
'''simple docstring'''






def 		A_       (	_lowerCAmelCase   :    int				,	_lowerCAmelCase   :    int							):



      """simple docstring"""




      while b:
            _lowerCamelCase				:   List[str]								=   b, a % b
      return a







def 		A_       (	_lowerCAmelCase   :    int				,	_lowerCAmelCase   :    int							):



      """simple docstring"""




      return a if b == 0 else euclidean_gcd_recursive(_lowerCAmelCase				,	a % b							)







def 		A_       (	):



      """simple docstring"""




      print(F'euclidean_gcd(3, 5) = {euclidean_gcd(3				,	5							)}'							)
      print(F'euclidean_gcd(5, 3) = {euclidean_gcd(5				,	3							)}'							)
      print(F'euclidean_gcd(1, 3) = {euclidean_gcd(1				,	3							)}'							)
      print(F'euclidean_gcd(3, 6) = {euclidean_gcd(3				,	6							)}'							)
      print(F'euclidean_gcd(6, 3) = {euclidean_gcd(6				,	3							)}'							)

      print(F'euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3				,	5							)}'							)
      print(F'euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5				,	3							)}'							)
      print(F'euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1				,	3							)}'							)
      print(F'euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3				,	6							)}'							)
      print(F'euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6				,	3							)}'							)


if __name__ == "__main__":
 main()



'''simple docstring'''






def 		A_       (	_lowerCAmelCase   :    float							):



      """simple docstring"""




      return 10 - x * x







def 		A_       (	_lowerCAmelCase   :    float				,	_lowerCAmelCase   :    float							):



      """simple docstring"""




      if equation(_lowerCAmelCase							) * equation(_lowerCAmelCase							) >= 0:
            raise ValueError("Wrong space!"							)

      _lowerCamelCase				:   List[str]								=   a
      while (b - a) >= 0.0_1:
            # Find middle point
            _lowerCamelCase				:   Union[str, Any]								=   (a + b) / 2
            # Check if middle point is root
            if equation(_lowerCAmelCase							) == 0.0:
                  break
            # Decide the side to repeat the steps
            if equation(_lowerCAmelCase							) * equation(_lowerCAmelCase							) < 0:
                  _lowerCamelCase				:   Union[str, Any]								=   c
            else:
                  _lowerCamelCase				:   Any								=   c
      return c


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 print(bisection(-2, 5))
 print(bisection(0, 6))