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<p>for IO operations
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<table class="memberdecls">
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Classes</h2></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d4f/structmath_1_1_point.html">Point</a></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:ab37f3a7302a84179aae682c79d8390bf"><td class="memItemLeft" align="right" valign="top">uint64_t </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ab37f3a7302a84179aae682c79d8390bf">aliquot_sum</a> (const uint64_t num)</td></tr>
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<tr class="separator:ab37f3a7302a84179aae682c79d8390bf"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:abf7f2a6d91f1ca6c89698792aea3f188"><td class="memItemLeft" align="right" valign="top">double </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#abf7f2a6d91f1ca6c89698792aea3f188">approximate_pi</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< <a class="el" href="../../de/d4f/structmath_1_1_point.html">Point</a> > &pts)</td></tr>
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<tr class="separator:abf7f2a6d91f1ca6c89698792aea3f188"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a971ce57e368f2f631cf1f4ff3f864049"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a971ce57e368f2f631cf1f4ff3f864049"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a971ce57e368f2f631cf1f4ff3f864049">square_area</a> (T length)</td></tr>
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<tr class="memdesc:a971ce57e368f2f631cf1f4ff3f864049"><td class="mdescLeft"> </td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Square" target="_blank">square</a> (l * l) <br /></td></tr>
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<tr class="separator:a971ce57e368f2f631cf1f4ff3f864049"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ab31d141f7c5b551746b1eee0eb4dedca"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:ab31d141f7c5b551746b1eee0eb4dedca"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ab31d141f7c5b551746b1eee0eb4dedca">rect_area</a> (T length, T width)</td></tr>
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<tr class="memdesc:ab31d141f7c5b551746b1eee0eb4dedca"><td class="mdescLeft"> </td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Rectangle" target="_blank">rectangle</a> (l * w) <br /></td></tr>
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<tr class="separator:ab31d141f7c5b551746b1eee0eb4dedca"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ab3b920cc56442abd92279ba23b50f4dc"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:ab3b920cc56442abd92279ba23b50f4dc"><td class="memTemplItemLeft" align="right" valign="top">T </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>
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<tr class="memdesc:ab3b920cc56442abd92279ba23b50f4dc"><td class="mdescLeft"> </td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Triangle" target="_blank">triangle</a> (b * h / 2) <br /></td></tr>
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<tr class="separator:ab3b920cc56442abd92279ba23b50f4dc"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a40e36c67da78d2131408c57ee091ad75"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a40e36c67da78d2131408c57ee091ad75"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a40e36c67da78d2131408c57ee091ad75">circle_area</a> (T radius)</td></tr>
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<tr class="memdesc:a40e36c67da78d2131408c57ee091ad75"><td class="mdescLeft"> </td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Area_of_a_circle" target="_blank">circle</a> (pi <br /></td></tr>
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<tr class="separator:a40e36c67da78d2131408c57ee091ad75"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a5de184925e68658f15415dd53954df4f"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a5de184925e68658f15415dd53954df4f"><td class="memTemplItemLeft" align="right" valign="top">T </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>
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<tr class="memdesc:a5de184925e68658f15415dd53954df4f"><td class="mdescLeft"> </td><td class="mdescRight">area of a <a href="https://en.wikipedia.org/wiki/Parallelogram" target="_blank">parallelogram</a> (b * h) <br /></td></tr>
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<tr class="separator:a5de184925e68658f15415dd53954df4f"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:abc46c784a297fc1d2eb8b33a327fba4c"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:abc46c784a297fc1d2eb8b33a327fba4c"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#abc46c784a297fc1d2eb8b33a327fba4c">cube_surface_area</a> (T length)</td></tr>
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<tr class="memdesc:abc46c784a297fc1d2eb8b33a327fba4c"><td class="mdescLeft"> </td><td class="mdescRight">surface area of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> ( 6 * (l <br /></td></tr>
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<tr class="separator:abc46c784a297fc1d2eb8b33a327fba4c"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ab7f29862d30df351c317eedd60a0c656"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:ab7f29862d30df351c317eedd60a0c656"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ab7f29862d30df351c317eedd60a0c656">sphere_surface_area</a> (T radius)</td></tr>
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<tr class="memdesc:ab7f29862d30df351c317eedd60a0c656"><td class="mdescLeft"> </td><td class="mdescRight">surface area of a <a href="https://en.wikipedia.org/wiki/Sphere" target="_blank">sphere</a> ( 4 * pi * r^2) <br /></td></tr>
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<tr class="separator:ab7f29862d30df351c317eedd60a0c656"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ac5803413618fcfb922cb32c6db0fc864"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:ac5803413618fcfb922cb32c6db0fc864"><td class="memTemplItemLeft" align="right" valign="top">T </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>
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<tr class="memdesc:ac5803413618fcfb922cb32c6db0fc864"><td class="mdescLeft"> </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) <br /></td></tr>
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<tr class="separator:ac5803413618fcfb922cb32c6db0fc864"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:aec65db4e5c7317323227f026fe50ef11"><td class="memItemLeft" align="right" valign="top">double </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>< double(double)> &func, double delta=.0001)</td></tr>
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<tr class="memdesc:aec65db4e5c7317323227f026fe50ef11"><td class="mdescLeft"> </td><td class="mdescRight">Computes integral approximation. <br /></td></tr>
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<tr class="separator:aec65db4e5c7317323227f026fe50ef11"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a50936ee98f4d40f17823befc65a32aec"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a50936ee98f4d40f17823befc65a32aec">test_eval</a> (double approx, double expected, double threshold)</td></tr>
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<tr class="memdesc:a50936ee98f4d40f17823befc65a32aec"><td class="mdescLeft"> </td><td class="mdescRight">Wrapper to evaluate if the approximated value is within <code>.XX%</code> threshold of the exact value. <br /></td></tr>
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<tr class="separator:a50936ee98f4d40f17823befc65a32aec"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:afa39ec943a4836c878e1614fd89b146f"><td class="memItemLeft" align="right" valign="top">uint64_t </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#afa39ec943a4836c878e1614fd89b146f">largestPower</a> (uint32_t n, const uint16_t &p)</td></tr>
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<tr class="memdesc:afa39ec943a4836c878e1614fd89b146f"><td class="mdescLeft"> </td><td class="mdescRight">Function to calculate largest power. <br /></td></tr>
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<tr class="separator:afa39ec943a4836c878e1614fd89b146f"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a04065193d190d605e1f0d0d93a87e244"><td class="memItemLeft" align="right" valign="top">uint64_t </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a04065193d190d605e1f0d0d93a87e244">lcmSum</a> (const uint16_t &num)</td></tr>
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<tr class="separator:a04065193d190d605e1f0d0d93a87e244"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a8d8e81a7cd59644b311ef9adb268f5f0"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a8d8e81a7cd59644b311ef9adb268f5f0">magic_number</a> (const uint64_t &n)</td></tr>
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<tr class="separator:a8d8e81a7cd59644b311ef9adb268f5f0"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:afcd07701d73ed65cd616bcba02737f3d"><td class="memItemLeft" align="right" valign="top">uint64_t </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#afcd07701d73ed65cd616bcba02737f3d">power</a> (uint64_t a, uint64_t b, uint64_t c)</td></tr>
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<tr class="memdesc:afcd07701d73ed65cd616bcba02737f3d"><td class="mdescLeft"> </td><td class="mdescRight">This function calculates a raised to exponent b under modulo c using modular exponentiation. <br /></td></tr>
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<tr class="separator:afcd07701d73ed65cd616bcba02737f3d"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a6e2dff75c5de70455b90c799d6ad6967"><td class="memTemplParams" colspan="2">template<class T > </td></tr>
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<tr class="memitem:a6e2dff75c5de70455b90c799d6ad6967"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a6e2dff75c5de70455b90c799d6ad6967">n_choose_r</a> (T n, T r)</td></tr>
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<tr class="memdesc:a6e2dff75c5de70455b90c799d6ad6967"><td class="mdescLeft"> </td><td class="mdescRight">This is the function implementation of \( \binom{n}{r} \). <br /></td></tr>
