arr, const int &amp;size)</div><div class="ttdoc">Utility function to print the array contents.</div><div class="ttdef"><b>Definition</b> quick_sort.cpp:124</div></div>
<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
<div class="ttc" id="atime_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a></div><div class="ttdeci">T time(T... args)</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
@@ -287,22 +288,22 @@ template&lt;typename T &gt; </div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>index of the smaller element </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 58</span> {</div>
<div class="line"><span class="lineno"> 59</span> T pivot = (*arr)[high]; <span class="comment">// taking the last element as pivot</span></div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordtype">int</span> i = (low - 1); <span class="comment">// Index of smaller element</span></div>
<div class="line"><span class="lineno"> 61</span> </div>
<div class="line"><span class="lineno"> 62</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = low; j &lt; high; j++) {</div>
<div class="line"><span class="lineno"> 63</span> <span class="comment">// If current element is smaller than or</span></div>
<div class="line"><span class="lineno"> 64</span> <span class="comment">// equal to pivot</span></div>
<div class="line"><span class="lineno"> 65</span> <span class="keywordflow">if</span> ((*arr)[j] &lt;= pivot) {</div>
<div class="line"><span class="lineno"> 66</span> i++; <span class="comment">// increment index of smaller element</span></div>
<div class="line"><span class="lineno"> 67</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>((*arr)[i], (*arr)[j]);</div>
<div class="line"><span class="lineno"> 68</span> }</div>
<div class="line"><span class="lineno"> 69</span> }</div>
<div class="line"><span class="lineno"> 70</span> </div>
<div class="line"><span class="lineno"> 71</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>((*arr)[i + 1], (*arr)[high]);</div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordflow">return</span> (i + 1);</div>
<div class="line"><span class="lineno"> 73</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 59</span> {</div>
<div class="line"><span class="lineno"> 60</span> T pivot = (*arr)[high]; <span class="comment">// taking the last element as pivot</span></div>
<div class="line"><span class="lineno"> 61</span> <span class="keywordtype">int</span> i = (low - 1); <span class="comment">// Index of smaller element</span></div>
<div class="line"><span class="lineno"> 62</span> </div>
<div class="line"><span class="lineno"> 63</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = low; j &lt; high; j++) {</div>
<div class="line"><span class="lineno"> 64</span> <span class="comment">// If current element is smaller than or</span></div>
<div class="line"><span class="lineno"> 65</span> <span class="comment">// equal to pivot</span></div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">if</span> ((*arr)[j] &lt;= pivot) {</div>
<div class="line"><span class="lineno"> 67</span> i++; <span class="comment">// increment index of smaller element</span></div>
<div class="line"><span class="lineno"> 68</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>((*arr)[i], (*arr)[j]);</div>
<div class="line"><span class="lineno"> 69</span> }</div>
<div class="line"><span class="lineno"> 70</span> }</div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>((*arr)[i + 1], (*arr)[high]);</div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordflow">return</span> (i + 1);</div>
<div class="line"><span class="lineno"> 74</span>}</div>
<div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
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@@ -353,14 +354,14 @@ template&lt;typename T &gt; </div>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 86</span> {</div>
<div class="line"><span class="lineno"> 87</span> <span class="keywordflow">if</span> (low &lt; high) {</div>
<div class="line"><span class="lineno"> 88</span> <span class="keywordtype">int</span> p = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/partition.html">partition</a>(arr, low, high);</div>
<div class="line"><span class="lineno"> 89</span> </div>
<div class="line"><span class="lineno"> 90</span> <a class="code hl_namespace" href="../../d0/d2b/namespacequick__sort.html">quick_sort</a>(arr, low, p - 1);</div>
<div class="line"><span class="lineno"> 91</span> <a class="code hl_namespace" href="../../d0/d2b/namespacequick__sort.html">quick_sort</a>(arr, p + 1, high);</div>
<div class="line"><span class="lineno"> 92</span> }</div>
<div class="line"><span class="lineno"> 93</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 87</span> {</div>
<div class="line"><span class="lineno"> 88</span> <span class="keywordflow">if</span> (low &lt; high) {</div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordtype">int</span> p = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/partition.html">partition</a>(arr, low, high);</div>
<div class="line"><span class="lineno"> 90</span> </div>
<div class="line"><span class="lineno"> 91</span> <a class="code hl_namespace" href="../../d0/d2b/namespacequick__sort.html">quick_sort</a>(arr, low, p - 1);</div>
<div class="line"><span class="lineno"> 92</span> <a class="code hl_namespace" href="../../d0/d2b/namespacequick__sort.html">quick_sort</a>(arr, p + 1, high);</div>
<div class="line"><span class="lineno"> 93</span> }</div>
<div class="line"><span class="lineno"> 94</span>}</div>
<div class="ttc" id="anamespacequick__sort_html"><div class="ttname"><a href="../../d0/d2b/namespacequick__sort.html">quick_sort</a></div><div class="ttdoc">Functions for the Quick sort implementation in C++.</div></div>
<div class="ttc" id="apartition_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/partition.html">std::partition</a></div><div class="ttdeci">T partition(T... args)</div></div>
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@@ -407,15 +408,15 @@ template&lt;typename T &gt; </div>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 106</span> {</div>
<div class="line"><span class="lineno"> 107</span> <span class="keywordflow">if</span> (low &lt; high) {</div>
<div class="line"><span class="lineno"> 108</span> <span class="keywordtype">int</span> p = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/partition.html">partition</a>(&amp;arr, low, high);</div>
<div class="line"><span class="lineno"> 109</span> </div>
<div class="line"><span class="lineno"> 110</span> <a class="code hl_namespace" href="../../d0/d2b/namespacequick__sort.html">quick_sort</a>(&amp;arr, low, p - 1);</div>
<div class="line"><span class="lineno"> 111</span> <a class="code hl_namespace" href="../../d0/d2b/namespacequick__sort.html">quick_sort</a>(&amp;arr, p + 1, high);</div>
<div class="line"><span class="lineno"> 112</span> }</div>
<div class="line"><span class="lineno"> 113</span> <span class="keywordflow">return</span> arr;</div>
<div class="line"><span class="lineno"> 114</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 107</span> {</div>
<div class="line"><span class="lineno"> 108</span> <span class="keywordflow">if</span> (low &lt; high) {</div>
<div class="line"><span class="lineno"> 109</span> <span class="keywordtype">int</span> p = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/partition.html">partition</a>(&amp;arr, low, high);</div>
<div class="line"><span class="lineno"> 110</span> </div>
<div class="line"><span class="lineno"> 111</span> <a class="code hl_namespace" href="../../d0/d2b/namespacequick__sort.html">quick_sort</a>(&amp;arr, low, p - 1);</div>
<div class="line"><span class="lineno"> 112</span> <a class="code hl_namespace" href="../../d0/d2b/namespacequick__sort.html">quick_sort</a>(&amp;arr, p + 1, high);</div>
<div class="line"><span class="lineno"> 113</span> }</div>
<div class="line"><span class="lineno"> 114</span> <span class="keywordflow">return</span> arr;</div>
<div class="line"><span class="lineno"> 115</span>}</div>
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@@ -449,10 +450,10 @@ template&lt;typename T &gt; </div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 123</span> {</div>
<div class="line"><span class="lineno"> 124</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; size; i++) <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; arr[i] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><span class="lineno"> 125</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;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 126</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 124</span> {</div>
