


'''simple docstring'''
from random import randint
from tempfile import TemporaryFile

import numpy as np


def 			_lowercase       (				UpperCamelCase__       :					Union[str, Any],				UpperCamelCase__       :					Any,				UpperCamelCase__       :					Dict			):
 __A  :		Optional[Any]       =			0
 if start < end:
  __A  :		Any       =			randint(UpperCamelCase__,				UpperCamelCase__			)
  __A  :		Optional[Any]       =			a[end]
  __A  :		str       =			a[pivot]
  __A  :		Tuple       =			temp

  __A  :		str       =			_in_place_partition(UpperCamelCase__,				UpperCamelCase__,				UpperCamelCase__			)
  count += _in_place_quick_sort(UpperCamelCase__,				UpperCamelCase__,				p - 1			)
  count += _in_place_quick_sort(UpperCamelCase__,				p + 1,				UpperCamelCase__			)
 return count


def 			_lowercase       (				UpperCamelCase__       :					List[str],				UpperCamelCase__       :					Tuple,				UpperCamelCase__       :					Any			):
 __A  :		int       =			0
 __A  :		List[Any]       =			randint(UpperCamelCase__,				UpperCamelCase__			)
 __A  :		int       =			a[end]
 __A  :		Union[str, Any]       =			a[pivot]
 __A  :		List[str]       =			temp
 __A  :		str       =			start - 1
 for index in range(UpperCamelCase__,				UpperCamelCase__			):
  count += 1
  if a[index] < a[end]:  # check if current val is less than pivot value
   __A  :		Tuple       =			new_pivot_index + 1
   __A  :		List[Any]       =			a[new_pivot_index]
   __A  :		Union[str, Any]       =			a[index]
   __A  :		Tuple       =			temp

 __A  :		Any       =			a[new_pivot_index + 1]
 __A  :		Dict       =			a[end]
 __A  :		str       =			temp
 return new_pivot_index + 1, count


UpperCAmelCase_ :     int								=      TemporaryFile()
UpperCAmelCase_ :     str								=      100  # 1000 elements are to be sorted


UpperCAmelCase_ :     str								=      0, 1  # mean and standard deviation
UpperCAmelCase_ :     str								=      np.random.normal(mu, sigma, p)
np.save(outfile, X)
print('The array is')
print(X)


outfile.seek(0)  # using the same array
UpperCAmelCase_ :     Dict								=      np.load(outfile)
UpperCAmelCase_ :     str								=      len(M) - 1
UpperCAmelCase_ :     Union[str, Any]								=      _in_place_quick_sort(M, 0, r)

print(
    'No of Comparisons for 100 elements selected from a standard normal distribution'
    'is :'
)


print(z)










'''simple docstring'''
from __future__ import annotations

class 						_lowerCamelCase					:




 '''simple docstring'''


 def __init__(      self      ,      __lowercase						):

  """simple docstring"""







  __A  :		Dict       =			order

  # a_{0} ... a_{k}
  __A  :		str       =			[1.0] + [0.0] * order
  # b_{0} ... b_{k}
  __A  :		Any       =			[1.0] + [0.0] * order

  # x[n-1] ... x[n-k]
  __A  :		Optional[int]       =			[0.0] * self.order
  # y[n-1] ... y[n-k]
  __A  :		Dict       =			[0.0] * self.order


 def  snake_case__   (      self      ,      __lowercase      ,      __lowercase						):

  """simple docstring"""







  if len(__lowercase						) < self.order:
   __A  :		List[Any]       =			[1.0, *a_coeffs]

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

  if len(__lowercase						) != self.order + 1:
   __A  :		List[Any]       =			(
       F"""Expected b_coeffs to have {self.order + 1} elements """
       F"""for {self.order}-order filter, got {len(__lowercase						)}"""
   )
   raise ValueError(__lowercase						)

  __A  :		Optional[int]       =			a_coeffs
  __A  :		Optional[int]       =			b_coeffs







 def  snake_case__   (      self      ,      __lowercase						):

  """simple docstring"""







  __A  :		Union[str, Any]       =			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  :		Optional[int]       =			(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

  __A  :		List[str]       =			self.input_history[:-1]
  __A  :		Optional[int]       =			self.output_history[:-1]

  __A  :		Optional[int]       =			sample
  __A  :		Dict       =			result

  return result