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<tr class="separator:a6e2dff75c5de70455b90c799d6ad6967"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a9236348755183644f1225e162d01ab14"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a9236348755183644f1225e162d01ab14"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a9236348755183644f1225e162d01ab14">square_perimeter</a> (T length)</td></tr>
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<tr class="memdesc:a9236348755183644f1225e162d01ab14"><td class="mdescLeft"> </td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/Square" target="_blank">square</a> (4 * l) <br /></td></tr>
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<tr class="separator:a9236348755183644f1225e162d01ab14"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a428769a16e9525e56588d7c7709d25a6"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a428769a16e9525e56588d7c7709d25a6"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a428769a16e9525e56588d7c7709d25a6">rect_perimeter</a> (T length, T width)</td></tr>
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<tr class="memdesc:a428769a16e9525e56588d7c7709d25a6"><td class="mdescLeft"> </td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/Rectangle" target="_blank">rectangle</a> ( 2(l + w) ) <br /></td></tr>
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<tr class="memitem:a3d1e4db743b189f309327572663415f3"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a3d1e4db743b189f309327572663415f3"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a3d1e4db743b189f309327572663415f3">triangle_perimeter</a> (T base, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>, T hypotenuse)</td></tr>
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<tr class="memdesc:a3d1e4db743b189f309327572663415f3"><td class="mdescLeft"> </td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/Triangle" target="_blank">triangle</a> (a + b + c) <br /></td></tr>
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<tr class="separator:a3d1e4db743b189f309327572663415f3"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ad0acf82b7bc920182bf8322d1e103953"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:ad0acf82b7bc920182bf8322d1e103953"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ad0acf82b7bc920182bf8322d1e103953">circle_perimeter</a> (T radius)</td></tr>
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<tr class="memdesc:ad0acf82b7bc920182bf8322d1e103953"><td class="mdescLeft"> </td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/perimeter_of_a_circle" target="_blank">circle</a> (2 * pi * r) <br /></td></tr>
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<tr class="separator:ad0acf82b7bc920182bf8322d1e103953"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a0efb235330ff48e14fd31faaccbcebb3"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a0efb235330ff48e14fd31faaccbcebb3"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a0efb235330ff48e14fd31faaccbcebb3">parallelogram_perimeter</a> (T base, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
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<tr class="memdesc:a0efb235330ff48e14fd31faaccbcebb3"><td class="mdescLeft"> </td><td class="mdescRight">perimeter of a <a href="https://en.wikipedia.org/wiki/Parallelogram" target="_blank">parallelogram</a> 2(b + h) <br /></td></tr>
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<tr class="separator:a0efb235330ff48e14fd31faaccbcebb3"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a8998ca7b1886d1d7d00aef3b457a9b1b"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a8998ca7b1886d1d7d00aef3b457a9b1b"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a8998ca7b1886d1d7d00aef3b457a9b1b">cube_surface_perimeter</a> (T length)</td></tr>
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<tr class="memdesc:a8998ca7b1886d1d7d00aef3b457a9b1b"><td class="mdescLeft"> </td><td class="mdescRight">surface perimeter of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> ( 12 <br /></td></tr>
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<tr class="separator:a8998ca7b1886d1d7d00aef3b457a9b1b"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:aa8592c3279c41a2c6d4d64eeb488f63f"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:aa8592c3279c41a2c6d4d64eeb488f63f"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#aa8592c3279c41a2c6d4d64eeb488f63f">n_polygon_surface_perimeter</a> (T sides, T length)</td></tr>
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<tr class="memdesc:aa8592c3279c41a2c6d4d64eeb488f63f"><td class="mdescLeft"> </td><td class="mdescRight">surface perimeter of a <a href="https://www.cuemath.com/measurement/perimeter-of-polygon/" target="_blank">n-polygon</a> ( n * l) <br /></td></tr>
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<tr class="separator:aa8592c3279c41a2c6d4d64eeb488f63f"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a1d4df7a4e43a2eac1acc0ac610487c73"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a1d4df7a4e43a2eac1acc0ac610487c73"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a1d4df7a4e43a2eac1acc0ac610487c73">cylinder_surface_perimeter</a> (T radius, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
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<tr class="memdesc:a1d4df7a4e43a2eac1acc0ac610487c73"><td class="mdescLeft"> </td><td class="mdescRight">surface perimeter of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> (2 * radius + 2 * height) <br /></td></tr>
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<tr class="separator:a1d4df7a4e43a2eac1acc0ac610487c73"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a8a48be4d7f14e34c5c92925bc1cbf3bb"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a8a48be4d7f14e34c5c92925bc1cbf3bb">power_of_two</a> (int n)</td></tr>
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<tr class="memdesc:a8a48be4d7f14e34c5c92925bc1cbf3bb"><td class="mdescLeft"> </td><td class="mdescRight">This function finds whether a number is power of 2 or not. <br /></td></tr>
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<tr class="separator:a8a48be4d7f14e34c5c92925bc1cbf3bb"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ae1ca505751f5a6d3977b86372cfe75ea"><td class="memItemLeft" align="right" valign="top">uint64_t </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ae1ca505751f5a6d3977b86372cfe75ea">binomialCoeffSum</a> (uint64_t n)</td></tr>
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<tr class="separator:ae1ca505751f5a6d3977b86372cfe75ea"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ae413098478fa38acaac887b7654f0725"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:ae413098478fa38acaac887b7654f0725"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ae413098478fa38acaac887b7654f0725">cube_volume</a> (T length)</td></tr>
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<tr class="memdesc:ae413098478fa38acaac887b7654f0725"><td class="mdescLeft"> </td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> <br /></td></tr>
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<tr class="separator:ae413098478fa38acaac887b7654f0725"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3fdc74c24697ec5bb5c3698c96117c12"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a3fdc74c24697ec5bb5c3698c96117c12"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a3fdc74c24697ec5bb5c3698c96117c12">rect_prism_volume</a> (T length, T width, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
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<tr class="memdesc:a3fdc74c24697ec5bb5c3698c96117c12"><td class="mdescLeft"> </td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cuboid" target="_blank">rectangular</a> prism. <br /></td></tr>
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<tr class="separator:a3fdc74c24697ec5bb5c3698c96117c12"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3fe35440c27758ecc2287e08217d63a7"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a3fe35440c27758ecc2287e08217d63a7"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a3fe35440c27758ecc2287e08217d63a7">cone_volume</a> (T radius, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>, double PI=3.14)</td></tr>
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<tr class="memdesc:a3fe35440c27758ecc2287e08217d63a7"><td class="mdescLeft"> </td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cone" target="_blank">cone</a> <br /></td></tr>
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<tr class="separator:a3fe35440c27758ecc2287e08217d63a7"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a2d704a7b72a6b2db8b76c8581b577b2c"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a2d704a7b72a6b2db8b76c8581b577b2c"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a2d704a7b72a6b2db8b76c8581b577b2c">triangle_prism_volume</a> (T base, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>, T depth)</td></tr>
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<tr class="memdesc:a2d704a7b72a6b2db8b76c8581b577b2c"><td class="mdescLeft"> </td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Triangular_prism" target="_blank">triangular</a> prism. <br /></td></tr>
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<tr class="separator:a2d704a7b72a6b2db8b76c8581b577b2c"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a94db02b3c9e55a69ac1696f30e2f761c"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a94db02b3c9e55a69ac1696f30e2f761c"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a94db02b3c9e55a69ac1696f30e2f761c">pyramid_volume</a> (T length, T width, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>)</td></tr>
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<tr class="memdesc:a94db02b3c9e55a69ac1696f30e2f761c"><td class="mdescLeft"> </td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Pyramid_(geometry)" target="_blank">pyramid</a> <br /></td></tr>
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<tr class="separator:a94db02b3c9e55a69ac1696f30e2f761c"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a34d66a77c19ce9b8b3a3d14352b34551"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a34d66a77c19ce9b8b3a3d14352b34551"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a34d66a77c19ce9b8b3a3d14352b34551">sphere_volume</a> (T radius, double PI=3.14)</td></tr>
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<tr class="memdesc:a34d66a77c19ce9b8b3a3d14352b34551"><td class="mdescLeft"> </td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Sphere" target="_blank">sphere</a> <br /></td></tr>