<div class="line"><span class="lineno"> 125</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; size; i++) <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; arr[i] &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;</div>
<div class="line"><span class="lineno"> 126</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;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 127</span>}</div>
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@@ -481,67 +482,67 @@ template&lt;typename T &gt; </div>
<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 135</span> {</div>
<div class="line"><span class="lineno"> 136</span> <span class="comment">// 1st test (normal numbers)</span></div>
<div class="line"><span class="lineno"> 137</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr = {5, 3, 8, 12, 14, 16, 28, 96, 2, 5977};</div>
<div class="line"><span class="lineno"> 138</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr_sorted = <a class="code hl_function" href="#a5e6213e8008356ac6eda9427f3f4b394">sorting::quick_sort::quick_sort</a>(</div>
<div class="line"><span class="lineno"> 139</span> arr, 0, <span class="keywordtype">int</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr)) - 1);</div>
<div class="line"><span class="lineno"> 140</span> </div>
<div class="line"><span class="lineno"> 141</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr_sorted), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr_sorted)));</div>
<div class="line"><span class="lineno"> 142</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;\n1st test: passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 143</span> </div>
<div class="line"><span class="lineno"> 144</span> <span class="comment">// 2nd test (normal and negative numbers)</span></div>
<div class="line"><span class="lineno"> 145</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr2 = {9, 15, 28, 96, 500, -4, -58,</div>
<div class="line"><span class="lineno"> 146</span> -977, -238, -800, -21, -53, -55};</div>
<div class="line"><span class="lineno"> 147</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr_sorted2 = <a class="code hl_function" href="#a5e6213e8008356ac6eda9427f3f4b394">sorting::quick_sort::quick_sort</a>(</div>
<div class="line"><span class="lineno"> 148</span> arr2, 0, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr2) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr2));</div>
<div class="line"><span class="lineno"> 149</span> </div>
<div class="line"><span class="lineno"> 150</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr_sorted2), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr_sorted2)));</div>
<div class="line"><span class="lineno"> 151</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;2nd test: passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 152</span> </div>
<div class="line"><span class="lineno"> 153</span> <span class="comment">// 3rd test (decimal and normal numbers)</span></div>
<div class="line"><span class="lineno"> 154</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> arr3 = {29, 36, 1100, 0, 77, 1,</div>
<div class="line"><span class="lineno"> 155</span> 6.7, 8.97, 1.74, 950.10, -329.65};</div>
<div class="line"><span class="lineno"> 156</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> arr_sorted3 = <a class="code hl_function" href="#a5e6213e8008356ac6eda9427f3f4b394">sorting::quick_sort::quick_sort</a>(</div>
<div class="line"><span class="lineno"> 157</span> arr3, 0, <span class="keywordtype">int</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr3) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr3)) - 1);</div>
<div class="line"><span class="lineno"> 158</span> </div>
<div class="line"><span class="lineno"> 159</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr_sorted3), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr_sorted3)));</div>
<div class="line"><span class="lineno"> 160</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;3rd test: passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 161</span> </div>
<div class="line"><span class="lineno"> 162</span> <span class="comment">// 4th test (random decimal and negative numbers)</span></div>
<div class="line"><span class="lineno"> 163</span> <span class="keywordtype">size_t</span> size = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 750 + 100;</div>
<div class="line"><span class="lineno"> 164</span> </div>
<div class="line"><span class="lineno"> 165</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> arr4(size);</div>
<div class="line"><span class="lineno"> 166</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; size; i++) {</div>
<div class="line"><span class="lineno"> 167</span> arr4[i] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>()) /</div>
<div class="line"><span class="lineno"> 168</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(RAND_MAX / 999.99 - 0.99) -</div>
<div class="line"><span class="lineno"> 169</span> 250;</div>
<div class="line"><span class="lineno"> 170</span> }</div>
<div class="line"><span class="lineno"> 171</span> </div>
<div class="line"><span class="lineno"> 172</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> arr4_sorted = <a class="code hl_function" href="#a5e6213e8008356ac6eda9427f3f4b394">sorting::quick_sort::quick_sort</a>(</div>
<div class="line"><span class="lineno"> 173</span> arr4, 0, <span class="keywordtype">int</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4)) - 1);</div>
<div class="line"><span class="lineno"> 174</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4_sorted), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4_sorted)));</div>
<div class="line"><span class="lineno"> 175</span> </div>
<div class="line"><span class="lineno"> 176</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;4th test: passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 177</span> </div>
<div class="line"><span class="lineno"> 178</span> <span class="comment">// Printing all sorted arrays</span></div>
<div class="line"><span class="lineno"> 179</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;\n\tPrinting all sorted arrays:\t\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 180</span> </div>
<div class="line"><span class="lineno"> 181</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;1st array:\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 182</span> <a class="code hl_function" href="#aeccefcf6fcca62c54939c5ec9a93109b">sorting::quick_sort::show</a>(arr_sorted, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr));</div>
<div class="line"><span class="lineno"> 183</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &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"> 184</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;2nd array:\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 185</span> <a class="code hl_function" href="#aeccefcf6fcca62c54939c5ec9a93109b">sorting::quick_sort::show</a>(arr_sorted2, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr2) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr2));</div>
<div class="line"><span class="lineno"> 186</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &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"> 187</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;3rd array:\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 188</span> <a class="code hl_function" href="#aeccefcf6fcca62c54939c5ec9a93109b">sorting::quick_sort::show</a>(arr_sorted3,</div>
<div class="line"><span class="lineno"> 189</span> <span class="keywordtype">int</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr3) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr3)) - 1);</div>
<div class="line"><span class="lineno"> 190</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &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"> 191</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;Start: 4th array:\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 192</span> <a class="code hl_function" href="#aeccefcf6fcca62c54939c5ec9a93109b">sorting::quick_sort::show</a>(</div>
<div class="line"><span class="lineno"> 193</span> arr4_sorted, <span class="keywordtype">int</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4_sorted) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4_sorted)) - 1);</div>
<div class="line"><span class="lineno"> 194</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;\nEnd: 4th array.\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 195</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 136</span> {</div>
<div class="line"><span class="lineno"> 137</span> <span class="comment">// 1st test (normal numbers)</span></div>
<div class="line"><span class="lineno"> 138</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr = {5, 3, 8, 12, 14, 16, 28, 96, 2, 5977};</div>
