'''simple docstring'''





from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean





def       lowerCAmelCase_							(   snake_case_			:					int     )       -> str:


     '''simple docstring'''




     def is_in_circle(snake_case_			:					float   ,       snake_case_			:					float     ) -> bool:
          UpperCAmelCase_			       =  sqrt((x**2) + (y**2)     )
          # Our circle has a radius of 1, so a distance
          # greater than 1 would land outside the circle.
          return distance_from_centre <= 1

     # The proportion of guesses that landed in the circle
     UpperCAmelCase_			       =  mean(
         int(is_in_circle(uniform(-1.0   ,       1.0     )   ,       uniform(-1.0   ,       1.0     )     )     )
         for _ in range(snake_case_     )     )
     # The ratio of the area for circle to square is pi/4.
     UpperCAmelCase_			       =  proportion * 4
     print(f"""The estimated value of pi is {pi_estimate}"""     )
     print(f"""The numpy value of pi is {pi}"""     )
     print(f"""The total error is {abs(pi - pi_estimate     )}"""     )





def       lowerCAmelCase_							(   snake_case_			:					int   ,       snake_case_			:					Callable[[float], float]   ,       snake_case_			:					float = 0.0   ,       snake_case_			:					float = 1.0   ,       )       -> float:


     '''simple docstring'''




     return mean(
         function_to_integrate(uniform(snake_case_   ,       snake_case_     )     ) for _ in range(snake_case_     )     ) * (max_value - min_value)





def       lowerCAmelCase_							(   snake_case_			:					int   ,       snake_case_			:					float = 0.0   ,       snake_case_			:					float = 1.0     )       -> None:


     '''simple docstring'''




     def identity_function(snake_case_			:					float     ) -> float:
          return x

     UpperCAmelCase_			       =  area_under_curve_estimator(
         snake_case_   ,       snake_case_   ,       snake_case_   ,       snake_case_     )
     UpperCAmelCase_			       =  (max_value * max_value - min_value * min_value) / 2

     print("******************"     )
     print(f"""Estimating area under y=x where x varies from {min_value} to {max_value}"""     )
     print(f"""Estimated value is {estimated_value}"""     )
     print(f"""Expected value is {expected_value}"""     )
     print(f"""Total error is {abs(estimated_value - expected_value     )}"""     )
     print("******************"     )





def       lowerCAmelCase_							(   snake_case_			:					int     )       -> None:


     '''simple docstring'''




     def function_to_integrate(snake_case_			:					float     ) -> float:
          return sqrt(4.0 - x * x     )

     UpperCAmelCase_			       =  area_under_curve_estimator(
         snake_case_   ,       snake_case_   ,       0.0   ,       2.0     )

     print("******************"     )
     print("Estimating pi using area_under_curve_estimator"     )
     print(f"""Estimated value is {estimated_value}"""     )
     print(f"""Expected value is {pi}"""     )
     print(f"""Total error is {abs(estimated_value - pi     )}"""     )
     print("******************"     )


if __name__ == "__main__":
    import doctest

    doctest.testmod()











from __future__ import annotations

def      UpperCAmelCase_    (    _UpperCAmelCase							:list[float]  ,						_UpperCAmelCase							:list[float]				)	->				float:
     '''simple docstring'''


     A_          =       sorted(numsa + numsa				)
     A_   ,    A_          =       divmod(len(_UpperCAmelCase				)  ,						2				)
     if mod == 1:
          return all_numbers[div]
     else:
          return (all_numbers[div] + all_numbers[div - 1]) / 2


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      a__      :     Optional[Any]         =		[float(x) for x in input('Enter the elements of first array: ').split()]
      a__      :     int         =		[float(x) for x in input('Enter the elements of second array: ').split()]
      print(f'''The median of two arrays is: {median_of_two_arrays(array_a, array_a)}''')