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<tr class="separator:a34d66a77c19ce9b8b3a3d14352b34551"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:abde24398be43538c62e4a496968e60ca"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:abde24398be43538c62e4a496968e60ca"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#abde24398be43538c62e4a496968e60ca">cylinder_volume</a> (T radius, T <a class="el" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>, double PI=3.14)</td></tr>
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<tr class="memdesc:abde24398be43538c62e4a496968e60ca"><td class="mdescLeft"> </td><td class="mdescRight">The volume of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> <br /></td></tr>
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<tr class="separator:abde24398be43538c62e4a496968e60ca"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>for IO operations </p>
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<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>
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<p>for io operations</p>
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<p>Evaluate recurrence relation using <a href="https://www.hackerearth.com/practice/notes/matrix-exponentiation-1/" target="_blank">matrix exponentiation</a>.</p>
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<p>for assert</p>
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<p>Math algorithms.</p>
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<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
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<p>for M_PI definition and pow()</p>
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<p>for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></p>
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<p>for assert</p>
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<p>Mathematical algorithms</p>
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<p>for IO operations for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
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<p>Mathematical algorithms</p>
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<p>for assert for uint16_t datatype for IO operations</p>
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<p>Mathematical algorithms</p>
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<p>for assert for int32_t type for atoi</p>
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<p>Mathematical algorithms</p>
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<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>
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<p>Mathematical algorithms</p>
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<p>for assert for mathematical functions for passing in functions</p>
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<p>Mathematical functions</p>
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<p>for math functions for fixed size data types for time to initialize rng for function pointers for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> for random number generation for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></p>
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<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>
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<p>Mathematical algorithms</p>
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<p>Given a recurrence relation; evaluate the value of nth term. For e.g., For fibonacci series, recurrence series is <code>f(n) = f(n-1) + f(n-2)</code> where <code>f(0) = 0</code> and <code>f(1) = 1</code>. Note that the method used only demonstrates recurrence relation with one variable (n), unlike <code>nCr</code> problem, since it has two (n, r)</p>
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<h3><a class="anchor" id="autotoc_md84"></a>
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Algorithm</h3>
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<p>This problem can be solved using matrix exponentiation method. </p><dl class="section see"><dt>See also</dt><dd>here for simple <a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_exponentiation.cpp" target="_blank">number exponentiation algorithm</a> or <a href="https://en.wikipedia.org/wiki/Exponentiation_by_squaring" target="_blank">explaination here</a>. </dd></dl>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/AshishYUO" target="_blank">Ashish Daulatabad</a> for assert for IO operations for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> STL</dd></dl>
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<p>Mathematical algorithms</p>
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<p>for std::is_equal, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a> for assert for IO operations</p>
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<p>Mathematical algorithms</p>
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<p>for assert for io operations</p>
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<p>Mathematical algorithms</p>
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<p>for assert for M_PI definition and pow() for uint16_t datatype</p>
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<p>Mathematical algorithms</p>
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<p>for IO operations</p>
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<p>Mathematical algorithms</p>
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<p>for assert for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a> for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/integer.html">std::uint32_t</a></p>
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<p>Mathematical algorithms </p>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="ab37f3a7302a84179aae682c79d8390bf" name="ab37f3a7302a84179aae682c79d8390bf"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ab37f3a7302a84179aae682c79d8390bf">◆ </a></span>aliquot_sum()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">uint64_t math::aliquot_sum </td>
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<td>(</td>
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<td class="paramtype">const uint64_t </td>
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<td class="paramname"><em>num</em></td><td>)</td>
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<td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Function to return the aliquot sum of a number </p><dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">num</td><td>The input number </td></tr>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><span class="lineno"> 26</span> {</div>
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<div class="line"><span class="lineno"> 27</span> <span class="keywordflow">if</span> (num == 0 || num == 1) {</div>
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<div class="line"><span class="lineno"> 28</span> <span class="keywordflow">return</span> 0; <span class="comment">// The aliquot sum for 0 and 1 is 0</span></div>
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<div class="line"><span class="lineno"> 29</span> }</div>
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<div class="line"><span class="lineno"> 30</span> </div>
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<div class="line"><span class="lineno"> 31</span> uint64_t sum = 0;</div>
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<div class="line"><span class="lineno"> 32</span> </div>
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<div class="line"><span class="lineno"> 33</span> <span class="keywordflow">for</span> (uint64_t i = 1; i <= num / 2; i++) {</div>
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<div class="line"><span class="lineno"> 34</span> <span class="keywordflow">if</span> (num % i == 0) {</div>
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<div class="line"><span class="lineno"> 35</span> sum += i;</div>
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<div class="line"><span class="lineno"> 36</span> }</div>
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<div class="line"><span class="lineno"> 37</span> }</div>
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<div class="line"><span class="lineno"> 38</span> </div>
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<div class="line"><span class="lineno"> 39</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>;</div>
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<div class="line"><span class="lineno"> 40</span>}</div>
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<div class="ttc" id="anamespacemachine__learning_html_a6f1c98c016ad34ff3d9f39372161bd35"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector< std::valarray< T > > &A)</div><div class="ttdef"><b>Definition:</b> vector_ops.hpp:232</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#abf7f2a6d91f1ca6c89698792aea3f188">◆ </a></span>approximate_pi()</h2>
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<td class="memname">double math::approximate_pi </td>
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<td>(</td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< <a class="el" href="../../de/d4f/structmath_1_1_point.html">Point</a> > & </td>
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<td class="paramname"><em>pts</em></td><td>)</td>
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<p>This function use the points pts (drawn at random) to return an estimate of the number π using the given points </p><dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">pts</td><td>Each item of pts contains a point. A point is represented by a structure containing exactly two numbers, respectively x and y such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. pts always contains at least one item </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>an estimate of the number π</dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 35</span> {<span class="comment"></span></div>
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<div class="line"><span class="lineno"> 36</span><span class="comment"> /**</span></div>
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<div class="line"><span class="lineno"> 37</span><span class="comment"> * This function use the points pts (drawn at random) to return an estimate of the number π using the given points</span></div>
