



from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean
def 		UpperCamelCase	(   snake_case__       :    int	)	->     Dict:

   # A local function to see if a dot lands in the circle.
   def is_in_circle(snake_case__       :    float       ,     snake_case__       :    float	) -> bool:
      UpperCamelCase    :  Union[str, Any]							=	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    :  Tuple							=	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    :  Optional[int]							=	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 		UpperCamelCase	(   snake_case__       :    int       ,     snake_case__       :    Callable[[float], float]       ,     snake_case__       :    float = 0.0       ,     snake_case__       :    float = 1.0       ,     )	->     float:
   return mean(
       function_to_integrate(uniform(snake_case__       ,     snake_case__	)	) for _ in range(snake_case__	)	) * (max_value - min_value)
def 		UpperCamelCase	(   snake_case__       :    int       ,     snake_case__       :    float = 0.0       ,     snake_case__       :    float = 1.0	)	->     None:

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

   UpperCamelCase    :  Optional[int]							=	area_under_curve_estimator(
       snake_case__       ,     snake_case__       ,     snake_case__       ,     snake_case__	)
   UpperCamelCase    :  List[Any]							=	(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 		UpperCamelCase	(   snake_case__       :    int	)	->     None:

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

   UpperCamelCase    :  str							=	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

from itertools import permutations
from random import randint
from timeit import repeat
def 		UpperCamelCase	(   )	->     tuple[list[int], int]:
   UpperCamelCase    :  int							=	[randint(-1000       ,     1000	) for i in range(10	)]
   UpperCamelCase    :  Dict							=	randint(-5000       ,     5000	)
   return (arr, r)


__UpperCAmelCase          =       make_dataset()
def 		UpperCamelCase	(   snake_case__       :    list[int]       ,     snake_case__       :    int	)	->     tuple[int, ...]:
   for triplet in permutations(snake_case__       ,     3	):
      if sum(snake_case__	) == target:
         return tuple(sorted(snake_case__	)	)
   return (0, 0, 0)
def 		UpperCamelCase	(   snake_case__       :    list[int]       ,     snake_case__       :    int	)	->     tuple[int, int, int]:
   arr.sort()
   UpperCamelCase    :  List[str]							=	len(snake_case__	)
   for i in range(n - 1	):
      UpperCamelCase	,     UpperCamelCase    :  Optional[Any]							=	i + 1, n - 1
      while left < right:
         if arr[i] + arr[left] + arr[right] == target:
            return (arr[i], arr[left], arr[right])
         elif arr[i] + arr[left] + arr[right] < target:
            left += 1
         elif arr[i] + arr[left] + arr[right] > target:
            right -= 1
   return (0, 0, 0)
def 		UpperCamelCase	(   )	->     tuple[float, float]:
   UpperCamelCase    :  Any							=	'\nfrom __main__ import dataset, triplet_sum1, triplet_sum2\n'
   UpperCamelCase    :  Optional[Any]							=	'\ntriplet_sum1(*dataset)\n'
   UpperCamelCase    :  Dict							=	'\ntriplet_sum2(*dataset)\n'
   UpperCamelCase    :  Optional[int]							=	repeat(setup=snake_case__       ,     stmt=snake_case__       ,     repeat=5       ,     number=10000	)
   UpperCamelCase    :  Any							=	repeat(setup=snake_case__       ,     stmt=snake_case__       ,     repeat=5       ,     number=10000	)
   return (min(snake_case__	), min(snake_case__	))


if __name__ == "__main__":
    from doctest import testmod

    testmod()
    __UpperCAmelCase          =       solution_times()
    print(F"""The time for naive implementation is {times[0]}.""")
    print(F"""The time for optimized implementation is {times[1]}.""")



