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<p>Compute <a href="https://en.wikipedia.org/wiki/Double_factorial" target="_blank">double factorial</a>: \(n!!\).
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cstdint&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for double_factorial.cpp:</div>
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<p><a href="../../d7/d89/double__factorial_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a0a3c417360400093891a9ccddaa4be26" id="r_a0a3c417360400093891a9ccddaa4be26"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a0a3c417360400093891a9ccddaa4be26">double_factorial_iterative</a> (uint64_t n)</td></tr>
<tr class="memitem:a68ba20fed2ce427f6469c7689437829d" id="r_a68ba20fed2ce427f6469c7689437829d"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a68ba20fed2ce427f6469c7689437829d">double_factorial_recursive</a> (uint64_t n)</td></tr>
<tr class="memitem:abbbcebf3a2d0c67f4c3cfb5511a97981" id="r_abbbcebf3a2d0c67f4c3cfb5511a97981"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#abbbcebf3a2d0c67f4c3cfb5511a97981">test</a> (uint64_t n, uint64_t expected)</td></tr>
<tr class="memitem:a88ec9ad42717780d6caaff9d3d6977f9" id="r_a88ec9ad42717780d6caaff9d3d6977f9"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a> ()</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Compute <a href="https://en.wikipedia.org/wiki/Double_factorial" target="_blank">double factorial</a>: \(n!!\). </p>
<p>Double factorial of a non-negative integer <span class="tt">n</span>, is defined as the product of all the integers from 1 to n that have the same parity (odd or even) as n. <br />
It is also called as semifactorial of a number and is denoted by \(n!!\) </p>
<p class="definition">Definition in file <a class="el" href="../../d7/d89/double__factorial_8cpp_source.html">double_factorial.cpp</a>.</p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="a0a3c417360400093891a9ccddaa4be26" name="a0a3c417360400093891a9ccddaa4be26"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0a3c417360400093891a9ccddaa4be26">&#9670;&#160;</a></span>double_factorial_iterative()</h2>
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<td class="memname">uint64_t double_factorial_iterative </td>
<td>(</td>
<td class="paramtype">uint64_t</td> <td class="paramname"><span class="paramname"><em>n</em></span></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Compute double factorial using iterative method </p>
<p class="definition">Definition at line <a class="el" href="../../d7/d89/double__factorial_8cpp_source.html#l00018">18</a> of file <a class="el" href="../../d7/d89/double__factorial_8cpp_source.html">double_factorial.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 18</span> {</div>
<div class="line"><span class="lineno"> 19</span> uint64_t res = 1;</div>
<div class="line"><span class="lineno"> 20</span> <span class="keywordflow">for</span> (uint64_t i = n;; i -= 2) {</div>
<div class="line"><span class="lineno"> 21</span> <span class="keywordflow">if</span> (i == 0 || i == 1)</div>
<div class="line"><span class="lineno"> 22</span> <span class="keywordflow">return</span> res;</div>
<div class="line"><span class="lineno"> 23</span> res *= i;</div>
<div class="line"><span class="lineno"> 24</span> }</div>
<div class="line"><span class="lineno"> 25</span> <span class="keywordflow">return</span> res;</div>
<div class="line"><span class="lineno"> 26</span>}</div>
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<a id="a68ba20fed2ce427f6469c7689437829d" name="a68ba20fed2ce427f6469c7689437829d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a68ba20fed2ce427f6469c7689437829d">&#9670;&#160;</a></span>double_factorial_recursive()</h2>
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<td class="memname">uint64_t double_factorial_recursive </td>
<td>(</td>
<td class="paramtype">uint64_t</td> <td class="paramname"><span class="paramname"><em>n</em></span></td><td>)</td>
<td></td>
</tr>
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</div><div class="memdoc">
<p>Compute double factorial using resursive method. <br />
Recursion can be costly for large numbers. </p>
<p class="definition">Definition at line <a class="el" href="../../d7/d89/double__factorial_8cpp_source.html#l00031">31</a> of file <a class="el" href="../../d7/d89/double__factorial_8cpp_source.html">double_factorial.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 31</span> {</div>
<div class="line"><span class="lineno"> 32</span> <span class="keywordflow">if</span> (n &lt;= 1)</div>
<div class="line"><span class="lineno"> 33</span> <span class="keywordflow">return</span> 1;</div>
<div class="line"><span class="lineno"> 34</span> <span class="keywordflow">return</span> n * <a class="code hl_function" href="#a68ba20fed2ce427f6469c7689437829d">double_factorial_recursive</a>(n - 2);</div>
<div class="line"><span class="lineno"> 35</span>}</div>
<div class="ttc" id="adouble__factorial_8cpp_html_a68ba20fed2ce427f6469c7689437829d"><div class="ttname"><a href="#a68ba20fed2ce427f6469c7689437829d">double_factorial_recursive</a></div><div class="ttdeci">uint64_t double_factorial_recursive(uint64_t n)</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d89/double__factorial_8cpp_source.html#l00031">double_factorial.cpp:31</a></div></div>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