<div class="line"><span class="lineno"> 139</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;uint64_t&gt;</a> arr_sorted = <a class="code hl_function" href="#a5e6213e8008356ac6eda9427f3f4b394">sorting::quick_sort::quick_sort</a>(</div>
<div class="line"><span class="lineno"> 140</span> arr, 0, <span class="keywordtype">int</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr)) - 1);</div>
<div class="line"><span class="lineno"> 141</span> </div>
<div class="line"><span class="lineno"> 142</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr_sorted), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr_sorted)));</div>
<div class="line"><span class="lineno"> 143</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;\n1st test: passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 144</span> </div>
<div class="line"><span class="lineno"> 145</span> <span class="comment">// 2nd test (normal and negative numbers)</span></div>
<div class="line"><span class="lineno"> 146</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr2 = {9, 15, 28, 96, 500, -4, -58,</div>
<div class="line"><span class="lineno"> 147</span> -977, -238, -800, -21, -53, -55};</div>
<div class="line"><span class="lineno"> 148</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;int64_t&gt;</a> arr_sorted2 = <a class="code hl_function" href="#a5e6213e8008356ac6eda9427f3f4b394">sorting::quick_sort::quick_sort</a>(</div>
<div class="line"><span class="lineno"> 149</span> arr2, 0, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr2) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr2));</div>
<div class="line"><span class="lineno"> 150</span> </div>
<div class="line"><span class="lineno"> 151</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr_sorted2), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr_sorted2)));</div>
<div class="line"><span class="lineno"> 152</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;2nd test: passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 153</span> </div>
<div class="line"><span class="lineno"> 154</span> <span class="comment">// 3rd test (decimal and normal numbers)</span></div>
<div class="line"><span class="lineno"> 155</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> arr3 = {29, 36, 1100, 0, 77, 1,</div>
<div class="line"><span class="lineno"> 156</span> 6.7, 8.97, 1.74, 950.10, -329.65};</div>
<div class="line"><span class="lineno"> 157</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> arr_sorted3 = <a class="code hl_function" href="#a5e6213e8008356ac6eda9427f3f4b394">sorting::quick_sort::quick_sort</a>(</div>
<div class="line"><span class="lineno"> 158</span> arr3, 0, <span class="keywordtype">int</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr3) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr3)) - 1);</div>
<div class="line"><span class="lineno"> 159</span> </div>
<div class="line"><span class="lineno"> 160</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr_sorted3), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr_sorted3)));</div>
<div class="line"><span class="lineno"> 161</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;3rd test: passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 162</span> </div>
<div class="line"><span class="lineno"> 163</span> <span class="comment">// 4th test (random decimal and negative numbers)</span></div>
<div class="line"><span class="lineno"> 164</span> <span class="keywordtype">size_t</span> size = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 750 + 100;</div>
<div class="line"><span class="lineno"> 165</span> </div>
<div class="line"><span class="lineno"> 166</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> arr4(size);</div>
<div class="line"><span class="lineno"> 167</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; size; i++) {</div>
<div class="line"><span class="lineno"> 168</span> arr4[i] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>()) /</div>
<div class="line"><span class="lineno"> 169</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">float</span><span class="keyword">&gt;</span>(RAND_MAX / 999.99 - 0.99) -</div>
<div class="line"><span class="lineno"> 170</span> 250;</div>
<div class="line"><span class="lineno"> 171</span> }</div>
<div class="line"><span class="lineno"> 172</span> </div>
<div class="line"><span class="lineno"> 173</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;float&gt;</a> arr4_sorted = <a class="code hl_function" href="#a5e6213e8008356ac6eda9427f3f4b394">sorting::quick_sort::quick_sort</a>(</div>
<div class="line"><span class="lineno"> 174</span> arr4, 0, <span class="keywordtype">int</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4)) - 1);</div>
<div class="line"><span class="lineno"> 175</span> assert(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/is_sorted.html">std::is_sorted</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4_sorted), <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4_sorted)));</div>
<div class="line"><span class="lineno"> 176</span> </div>
<div class="line"><span class="lineno"> 177</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;4th test: passed!\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 178</span> </div>
<div class="line"><span class="lineno"> 179</span> <span class="comment">// Printing all sorted arrays</span></div>
<div class="line"><span class="lineno"> 180</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;\n\tPrinting all sorted arrays:\t\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 181</span> </div>
<div class="line"><span class="lineno"> 182</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;1st array:\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 183</span> <a class="code hl_function" href="#aeccefcf6fcca62c54939c5ec9a93109b">sorting::quick_sort::show</a>(arr_sorted, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr));</div>
<div class="line"><span class="lineno"> 184</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &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"> 185</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;2nd array:\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 186</span> <a class="code hl_function" href="#aeccefcf6fcca62c54939c5ec9a93109b">sorting::quick_sort::show</a>(arr_sorted2, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr2) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr2));</div>
<div class="line"><span class="lineno"> 187</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &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"> 188</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;3rd array:\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 189</span> <a class="code hl_function" href="#aeccefcf6fcca62c54939c5ec9a93109b">sorting::quick_sort::show</a>(arr_sorted3,</div>
<div class="line"><span class="lineno"> 190</span> <span class="keywordtype">int</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr3) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr3)) - 1);</div>
<div class="line"><span class="lineno"> 191</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &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"> 192</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;Start: 4th array:\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 193</span> <a class="code hl_function" href="#aeccefcf6fcca62c54939c5ec9a93109b">sorting::quick_sort::show</a>(</div>
<div class="line"><span class="lineno"> 194</span> arr4_sorted, <span class="keywordtype">int</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a>(arr4_sorted) - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/begin.html">std::begin</a>(arr4_sorted)) - 1);</div>
<div class="line"><span class="lineno"> 195</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;\nEnd: 4th array.\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 196</span>}</div>
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<div class="textblock"><code>#include &lt;algorithm&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
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<div class="line"><span class="lineno"> 57</span> arr); <span class="comment">// create a copy of input vector. this way, the original input</span></div>
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<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; size; i += 2) {</div>
<div class="line"><span class="lineno"> 62</span> <span class="keywordflow">if</span> (i &gt; 0 &amp;&amp; out[i - 1] &gt; out[i]) {</div>
<div class="line"><span class="lineno"> 63</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(out[i], out[i - 1]); <span class="comment">// swapping the two values</span></div>