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<div class="line"><span class="lineno"> 38</span><span class="comment"> * @param pts Each item of pts contains a point. A point is represented by a structure containing exactly </span></div>
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<div class="line"><span class="lineno"> 39</span><span class="comment"> * two numbers, respectively x and y such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. </span></div>
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<div class="line"><span class="lineno"> 40</span><span class="comment"> * pts always contains at least one item</span></div>
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<div class="line"><span class="lineno"> 41</span><span class="comment"> * @return an estimate of the number π</span></div>
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<div class="line"><span class="lineno"> 42</span><span class="comment"> */</span></div>
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<div class="line"><span class="lineno"> 43</span> {</div>
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<div class="line"><span class="lineno"> 44</span> <span class="keywordtype">int</span> count =0; <span class="comment">// Points in cercle</span></div>
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<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">for</span>(<a class="code hl_struct" href="../../de/d4f/structmath_1_1_point.html">Point</a> p:pts)</div>
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<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">if</span>(p.x * p.x + p.y*p.y <= 1)</div>
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<div class="line"><span class="lineno"> 47</span> ++count;</div>
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<div class="line"><span class="lineno"> 48</span> </div>
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<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">return</span> 4.0*count/pts.size();</div>
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<div class="line"><span class="lineno"> 50</span> }</div>
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<div class="line"><span class="lineno"> 51</span> }</div>
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<div class="ttc" id="astructmath_1_1_point_html"><div class="ttname"><a href="../../de/d4f/structmath_1_1_point.html">math::Point</a></div><div class="ttdef"><b>Definition:</b> approximate_pi.cpp:30</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae1ca505751f5a6d3977b86372cfe75ea">◆ </a></span>binomialCoeffSum()</h2>
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<td class="memname">uint64_t math::binomialCoeffSum </td>
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<td>(</td>
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<td class="paramtype">uint64_t </td>
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<td class="paramname"><em>n</em></td><td>)</td>
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<p>Function to calculate sum of binomial coefficients </p><dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">n</td><td>number </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>Sum of binomial coefficients of number </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 26</span> {</div>
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<div class="line"><span class="lineno"> 27</span> <span class="comment">// Calculating 2^n</span></div>
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<div class="line"><span class="lineno"> 28</span> <span class="keywordflow">return</span> (1 << n);</div>
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<div class="line"><span class="lineno"> 29</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a40e36c67da78d2131408c57ee091ad75">◆ </a></span>circle_area()</h2>
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<td class="memname">T math::circle_area </td>
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<td>(</td>
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<td class="paramname"><em>radius</em></td><td>)</td>
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<p>area of a <a href="https://en.wikipedia.org/wiki/Area_of_a_circle" target="_blank">circle</a> (pi </p>
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<ul>
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<li>r^2) <dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">radius</td><td>is the radius of the circle </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>area of the circle </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 63</span> {</div>
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<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">return</span> M_PI * pow(radius, 2);</div>
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<div class="line"><span class="lineno"> 65</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ad0acf82b7bc920182bf8322d1e103953">◆ </a></span>circle_perimeter()</h2>
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<td class="memname">T math::circle_perimeter </td>
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<td>(</td>
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<td class="paramname"><em>radius</em></td><td>)</td>
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<p>perimeter of a <a href="https://en.wikipedia.org/wiki/perimeter_of_a_circle" target="_blank">circle</a> (2 * pi * r) </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">radius</td><td>is the radius of the circle </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>perimeter of the circle </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 63</span> {</div>
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<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">return</span> 2 * M_PI * radius;</div>
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<div class="line"><span class="lineno"> 65</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a3fe35440c27758ecc2287e08217d63a7">◆ </a></span>cone_volume()</h2>
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<td class="memname">T math::cone_volume </td>
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<td class="paramname"><em>radius</em>, </td>
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<td class="paramkey"></td>
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<td class="paramname"><em>height</em>, </td>
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<p>The volume of a <a href="https://en.wikipedia.org/wiki/Cone" target="_blank">cone</a> </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">radius</td><td>The radius of the base circle </td></tr>
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<tr><td class="paramname">height</td><td>The height of the cone </td></tr>
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<tr><td class="paramname">PI</td><td>The definition of the constant PI </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>The volume of the cone </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 53</span> {</div>
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<div class="line"><span class="lineno"> 54</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(radius, 2) * PI * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> / 3;</div>
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<div class="line"><span class="lineno"> 55</span>}</div>
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<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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<div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#abc46c784a297fc1d2eb8b33a327fba4c">◆ </a></span>cube_surface_area()</h2>
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<p>surface area of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> ( 6 * (l </p>
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<li>l)) <dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>surface area of the cube </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 86</span> {</div>
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<div class="line"><span class="lineno"> 87</span> <span class="keywordflow">return</span> 6 * length * length;</div>
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<div class="line"><span class="lineno"> 88</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a8998ca7b1886d1d7d00aef3b457a9b1b">◆ </a></span>cube_surface_perimeter()</h2>
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<p>surface perimeter of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> ( 12 </p>
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<dl class="section return"><dt>Returns</dt><dd>surface perimeter of the cube </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 86</span> {</div>
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<div class="line"><span class="lineno"> 87</span> <span class="keywordflow">return</span> 12 * length;</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae413098478fa38acaac887b7654f0725">◆ </a></span>cube_volume()</h2>
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<p>The volume of a <a href="https://en.wikipedia.org/wiki/Cube" target="_blank">cube</a> </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<dl class="section return"><dt>Returns</dt><dd>The volume of the cube </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 28</span> {</div>
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<div class="line"><span class="lineno"> 29</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(length, 3);</div>
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<div class="line"><span class="lineno"> 30</span>}</div>
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d47/namespacemath_ae413098478fa38acaac887b7654f0725_cgraph.svg" width="267" height="36"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<h2 class="memtitle"><span class="permalink"><a href="#ac5803413618fcfb922cb32c6db0fc864">◆ </a></span>cylinder_surface_area()</h2>
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<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>
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<tr><td class="paramname">radius</td><td>is the radius of the cylinder </td></tr>
