

'''simple docstring'''



from random import randint
from tempfile import TemporaryFile

import numpy as np

def 	lowerCamelCase__							(   a__      ,   a__      ,   a__)		->     List[Any]:



    """simple docstring"""







    _snake_case			:			str				       =		0
    if start < end:
        _snake_case			:			Union[str, Any]				       =		randint(lowerCAmelCase__      ,   lowerCAmelCase__)
        _snake_case			:			Optional[Any]				       =		a[end]
        _snake_case			:			Dict				       =		a[pivot]
        _snake_case			:			Any				       =		temp

        _snake_case       ,				_snake_case			:			str				       =		_in_place_partition(lowerCAmelCase__      ,   lowerCAmelCase__      ,   lowerCAmelCase__)
        count += _in_place_quick_sort(lowerCAmelCase__      ,   lowerCAmelCase__      ,   p - 1)
        count += _in_place_quick_sort(lowerCAmelCase__      ,   p + 1      ,   lowerCAmelCase__)
    return count

def 	lowerCamelCase__							(   a__      ,   a__      ,   a__)		->     Any:



    """simple docstring"""







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

    _snake_case			:			str				       =		a[new_pivot_index + 1]
    _snake_case			:			Tuple				       =		a[end]
    _snake_case			:			List[Any]				       =		temp
    return new_pivot_index + 1, count


SCREAMING_SNAKE_CASE_     = TemporaryFile()
SCREAMING_SNAKE_CASE_     = 100  # 1000 elements are to be sorted


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


outfile.seek(0)  # using the same array
SCREAMING_SNAKE_CASE_     = np.load(outfile)
SCREAMING_SNAKE_CASE_     = len(M) - 1
SCREAMING_SNAKE_CASE_     = _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"""






def      UpperCAmelCase__			(							lowerCAmelCase__	:int = 5_0						)					->       int:
      '''simple docstring'''


      lowercase								=      [1] * (length + 1)

      for row_length in range(3   ,						length + 1						):
            for block_length in range(3   ,						row_length + 1						):
                  for block_start in range(row_length - block_length						):
                        ways_number[row_length] += ways_number[
                            row_length - block_start - block_length - 1
                        ]

                  ways_number[row_length] += 1

      return ways_number[length]


if __name__ == "__main__":
       print(F"""{solution() = }""")