<div class="line"><span class="lineno"> 64</span> }</div>
<div class="line"><span class="lineno"> 65</span> </div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">if</span> (i &lt; size - 1 &amp;&amp; out[i] &lt; out[i + 1]) {</div>
<div class="line"><span class="lineno"> 67</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(out[i], out[i + 1]); <span class="comment">// swapping the two values</span></div>
<div class="line"><span class="lineno"> 68</span> }</div>
<div class="line"><span class="lineno"> 69</span> }</div>
<div class="line"><span class="lineno"> 70</span> </div>
<div class="line"><span class="lineno"> 71</span> <span class="keywordflow">return</span> out; <span class="comment">// returns the sorted vector</span></div>
<div class="line"><span class="lineno"> 72</span>}</div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
<div class="ttc" id="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>

View File

@@ -129,7 +129,7 @@ Functions</h2></td></tr>
<div class="textblock"><p>for assert </p>
<p>Numerical Methods.</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/map.html">std::map</a> container</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
<p>for storing points and coefficents</p>
<p>for io operations</p>
<p>for math functions</p>
<p>for IO operations</p>
@@ -138,7 +138,7 @@ Functions</h2></td></tr>
<p>Numerical algorithms/methods</p>
<p>for math operations</p>
<p>Numerical methods</p>
<p>for assert for mathematical-related functions for storing points and coefficents for IO operations</p>
<p>for assert for mathematical-related functions for IO operations for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
<p>Numerical algorithms/methods</p>
<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a> for assert for fabs</p>
<p>Numerical Methods algorithms</p>
@@ -251,61 +251,61 @@ y if n!=1 </dd></dl>
<p>Updating the last n/2 elements</p>
<p>Deleting dynamic array ye</p>
<p>Deleting dynamic array yo</p>
<div class="fragment"><div class="line"><span class="lineno"> 41</span> {</div>
<div class="line"><span class="lineno"> 42</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><span class="lineno"> 43</span> <span class="keywordflow">return</span> p; <span class="comment">/// Base Case To return</span></div>
<div class="line"><span class="lineno"> 44</span> }</div>
<div class="line"><span class="lineno"> 45</span> </div>
<div class="line"><span class="lineno"> 46</span> <span class="keywordtype">double</span> pi = 2 * asin(1.0); <span class="comment">/// Declaring value of pi</span></div>
<div class="line"><span class="lineno"> 47</span> </div>
<div class="line"><span class="lineno"> 48</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> om = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(</div>
<div class="line"><span class="lineno"> 49</span> cos(2 * pi / n), sin(2 * pi / n)); <span class="comment">/// Calculating value of omega</span></div>
<div class="line"><span class="lineno"> 50</span> </div>
<div class="line"><span class="lineno"> 51</span> <span class="keyword">auto</span> *pe = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of even power</span></div>
<div class="line"><span class="lineno"> 52</span> </div>
<div class="line"><span class="lineno"> 53</span> <span class="keyword">auto</span> *po = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of odd power</span></div>
<div class="line"><span class="lineno"> 54</span> </div>
<div class="line"><span class="lineno"> 55</span> <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 56</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><span class="lineno"> 57</span> <span class="keywordflow">if</span> (j % 2 == 0) {</div>
<div class="line"><span class="lineno"> 58</span> pe[k1++] = p[j]; <span class="comment">/// Assigning values of even Coefficients</span></div>
<div class="line"><span class="lineno"> 59</span> </div>
<div class="line"><span class="lineno"> 60</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 61</span> po[k2++] = p[j]; <span class="comment">/// Assigning value of odd Coefficients</span></div>
<div class="line"><span class="lineno"> 62</span> }</div>
<div class="line"><span class="lineno"> 63</span> }</div>
<div class="line"><span class="lineno"> 64</span> </div>
<div class="line"><span class="lineno"> 65</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *ye =</div>
<div class="line"><span class="lineno"> 66</span> <a class="code hl_function" href="#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(pe, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><span class="lineno"> 67</span> </div>
<div class="line"><span class="lineno"> 68</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *yo =</div>
<div class="line"><span class="lineno"> 69</span> <a class="code hl_function" href="#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(po, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><span class="lineno"> 70</span> </div>
<div class="line"><span class="lineno"> 71</span> <span class="keyword">auto</span> *y = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n]; <span class="comment">/// Final value representation list</span></div>
<div class="line"><span class="lineno"> 72</span> </div>
<div class="line"><span class="lineno"> 73</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 74</span> </div>
<div class="line"><span class="lineno"> 75</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n / 2; i++) {</div>
<div class="line"><span class="lineno"> 76</span> y[i] =</div>
<div class="line"><span class="lineno"> 77</span> ye[k1] + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the first n/2 elements</span></div>
<div class="line"><span class="lineno"> 78</span> y[i + n / 2] =</div>
<div class="line"><span class="lineno"> 79</span> ye[k1] - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the last n/2 elements</span></div>
<div class="line"><span class="lineno"> 80</span> </div>
<div class="line"><span class="lineno"> 81</span> k1++;</div>
<div class="line"><span class="lineno"> 82</span> k2++;</div>
<div class="line"><span class="lineno"> 83</span> }</div>
<div class="line"><span class="lineno"> 84</span> </div>
<div class="line"><span class="lineno"> 85</span> <span class="keywordflow">if</span> (n != 2) {</div>
<div class="line"><span class="lineno"> 86</span> <span class="keyword">delete</span>[] pe;</div>
<div class="line"><span class="lineno"> 87</span> <span class="keyword">delete</span>[] po;</div>
<div class="line"><span class="lineno"> 88</span> }</div>
<div class="line"><span class="lineno"> 89</span> </div>
<div class="line"><span class="lineno"> 90</span> <span class="keyword">delete</span>[] ye; <span class="comment">/// Deleting dynamic array ye</span></div>
<div class="line"><span class="lineno"> 91</span> <span class="keyword">delete</span>[] yo; <span class="comment">/// Deleting dynamic array yo</span></div>
<div class="line"><span class="lineno"> 92</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><span class="lineno"> 93</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 42</span> {</div>
<div class="line"><span class="lineno"> 43</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">return</span> p; <span class="comment">/// Base Case To return</span></div>
<div class="line"><span class="lineno"> 45</span> }</div>
<div class="line"><span class="lineno"> 46</span> </div>
<div class="line"><span class="lineno"> 47</span> <span class="keywordtype">double</span> pi = 2 * asin(1.0); <span class="comment">/// Declaring value of pi</span></div>
<div class="line"><span class="lineno"> 48</span> </div>
<div class="line"><span class="lineno"> 49</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> om = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(</div>
<div class="line"><span class="lineno"> 50</span> cos(2 * pi / n), sin(2 * pi / n)); <span class="comment">/// Calculating value of omega</span></div>
<div class="line"><span class="lineno"> 51</span> </div>
<div class="line"><span class="lineno"> 52</span> <span class="keyword">auto</span> *pe = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of even power</span></div>
<div class="line"><span class="lineno"> 53</span> </div>
<div class="line"><span class="lineno"> 54</span> <span class="keyword">auto</span> *po = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of odd power</span></div>
<div class="line"><span class="lineno"> 55</span> </div>
<div class="line"><span class="lineno"> 56</span> <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 57</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><span class="lineno"> 58</span> <span class="keywordflow">if</span> (j % 2 == 0) {</div>
<div class="line"><span class="lineno"> 59</span> pe[k1++] = p[j]; <span class="comment">/// Assigning values of even Coefficients</span></div>
