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@@ -96,11 +96,43 @@ $(document).ready(function(){initNavTree('dd/d47/namespacemath.html','../../');
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<p>for IO operations
<p>for assert
<a href="../../dd/d47/namespacemath.html#details">More...</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a971ce57e368f2f631cf1f4ff3f864049"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a971ce57e368f2f631cf1f4ff3f864049"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a971ce57e368f2f631cf1f4ff3f864049">square_area</a> (T length)</td></tr>
<tr class="memdesc:a971ce57e368f2f631cf1f4ff3f864049"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Square" target="_blank">square</a> (l * l) <a href="../../dd/d47/namespacemath.html#a971ce57e368f2f631cf1f4ff3f864049">More...</a><br /></td></tr>
<tr class="separator:a971ce57e368f2f631cf1f4ff3f864049"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab31d141f7c5b551746b1eee0eb4dedca"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ab31d141f7c5b551746b1eee0eb4dedca"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ab31d141f7c5b551746b1eee0eb4dedca">rect_area</a> (T length, T width)</td></tr>
<tr class="memdesc:ab31d141f7c5b551746b1eee0eb4dedca"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Rectangle" target="_blank">rectangle</a> (l * w) <a href="../../dd/d47/namespacemath.html#ab31d141f7c5b551746b1eee0eb4dedca">More...</a><br /></td></tr>
<tr class="separator:ab31d141f7c5b551746b1eee0eb4dedca"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab3b920cc56442abd92279ba23b50f4dc"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ab3b920cc56442abd92279ba23b50f4dc"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ab3b920cc56442abd92279ba23b50f4dc">triangle_area</a> (T base, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
<tr class="memdesc:ab3b920cc56442abd92279ba23b50f4dc"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Triangle" target="_blank">triangle</a> (b * h / 2) <a href="../../dd/d47/namespacemath.html#ab3b920cc56442abd92279ba23b50f4dc">More...</a><br /></td></tr>
<tr class="separator:ab3b920cc56442abd92279ba23b50f4dc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a40e36c67da78d2131408c57ee091ad75"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a40e36c67da78d2131408c57ee091ad75"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a40e36c67da78d2131408c57ee091ad75">circle_area</a> (T radius)</td></tr>
<tr class="memdesc:a40e36c67da78d2131408c57ee091ad75"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Area_of_a_circle" target="_blank">circle</a> (pi <a href="../../dd/d47/namespacemath.html#a40e36c67da78d2131408c57ee091ad75">More...</a><br /></td></tr>
<tr class="separator:a40e36c67da78d2131408c57ee091ad75"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5de184925e68658f15415dd53954df4f"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a5de184925e68658f15415dd53954df4f"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a5de184925e68658f15415dd53954df4f">parallelogram_area</a> (T base, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
<tr class="memdesc:a5de184925e68658f15415dd53954df4f"><td class="mdescLeft">&#160;</td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Parallelogram" target="_blank">parallelogram</a> (b * h) <a href="../../dd/d47/namespacemath.html#a5de184925e68658f15415dd53954df4f">More...</a><br /></td></tr>
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<tr class="memitem:abc46c784a297fc1d2eb8b33a327fba4c"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:abc46c784a297fc1d2eb8b33a327fba4c"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#abc46c784a297fc1d2eb8b33a327fba4c">cube_surface_area</a> (T length)</td></tr>
<tr class="memdesc:abc46c784a297fc1d2eb8b33a327fba4c"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface area of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> ( 6 * (l <a href="../../dd/d47/namespacemath.html#abc46c784a297fc1d2eb8b33a327fba4c">More...</a><br /></td></tr>
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<tr class="memitem:ab7f29862d30df351c317eedd60a0c656"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ab7f29862d30df351c317eedd60a0c656"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ab7f29862d30df351c317eedd60a0c656">sphere_surface_area</a> (T radius)</td></tr>
<tr class="memdesc:ab7f29862d30df351c317eedd60a0c656"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface area of a <a href="https://en.wikipedia.org/wiki/Sphere" target="_blank">sphere</a> ( 4 * pi * r^2) <a href="../../dd/d47/namespacemath.html#ab7f29862d30df351c317eedd60a0c656">More...</a><br /></td></tr>
<tr class="separator:ab7f29862d30df351c317eedd60a0c656"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac5803413618fcfb922cb32c6db0fc864"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ac5803413618fcfb922cb32c6db0fc864"><td class="memTemplItemLeft" align="right" valign="top">T&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ac5803413618fcfb922cb32c6db0fc864">cylinder_surface_area</a> (T radius, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
<tr class="memdesc:ac5803413618fcfb922cb32c6db0fc864"><td class="mdescLeft">&#160;</td><td class="mdescRight">surface area of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> (2 * pi * r * h + 2 * pi * r^2) <a href="../../dd/d47/namespacemath.html#ac5803413618fcfb922cb32c6db0fc864">More...</a><br /></td></tr>
