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<div class="headertitle"><div class="title">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/math/quadratic_equations_complex_numbers.cpp</div></div>
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<p>int <a class="el" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4" title="Main function.">main()</a> { using <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>; using <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>; using <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>array<complex<long double, 2> solutions = quadraticEquation(1, 2, 1); cout << solutions[0] << " " << solutions[1] << "\n";</p>
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<p>solutions = quadraticEquation(1, 1, 1); // Reusing solutions. cout << solutions[0] << " " << solutions[1] << "\n"; return 0; }</p>
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<p>Output: (-1, 0) (-1, 0) (-0.5,0.866025) (-0.5,0.866025)</p>
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<div class="fragment"><div class="line"><span class="comment">/**</span></div>
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<div class="line"><span class="comment"> * @file</span></div>
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<div class="line"><span class="comment"> * @brief Calculate quadratic equation with complex roots, i.e. b^2 - 4ac < 0.</span></div>
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||||
<div class="line"><span class="comment"> *</span></div>
|
||||
<div class="line"><span class="comment"> * @author [Renjian-buchai](https://github.com/Renjian-buchai)</span></div>
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<div class="line"><span class="comment"> *</span></div>
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||||
<div class="line"><span class="comment"> * @description Calculates any quadratic equation in form ax^2 + bx + c.</span></div>
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||||
<div class="line"><span class="comment"> *</span></div>
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<div class="line"><span class="comment"> * Quadratic equation:</span></div>
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<div class="line"><span class="comment"> * x = (-b +/- sqrt(b^2 - 4ac)) / 2a</span></div>
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||||
<div class="line"><span class="comment"> *</span></div>
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||||
<div class="line"><span class="comment"> * @example</span></div>
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||||
<div class="line"><span class="comment"> * int main() {</span></div>
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||||
<div class="line"><span class="comment"> * using std::array;</span></div>
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<div class="line"><span class="comment"> * using std::complex;</span></div>
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||||
<div class="line"><span class="comment"> * using std::cout;</span></div>
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<div class="line"><span class="comment"> *</span></div>
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||||
<div class="line"><span class="comment"> * array<complex<long double, 2> solutions = quadraticEquation(1, 2, 1);</span></div>
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||||
<div class="line"><span class="comment"> * cout << solutions[0] << " " << solutions[1] << "\n";</span></div>
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<div class="line"><span class="comment"> *</span></div>
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<div class="line"><span class="comment"> * solutions = quadraticEquation(1, 1, 1); // Reusing solutions.</span></div>
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<div class="line"><span class="comment"> * cout << solutions[0] << " " << solutions[1] << "\n";</span></div>
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||||
<div class="line"><span class="comment"> * return 0;</span></div>
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||||
<div class="line"><span class="comment"> * }</span></div>
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<div class="line"><span class="comment"> *</span></div>
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||||
<div class="line"><span class="comment"> * Output:</span></div>
|
||||
<div class="line"><span class="comment"> * (-1, 0) (-1, 0)</span></div>
|
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<div class="line"><span class="comment"> * (-0.5,0.866025) (-0.5,0.866025)</span></div>
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<div class="line"><span class="comment"> */</span></div>
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<div class="line"> </div>
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<div class="line"><span class="preprocessor">#include <array></span> <span class="comment">/// std::array</span></div>
|
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<div class="line"><span class="preprocessor">#include <cassert></span> <span class="comment">/// assert</span></div>
|
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<div class="line"><span class="preprocessor">#include <cmath></span> <span class="comment">/// std::sqrt, std::trunc, std::pow</span></div>
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||||
<div class="line"><span class="preprocessor">#include <complex></span> <span class="comment">/// std::complex</span></div>
