

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





def      A__					(			__A  :						int			)					->int:

      # A local function to see if a dot lands in the circle.
      def is_in_circle(__A  :						float     ,				__A  :						float			) -> bool:
            __A    =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
      __A    =mean(
          int(is_in_circle(uniform(-1.0     ,				1.0			)     ,				uniform(-1.0     ,				1.0			)			)			)
          for _ in range(__A			)			)
      # The ratio of the area for circle to square is pi/4.
      __A    =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      A__					(			__A  :						int     ,				__A  :						Callable[[float], float]     ,				__A  :						float = 0.0     ,				__A  :						float = 1.0     ,				)					->float:
      return mean(
          function_to_integrate(uniform(__A     ,				__A			)			) for _ in range(__A			)			) * (max_value - min_value)





def      A__					(			__A  :						int     ,				__A  :						float = 0.0     ,				__A  :						float = 1.0			)					->None:

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

      __A    =area_under_curve_estimator(
          __A     ,				__A     ,				__A     ,				__A			)
      __A    =(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      A__					(			__A  :						int			)					->None:

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

      __A    =area_under_curve_estimator(
          __A     ,				__A     ,				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()





def      A__					(			__A  :						str     ,				__A  :						str			)					->str:

      if not (isinstance(__A     ,				__A			) and isinstance(__A     ,				__A			)):
            raise ValueError('''longest_common_substring() takes two strings for inputs'''			)

      __A    =len(__A			)
      __A    =len(__A			)

      __A    =[[0] * (texta_length + 1) for _ in range(texta_length + 1			)]
      __A    =0
      __A    =0

      for i in range(1     ,				texta_length + 1			):
            for j in range(1     ,				texta_length + 1			):
                  if texta[i - 1] == texta[j - 1]:
                        __A    =1 + dp[i - 1][j - 1]
                        if dp[i][j] > ans_length:
                              __A    =i
                              __A    =dp[i][j]

      return texta[ans_index - ans_length : ans_index]


if __name__ == "__main__":
   import doctest

   doctest.testmod()


