





from random import randint
from tempfile import TemporaryFile

import numpy as np







def       UpperCAmelCase							(     _lowerCamelCase      :  Optional[int]			,   _lowerCamelCase      :  int			,   _lowerCamelCase      :  Union[str, Any]     ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__     :				Optional[Any]   =					0
						if start < end:
												SCREAMING_SNAKE_CASE__     :				Union[str, Any]   =					randint(_lowerCamelCase			,   _lowerCamelCase     )
												SCREAMING_SNAKE_CASE__     :				str   =					a[end]
												SCREAMING_SNAKE_CASE__     :				List[str]   =					a[pivot]
												SCREAMING_SNAKE_CASE__     :				Tuple   =					temp

												SCREAMING_SNAKE_CASE__,							SCREAMING_SNAKE_CASE__     :				int   =					_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       UpperCAmelCase							(     _lowerCamelCase      :  Union[str, Any]			,   _lowerCamelCase      :  Tuple			,   _lowerCamelCase      :  List[Any]     ):





						'''simple docstring'''


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

						SCREAMING_SNAKE_CASE__     :				List[Any]   =					a[new_pivot_index + 1]
						SCREAMING_SNAKE_CASE__     :				Dict   =					a[end]
						SCREAMING_SNAKE_CASE__     :				Optional[Any]   =					temp
						return new_pivot_index + 1, count


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


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


outfile.seek(0)  # using the same array
__lowercase       :Tuple       =  np.load(outfile)
__lowercase       :int       =  len(M) - 1
__lowercase       :Tuple       =  _in_place_quick_sort(M, 0, r)

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



print(z)






from __future__ import annotations







def       UpperCAmelCase							(     _lowerCamelCase      :  list[int | float]			,   _lowerCamelCase      :  int			,   _lowerCamelCase      :  int     ):





						'''simple docstring'''


						if len(_lowerCamelCase     ) == 0:
												raise ValueError("find_max() arg is an empty sequence"     )
						if (
						    left >= len(_lowerCamelCase     )
						    or left < -len(_lowerCamelCase     )
						    or right >= len(_lowerCamelCase     )
						    or right < -len(_lowerCamelCase     )
						):
												raise IndexError("list index out of range"     )
						if left == right:
												return nums[left]
						SCREAMING_SNAKE_CASE__     :				Optional[int]   =					(left + right) >> 1  # the middle
						SCREAMING_SNAKE_CASE__     :				List[Any]   =					find_max(_lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase     )  # find max in range[left, mid]
						SCREAMING_SNAKE_CASE__     :				Optional[int]   =					find_max(_lowerCamelCase			,   mid + 1			,   _lowerCamelCase     )  # find max in range[mid + 1, right]

						return left_max if left_max >= right_max else right_max


if __name__ == "__main__":
				import doctest

				doctest.testmod(verbose=True)