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||||
<div class="line"><span class="preprocessor">#include <exception></span> <span class="comment">/// std::invalid_argument</span></div>
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<div class="line"><span class="preprocessor">#include <iomanip></span> <span class="comment">/// std::setprecision</span></div>
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<div class="line"><span class="preprocessor">#include <iostream></span> <span class="comment">/// std::cout</span></div>
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<div class="line"><span class="comment"></span> </div>
|
||||
<div class="line"><span class="comment">/**</span></div>
|
||||
<div class="line"><span class="comment"> * @namespace</span></div>
|
||||
<div class="line"><span class="comment"> * @brief Mathematical algorithms</span></div>
|
||||
<div class="line"><span class="comment"> */</span></div>
|
||||
<div class="line"><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/d47/namespacemath.html">math</a> {</div>
|
||||
<div class="line"><span class="comment"></span> </div>
|
||||
<div class="line"><span class="comment">/**</span></div>
|
||||
<div class="line"><span class="comment"> * @brief Quadratic equation calculator.</span></div>
|
||||
<div class="line"><span class="comment"> * @param a quadratic coefficient.</span></div>
|
||||
<div class="line"><span class="comment"> * @param b linear coefficient.</span></div>
|
||||
<div class="line"><span class="comment"> * @param c constant</span></div>
|
||||
<div class="line"><span class="comment"> * @return Array containing the roots of quadratic equation, incl. complex</span></div>
|
||||
<div class="line"><span class="comment"> * root.</span></div>
|
||||
<div class="line"><span class="comment"> */</span></div>
|
||||
<div class="line"><a id="_a0" name="_a0"></a><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::complex<long double></a>, 2> <a id="a1" name="a1"></a><a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">quadraticEquation</a>(<span class="keywordtype">long</span> <span class="keywordtype">double</span> a,</div>
|
||||
<div class="line"> <span class="keywordtype">long</span> <span class="keywordtype">double</span> b,</div>
|
||||
<div class="line"> <span class="keywordtype">long</span> <span class="keywordtype">double</span> c) {</div>
|
||||
<div class="line"> <span class="keywordflow">if</span> (a == 0) {</div>
|
||||
<div class="line"> <span class="keywordflow">throw</span> <a id="_a2" name="_a2"></a><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>(<span class="stringliteral">"quadratic coefficient cannot be 0"</span>);</div>
|
||||
<div class="line"> }</div>
|
||||
<div class="line"> </div>
|
||||
<div class="line"> <span class="keywordtype">long</span> <span class="keywordtype">double</span> discriminant = b * b - 4 * a * c;</div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::complex<long double></a>, 2> solutions{0, 0};</div>
|
||||
<div class="line"> </div>
|
||||
<div class="line"> <span class="keywordflow">if</span> (discriminant == 0) {</div>
|
||||
<div class="line"> solutions[0] = -b * 0.5 / a;</div>
|
||||
<div class="line"> solutions[1] = -b * 0.5 / a;</div>
|
||||
<div class="line"> <span class="keywordflow">return</span> solutions;</div>
|
||||
<div class="line"> }</div>
|
||||
<div class="line"> </div>
|
||||
<div class="line"> <span class="comment">// Complex root (discriminant < 0)</span></div>
|
||||
<div class="line"> <span class="comment">// Note that the left term (-b / 2a) is always real. The imaginary part</span></div>
|
||||
<div class="line"> <span class="comment">// appears when b^2 - 4ac < 0, so sqrt(b^2 - 4ac) has no real roots. So,</span></div>
|
||||
<div class="line"> <span class="comment">// the imaginary component is i * (+/-)sqrt(abs(b^2 - 4ac)) / 2a.</span></div>
|
||||
<div class="line"> <span class="keywordflow">if</span> (discriminant > 0) {</div>
|
||||
<div class="line"> <span class="comment">// Since discriminant > 0, there are only real roots. Therefore,</span></div>
|
||||
<div class="line"> <span class="comment">// imaginary component = 0.</span></div>
|
||||
<div class="line"> solutions[0] = <a id="_a3" name="_a3"></a><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>{</div>
|
||||
<div class="line"> (-b - <a id="a4" name="a4"></a><a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(discriminant)) * 0.5 / a, 0};</div>
|
||||
<div class="line"> solutions[1] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>{</div>
|
||||
<div class="line"> (-b + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(discriminant)) * 0.5 / a, 0};</div>
|
||||
<div class="line"> <span class="keywordflow">return</span> solutions;</div>
|
||||
<div class="line"> }</div>
|
||||
<div class="line"> <span class="comment">// Since b^2 - 4ac is < 0, for faster computation, -discriminant is</span></div>
|
||||
<div class="line"> <span class="comment">// enough to make it positive.</span></div>
|
||||
<div class="line"> solutions[0] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>{</div>
|
||||
<div class="line"> -b * 0.5 / a, -<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(-discriminant) * 0.5 / a};</div>
|
||||
<div class="line"> solutions[1] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>{</div>
|
||||
<div class="line"> -b * 0.5 / a, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(-discriminant) * 0.5 / a};</div>
|
||||
<div class="line"> </div>
|
||||
