






from __future__ import annotations

from itertools import permutations
from random import randint
from timeit import repeat
def 		_a       ( )				->     tuple[list[int], int]:
 a						    = [randint(-1_000      ,				1_000					) for i in range(10					)]
 a						    = randint(-5_000      ,				5_000					)
 return (arr, r)


UpperCAmelCase__							  =						make_dataset()
def 		_a       ( a					:list[int]      ,				a					:int					)				->     tuple[int, ...]:
 for triplet in permutations(a      ,				3					):
  if sum(a					) == target:
   return tuple(sorted(a					)					)
 return (0, 0, 0)
def 		_a       ( a					:list[int]      ,				a					:int					)				->     tuple[int, int, int]:
 arr.sort()
 a						    = len(a					)
 for i in range(n - 1					):
  a    ,	a						    = 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 		_a       ( )				->     tuple[float, float]:
 a						    = '''
from __main__ import dataset, triplet_sum1, triplet_sum2
'''
 a						    = '''
triplet_sum1(*dataset)
'''
 a						    = '''
triplet_sum2(*dataset)
'''
 a						    = repeat(setup=a      ,				stmt=a      ,				repeat=5      ,				number=10_000					)
 a						    = repeat(setup=a      ,				stmt=a      ,				repeat=5      ,				number=10_000					)
 return (min(a					), min(a					))


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]}.""")










from __future__ import annotations






class 						lowercase_   :






      '''simple docstring'''




      def __init__( self :		List[str]					,   __UpperCAmelCase :		int    )       ->None:




       """simple docstring"""


       a						    = order

       # a_{0} ... a_{k}
       a						    = [1.0] + [0.0] * order
       # b_{0} ... b_{k}
       a						    = [1.0] + [0.0] * order

       # x[n-1] ... x[n-k]
       a						    = [0.0] * self.order
       # y[n-1] ... y[n-k]
       a						    = [0.0] * self.order







      def  __lowerCAmelCase   ( self :		Union[str, Any]					,   __UpperCAmelCase :		list[float]					,   __UpperCAmelCase :		list[float]    )       ->None:




       """simple docstring"""


       if len(__UpperCAmelCase    ) < self.order:
        a						    = [1.0, *a_coeffs]

       if len(__UpperCAmelCase    ) != self.order + 1:
        a						    = (
            F"""Expected a_coeffs to have {self.order + 1} elements """
            F"""for {self.order}-order filter, got {len(__UpperCAmelCase    )}"""
        )
        raise ValueError(__UpperCAmelCase    )

       if len(__UpperCAmelCase    ) != self.order + 1:
        a						    = (
            F"""Expected b_coeffs to have {self.order + 1} elements """
            F"""for {self.order}-order filter, got {len(__UpperCAmelCase    )}"""
        )
        raise ValueError(__UpperCAmelCase    )

       a						    = a_coeffs
       a						    = b_coeffs







      def  __lowerCAmelCase   ( self :		Any					,   __UpperCAmelCase :		float    )       ->float:




       """simple docstring"""


       a						    = 0.0

       # Start at index 1 and do index 0 at the end.
       for i in range(1					,   self.order + 1    ):
        result += (
            self.b_coeffs[i] * self.input_history[i - 1]
            - self.a_coeffs[i] * self.output_history[i - 1]
        )

       a						    = (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

       a						    = self.input_history[:-1]
       a						    = self.output_history[:-1]

       a						    = sample
       a						    = result

       return result