<div class="line"><span class="lineno"> 60</span> </div>
<div class="line"><span class="lineno"> 61</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 62</span> po[k2++] = p[j]; <span class="comment">/// Assigning value of odd Coefficients</span></div>
<div class="line"><span class="lineno"> 63</span> }</div>
<div class="line"><span class="lineno"> 64</span> }</div>
<div class="line"><span class="lineno"> 65</span> </div>
<div class="line"><span class="lineno"> 66</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *ye =</div>
<div class="line"><span class="lineno"> 67</span> <a class="code hl_function" href="#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(pe, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><span class="lineno"> 68</span> </div>
<div class="line"><span class="lineno"> 69</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *yo =</div>
<div class="line"><span class="lineno"> 70</span> <a class="code hl_function" href="#a158fd271b9a53e8f3f60b08b18857150">FastFourierTransform</a>(po, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</span> <span class="keyword">auto</span> *y = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n]; <span class="comment">/// Final value representation list</span></div>
<div class="line"><span class="lineno"> 73</span> </div>
<div class="line"><span class="lineno"> 74</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 75</span> </div>
<div class="line"><span class="lineno"> 76</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n / 2; i++) {</div>
<div class="line"><span class="lineno"> 77</span> y[i] =</div>
<div class="line"><span class="lineno"> 78</span> ye[k1] + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the first n/2 elements</span></div>
<div class="line"><span class="lineno"> 79</span> y[i + n / 2] =</div>
<div class="line"><span class="lineno"> 80</span> ye[k1] - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the last n/2 elements</span></div>
<div class="line"><span class="lineno"> 81</span> </div>
<div class="line"><span class="lineno"> 82</span> k1++;</div>
<div class="line"><span class="lineno"> 83</span> k2++;</div>
<div class="line"><span class="lineno"> 84</span> }</div>
<div class="line"><span class="lineno"> 85</span> </div>
<div class="line"><span class="lineno"> 86</span> <span class="keywordflow">if</span> (n != 2) {</div>
<div class="line"><span class="lineno"> 87</span> <span class="keyword">delete</span>[] pe;</div>
<div class="line"><span class="lineno"> 88</span> <span class="keyword">delete</span>[] po;</div>
<div class="line"><span class="lineno"> 89</span> }</div>
<div class="line"><span class="lineno"> 90</span> </div>
<div class="line"><span class="lineno"> 91</span> <span class="keyword">delete</span>[] ye; <span class="comment">/// Deleting dynamic array ye</span></div>
<div class="line"><span class="lineno"> 92</span> <span class="keyword">delete</span>[] yo; <span class="comment">/// Deleting dynamic array yo</span></div>
<div class="line"><span class="lineno"> 93</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><span class="lineno"> 94</span>}</div>
<div class="ttc" id="acomplex_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a></div></div>
<div class="ttc" id="anamespacenumerical__methods_html_a158fd271b9a53e8f3f60b08b18857150"><div class="ttname"><a href="#a158fd271b9a53e8f3f60b08b18857150">numerical_methods::FastFourierTransform</a></div><div class="ttdeci">std::complex&lt; double &gt; * FastFourierTransform(std::complex&lt; double &gt; *p, uint8_t n)</div><div class="ttdoc">FastFourierTransform is a recursive function which returns list of complex numbers.</div><div class="ttdef"><b>Definition</b> fast_fourier_transform.cpp:41</div></div>
<div class="ttc" id="anamespacenumerical__methods_html_a158fd271b9a53e8f3f60b08b18857150"><div class="ttname"><a href="#a158fd271b9a53e8f3f60b08b18857150">numerical_methods::FastFourierTransform</a></div><div class="ttdeci">std::complex&lt; double &gt; * FastFourierTransform(std::complex&lt; double &gt; *p, uint8_t n)</div><div class="ttdoc">FastFourierTransform is a recursive function which returns list of complex numbers.</div><div class="ttdef"><b>Definition</b> fast_fourier_transform.cpp:42</div></div>
<div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
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@@ -361,64 +361,64 @@ y if n!=1 </dd></dl>
<p>Updating the last n/2 elements</p>
<p>Deleting dynamic array ye</p>
<p>Deleting dynamic array yo</p>
<div class="fragment"><div class="line"><span class="lineno"> 34</span> {</div>
<div class="line"><span class="lineno"> 35</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><span class="lineno"> 36</span> <span class="keywordflow">return</span> p; <span class="comment">/// Base Case To return</span></div>
<div class="line"><span class="lineno"> 37</span> }</div>
<div class="line"><span class="lineno"> 38</span> </div>
<div class="line"><span class="lineno"> 39</span> <span class="keywordtype">double</span> pi = 2 * asin(1.0); <span class="comment">/// Declaring value of pi</span></div>
<div class="line"><span class="lineno"> 40</span> </div>
<div class="line"><span class="lineno"> 41</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> om = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(</div>
<div class="line"><span class="lineno"> 42</span> cos(2 * pi / n), sin(2 * pi / n)); <span class="comment">/// Calculating value of omega</span></div>
<div class="line"><span class="lineno"> 43</span> </div>
<div class="line"><span class="lineno"> 44</span> om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>(om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() / n); <span class="comment">/// One change in comparison with DFT</span></div>
<div class="line"><span class="lineno"> 45</span> om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>(om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>() / n); <span class="comment">/// One change in comparison with DFT</span></div>
<div class="line"><span class="lineno"> 46</span> </div>
<div class="line"><span class="lineno"> 47</span> <span class="keyword">auto</span> *pe = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of even power</span></div>
<div class="line"><span class="lineno"> 48</span> </div>
<div class="line"><span class="lineno"> 49</span> <span class="keyword">auto</span> *po = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of odd power</span></div>
<div class="line"><span class="lineno"> 50</span> </div>
<div class="line"><span class="lineno"> 51</span> <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">if</span> (j % 2 == 0) {</div>
<div class="line"><span class="lineno"> 54</span> pe[k1++] = p[j]; <span class="comment">/// Assigning values of even Coefficients</span></div>
<div class="line"><span class="lineno"> 55</span> </div>
<div class="line"><span class="lineno"> 56</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 57</span> po[k2++] = p[j]; <span class="comment">/// Assigning value of odd Coefficients</span></div>
<div class="line"><span class="lineno"> 58</span> }</div>
<div class="line"><span class="lineno"> 59</span> }</div>
<div class="line"><span class="lineno"> 60</span> </div>
<div class="line"><span class="lineno"> 61</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *ye =</div>
<div class="line"><span class="lineno"> 62</span> <a class="code hl_function" href="#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(pe, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><span class="lineno"> 63</span> </div>
<div class="line"><span class="lineno"> 64</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *yo =</div>
<div class="line"><span class="lineno"> 65</span> <a class="code hl_function" href="#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(po, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><span class="lineno"> 66</span> </div>
<div class="line"><span class="lineno"> 67</span> <span class="keyword">auto</span> *y = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n]; <span class="comment">/// Final value representation list</span></div>
<div class="line"><span class="lineno"> 68</span> </div>
<div class="line"><span class="lineno"> 69</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 70</span> </div>
<div class="line"><span class="lineno"> 71</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n / 2; i++) {</div>
<div class="line"><span class="lineno"> 72</span> y[i] =</div>
<div class="line"><span class="lineno"> 73</span> ye[k1] + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the first n/2 elements</span></div>
<div class="line"><span class="lineno"> 74</span> y[i + n / 2] =</div>