<div class="line"> <span class="keywordflow">return</span> solutions;</div>
|
||||
<div class="line">}</div>
|
||||
<div class="line"> </div>
|
||||
<div class="line">} <span class="comment">// namespace math</span></div>
|
||||
<div class="line"><span class="comment"></span> </div>
|
||||
<div class="line"><span class="comment">/**</span></div>
|
||||
<div class="line"><span class="comment"> * @brief Asserts an array of complex numbers.</span></div>
|
||||
<div class="line"><span class="comment"> * @param input Input array of complex numbers. .</span></div>
|
||||
<div class="line"><span class="comment"> * @param expected Expected array of complex numbers.</span></div>
|
||||
<div class="line"><span class="comment"> * @param precision Precision to be asserted. Default=10</span></div>
|
||||
<div class="line"><span class="comment"> */</span></div>
|
||||
<div class="line"><span class="keywordtype">void</span> <a id="a5" name="a5"></a><a class="code hl_function" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#af7a6d4e3dc85a6288c8f1f7094830c5a">assertArray</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a><<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>, 2> input,</div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a><<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>, 2> expected,</div>
|
||||
<div class="line"> <span class="keywordtype">size_t</span> precision = 10) {</div>
|
||||
<div class="line"> <span class="keywordtype">long</span> <span class="keywordtype">double</span> exponent = <a id="a6" name="a6"></a><a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(10, precision);</div>
|
||||
<div class="line"> input[0].real(<a id="a7" name="a7"></a><a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(input[0].real() * exponent));</div>
|
||||
<div class="line"> input[1].real(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(input[1].real() * exponent));</div>
|
||||
<div class="line"> input[0].imag(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(input[0].imag() * exponent));</div>
|
||||
<div class="line"> input[1].imag(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(input[1].imag() * exponent));</div>
|
||||
<div class="line"> </div>
|
||||
<div class="line"> expected[0].real(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(expected[0].real() * exponent));</div>
|
||||
<div class="line"> expected[1].real(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(expected[1].real() * exponent));</div>
|
||||
<div class="line"> expected[0].imag(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(expected[0].imag() * exponent));</div>
|
||||
<div class="line"> expected[1].imag(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(expected[1].imag() * exponent));</div>
|
||||
<div class="line"> </div>
|
||||
<div class="line"> assert(input == expected);</div>
|
||||
<div class="line">}</div>
|
||||
<div class="line"><span class="comment"></span> </div>
|
||||
<div class="line"><span class="comment">/**</span></div>
|
||||
<div class="line"><span class="comment"> * @brief Self-test implementations to test quadraticEquation function.</span></div>
|
||||
<div class="line"><span class="comment"> * @note There are 4 different types of solutions: Real and equal, real,</span></div>
|
||||
<div class="line"><span class="comment"> * complex, complex and equal.</span></div>
|
||||
<div class="line"><span class="comment"> */</span></div>
|
||||
<div class="line"><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>() {</div>
|
||||
<div class="line"> <span class="comment">// Values are equal and real.</span></div>
|
||||
<div class="line"> <a id="_a8" name="_a8"></a><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Input: \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"a=1 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"b=-2 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"c=1 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"Expected output: \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"(1, 0), (1, 0)\n\n"</span>;</div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::complex<long double></a>, 2> equalCase{</div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>{1, 0}, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>{1, 0}};</div>
|
||||
<div class="line"> assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(1, -2, 1) == equalCase);</div>
|
||||
<div class="line"> </div>
|
||||
<div class="line"> <span class="comment">// Values are equal and complex.</span></div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Input: \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"a=1 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"b=4 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"c=5 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"Expected output: \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"(-2, -1), (-2, 1)\n\n"</span>;</div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::complex<long double></a>, 2> complexCase{</div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>{-2, -1}, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>{-2, 1}};</div>
|
||||
<div class="line"> assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(1, 4, 5) == complexCase);</div>
|
||||
<div class="line"> </div>
|
||||