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<tr><td class="paramname">height</td><td>is the height of the cylinder </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>surface area of the cylinder </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 109</span> {</div>
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<div class="line"><span class="lineno"> 110</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>
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<div class="line"><span class="lineno"> 111</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a1d4df7a4e43a2eac1acc0ac610487c73">◆ </a></span>cylinder_surface_perimeter()</h2>
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<td class="memname">T math::cylinder_surface_perimeter </td>
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<td>(</td>
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<td class="paramname"><em>radius</em>, </td>
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<p>surface perimeter of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> (2 * radius + 2 * height) </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">radius</td><td>is the radius of the cylinder </td></tr>
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<tr><td class="paramname">height</td><td>is the height of the cylinder </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>surface perimeter of the cylinder </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 111</span> {</div>
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<div class="line"><span class="lineno"> 112</span> <span class="keywordflow">return</span> (2 * radius) + (2 * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>);</div>
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<div class="line"><span class="lineno"> 113</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#abde24398be43538c62e4a496968e60ca">◆ </a></span>cylinder_volume()</h2>
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<td class="memname">T math::cylinder_volume </td>
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<td>(</td>
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<p>The volume of a <a href="https://en.wikipedia.org/wiki/Cylinder" target="_blank">cylinder</a> </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">radius</td><td>The radius of the base circle </td></tr>
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<tr><td class="paramname">height</td><td>The height of the cylinder </td></tr>
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<tr><td class="paramname">PI</td><td>The definition of the constant PI </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>The volume of the cylinder </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 103</span> {</div>
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<div class="line"><span class="lineno"> 104</span> <span class="keywordflow">return</span> PI * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(radius, 2) * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>;</div>
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<div class="line"><span class="lineno"> 105</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aec65db4e5c7317323227f026fe50ef11">◆ </a></span>integral_approx()</h2>
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<td class="memname">double math::integral_approx </td>
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<td class="paramtype">double </td>
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<td class="paramname"><em>lb</em>, </td>
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<td class="paramtype">double </td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>< double(double)> & </td>
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<p>Computes integral approximation. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">lb</td><td>lower bound </td></tr>
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<tr><td class="paramname">ub</td><td>upper bound </td></tr>
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<tr><td class="paramname">func</td><td>function passed in </td></tr>
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<tr><td class="paramname">delta</td><td></td></tr>
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<dl class="section return"><dt>Returns</dt><dd>integral approximation of function from [lb, ub] </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 33</span> {</div>
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<div class="line"><span class="lineno"> 34</span> <span class="keywordtype">double</span> result = 0;</div>
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<div class="line"><span class="lineno"> 35</span> uint64_t numDeltas = <span class="keyword">static_cast<</span>uint64_t<span class="keyword">></span>((ub - lb) / delta);</div>
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<div class="line"><span class="lineno"> 36</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < numDeltas; i++) {</div>
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<div class="line"><span class="lineno"> 37</span> <span class="keywordtype">double</span> begin = lb + i * delta;</div>
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<div class="line"><span class="lineno"> 38</span> <span class="keywordtype">double</span> end = lb + (i + 1) * delta;</div>
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<div class="line"><span class="lineno"> 39</span> result += delta * (func(begin) + func(end)) / 2;</div>
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<div class="line"><span class="lineno"> 40</span> }</div>
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<div class="line"><span class="lineno"> 41</span> <span class="keywordflow">return</span> result;</div>
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<div class="line"><span class="lineno"> 42</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#afa39ec943a4836c878e1614fd89b146f">◆ </a></span>largestPower()</h2>
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<td class="memname">uint64_t math::largestPower </td>
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<td>(</td>
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<td class="paramtype">uint32_t </td>
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<p>Function to calculate largest power. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">n</td><td>number </td></tr>
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<tr><td class="paramname">p</td><td>prime number </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>largest power </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 27</span> { </div>
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<div class="line"><span class="lineno"> 28</span> <span class="comment">// Initialize result </span></div>
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<div class="line"><span class="lineno"> 29</span> <span class="keywordtype">int</span> x = 0; </div>
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<div class="line"><span class="lineno"> 30</span> </div>
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<div class="line"><span class="lineno"> 31</span> <span class="comment">// Calculate result </span></div>
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<div class="line"><span class="lineno"> 32</span> <span class="keywordflow">while</span> (n) </div>
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<div class="line"><span class="lineno"> 33</span> { </div>
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<div class="line"><span class="lineno"> 34</span> n /= p; </div>
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<div class="line"><span class="lineno"> 35</span> x += n; </div>
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<div class="line"><span class="lineno"> 36</span> } </div>
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<div class="line"><span class="lineno"> 37</span> <span class="keywordflow">return</span> x; </div>
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<div class="line"><span class="lineno"> 38</span> }</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a04065193d190d605e1f0d0d93a87e244">◆ </a></span>lcmSum()</h2>
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<td class="memname">uint64_t math::lcmSum </td>
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<p>Function to compute sum of euler totients in sumOfEulerTotient vector </p><dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">num</td><td>input number </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>int Sum of LCMs, i.e. ∑LCM(i, num) from i = 1 to num </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 29</span> {</div>
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<div class="line"><span class="lineno"> 30</span> uint64_t i = 0, j = 0;</div>
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<div class="line"><span class="lineno"> 31</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<uint64_t></a> eulerTotient(num + 1);</div>
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<div class="line"><span class="lineno"> 32</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<uint64_t></a> sumOfEulerTotient(num + 1);</div>
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<div class="line"><span class="lineno"> 33</span> </div>
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<div class="line"><span class="lineno"> 34</span> <span class="comment">// storing initial values in eulerTotient vector</span></div>
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<div class="line"><span class="lineno"> 35</span> <span class="keywordflow">for</span> (i = 1; i <= num; i++) {</div>
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<div class="line"><span class="lineno"> 36</span> eulerTotient[i] = i;</div>
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<div class="line"><span class="lineno"> 37</span> }</div>
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<div class="line"><span class="lineno"> 38</span> </div>
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<div class="line"><span class="lineno"> 39</span> <span class="comment">// applying totient sieve</span></div>
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<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">for</span> (i = 2; i <= num; i++) {</div>
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<div class="line"><span class="lineno"> 41</span> <span class="keywordflow">if</span> (eulerTotient[i] == i) {</div>
