


"""simple docstring"""






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







def        lowerCamelCase_(		_lowerCamelCase       )    ->     Tuple:
   '''simple docstring'''





   def is_in_circle(_lowerCamelCase			,		_lowerCamelCase       ) -> bool:
      _lowerCamelCase   :				int							=     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
   _lowerCamelCase   :				Tuple							=     mean(
       int(is_in_circle(uniform(-1.0			,		1.0       )			,		uniform(-1.0			,		1.0       )       )       )
       for _ in range(_lowerCamelCase       )       )
   # The ratio of the area for circle to square is pi/4.
   _lowerCamelCase   :				List[Any]							=     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_(		_lowerCamelCase			,		_lowerCamelCase			,		_lowerCamelCase = 0.0			,		_lowerCamelCase = 1.0			,		)    ->     float:
   '''simple docstring'''





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







def        lowerCamelCase_(		_lowerCamelCase			,		_lowerCamelCase = 0.0			,		_lowerCamelCase = 1.0       )    ->     None:
   '''simple docstring'''





   def identity_function(_lowerCamelCase       ) -> float:
      return x

   _lowerCamelCase   :				Union[str, Any]							=     area_under_curve_estimator(
       _lowerCamelCase			,		_lowerCamelCase			,		_lowerCamelCase			,		_lowerCamelCase       )
   _lowerCamelCase   :				Tuple							=     (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_(		_lowerCamelCase       )    ->     None:
   '''simple docstring'''





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

   _lowerCamelCase   :				int							=     area_under_curve_estimator(
       _lowerCamelCase			,		_lowerCamelCase			,		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()




'''simple docstring'''





def 							lowerCamelCase	(					_snake_case	:    Optional[Any]  ,_snake_case	:    Union[str, Any]  ,_snake_case	:    Dict  ,_snake_case	:    List[str]  ,_snake_case	:    List[str]  ,_snake_case	:    List[str]							):





    '''simple docstring'''


    if index == r:
        for j in range(_snake_case							):
            print(data[j]  ,end=" "							)
        print(" "							)
        return
    #  When no more elements are there to put in data[]
    if i >= n:
        return
    # current is included, put next at next location
    lowercase__									=    arr[i]
    combination_util(_snake_case  ,_snake_case  ,_snake_case  ,index + 1  ,_snake_case  ,i + 1							)
    # current is excluded, replace it with
    # next (Note that i+1 is passed, but
    # index is not changed)
    combination_util(_snake_case  ,_snake_case  ,_snake_case  ,_snake_case  ,_snake_case  ,i + 1							)
    # The main function that prints all combinations
    # of size r in arr[] of size n. This function
    # mainly uses combinationUtil()




def 							lowerCamelCase	(					_snake_case	:    Optional[Any]  ,_snake_case	:    Tuple  ,_snake_case	:    Union[str, Any]							):





    '''simple docstring'''


    lowercase__									=    [0] * r
    # Print all combination using temporary array 'data[]'
    combination_util(_snake_case  ,_snake_case  ,_snake_case  ,0  ,_snake_case  ,0							)


if __name__ == "__main__":
 # Driver code to check the function above
 SCREAMING_SNAKE_CASE__          =  [10, 20, 30, 40, 50]
 print_combination(arr, len(arr), 3)
 # This code is contributed by Ambuj sahu