<div class="line"> <span class="comment">// Values are real.</span></div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Input: \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"a=1 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"b=5 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"c=1 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"Expected output: \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"(-4.7912878475, 0), (-0.2087121525, 0)\n\n"</span>;</div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::complex<long double></a>, 2> floatCase{</div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>{-4.7912878475, 0},</div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>{-0.2087121525, 0}};</div>
|
||||
<div class="line"> <a class="code hl_function" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#af7a6d4e3dc85a6288c8f1f7094830c5a">assertArray</a>(<a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(1, 5, 1), floatCase);</div>
|
||||
<div class="line"> </div>
|
||||
<div class="line"> <span class="comment">// Values are complex.</span></div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Input: \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"a=1 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"b=1 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"c=1 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"Expected output: \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"(-0.5, -0.8660254038), (-0.5, 0.8660254038)\n\n"</span>;</div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::complex<long double></a>, 2> ifloatCase{</div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>{-0.5, -0.8660254038},</div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a>{-0.5, 0.8660254038}};</div>
|
||||
<div class="line"> <a class="code hl_function" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#af7a6d4e3dc85a6288c8f1f7094830c5a">assertArray</a>(<a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(1, 1, 1), ifloatCase);</div>
|
||||
<div class="line"> </div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Exception test: \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"Input: \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"a=0 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"b=0 \n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"c=0\n"</span></div>
|
||||
<div class="line"> <span class="stringliteral">"Expected output: Exception thrown \n"</span>;</div>
|
||||
<div class="line"> <span class="keywordflow">try</span> {</div>
|
||||
<div class="line"> <a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(0, 0, 0);</div>
|
||||
<div class="line"> } <span class="keywordflow">catch</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>& e) {</div>
|
||||
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Exception thrown successfully \n"</span>;</div>
|
||||
<div class="line"> }</div>
|
||||
<div class="line">}</div>
|
||||
<div class="line"><span class="comment"></span> </div>
|
||||
<div class="line"><span class="comment">/**</span></div>
|
||||
<div class="line"><span class="comment"> * @brief Main function</span></div>
|
||||
<div class="line"><span class="comment"> * @returns 0 on exit</span></div>
|
||||
<div class="line"><span class="comment"> */</span></div>
|
||||
<div class="line"><span class="keywordtype">int</span> <a id="a9" name="a9"></a><a class="code hl_function" href="../../d3/d40/graph__coloring_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
|
||||
<div class="line"> <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>(); <span class="comment">// Run self-test implementation.</span></div>
|
||||
<div class="line"> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line">}</div>
|
||||
<div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a></div></div>
|
||||
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
|
||||
<div class="ttc" id="acaesar__cipher_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition:</b> caesar_cipher.cpp:100</div></div>
|
||||
<div class="ttc" id="acomplex_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a></div></div>
|
||||
<div class="ttc" id="agraph__coloring_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d3/d40/graph__coloring_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition:</b> graph_coloring.cpp:112</div></div>
|
||||
<div class="ttc" id="ainvalid_argument_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a></div></div>
|
||||
<div class="ttc" id="anamespacemath_html"><div class="ttname"><a href="../../dd/d47/namespacemath.html">math</a></div><div class="ttdoc">for IO operations</div></div>
|
||||
<div class="ttc" id="anamespacemath_html_aacb1411ef2029e81f249c21e17c96fdb"><div class="ttname"><a href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a></div><div class="ttdeci">std::array< std::complex< long double >, 2 > quadraticEquation(long double a, long double b, long double c)</div><div class="ttdoc">Quadratic equation calculator.</div><div class="ttdef"><b>Definition:</b> quadratic_equations_complex_numbers.cpp:53</div></div>
|
||||
<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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<div class="ttc" id="aquadratic__equations__complex__numbers_8cpp_html_af7a6d4e3dc85a6288c8f1f7094830c5a"><div class="ttname"><a href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#af7a6d4e3dc85a6288c8f1f7094830c5a">assertArray</a></div><div class="ttdeci">void assertArray(std::array< std::complex< long double >, 2 > input, std::array< std::complex< long double >, 2 > expected, size_t precision=10)</div><div class="ttdoc">Asserts an array of complex numbers.</div><div class="ttdef"><b>Definition:</b> quadratic_equations_complex_numbers.cpp:100</div></div>
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