






from random import randint
from tempfile import TemporaryFile

import numpy as np





def 						__UpperCAmelCase			(     a_							,     a_							,     a_):
							snake_case_				=							0
							if start < end:
														snake_case_				=							randint(__a							,     __a)
														snake_case_				=							a[end]
														snake_case_				=							a[pivot]
														snake_case_				=							temp

														snake_case_			,		snake_case_				=							_in_place_partition(__a							,     __a							,     __a)
														count += _in_place_quick_sort(__a							,     __a							,     p - 1)
														count += _in_place_quick_sort(__a							,     p + 1							,     __a)
							return count





def 						__UpperCAmelCase			(     a_							,     a_							,     a_):
							snake_case_				=							0
							snake_case_				=							randint(__a							,     __a)
							snake_case_				=							a[end]
							snake_case_				=							a[pivot]
							snake_case_				=							temp
							snake_case_				=							start - 1
							for index in range(__a							,     __a):
														count += 1
														if a[index] < a[end]:  # check if current val is less than pivot value
																					snake_case_				=							new_pivot_index + 1
																					snake_case_				=							a[new_pivot_index]
																					snake_case_				=							a[index]
																					snake_case_				=							temp

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


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


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


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

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




print(z)












def    __lowerCamelCase					(							__a   :int = 1_0_0_0_0_0_0    )		->				int:






		"""simple docstring"""

		A__        =   limit + 1
		A__        =   [0] * limit
		for first_term in range(1    ,     __a    ):
				for n in range(__a    ,     __a    ,     __a    ):
						A__        =   first_term + n / first_term
						if common_difference % 4:  # d must be divisble by 4
								continue
						else:
								common_difference /= 4
								if (
								    first_term > common_difference
								    and first_term < 4 * common_difference
								):  # since x,y,z are positive integers
										frequency[n] += 1  # so z>0 and a>d ,also 4d<a

		A__        =   sum(1 for x in frequency[1:limit] if x == 1_0    )

		return count


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



