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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;cassert&gt;</code><br />
<code>#include &lt;cstdlib&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for approximate_pi.cpp:</div>
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<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <br /></td></tr>
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Typedefs</h2></td></tr>
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using&#160;</td><td class="memItemRight" valign="bottom"><b>math::Point</b> = { double x</td></tr>
<tr class="memdesc:a937dc0c826acf3e6c0d2785527f7e9d7"><td class="mdescLeft">&#160;</td><td class="mdescRight">structure of points containing two numbers, x and y, such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. <br /></td></tr>
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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="../../dd/d47/namespacemath.html#a937dc0c826acf3e6c0d2785527f7e9d7">Point</a> &gt; &amp;pts)</td></tr>
<tr class="memdesc:abf7f2a6d91f1ca6c89698792aea3f188"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function uses the points in a given vector 'pts' (drawn at random) to return an approximation of the number π. <br /></td></tr>
<tr class="separator:abf7f2a6d91f1ca6c89698792aea3f188"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a483bb8ccf42aaf7375a83e91490eda1e"><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#a483bb8ccf42aaf7375a83e91490eda1e">tests</a> ()</td></tr>
<tr class="memdesc:a483bb8ccf42aaf7375a83e91490eda1e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><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#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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Variables</h2></td></tr>
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double&#160;</td><td class="memItemRight" valign="bottom"><b>math::y</b></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, else 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="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<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"> 80</span> {</div>
<div class="line"><span class="lineno"> 81</span> <a class="code hl_function" href="../../d0/d51/approximate__pi_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 83</span>}</div>
<div class="ttc" id="aapproximate__pi_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="../../d0/d51/approximate__pi_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> approximate_pi.cpp:62</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">&#9670;&#160;</a></span>tests()</h2>
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<td class="memname">static void tests </td>
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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"> 62</span> {</div>
<div class="line"><span class="lineno"> 63</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"> 64</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"> 65</span> <a class="code hl_typedef" href="../../dd/d47/namespacemath.html#a937dc0c826acf3e6c0d2785527f7e9d7">math::Point</a> p;</div>
<div class="line"><span class="lineno"> 66</span> p.x = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">rand</a>() / <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(RAND_MAX); <span class="comment">// 0 &lt;= x &lt;= 1</span></div>
<div class="line"><span class="lineno"> 67</span> p.y = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">rand</a>() / <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(RAND_MAX); <span class="comment">// 0 &lt;= y &lt;= 1</span></div>
<div class="line"><span class="lineno"> 68</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"> 69</span> }</div>
<div class="line"><span class="lineno"> 70</span> assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#abf7f2a6d91f1ca6c89698792aea3f188">math::approximate_pi</a>(rands) &gt; 3.135);</div>
<div class="line"><span class="lineno"> 71</span> assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#abf7f2a6d91f1ca6c89698792aea3f188">math::approximate_pi</a>(rands) &lt; 3.145);</div>
<div class="line"><span class="lineno"> 72</span> </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;All tests have successfully 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"> 74</span>}</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="ttdoc">This function uses the points in a given vector 'pts' (drawn at random) to return an approximation of...</div><div class="ttdef"><b>Definition</b> approximate_pi.cpp:47</div></div>
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