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<p>Main function </p>
<p class="definition">Definition at line <a class="el" href="../../d7/d89/double__factorial_8cpp_source.html#l00068">68</a> of file <a class="el" href="../../d7/d89/double__factorial_8cpp_source.html">double_factorial.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 68</span> {</div>
<div class="line"><span class="lineno"> 69</span> <a class="code hl_function" href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a>();</div>
<div class="line"><span class="lineno"> 70</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 71</span>}</div>
<div class="ttc" id="adouble__factorial_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d89/double__factorial_8cpp_source.html#l00051">double_factorial.cpp:51</a></div></div>
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<a id="abbbcebf3a2d0c67f4c3cfb5511a97981" name="abbbcebf3a2d0c67f4c3cfb5511a97981"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abbbcebf3a2d0c67f4c3cfb5511a97981">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">void test </td>
<td>(</td>
<td class="paramtype">uint64_t</td> <td class="paramname"><span class="paramname"><em>n</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint64_t</td> <td class="paramname"><span class="paramname"><em>expected</em></span>&#160;)</td>
</tr>
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</div><div class="memdoc">
<p>Wrapper to run tests using both recursive and iterative implementations. The checks are only valid in debug builds due to the use of <span class="tt">assert()</span> statements. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">n</td><td>number to check double factorial for </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">expected</td><td>expected result </td></tr>
</table>
</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="../../d7/d89/double__factorial_8cpp_source.html#l00043">43</a> of file <a class="el" href="../../d7/d89/double__factorial_8cpp_source.html">double_factorial.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 43</span> {</div>
<div class="line"><span class="lineno"> 44</span> assert(<a class="code hl_function" href="#a0a3c417360400093891a9ccddaa4be26">double_factorial_iterative</a>(n) == expected);</div>
<div class="line"><span class="lineno"> 45</span> assert(<a class="code hl_function" href="#a68ba20fed2ce427f6469c7689437829d">double_factorial_recursive</a>(n) == expected);</div>
<div class="line"><span class="lineno"> 46</span>}</div>
<div class="ttc" id="adouble__factorial_8cpp_html_a0a3c417360400093891a9ccddaa4be26"><div class="ttname"><a href="#a0a3c417360400093891a9ccddaa4be26">double_factorial_iterative</a></div><div class="ttdeci">uint64_t double_factorial_iterative(uint64_t n)</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d89/double__factorial_8cpp_source.html#l00018">double_factorial.cpp:18</a></div></div>
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<a id="a88ec9ad42717780d6caaff9d3d6977f9" name="a88ec9ad42717780d6caaff9d3d6977f9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a88ec9ad42717780d6caaff9d3d6977f9">&#9670;&#160;</a></span>tests()</h2>
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<td class="memname">void tests </td>
<td>(</td>
<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
</tr>
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<p>Test implementations </p>
<p class="definition">Definition at line <a class="el" href="../../d7/d89/double__factorial_8cpp_source.html#l00051">51</a> of file <a class="el" href="../../d7/d89/double__factorial_8cpp_source.html">double_factorial.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 51</span> {</div>
<div class="line"><span class="lineno"> 52</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 1:\t n=5\t...&quot;</span>;</div>
<div class="line"><span class="lineno"> 53</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(5, 15);</div>
<div class="line"><span class="lineno"> 54</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 55</span> </div>
<div class="line"><span class="lineno"> 56</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 2:\t n=15\t...&quot;</span>;</div>
<div class="line"><span class="lineno"> 57</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(15, 2027025);</div>
<div class="line"><span class="lineno"> 58</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 59</span> </div>
<div class="line"><span class="lineno"> 60</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 3:\t n=0\t...&quot;</span>;</div>
<div class="line"><span class="lineno"> 61</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(0, 1);</div>
<div class="line"><span class="lineno"> 62</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 63</span>}</div>
<div class="ttc" id="agenerate__parentheses_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00082">generate_parentheses.cpp:82</a></div></div>
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