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<div class="line"><span class="lineno"> 42</span> <span class="keywordflow">for</span> (j = i; j <= num; j += i) {</div>
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<div class="line"><span class="lineno"> 43</span> eulerTotient[j] = eulerTotient[j] / i;</div>
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<div class="line"><span class="lineno"> 44</span> eulerTotient[j] = eulerTotient[j] * (i - 1);</div>
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<div class="line"><span class="lineno"> 45</span> }</div>
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<div class="line"><span class="lineno"> 46</span> }</div>
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<div class="line"><span class="lineno"> 47</span> }</div>
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<div class="line"><span class="lineno"> 48</span> </div>
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<div class="line"><span class="lineno"> 49</span> <span class="comment">// computing sum of euler totients</span></div>
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<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">for</span> (i = 1; i <= num; i++) {</div>
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<div class="line"><span class="lineno"> 51</span> <span class="keywordflow">for</span> (j = i; j <= num; j += i) {</div>
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<div class="line"><span class="lineno"> 52</span> sumOfEulerTotient[j] += eulerTotient[i] * i;</div>
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<div class="line"><span class="lineno"> 53</span> }</div>
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<div class="line"><span class="lineno"> 54</span> }</div>
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<div class="line"><span class="lineno"> 55</span> </div>
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<div class="line"><span class="lineno"> 56</span> <span class="keywordflow">return</span> ((sumOfEulerTotient[num] + 1) * num) / 2;</div>
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<div class="line"><span class="lineno"> 57</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a8d8e81a7cd59644b311ef9adb268f5f0">◆ </a></span>magic_number()</h2>
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<p>Function to check if the given number is magic number or not. </p><dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">n</td><td>number to be checked. </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>if number is a magic number, returns true, else false. </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 32</span> {</div>
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<div class="line"><span class="lineno"> 33</span> <span class="keywordflow">if</span> (n <= 0) {</div>
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<div class="line"><span class="lineno"> 34</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><span class="lineno"> 35</span> }</div>
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<div class="line"><span class="lineno"> 36</span> <span class="comment">// result stores the modulus of @param n with 9</span></div>
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<div class="line"><span class="lineno"> 37</span> uint64_t result = n % 9;</div>
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<div class="line"><span class="lineno"> 38</span> <span class="comment">// if result is 1 then the number is a magic number else not</span></div>
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<div class="line"><span class="lineno"> 39</span> <span class="keywordflow">if</span> (result == 1) {</div>
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<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><span class="lineno"> 41</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><span class="lineno"> 42</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><span class="lineno"> 43</span> }</div>
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<div class="line"><span class="lineno"> 44</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6e2dff75c5de70455b90c799d6ad6967">◆ </a></span>n_choose_r()</h2>
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template<class T > </div>
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<p>This is the function implementation of \( \binom{n}{r} \). </p>
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<p>We are calculating the ans with iterations instead of calculating three different factorials. Also, we are using the fact that \( \frac{n!}{r! (n-r)!} = \frac{(n - r + 1) \times \cdots \times n}{1 \times
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\cdots \times r} \) </p><dl class="tparams"><dt>Template Parameters</dt><dd>
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<tr><td class="paramname">T</td><td>Only for integer types such as long, int_64 etc </td></tr>
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<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">n</td><td>\( n \) in \( \binom{n}{r} \) </td></tr>
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<tr><td class="paramname">r</td><td>\( r \) in \( \binom{n}{r} \) </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>ans \( \binom{n}{r} \) </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 35</span> {</div>
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<div class="line"><span class="lineno"> 36</span> <span class="keywordflow">if</span> (r > n / 2) {</div>
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<div class="line"><span class="lineno"> 37</span> r = n - r; <span class="comment">// Because of the fact that nCr(n, r) == nCr(n, n - r)</span></div>
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<div class="line"><span class="lineno"> 38</span> }</div>
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<div class="line"><span class="lineno"> 39</span> T ans = 1;</div>
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<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i <= r; i++) {</div>
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<div class="line"><span class="lineno"> 41</span> ans *= n - r + i;</div>
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<div class="line"><span class="lineno"> 42</span> ans /= i;</div>
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<div class="line"><span class="lineno"> 43</span> }</div>
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<div class="line"><span class="lineno"> 44</span> <span class="keywordflow">return</span> ans;</div>
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<div class="line"><span class="lineno"> 45</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8592c3279c41a2c6d4d64eeb488f63f">◆ </a></span>n_polygon_surface_perimeter()</h2>
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<td class="memname">T math::n_polygon_surface_perimeter </td>
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<td>(</td>
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<td class="paramname"><em>sides</em>, </td>
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<td class="paramname"><em>length</em> </td>
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<p>surface perimeter of a <a href="https://www.cuemath.com/measurement/perimeter-of-polygon/" target="_blank">n-polygon</a> ( n * l) </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">length</td><td>is the length of the polygon </td></tr>
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<tr><td class="paramname">sides</td><td>is the number of sides of the polygon </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>surface perimeter of the polygon </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 99</span> {</div>
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<div class="line"><span class="lineno"> 100</span> <span class="keywordflow">return</span> sides * length;</div>
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<div class="line"><span class="lineno"> 101</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a5de184925e68658f15415dd53954df4f">◆ </a></span>parallelogram_area()</h2>
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<td class="memname">T math::parallelogram_area </td>
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<td>(</td>
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<td class="paramname"><em>base</em>, </td>
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<td class="paramname"><em>height</em> </td>
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<p>area of a <a href="https://en.wikipedia.org/wiki/Parallelogram" target="_blank">parallelogram</a> (b * h) </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">base</td><td>is the length of the bottom side of the parallelogram </td></tr>
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<tr><td class="paramname">height</td><td>is the length of the tallest point in the parallelogram </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>area of the parallelogram </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 75</span> {</div>
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<div class="line"><span class="lineno"> 76</span> <span class="keywordflow">return</span> base * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>;</div>
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<div class="line"><span class="lineno"> 77</span>}</div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d47/namespacemath_a5de184925e68658f15415dd53954df4f_cgraph.svg" width="406" height="60"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<a id="a0efb235330ff48e14fd31faaccbcebb3" name="a0efb235330ff48e14fd31faaccbcebb3"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a0efb235330ff48e14fd31faaccbcebb3">◆ </a></span>parallelogram_perimeter()</h2>
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template<typename T > </div>
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<td class="memname">T math::parallelogram_perimeter </td>
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<td>(</td>
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<td class="paramtype">T </td>
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<td class="paramname"><em>base</em>, </td>
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<td class="paramtype">T </td>
