


'''simple docstring'''

from random import randint
from tempfile import TemporaryFile

import numpy as np





def __snake_case      (   UpperCAmelCase_		:		Optional[Any]      ,       UpperCAmelCase_		:		Any      ,       UpperCAmelCase_		:		List[str]	):
 lowerCamelCase_  				=						0
 if start < end:
  lowerCamelCase_  				=						randint(UpperCAmelCase_      ,       UpperCAmelCase_	)
  lowerCamelCase_  				=						a[end]
  lowerCamelCase_  				=						a[pivot]
  lowerCamelCase_  				=						temp

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

 lowerCamelCase_  				=						a[new_pivot_index + 1]
 lowerCamelCase_  				=						a[end]
 lowerCamelCase_  				=						temp
 return new_pivot_index + 1, count


a_						:       Union[str, Any]      			=				TemporaryFile()
a_						:       List[Any]      			=				100  # 1000 elements are to be sorted


a_			,     a_						:       Optional[Any]      			=				0, 1  # mean and standard deviation
a_						:       Any      			=				np.random.normal(mu, sigma, p)
np.save(outfile, X)
print("""The array is""")
print(X)


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





def __snake_case      (   UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int	):
 if b == 0:
  return (1, 0)
 ((lowerCamelCase_)				,(lowerCamelCase_))  				=						extended_euclid(UpperCAmelCase_      ,       a % b	)
 lowerCamelCase_  				=						a // b
 return (y, x - k * y)





def __snake_case      (   UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int	):
 ((lowerCamelCase_)				,(lowerCamelCase_))  				=						extended_euclid(UpperCAmelCase_      ,       UpperCAmelCase_	)
 lowerCamelCase_  				=						na * na
 lowerCamelCase_  				=						ra * x * na + ra * y * na
 return (n % m + m) % m





def __snake_case      (   UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int	):
 ((lowerCamelCase_)				,(lowerCamelCase_))  				=						extended_euclid(UpperCAmelCase_      ,       UpperCAmelCase_	)
 if b < 0:
  lowerCamelCase_  				=						(b % n + n) % n
 return b





def __snake_case      (   UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int      ,       UpperCAmelCase_		:		int	):
 lowerCamelCase_				,lowerCamelCase_  				=						invert_modulo(UpperCAmelCase_      ,       UpperCAmelCase_	), invert_modulo(UpperCAmelCase_      ,       UpperCAmelCase_	)
 lowerCamelCase_  				=						na * na
 lowerCamelCase_  				=						ra * x * na + ra * y * na
 return (n % m + m) % m


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

     testmod(name="""chinese_remainder_theorem""", verbose=True)
     testmod(name="""chinese_remainder_theorem2""", verbose=True)
     testmod(name="""invert_modulo""", verbose=True)
     testmod(name="""extended_euclid""", verbose=True)