<div class="line"><span class="lineno"> 75</span> ye[k1] - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the last n/2 elements</span></div>
<div class="line"><span class="lineno"> 76</span> </div>
<div class="line"><span class="lineno"> 77</span> k1++;</div>
<div class="line"><span class="lineno"> 78</span> k2++;</div>
<div class="line"><span class="lineno"> 79</span> }</div>
<div class="line"><span class="lineno"> 80</span> </div>
<div class="line"><span class="lineno"> 81</span> <span class="keywordflow">if</span> (n != 2) {</div>
<div class="line"><span class="lineno"> 82</span> <span class="keyword">delete</span>[] pe;</div>
<div class="line"><span class="lineno"> 83</span> <span class="keyword">delete</span>[] po;</div>
<div class="line"><span class="lineno"> 84</span> }</div>
<div class="line"><span class="lineno"> 85</span> </div>
<div class="line"><span class="lineno"> 86</span> <span class="keyword">delete</span>[] ye; <span class="comment">/// Deleting dynamic array ye</span></div>
<div class="line"><span class="lineno"> 87</span> <span class="keyword">delete</span>[] yo; <span class="comment">/// Deleting dynamic array yo</span></div>
<div class="line"><span class="lineno"> 88</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><span class="lineno"> 89</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 35</span> {</div>
<div class="line"><span class="lineno"> 36</span> <span class="keywordflow">if</span> (n == 1) {</div>
<div class="line"><span class="lineno"> 37</span> <span class="keywordflow">return</span> p; <span class="comment">/// Base Case To return</span></div>
<div class="line"><span class="lineno"> 38</span> }</div>
<div class="line"><span class="lineno"> 39</span> </div>
<div class="line"><span class="lineno"> 40</span> <span class="keywordtype">double</span> pi = 2 * asin(1.0); <span class="comment">/// Declaring value of pi</span></div>
<div class="line"><span class="lineno"> 41</span> </div>
<div class="line"><span class="lineno"> 42</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> om = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>(</div>
<div class="line"><span class="lineno"> 43</span> cos(2 * pi / n), sin(2 * pi / n)); <span class="comment">/// Calculating value of omega</span></div>
<div class="line"><span class="lineno"> 44</span> </div>
<div class="line"><span class="lineno"> 45</span> om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>(om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>() / n); <span class="comment">/// One change in comparison with DFT</span></div>
<div class="line"><span class="lineno"> 46</span> om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>(om.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>() / n); <span class="comment">/// One change in comparison with DFT</span></div>
<div class="line"><span class="lineno"> 47</span> </div>
<div class="line"><span class="lineno"> 48</span> <span class="keyword">auto</span> *pe = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of even power</span></div>
<div class="line"><span class="lineno"> 49</span> </div>
<div class="line"><span class="lineno"> 50</span> <span class="keyword">auto</span> *po = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n / 2]; <span class="comment">/// Coefficients of odd power</span></div>
<div class="line"><span class="lineno"> 51</span> </div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordtype">int</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; n; j++) {</div>
<div class="line"><span class="lineno"> 54</span> <span class="keywordflow">if</span> (j % 2 == 0) {</div>
<div class="line"><span class="lineno"> 55</span> pe[k1++] = p[j]; <span class="comment">/// Assigning values of even Coefficients</span></div>
<div class="line"><span class="lineno"> 56</span> </div>
<div class="line"><span class="lineno"> 57</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><span class="lineno"> 58</span> po[k2++] = p[j]; <span class="comment">/// Assigning value of odd Coefficients</span></div>
<div class="line"><span class="lineno"> 59</span> }</div>
<div class="line"><span class="lineno"> 60</span> }</div>
<div class="line"><span class="lineno"> 61</span> </div>
<div class="line"><span class="lineno"> 62</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *ye =</div>
<div class="line"><span class="lineno"> 63</span> <a class="code hl_function" href="#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(pe, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><span class="lineno"> 64</span> </div>
<div class="line"><span class="lineno"> 65</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a> *yo =</div>
<div class="line"><span class="lineno"> 66</span> <a class="code hl_function" href="#aee56dc85997b8cd42bad71a5d6bd2d93">InverseFastFourierTransform</a>(po, n / 2); <span class="comment">/// Recursive Call</span></div>
<div class="line"><span class="lineno"> 67</span> </div>
<div class="line"><span class="lineno"> 68</span> <span class="keyword">auto</span> *y = <span class="keyword">new</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;double&gt;</a>[n]; <span class="comment">/// Final value representation list</span></div>
<div class="line"><span class="lineno"> 69</span> </div>
<div class="line"><span class="lineno"> 70</span> k1 = 0, k2 = 0;</div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n / 2; i++) {</div>
<div class="line"><span class="lineno"> 73</span> y[i] =</div>
<div class="line"><span class="lineno"> 74</span> ye[k1] + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the first n/2 elements</span></div>
<div class="line"><span class="lineno"> 75</span> y[i + n / 2] =</div>
<div class="line"><span class="lineno"> 76</span> ye[k1] - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(om, i) * yo[k2]; <span class="comment">/// Updating the last n/2 elements</span></div>
<div class="line"><span class="lineno"> 77</span> </div>
<div class="line"><span class="lineno"> 78</span> k1++;</div>
<div class="line"><span class="lineno"> 79</span> k2++;</div>
<div class="line"><span class="lineno"> 80</span> }</div>
<div class="line"><span class="lineno"> 81</span> </div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordflow">if</span> (n != 2) {</div>
<div class="line"><span class="lineno"> 83</span> <span class="keyword">delete</span>[] pe;</div>
<div class="line"><span class="lineno"> 84</span> <span class="keyword">delete</span>[] po;</div>
<div class="line"><span class="lineno"> 85</span> }</div>
<div class="line"><span class="lineno"> 86</span> </div>
<div class="line"><span class="lineno"> 87</span> <span class="keyword">delete</span>[] ye; <span class="comment">/// Deleting dynamic array ye</span></div>
<div class="line"><span class="lineno"> 88</span> <span class="keyword">delete</span>[] yo; <span class="comment">/// Deleting dynamic array yo</span></div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><span class="lineno"> 90</span>}</div>
<div class="ttc" id="aimag_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">std::complex::imag</a></div><div class="ttdeci">T imag(T... args)</div></div>
<div class="ttc" id="anamespacenumerical__methods_html_aee56dc85997b8cd42bad71a5d6bd2d93"><div class="ttname"><a href="#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a></div><div class="ttdeci">std::complex&lt; double &gt; * InverseFastFourierTransform(std::complex&lt; double &gt; *p, uint8_t n)</div><div class="ttdoc">InverseFastFourierTransform is a recursive function which returns list of complex numbers.</div><div class="ttdef"><b>Definition</b> inverse_fast_fourier_transform.cpp:33</div></div>
<div class="ttc" id="anamespacenumerical__methods_html_aee56dc85997b8cd42bad71a5d6bd2d93"><div class="ttname"><a href="#aee56dc85997b8cd42bad71a5d6bd2d93">numerical_methods::InverseFastFourierTransform</a></div><div class="ttdeci">std::complex&lt; double &gt; * InverseFastFourierTransform(std::complex&lt; double &gt; *p, uint8_t n)</div><div class="ttdoc">InverseFastFourierTransform is a recursive function which returns list of complex numbers.</div><div class="ttdef"><b>Definition</b> inverse_fast_fourier_transform.cpp:34</div></div>
<div class="ttc" id="areal_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">std::complex::real</a></div><div class="ttdeci">T real(T... args)</div></div>
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@@ -115,18 +115,19 @@ $(function(){initNavTree('d1/de9/integral__approximation_8cpp.html','../../'); i
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;cstdint&gt;</code><br />
<code>#include &lt;functional&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for integral_approximation.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html">math</a></td></tr>