<tr class="separator:ac5803413618fcfb922cb32c6db0fc864"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aec65db4e5c7317323227f026fe50ef11"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">integral_approx</a> (double lb, double ub, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt; double(double)&gt; &amp;func, double delta=.0001)</td></tr>
<tr class="memdesc:aec65db4e5c7317323227f026fe50ef11"><td class="mdescLeft">&#160;</td><td class="mdescRight">Computes integral approximation. <a href="../../dd/d47/namespacemath.html#aec65db4e5c7317323227f026fe50ef11">More...</a><br /></td></tr>
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@@ -128,14 +160,16 @@ Functions</h2></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >for IO operations </p>
<div class="textblock"><p >for assert </p>
<p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> and <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></p>
<p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></p>
<p >for io operations</p>
<p >Evaluate recurrence relation using <a href="https://www.hackerearth.com/practice/notes/matrix-exponentiation-1/" target="_blank">matrix exponentiation</a>.</p>
<p >for assert</p>
<p >Math algorithms.</p>
<p >for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
<p >for IO operations</p>
<p >for M_PI definition and pow() for uint16_t datatype for IO operations</p>
<p >Mathematical algorithms</p>
<p >for assert for int32_t type for atoi</p>
<p >Mathematical algorithms</p>
<p >for assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> and <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></p>
@@ -186,6 +220,126 @@ Algorithm</h3>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keywordflow">return</span> (1 &lt;&lt; n);</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a40e36c67da78d2131408c57ee091ad75">&#9670;&nbsp;</a></span>circle_area()</h2>
<div class="memitem">
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template&lt;typename T &gt; </div>
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<td class="memname">T math::circle_area </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>radius</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>area of a <a href="https://en.wikipedia.org/wiki/Area_of_a_circle" target="_blank">circle</a> (pi </p>
<ul>
<li>r^2) <dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">radius</td><td>is the radius of the circle </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>area of the circle </dd></dl>
</li>
</ul>
<div class="fragment"><div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> {</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">return</span> M_PI * pow(radius, 2);</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#abc46c784a297fc1d2eb8b33a327fba4c">&#9670;&nbsp;</a></span>cube_surface_area()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">T math::cube_surface_area </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>length</em></td><td>)</td>
<td></td>
</tr>
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<p>surface area of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> ( 6 * (l </p>
<ul>
<li>l)) <dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">length</td><td>is the length of the cube </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>surface area of the cube </dd></dl>
</li>
</ul>
<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> {</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keywordflow">return</span> 6 * length * length;</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ac5803413618fcfb922cb32c6db0fc864">&#9670;&nbsp;</a></span>cylinder_surface_area()</h2>
<div class="memitem">
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template&lt;typename T &gt; </div>
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<td class="memname">T math::cylinder_surface_area </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>radius</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>height</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>surface area of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> (2 * pi * r * h + 2 * pi * r^2) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">radius</td><td>is the radius of the cylinder </td></tr>
<tr><td class="paramname">height</td><td>is the height of the cylinder </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>surface area of the cylinder </dd></dl>
<div class="fragment"><div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> {</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keywordflow">return</span> 2 * M_PI * radius * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> + 2 * M_PI * pow(radius, 2);</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span>}</div>
<div class="ttc" id="aavltree_8cpp_html_ae4a66d8b0c2b0d626aea45977e358c83"><div class="ttname"><a href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a></div><div class="ttdeci">int height(node *root)</div><div class="ttdef"><b>Definition:</b> avltree.cpp:31</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a5de184925e68658f15415dd53954df4f">&#9670;&nbsp;</a></span>parallelogram_area()</h2>