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<td class="paramname"><em>height</em> </td>
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<p>perimeter of a <a href="https://en.wikipedia.org/wiki/Parallelogram" target="_blank">parallelogram</a> 2(b + h) </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">base</td><td>is the length of the bottom side of the parallelogram </td></tr>
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<tr><td class="paramname">height</td><td>is the length of the tallest point in the parallelogram </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>perimeter of the parallelogram </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 75</span> {</div>
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<div class="line"><span class="lineno"> 76</span> <span class="keywordflow">return</span> 2 * (base + <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>);</div>
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<div class="line"><span class="lineno"> 77</span>}</div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d47/namespacemath_a0efb235330ff48e14fd31faaccbcebb3_cgraph.svg" width="374" height="68"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<a id="afcd07701d73ed65cd616bcba02737f3d" name="afcd07701d73ed65cd616bcba02737f3d"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#afcd07701d73ed65cd616bcba02737f3d">◆ </a></span>power()</h2>
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<td class="memname">uint64_t math::power </td>
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<td>(</td>
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<td class="paramtype">uint64_t </td>
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<td class="paramname"><em>a</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">uint64_t </td>
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<td class="paramtype">uint64_t </td>
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<td class="paramname"><em>c</em> </td>
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</div><div class="memdoc">
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<p>This function calculates a raised to exponent b under modulo c using modular exponentiation. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">a</td><td>integer base </td></tr>
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<tr><td class="paramname">b</td><td>unsigned integer exponent </td></tr>
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<tr><td class="paramname">c</td><td>integer modulo </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>a raised to power b modulo c </dd></dl>
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<p>Initialize the answer to be returned</p>
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<p>Update a if it is more than or equal to c</p>
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<p>In case a is divisible by c;</p>
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<p>If b is odd, multiply a with answer</p>
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<p>b must be even now</p>
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<p>b = b/2</p>
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<div class="fragment"><div class="line"><span class="lineno"> 35</span> {</div>
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<div class="line"><span class="lineno"> 36</span> uint64_t ans = 1; <span class="comment">/// Initialize the answer to be returned</span></div>
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<div class="line"><span class="lineno"> 37</span> a = a % c; <span class="comment">/// Update a if it is more than or equal to c</span></div>
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<div class="line"><span class="lineno"> 38</span> <span class="keywordflow">if</span> (a == 0) {</div>
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<div class="line"><span class="lineno"> 39</span> <span class="keywordflow">return</span> 0; <span class="comment">/// In case a is divisible by c;</span></div>
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<div class="line"><span class="lineno"> 40</span> }</div>
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<div class="line"><span class="lineno"> 41</span> <span class="keywordflow">while</span> (b > 0) {<span class="comment"></span></div>
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<div class="line"><span class="lineno"> 42</span><span class="comment"> /// If b is odd, multiply a with answer</span></div>
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<div class="line"><span class="lineno"> 43</span><span class="comment"></span> <span class="keywordflow">if</span> (b & 1) {</div>
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<div class="line"><span class="lineno"> 44</span> ans = ((ans % c) * (a % c)) % c;</div>
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<div class="line"><span class="lineno"> 45</span> }<span class="comment"></span></div>
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<div class="line"><span class="lineno"> 46</span><span class="comment"> /// b must be even now</span></div>
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<div class="line"><span class="lineno"> 47</span><span class="comment"></span> b = b >> 1; <span class="comment">/// b = b/2</span></div>
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<div class="line"><span class="lineno"> 48</span> a = ((a % c) * (a % c)) % c;</div>
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<div class="line"><span class="lineno"> 49</span> }</div>
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<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">return</span> ans;</div>
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<div class="line"><span class="lineno"> 51</span>}</div>
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</div><!-- fragment -->
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</div>
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<a id="a8a48be4d7f14e34c5c92925bc1cbf3bb" name="a8a48be4d7f14e34c5c92925bc1cbf3bb"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a8a48be4d7f14e34c5c92925bc1cbf3bb">◆ </a></span>power_of_two()</h2>
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<td class="memname">int math::power_of_two </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>n</em></td><td>)</td>
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<p>This function finds whether a number is power of 2 or not. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">n</td><td>value for which we want to check prints the result, as "Yes, the number n is a power of 2" or "No, the number is not a power of 2" without quotes </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>1 if <code>n</code> IS the power of 2 </dd>
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<dd>
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0 if n is NOT a power of 2 </dd></dl>
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<p>result stores the bitwise and of n and n-1</p>
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<div class="fragment"><div class="line"><span class="lineno"> 42</span> {<span class="comment"></span></div>
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<div class="line"><span class="lineno"> 43</span><span class="comment"> /// result stores the</span></div>
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<div class="line"><span class="lineno"> 44</span><span class="comment"> /// bitwise and of n and n-1</span></div>
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<div class="line"><span class="lineno"> 45</span><span class="comment"></span> <span class="keywordtype">int</span> result = n & (n - 1);</div>
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<div class="line"><span class="lineno"> 46</span> </div>
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<div class="line"><span class="lineno"> 47</span> <span class="keywordflow">if</span> (result == 0) {</div>
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<div class="line"><span class="lineno"> 48</span> <span class="keywordflow">return</span> 1;</div>
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<div class="line"><span class="lineno"> 49</span> }</div>
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<div class="line"><span class="lineno"> 50</span> </div>
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<div class="line"><span class="lineno"> 51</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 52</span>}</div>
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</div><!-- fragment -->
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<a id="a94db02b3c9e55a69ac1696f30e2f761c" name="a94db02b3c9e55a69ac1696f30e2f761c"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a94db02b3c9e55a69ac1696f30e2f761c">◆ </a></span>pyramid_volume()</h2>
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<td class="memname">T math::pyramid_volume </td>
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<td>(</td>
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<td class="paramname"><em>length</em>, </td>
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<p>The volume of a <a href="https://en.wikipedia.org/wiki/Pyramid_(geometry)" target="_blank">pyramid</a> </p>
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<dl class="params"><dt>Parameters</dt><dd>
|
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<table class="params">
|
|
<tr><td class="paramname">length</td><td>The length of the base shape (or base for triangles) </td></tr>
|
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<tr><td class="paramname">width</td><td>The width of the base shape (or height for triangles) </td></tr>
|
|
<tr><td class="paramname">height</td><td>The height of the pyramid </td></tr>
|
|
</table>
|
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</dd>
|
|
</dl>
|
|
<dl class="section return"><dt>Returns</dt><dd>The volume of the pyramid </dd></dl>
|
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<div class="fragment"><div class="line"><span class="lineno"> 80</span> {</div>
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<div class="line"><span class="lineno"> 81</span> <span class="keywordflow">return</span> length * width * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> / 3;</div>