<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <br /></td></tr>
<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for assert <br /></td></tr>
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@@ -166,10 +167,10 @@ Functions</h2></td></tr>
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 122</span> {</div>
<div class="line"><span class="lineno"> 123</span> <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 124</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 125</span>}</div>
<div class="fragment"><div class="line"><span class="lineno"> 133</span> {</div>
<div class="line"><span class="lineno"> 134</span> <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 135</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 136</span>}</div>
<div class="ttc" id="acaesar__cipher_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition</b> caesar_cipher.cpp:100</div></div>
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@@ -201,59 +202,59 @@ Here is the call graph for this function:</div>
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</div><div class="memdoc">
<div class="fragment"><div class="line"><span class="lineno"> 64</span> {</div>
<div class="line"><span class="lineno"> 65</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a> = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(</div>
<div class="line"><span class="lineno"> 66</span> 3.24, 7.56, [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(x) + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">exp</a>(x) + x; });</div>
<div class="line"><span class="lineno"> 67</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;Test Case 1&quot;</span> &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"> 68</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;function: log(x) + e^x + x&quot;</span> &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"> 69</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;range: [3.24, 7.56]&quot;</span> &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"> 70</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;value: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a> &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"> 71</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a>, 1924.80384023549, .001);</div>
<div class="line"><span class="lineno"> 72</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;Test 1 Passed!&quot;</span> &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"> 73</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;=====================&quot;</span> &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"> 74</span> </div>
<div class="line"><span class="lineno"> 75</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a> = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(0.023, 3.69, [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) {</div>
<div class="line"><span class="lineno"> 76</span> <span class="keywordflow">return</span> x * x + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(x) + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">exp</a>(x) + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(x);</div>
<div class="line"><span class="lineno"> 77</span> });</div>
<div class="line"><span class="lineno"> 78</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;Test Case 2&quot;</span> &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"> 79</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;function: x^2 + cos(x) + e^x + log^2(x)&quot;</span> &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"> 80</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;range: [.023, 3.69]&quot;</span> &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"> 81</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;value: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a> &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"> 82</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a>, 58.71291345202729, .001);</div>
<div class="line"><span class="lineno"> 83</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;Test 2 Passed!&quot;</span> &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="fragment"><div class="line"><span class="lineno"> 75</span> {</div>
<div class="line"><span class="lineno"> 76</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a> = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(</div>
<div class="line"><span class="lineno"> 77</span> 3.24, 7.56, [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(x) + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">exp</a>(x) + x; });</div>
<div class="line"><span class="lineno"> 78</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;Test Case 1&quot;</span> &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"> 79</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;function: log(x) + e^x + x&quot;</span> &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"> 80</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;range: [3.24, 7.56]&quot;</span> &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"> 81</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;value: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a> &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"> 82</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a34b8683a2b429de5cce57e6d733ec817">test_1</a>, 1924.80384023549, .001);</div>
<div class="line"><span class="lineno"> 83</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;Test 1 Passed!&quot;</span> &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"> 84</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;=====================&quot;</span> &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"> 85</span> </div>
<div class="line"><span class="lineno"> 86</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a> = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(</div>
<div class="line"><span class="lineno"> 87</span> 10.78, 24.899, [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> x * x * x - x * x + 378; });</div>
<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> &lt;&lt; <span class="stringliteral">&quot;Test Case 3&quot;</span> &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"> 89</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;function: x^3 - x^2 + 378&quot;</span> &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"> 90</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;range: [10.78, 24.899]&quot;</span> &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"> 91</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;value: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a> &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"> 92</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a>, 93320.65915078377, .001);</div>
<div class="line"><span class="lineno"> 93</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;Test 3 Passed!&quot;</span> &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"> 94</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;=====================&quot;</span> &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"> 95</span> </div>
<div class="line"><span class="lineno"> 96</span> <span class="keywordtype">double</span> test_4 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(</div>
<div class="line"><span class="lineno"> 97</span> .101, .505,</div>
<div class="line"><span class="lineno"> 98</span> [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/tan.html">tan</a>(x) * x * x + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">exp</a>(x); },</div>
<div class="line"><span class="lineno"> 99</span> .00001);</div>
<div class="line"><span class="lineno"> 100</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;Test Case 4&quot;</span> &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"> 101</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;function: cos(x)*tan(x)*x^2 + e^x&quot;</span> &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"> 102</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;range: [.101, .505]&quot;</span> &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"> 103</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;value: &quot;</span> &lt;&lt; test_4 &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"> 104</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(test_4, 0.566485986311631, .001);</div>
<div class="line"><span class="lineno"> 105</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;Test 4 Passed!&quot;</span> &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"> 106</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;=====================&quot;</span> &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"> 107</span> </div>
