一元二次方程式 (quadratic equation)
(include/emthrm/math/quadratic_equation.hpp)

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• Last update: 2022-12-15 22:18:37+09:00
• Include: #include "emthrm/math/quadratic_equation.hpp"

\[ax^2 + bx + c = 0\]

時間計算量

$O(1)$

仕様

名前	戻り値	要件
std::vector<double> quadratic_equation(double a, double b, double c, const double eps = 1e-8);	$ax^2 + bx + c = 0$ を満たす $x$	$a, b, c$ のいずれかは非零である。

参考文献

• https://yukicoder.me/problems/no/955/editorial

TODO

• 三次方程式 (cubic equation)
  • https://ja.wikipedia.org/wiki/%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B%E5%BC%8F
  • https://tubo28.me/compprog/algorithm/cubic/
  • https://cafecoder.top/contests/test003/tasks/test003_b

Submissons

https://onlinejudge.u-aizu.ac.jp/solutions/problem/1039/review/4338571/emthrm/C++14

Verified with

• 数学/一元二次方程式 (test/math/quadratic_equation.test.cpp)

Code

#ifndef EMTHRM_MATH_QUADRATIC_EQUATION_HPP_
#define EMTHRM_MATH_QUADRATIC_EQUATION_HPP_

#include <cassert>
#include <cmath>
#include <vector>

namespace emthrm {

std::vector<double> quadratic_equation(double a, double b, double c,
                                       const double eps = 1e-8) {
  if (std::abs(a) < eps) {
    if (std::abs(b) < eps) {
      assert(std::abs(c) >= eps);
      return {};
    }
    return {-c / b};
  }
  double d = b * b - 4 * a * c;
  if (d <= -eps) return {};
  if (d < eps) return {-0.5 * b / a};
  d = std::sqrt(d);
  const double x1 = -0.5 * (b >= 0 ? b + d : b - d) / a, x2 = c / (x1 * a);
  return x1 > x2 ? std::vector<double>{x2, x1} : std::vector<double>{x1, x2};
}

}  // namespace emthrm

#endif  // EMTHRM_MATH_QUADRATIC_EQUATION_HPP_

#line 1 "include/emthrm/math/quadratic_equation.hpp"



#include <cassert>
#include <cmath>
#include <vector>

namespace emthrm {

std::vector<double> quadratic_equation(double a, double b, double c,
                                       const double eps = 1e-8) {
  if (std::abs(a) < eps) {
    if (std::abs(b) < eps) {
      assert(std::abs(c) >= eps);
      return {};
    }
    return {-c / b};
  }
  double d = b * b - 4 * a * c;
  if (d <= -eps) return {};
  if (d < eps) return {-0.5 * b / a};
  d = std::sqrt(d);
  const double x1 = -0.5 * (b >= 0 ? b + d : b - d) / a, x2 = c / (x1 * a);
  return x1 > x2 ? std::vector<double>{x2, x1} : std::vector<double>{x1, x2};
}

}  // namespace emthrm

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