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<div class="memtemplate">
template&lt;typename T &gt; </div>
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<td class="memname">T math::parallelogram_area </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>base</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>height</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
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<p>area of a <a href="https://en.wikipedia.org/wiki/Parallelogram" target="_blank">parallelogram</a> (b * h) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">base</td><td>is the length of the bottom side of the parallelogram </td></tr>
<tr><td class="paramname">height</td><td>is the length of the tallest point in the parallelogram </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>area of the parallelogram </dd></dl>
<div class="fragment"><div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> {</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordflow">return</span> base * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ab31d141f7c5b551746b1eee0eb4dedca">&#9670;&nbsp;</a></span>rect_area()</h2>
<div class="memitem">
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template&lt;typename T &gt; </div>
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<td class="memname">T math::rect_area </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>length</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>width</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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<p>area of a <a href="https://en.wikipedia.org/wiki/Rectangle" target="_blank">rectangle</a> (l * w) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">length</td><td>is the length of the rectangle </td></tr>
<tr><td class="paramname">width</td><td>is the width of the rectangle </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>area of the rectangle </dd></dl>
<div class="fragment"><div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> {</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordflow">return</span> length * width;</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ab7f29862d30df351c317eedd60a0c656">&#9670;&nbsp;</a></span>sphere_surface_area()</h2>
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<td class="memname">T math::sphere_surface_area </td>
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<td class="paramname"><em>radius</em></td><td>)</td>
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<p>surface area of a <a href="https://en.wikipedia.org/wiki/Sphere" target="_blank">sphere</a> ( 4 * pi * r^2) </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">radius</td><td>is the radius of the sphere </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>surface area of the sphere </dd></dl>
<div class="fragment"><div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> {</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordflow">return</span> 4 * M_PI * pow(radius, 2);</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a971ce57e368f2f631cf1f4ff3f864049">&#9670;&nbsp;</a></span>square_area()</h2>
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<td class="memname">T math::square_area </td>
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<td class="paramname"><em>length</em></td><td>)</td>
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<p>area of a <a href="https://en.wikipedia.org/wiki/Square" target="_blank">square</a> (l * l) </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">length</td><td>is the length of the square </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>area of square </dd></dl>
<div class="fragment"><div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> {</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keywordflow">return</span> length * length;</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span>}</div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> assert(approx &lt;= expected * (1 + threshold));</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ab3b920cc56442abd92279ba23b50f4dc">&#9670;&nbsp;</a></span>triangle_area()</h2>
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<td class="memname">T math::triangle_area </td>
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<td class="paramname"><em>base</em>, </td>
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<td class="paramname"><em>height</em>&#160;</td>
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<p>area of a <a href="https://en.wikipedia.org/wiki/Triangle" target="_blank">triangle</a> (b * h / 2) </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">base</td><td>is the length of the bottom side of the triangle </td></tr>
<tr><td class="paramname">height</td><td>is the length of the tallest point in the triangle </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>area of the triangle </dd></dl>
<div class="fragment"><div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> {</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">return</span> base * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> / 2;</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span>}</div>
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