

'''simple docstring'''



from random import randint
from tempfile import TemporaryFile

import numpy as np
def 						__lowerCamelCase	(       __snake_case					:		Dict,		__snake_case					:		Dict,		__snake_case					:		Union[str, Any]	)	->							str:






						"""simple docstring"""





						A__					:       List[str]     =0
						if start < end:
												A__					:       Any     =randint(__snake_case,		__snake_case	)
												A__					:       List[Any]     =a[end]
												A__					:       Union[str, Any]     =a[pivot]
												A__					:       Union[str, Any]     =temp

												A__   ,						A__					:       Optional[int]     =_in_place_partition(__snake_case,		__snake_case,		__snake_case	)
												count += _in_place_quick_sort(__snake_case,		__snake_case,		p - 1	)
												count += _in_place_quick_sort(__snake_case,		p + 1,		__snake_case	)
						return count
def 						__lowerCamelCase	(       __snake_case					:		Tuple,		__snake_case					:		Union[str, Any],		__snake_case					:		int	)	->							Optional[Any]:






						"""simple docstring"""





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

						A__					:       Optional[int]     =a[new_pivot_index + 1]
						A__					:       str     =a[end]
						A__					:       str     =temp
						return new_pivot_index + 1, count


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


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


outfile.seek(0)  # using the same array
__snake_case			:     str										=      np.load(outfile)
__snake_case			:     Optional[Any]										=      len(M) - 1
__snake_case			:     Optional[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

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np



class lowerCamelCase			(  lowercase_						):



			'''simple docstring'''






			def lowercase__						(				self	:						Any		,      lowerCAmelCase_	:						float			)      ->		float:





									'''simple docstring'''
									return 0.0


def 						__lowerCamelCase	(       __snake_case					:		np.ndarray,		__snake_case					:		int	)	->							tuple[int | float, int | float]:






						"""simple docstring"""





						A__					:       Tuple     =min([-20, np.min(fft_results[1 : samplerate // 2 - 1]	)]	)
						A__					:       str     =max([20, np.max(fft_results[1 : samplerate // 2 - 1]	)]	)
						return lowest, highest
def 						__lowerCamelCase	(       __snake_case					:		FilterType,		__snake_case					:		int	)	->							None:






						"""simple docstring"""





						A__					:       Any     =512
						A__					:       int     =[1] + [0] * (size - 1)
						A__					:       int     =[filter_type.process(__snake_case	) for item in inputs]

						A__					:       Union[str, Any]     =[0] * (samplerate - size)  # zero-padding
						outputs += filler
						A__					:       List[Any]     =np.abs(np.fft.fft(__snake_case	)	)
						A__					:       int     =20 * np.logaa(__snake_case	)

						# Frequencies on log scale from 24 to nyquist frequency
						plt.xlim(24,		samplerate / 2 - 1	)
						plt.xlabel("""Frequency (Hz)"""	)
						plt.xscale("""log"""	)

						# Display within reasonable bounds
						A__					:       Union[str, Any]     =get_bounds(__snake_case,		__snake_case	)
						plt.ylim(max([-80, bounds[0]]	),		min([80, bounds[1]]	)	)
						plt.ylabel("""Gain (dB)"""	)

						plt.plot(__snake_case	)
						plt.show()
def 						__lowerCamelCase	(       __snake_case					:		FilterType,		__snake_case					:		int	)	->							None:






						"""simple docstring"""





						A__					:       List[Any]     =512
						A__					:       List[Any]     =[1] + [0] * (size - 1)
						A__					:       Dict     =[filter_type.process(__snake_case	) for item in inputs]

						A__					:       Union[str, Any]     =[0] * (samplerate - size)  # zero-padding
						outputs += filler
						A__					:       str     =np.angle(np.fft.fft(__snake_case	)	)

						# Frequencies on log scale from 24 to nyquist frequency
						plt.xlim(24,		samplerate / 2 - 1	)
						plt.xlabel("""Frequency (Hz)"""	)
						plt.xscale("""log"""	)

						plt.ylim(-2 * pi,		2 * pi	)
						plt.ylabel("""Phase shift (Radians)"""	)
						plt.plot(np.unwrap(__snake_case,		-2 * pi	)	)
						plt.show()

