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<p>Implementation to calculate an estimate of the <a href="https://en.wikipedia.org/wiki/File:Pi_30K.gif" target="_blank">number π (Pi)</a>.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
<code>#include &lt;cstdlib&gt;</code><br />
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Include dependency graph for approximate_pi.cpp:</div>
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<tr class="memitem:abf7f2a6d91f1ca6c89698792aea3f188"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#abf7f2a6d91f1ca6c89698792aea3f188">math::approximate_pi</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="el" href="../../d8/dc8/struct_point.html">Point</a> &gt; &amp;pts)</td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d51/approximate__pi_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <a href="../../d0/d51/approximate__pi_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
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<tr class="memitem:a0ddf1224851353fc92bfbff6f499fa97"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d0/d51/approximate__pi_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">main</a> (int argc, char *argv[])</td></tr>
<tr class="memdesc:a0ddf1224851353fc92bfbff6f499fa97"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d0/d51/approximate__pi_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">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 >Implementation to calculate an estimate of the <a href="https://en.wikipedia.org/wiki/File:Pi_30K.gif" target="_blank">number π (Pi)</a>. </p>
<p >We take a random point P with coordinates (x, y) such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. If x² + y² ≤ 1, then the point is inside the quarter disk of radius 1, otherwise the point is outside. We know that the probability of the point being inside the quarter disk is equal to π/4 double approx(vector&lt;Point&gt; &amp;pts) which will use the points pts (drawn at random) to return an estimate of the number π </p><dl class="section note"><dt>Note</dt><dd>This implementation is better than naive recursive or iterative approach.</dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Qannaf" target="_blank">Qannaf AL-SAHMI</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a0ddf1224851353fc92bfbff6f499fa97" name="a0ddf1224851353fc92bfbff6f499fa97"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a0ddf1224851353fc92bfbff6f499fa97">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<td class="paramtype">int&#160;</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 (ignored) </td></tr>
<tr><td class="paramname">argv</td><td>commandline array of arguments (ignored) </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 75</span> {</div>
<div class="line"><span class="lineno"> 76</span> <a class="code hl_function" href="../../d0/d51/approximate__pi_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 77</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 78</span>}</div>
<div class="ttc" id="aapproximate__pi_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d0/d51/approximate__pi_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> approximate_pi.cpp:58</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<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"> 58</span> {</div>
<div class="line"><span class="lineno"> 59</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;math::Point&gt;</a> rands;</div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">for</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a> i = 0; i &lt; 100000; i++) {</div>
<div class="line"><span class="lineno"> 61</span> <a class="code hl_struct" href="../../de/d4f/structmath_1_1_point.html">math::Point</a> p;</div>
<div class="line"><span class="lineno"> 62</span> p.x = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">rand</a>() / (double)RAND_MAX; <span class="comment">// 0 &lt;= x &lt;= 1</span></div>
<div class="line"><span class="lineno"> 63</span> p.y = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">rand</a>() / (double)RAND_MAX; <span class="comment">// 0 &lt;= y &lt;= 1</span></div>
<div class="line"><span class="lineno"> 64</span> rands.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(p);</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/io/basic_ostream.html">std::cout</a> &lt;&lt; <a class="code hl_function" href="../../dd/d47/namespacemath.html#abf7f2a6d91f1ca6c89698792aea3f188">math::approximate_pi</a>(rands) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>; <span class="comment">// ~3.14</span></div>
<div class="line"><span class="lineno"> 67</span>}</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>
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<div class="ttc" id="anamespacemath_html_abf7f2a6d91f1ca6c89698792aea3f188"><div class="ttname"><a href="../../dd/d47/namespacemath.html#abf7f2a6d91f1ca6c89698792aea3f188">math::approximate_pi</a></div><div class="ttdeci">double approximate_pi(const std::vector&lt; Point &gt; &amp;pts)</div><div class="ttdef"><b>Definition:</b> approximate_pi.cpp:35</div></div>
<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
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