from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np





class       lowercase__		(     UpperCamelCase_):


						def  __A ( self			:       Optional[int]					,	UpperCamelCase__			:       float		):





												'''simple docstring'''





												return 0.0






def    A			(					_lowercase	,						_lowercase		):
						SCREAMING_SNAKE_CASE							:					Optional[Any]           =							min([-20, np.min(fft_results[1 : samplerate // 2 - 1]		)]		)
						SCREAMING_SNAKE_CASE							:					Dict           =							max([20, np.max(fft_results[1 : samplerate // 2 - 1]		)]		)
						return lowest, highest
def    A			(					_lowercase	,						_lowercase		):
						SCREAMING_SNAKE_CASE							:					Optional[int]           =							512
						SCREAMING_SNAKE_CASE							:					Dict           =							[1] + [0] * (size - 1)
						SCREAMING_SNAKE_CASE							:					Dict           =							[filter_type.process(_lowercase		) for item in inputs]

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

						# 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
						SCREAMING_SNAKE_CASE							:					str           =							get_bounds(_lowercase	,						_lowercase		)
						plt.ylim(max([-80, bounds[0]]		)	,						min([80, bounds[1]]		)		)
						plt.ylabel('''Gain (dB)'''		)

						plt.plot(_lowercase		)
						plt.show()



def    A			(					_lowercase	,						_lowercase		):
						SCREAMING_SNAKE_CASE							:					List[str]           =							512
						SCREAMING_SNAKE_CASE							:					Any           =							[1] + [0] * (size - 1)
						SCREAMING_SNAKE_CASE							:					Optional[Any]           =							[filter_type.process(_lowercase		) for item in inputs]

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

						# 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(_lowercase	,						-2 * pi		)		)
						plt.show()






import random
def    A			(					_lowercase	,						_lowercase		):
						SCREAMING_SNAKE_CASE       ,						SCREAMING_SNAKE_CASE       ,						SCREAMING_SNAKE_CASE							:					Tuple           =							[], [], []
						for element in data:
												if element < pivot:
																		less.append(_lowercase		)
												elif element > pivot:
																		greater.append(_lowercase		)
												else:
																		equal.append(_lowercase		)
						return less, equal, greater



def    A			(					_lowercase	,						_lowercase		):
						# index = len(items) // 2 when trying to find the median
						#   (value of index when items is sorted)

						# invalid input
						if index >= len(_lowercase		) or index < 0:
												return None

						SCREAMING_SNAKE_CASE							:					Dict           =							items[random.randint(0	,						len(_lowercase		) - 1		)]
						SCREAMING_SNAKE_CASE							:					int           =							0
						SCREAMING_SNAKE_CASE       ,						SCREAMING_SNAKE_CASE       ,						SCREAMING_SNAKE_CASE							:					List[str]           =							_partition(_lowercase	,						_lowercase		)
						SCREAMING_SNAKE_CASE							:					List[Any]           =							len(_lowercase		)
						SCREAMING_SNAKE_CASE							:					Optional[Any]           =							len(_lowercase		)

						# index is the pivot
						if m <= index < m + count:
												return pivot
						# must be in smaller
						elif m > index:
												return quick_select(_lowercase	,						_lowercase		)
						# must be in larger
						else:
												return quick_select(_lowercase	,						index - (m + count)		)