<div class="line"><span class="lineno"> 108</span> <span class="keywordtype">double</span> test_5 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(</div>
<div class="line"><span class="lineno"> 109</span> -1, 1, [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">exp</a>(-1 / (x * x)); });</div>
<div class="line"><span class="lineno"> 110</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;Test Case 5&quot;</span> &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"> 111</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;function: e^(-1/x^2)&quot;</span> &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"> 112</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;range: [-1, 1]&quot;</span> &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"> 113</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;value: &quot;</span> &lt;&lt; test_5 &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"> 114</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(test_5, 0.1781477117815607, .001);</div>
<div class="line"><span class="lineno"> 115</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;Test 5 Passed!&quot;</span> &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"> 116</span>}</div>
<div class="line"><span class="lineno"> 86</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a> = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(0.023, 3.69, [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) {</div>
<div class="line"><span class="lineno"> 87</span> <span class="keywordflow">return</span> x * x + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(x) + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">exp</a>(x) + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">log</a>(x);</div>
<div class="line"><span class="lineno"> 88</span> });</div>
<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> &lt;&lt; <span class="stringliteral">&quot;Test Case 2&quot;</span> &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"> 90</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;function: x^2 + cos(x) + e^x + log^2(x)&quot;</span> &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"> 91</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;range: [.023, 3.69]&quot;</span> &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"> 92</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;value: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a> &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"> 93</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#a458410412185a5f09199deaff7157a8d">test_2</a>, 58.71291345202729, .001);</div>
<div class="line"><span class="lineno"> 94</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;Test 2 Passed!&quot;</span> &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"> 95</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;=====================&quot;</span> &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"> 96</span> </div>
<div class="line"><span class="lineno"> 97</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a> = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(</div>
<div class="line"><span class="lineno"> 98</span> 10.78, 24.899, [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> x * x * x - x * x + 378; });</div>
<div class="line"><span class="lineno"> 99</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;Test Case 3&quot;</span> &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"> 100</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;function: x^3 - x^2 + 378&quot;</span> &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"> 101</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;range: [10.78, 24.899]&quot;</span> &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"> 102</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;value: &quot;</span> &lt;&lt; <a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a> &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"> 103</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(<a class="code hl_function" href="../../d2/de9/heavy__light__decomposition_8cpp.html#af31ec5409537703d9c8a47350386b32a">test_3</a>, 93320.65915078377, .001);</div>
<div class="line"><span class="lineno"> 104</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;Test 3 Passed!&quot;</span> &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"> 105</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;=====================&quot;</span> &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"> 106</span> </div>
<div class="line"><span class="lineno"> 107</span> <span class="keywordtype">double</span> test_4 = <a class="code hl_function" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">math::integral_approx</a>(</div>
<div class="line"><span class="lineno"> 108</span> .101, .505,</div>
<div class="line"><span class="lineno"> 109</span> [](<span class="keyword">const</span> <span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">cos</a>(x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/tan.html">tan</a>(x) * x * x + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">exp</a>(x); },</div>
<div class="line"><span class="lineno"> 110</span> .00001);</div>
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<div class="line"><span class="lineno"> 114</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;value: &quot;</span> &lt;&lt; test_4 &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"> 115</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(test_4, 0.566485986311631, .001);</div>
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<div class="line"><span class="lineno"> 118</span> </div>
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<div class="line"><span class="lineno"> 123</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;range: [-1, 1]&quot;</span> &lt;&lt; <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"> 125</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">math::test_eval</a>(test_5, 0.1781477117815607, .001);</div>
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@@ -112,7 +112,7 @@ $(function(){initNavTree('d1/df6/class_easter_year_month_day.html','../../'); in
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<p>for IO operations
<p>for assert
<a href="#details">More...</a></p>
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<div class="textblock"><p>for IO operations </p>
<p>for assert </p>
<div class="textblock"><p>for assert </p>
<p>for IO operations </p>
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<div class="fragment"><div class="line"><span class="lineno"> 32</span> {</div>
<div class="line"><span class="lineno"> 33</span> <a class="code hl_variable" href="#a28d3cd09391390250932b7fb58fe61dc">year</a> = newYear; <span class="comment">// Assigns year to class</span></div>
<div class="line"><span class="lineno"> 34</span> <a class="code hl_variable" href="#a01a068eae0b6fa8f86f5f60c2840bbde">month</a> = newMonth;</div>
<div class="line"><span class="lineno"> 35</span> <a class="code hl_variable" href="#ade0b934e5b1af24e19ff959673b2ec51">day</a> = newDay;</div>
<div class="line"><span class="lineno"> 36</span> }</div>
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<div class="ttc" id="aclass_easter_year_month_day_html_a28d3cd09391390250932b7fb58fe61dc"><div class="ttname"><a href="#a28d3cd09391390250932b7fb58fe61dc">EasterYearMonthDay::year</a></div><div class="ttdeci">uint64_t year</div><div class="ttdoc">year Easter is on</div><div class="ttdef"><b>Definition</b> easter.cpp:28</div></div>
<div class="ttc" id="aclass_easter_year_month_day_html_ade0b934e5b1af24e19ff959673b2ec51"><div class="ttname"><a href="#ade0b934e5b1af24e19ff959673b2ec51">EasterYearMonthDay::day</a></div><div class="ttdeci">uint64_t day</div><div class="ttdoc">day Easter is on</div><div class="ttdef"><b>Definition</b> easter.cpp:30</div></div>
<div class="fragment"><div class="line"><span class="lineno"> 33</span> {</div>
<div class="line"><span class="lineno"> 34</span> <a class="code hl_variable" href="#a28d3cd09391390250932b7fb58fe61dc">year</a> = newYear; <span class="comment">// Assigns year to class</span></div>
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<div class="line"><span class="lineno"> 37</span> }</div>
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<div class="ttc" id="aclass_easter_year_month_day_html_ade0b934e5b1af24e19ff959673b2ec51"><div class="ttname"><a href="#ade0b934e5b1af24e19ff959673b2ec51">EasterYearMonthDay::day</a></div><div class="ttdeci">uint64_t day</div><div class="ttdoc">day Easter is on</div><div class="ttdef"><b>Definition</b> easter.cpp:31</div></div>
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