



from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np





class 		UpperCAmelCase						(						snake_case_				):





   def 	__lowerCAmelCase							(	self       ,     _lowerCAmelCase			):
         return 0.0






def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	np.ndarray     ,				_SCREAMING_SNAKE_CASE   :	int				)->tuple[int | float, int | float]:
      _lowerCAmelCase 			=  min([-2_0, np.min(fft_results[1 : samplerate // 2 - 1]				)]				)
      _lowerCAmelCase 			=  max([2_0, np.max(fft_results[1 : samplerate // 2 - 1]				)]				)
      return lowest, highest
def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	FilterType     ,				_SCREAMING_SNAKE_CASE   :	int				)->None:
      _lowerCAmelCase 			=  5_1_2
      _lowerCAmelCase 			=  [1] + [0] * (size - 1)
      _lowerCAmelCase 			=  [filter_type.process(_SCREAMING_SNAKE_CASE				) for item in inputs]

      _lowerCAmelCase 			=  [0] * (samplerate - size)  # zero-padding
      outputs += filler
      _lowerCAmelCase 			=  np.abs(np.fft.fft(_SCREAMING_SNAKE_CASE				)				)
      _lowerCAmelCase 			=  2_0 * np.logaa(_SCREAMING_SNAKE_CASE				)

      # Frequencies on log scale from 24 to nyquist frequency
      plt.xlim(2_4     ,				samplerate / 2 - 1				)
      plt.xlabel('''Frequency (Hz)'''				)
      plt.xscale('''log'''				)

      # Display within reasonable bounds
      _lowerCAmelCase 			=  get_bounds(_SCREAMING_SNAKE_CASE     ,				_SCREAMING_SNAKE_CASE				)
      plt.ylim(max([-8_0, bounds[0]]				)     ,				min([8_0, bounds[1]]				)				)
      plt.ylabel('''Gain (dB)'''				)

      plt.plot(_SCREAMING_SNAKE_CASE				)
      plt.show()


def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	FilterType     ,				_SCREAMING_SNAKE_CASE   :	int				)->None:
      _lowerCAmelCase 			=  5_1_2
      _lowerCAmelCase 			=  [1] + [0] * (size - 1)
      _lowerCAmelCase 			=  [filter_type.process(_SCREAMING_SNAKE_CASE				) for item in inputs]

      _lowerCAmelCase 			=  [0] * (samplerate - size)  # zero-padding
      outputs += filler
      _lowerCAmelCase 			=  np.angle(np.fft.fft(_SCREAMING_SNAKE_CASE				)				)

      # Frequencies on log scale from 24 to nyquist frequency
      plt.xlim(2_4     ,				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(_SCREAMING_SNAKE_CASE     ,				-2 * pi				)				)
      plt.show()




from __future__ import annotations
def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	list				)->list:
      if len(_SCREAMING_SNAKE_CASE				) == 0:
            return []
      _lowerCAmelCase			,   _lowerCAmelCase 			=  min(_SCREAMING_SNAKE_CASE				), max(_SCREAMING_SNAKE_CASE				)
      _lowerCAmelCase 			=  int(max_value - min_value				) + 1
      _lowerCAmelCase 			=  [[] for _ in range(_SCREAMING_SNAKE_CASE				)]

      for i in my_list:
            buckets[int(i - min_value				)].append(_SCREAMING_SNAKE_CASE				)

      return [v for bucket in buckets for v in sorted(_SCREAMING_SNAKE_CASE				)]


if __name__ == "__main__":
    from doctest import testmod

    testmod()
    assert bucket_sort([4, 5, 3, 2, 1]) == [1, 2, 3, 4, 5]
    assert bucket_sort([0, 1, -1_0, 1_5, 2, -2]) == [-1_0, -2, 0, 1, 2, 1_5]