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<div class="line"><span class="lineno"> 82</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ab31d141f7c5b551746b1eee0eb4dedca">◆ </a></span>rect_area()</h2>
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<td class="memname">T math::rect_area </td>
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<p>area of a <a href="https://en.wikipedia.org/wiki/Rectangle" target="_blank">rectangle</a> (l * w) </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">length</td><td>is the length of the rectangle </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>area of the rectangle </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 40</span> {</div>
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<div class="line"><span class="lineno"> 41</span> <span class="keywordflow">return</span> length * width;</div>
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<div class="line"><span class="lineno"> 42</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a428769a16e9525e56588d7c7709d25a6">◆ </a></span>rect_perimeter()</h2>
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<p>perimeter of a <a href="https://en.wikipedia.org/wiki/Rectangle" target="_blank">rectangle</a> ( 2(l + w) ) </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">length</td><td>is the length of the rectangle </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>perimeter of the rectangle </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 40</span> {</div>
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<div class="line"><span class="lineno"> 41</span> <span class="keywordflow">return</span> 2 * (length + width);</div>
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<div class="line"><span class="lineno"> 42</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a3fdc74c24697ec5bb5c3698c96117c12">◆ </a></span>rect_prism_volume()</h2>
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<p>The volume of a <a href="https://en.wikipedia.org/wiki/Cuboid" target="_blank">rectangular</a> prism. </p>
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<tr><td class="paramname">length</td><td>The length of the base rectangle </td></tr>
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<tr><td class="paramname">width</td><td>The width of the base rectangle </td></tr>
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<tr><td class="paramname">height</td><td>The height of the rectangular prism </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>The volume of the rectangular prism </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 41</span> {</div>
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<div class="line"><span class="lineno"> 42</span> <span class="keywordflow">return</span> length * width * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a>;</div>
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<div class="line"><span class="lineno"> 43</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ab7f29862d30df351c317eedd60a0c656">◆ </a></span>sphere_surface_area()</h2>
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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>
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<dl class="section return"><dt>Returns</dt><dd>surface area of the sphere </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 97</span> {</div>
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<div class="line"><span class="lineno"> 98</span> <span class="keywordflow">return</span> 4 * M_PI * pow(radius, 2);</div>
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<div class="line"><span class="lineno"> 99</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a34d66a77c19ce9b8b3a3d14352b34551">◆ </a></span>sphere_volume()</h2>
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<p>The volume of a <a href="https://en.wikipedia.org/wiki/Sphere" target="_blank">sphere</a> </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">radius</td><td>The radius of the sphere </td></tr>
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<tr><td class="paramname">PI</td><td>The definition of the constant PI </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>The volume of the sphere </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 91</span> {</div>
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<div class="line"><span class="lineno"> 92</span> <span class="keywordflow">return</span> PI * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(radius, 3) * 4 / 3;</div>
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<div class="line"><span class="lineno"> 93</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a971ce57e368f2f631cf1f4ff3f864049">◆ </a></span>square_area()</h2>
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<p>area of a <a href="https://en.wikipedia.org/wiki/Square" target="_blank">square</a> (l * l) </p>
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<dl class="section return"><dt>Returns</dt><dd>area of square </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 29</span> {</div>
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<div class="line"><span class="lineno"> 30</span> <span class="keywordflow">return</span> length * length;</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a9236348755183644f1225e162d01ab14">◆ </a></span>square_perimeter()</h2>
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<p>perimeter of a <a href="https://en.wikipedia.org/wiki/Square" target="_blank">square</a> (4 * l) </p>
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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>perimeter of square </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 28</span> {</div>
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<div class="line"><span class="lineno"> 29</span> <span class="keywordflow">return</span> 4 * length;</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a50936ee98f4d40f17823befc65a32aec">◆ </a></span>test_eval()</h2>
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<p>Wrapper to evaluate if the approximated value is within <code>.XX%</code> threshold of the exact value. </p>
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<tr><td class="paramname">approx</td><td>aprroximate value </td></tr>
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<tr><td class="paramname">exact</td><td>expected value </td></tr>
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<tr><td class="paramname">threshold</td><td>values from [0, 1) </td></tr>
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<div class="fragment"><div class="line"><span class="lineno"> 51</span> {</div>
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<div class="line"><span class="lineno"> 52</span> assert(approx >= expected * (1 - threshold));</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ab3b920cc56442abd92279ba23b50f4dc">◆ </a></span>triangle_area()</h2>
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<p>area of a <a href="https://en.wikipedia.org/wiki/Triangle" target="_blank">triangle</a> (b * h / 2) </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">base</td><td>is the length of the bottom side of the triangle </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>area of the triangle </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 52</span> {</div>
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<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">return</span> base * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> / 2;</div>
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<div class="line"><span class="lineno"> 54</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a3d1e4db743b189f309327572663415f3">◆ </a></span>triangle_perimeter()</h2>
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template<typename T > </div>
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<td class="memname">T math::triangle_perimeter </td>
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<td>(</td>
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<td class="paramtype">T </td>
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<td class="paramname"><em>base</em>, </td>
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<td class="paramname"><em>height</em>, </td>
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<p>perimeter of a <a href="https://en.wikipedia.org/wiki/Triangle" target="_blank">triangle</a> (a + b + c) </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">base</td><td>is the length of the bottom side of the triangle </td></tr>
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<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>perimeter of the triangle </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 52</span> {</div>
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<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">return</span> base + <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> + hypotenuse;</div>
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<div class="line"><span class="lineno"> 54</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a2d704a7b72a6b2db8b76c8581b577b2c">◆ </a></span>triangle_prism_volume()</h2>
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<td class="memname">T math::triangle_prism_volume </td>
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<p>The volume of a <a href="https://en.wikipedia.org/wiki/Triangular_prism" target="_blank">triangular</a> prism. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">base</td><td>The length of the base triangle </td></tr>
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<tr><td class="paramname">height</td><td>The height of the base triangles </td></tr>
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<tr><td class="paramname">depth</td><td>The depth of the triangular prism (the height of the whole prism) </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>The volume of the triangular prism </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 67</span> {</div>
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<div class="line"><span class="lineno"> 68</span> <span class="keywordflow">return</span> base * <a class="code hl_function" href="../../d8/dee/avltree_8cpp.html#ae4a66d8b0c2b0d626aea45977e358c83">height</a> * depth / 2;</div>
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<div class="line"><span class="lineno"> 69</span>}</div>
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