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<p>Program to calculate <a href="https://en.wikipedia.org/wiki/Binomial_coefficient" target="_blank">Binomial coefficients</a>
<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;cstdlib&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for binomial_calculate.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:dd/d47/namespacemath"><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 M_PI definition and pow() <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:d7/d7a/namespacebinomial"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d7a/namespacebinomial.html">binomial</a></td></tr>
<tr class="memdesc:d7/d7a/namespacebinomial"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Binomial_coefficient" target="_blank">Binomial coefficients</a> implementation. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:aae407a2a13362c4c64fbe509ff325978"><td class="memItemLeft" align="right" valign="top">size_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/db1/binomial__calculate_8cpp.html#aae407a2a13362c4c64fbe509ff325978">math::binomial::calculate</a> (int32_t n, int32_t k)</td></tr>
<tr class="memdesc:aae407a2a13362c4c64fbe509ff325978"><td class="mdescLeft">&#160;</td><td class="mdescRight">Function to calculate binomial coefficients. <a href="../../d8/db1/binomial__calculate_8cpp.html#aae407a2a13362c4c64fbe509ff325978">More...</a><br /></td></tr>
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<tr class="memitem:a483bb8ccf42aaf7375a83e91490eda1e"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/db1/binomial__calculate_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a> ()</td></tr>
<tr class="memdesc:a483bb8ccf42aaf7375a83e91490eda1e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test implementations. <a href="../../d8/db1/binomial__calculate_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">More...</a><br /></td></tr>
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<tr class="memitem:ac0f2228420376f4db7e1274f2b41667c"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/db1/binomial__calculate_8cpp.html#ac0f2228420376f4db7e1274f2b41667c">main</a> (int argc, const char *argv[])</td></tr>
<tr class="memdesc:ac0f2228420376f4db7e1274f2b41667c"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d8/db1/binomial__calculate_8cpp.html#ac0f2228420376f4db7e1274f2b41667c">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Program to calculate <a href="https://en.wikipedia.org/wiki/Binomial_coefficient" target="_blank">Binomial coefficients</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/astronmax" target="_blank">astronmax</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="aae407a2a13362c4c64fbe509ff325978" name="aae407a2a13362c4c64fbe509ff325978"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aae407a2a13362c4c64fbe509ff325978">&#9670;&nbsp;</a></span>calculate()</h2>
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<td class="memname">size_t math::binomial::calculate </td>
<td>(</td>
<td class="paramtype">int32_t&#160;</td>
<td class="paramname"><em>n</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int32_t&#160;</td>
<td class="paramname"><em>k</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Function to calculate binomial coefficients. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>first value </td></tr>
<tr><td class="paramname">k</td><td>second value </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>binomial coefficient for n and k </dd></dl>
<div class="fragment"><div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> {</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// basic cases</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordflow">if</span> (k &gt; (n / 2))</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> k = n - k;</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">if</span> (k == 1)</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordflow">return</span> n;</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordflow">if</span> (k == 0)</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordflow">return</span> 1;</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keywordtype">size_t</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = 1;</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">for</span> (int32_t i = 1; i &lt;= k; ++i) {</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> *= n - k + i;</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> /= i;</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> }</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</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"><a id="l00048" name="l00048"></a><span class="lineno"> 48</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>
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<h2 class="memtitle"><span class="permalink"><a href="#ac0f2228420376f4db7e1274f2b41667c">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>argc</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const char *&#160;</td>
<td class="paramname"><em>argv</em>[]&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Main function. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">argc</td><td>commandline argument count </td></tr>
<tr><td class="paramname">argv</td><td>commandline array of arguments </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> {</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <a class="code hl_function" href="../../d8/db1/binomial__calculate_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> </div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">if</span> (argc &lt; 3) {</div>
<div class="line"><a id="l00083" name="l00083"></a><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;Usage ./binomial_calculate {n} {k}&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"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> }</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> int32_t n = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> int32_t k = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[2]);</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a id="l00090" name="l00090"></a><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; <a class="code hl_function" href="../../d8/db1/binomial__calculate_8cpp.html#aae407a2a13362c4c64fbe509ff325978">math::binomial::calculate</a>(n, k) &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"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span>}</div>
<div class="ttc" id="aatoi_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a></div><div class="ttdeci">T atoi(T... args)</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="abinomial__calculate_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="../../d8/db1/binomial__calculate_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">Test implementations.</div><div class="ttdef"><b>Definition:</b> binomial_calculate.cpp:56</div></div>
<div class="ttc" id="abinomial__calculate_8cpp_html_aae407a2a13362c4c64fbe509ff325978"><div class="ttname"><a href="../../d8/db1/binomial__calculate_8cpp.html#aae407a2a13362c4c64fbe509ff325978">math::binomial::calculate</a></div><div class="ttdeci">size_t calculate(int32_t n, int32_t k)</div><div class="ttdoc">Function to calculate binomial coefficients.</div><div class="ttdef"><b>Definition:</b> binomial_calculate.cpp:32</div></div>
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">&#9670;&nbsp;</a></span>tests()</h2>
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<td class="memname">static void tests </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<p>Test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// tests for calculate function</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> assert(math::binomial::calculate(1, 1) == 1);</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> assert(math::binomial::calculate(57, 57) == 1);</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> assert(math::binomial::calculate(6, 3) == 20);</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> assert(math::binomial::calculate(10, 5) == 252);</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> assert(math::binomial::calculate(20, 10) == 184756);</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> assert(math::binomial::calculate(30, 15) == 155117520);</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> assert(math::binomial::calculate(40, 20) == 137846528820);</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> assert(math::binomial::calculate(50, 25) == 126410606437752);</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> assert(math::binomial::calculate(60, 30) == 118264581564861424);</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> assert(math::binomial::calculate(62, 31) == 465428353255261088);</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a id="l00069" name="l00069"></a><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;[+] Binomial coefficients calculate test completed&quot;</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</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"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span>}</div>
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