



'''simple docstring'''





from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np



class  snake_case__						(    SCREAMING_SNAKE_CASE_				):
 def A_   (   self						:							Optional[Any]      ,     __a						:							float  )      ->   float:







       '''simple docstring'''
       return 0.0





def   a_   (		_UpperCAmelCase    :      np.ndarray ,_UpperCAmelCase    :      int				)    ->  tuple[int | float, int | float]:
      __snake_case :   List[Any]													=    min([-20, np.min(fft_results[1 : samplerate // 2 - 1]				)]				)
      __snake_case :   List[str]													=    max([20, np.max(fft_results[1 : samplerate // 2 - 1]				)]				)
      return lowest, highest





def   a_   (		_UpperCAmelCase    :      FilterType ,_UpperCAmelCase    :      int				)    ->  None:
      __snake_case :   int													=    5_12
      __snake_case :   Optional[Any]													=    [1] + [0] * (size - 1)
      __snake_case :   Any													=    [filter_type.process(_UpperCAmelCase				) for item in inputs]

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

      # 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
      __snake_case :   List[Any]													=    get_bounds(_UpperCAmelCase ,_UpperCAmelCase				)
      plt.ylim(max([-80, bounds[0]]				) ,min([80, bounds[1]]				)				)
      plt.ylabel('Gain (dB)'				)

      plt.plot(_UpperCAmelCase				)
      plt.show()





def   a_   (		_UpperCAmelCase    :      FilterType ,_UpperCAmelCase    :      int				)    ->  None:
      __snake_case :   List[str]													=    5_12
      __snake_case :   Tuple													=    [1] + [0] * (size - 1)
      __snake_case :   Optional[int]													=    [filter_type.process(_UpperCAmelCase				) for item in inputs]

      __snake_case :   int													=    [0] * (samplerate - size)  # zero-padding
      outputs += filler
      __snake_case :   List[str]													=    np.angle(np.fft.fft(_UpperCAmelCase				)				)

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








'''simple docstring'''





import functools





def   a_   (		_UpperCAmelCase    :      list[int] ,_UpperCAmelCase    :      list[int]				)    ->  int:

      # Validation
      if not isinstance(_UpperCAmelCase ,_UpperCAmelCase				) or not all(isinstance(_UpperCAmelCase ,_UpperCAmelCase				) for day in days				):
            raise ValueError('The parameter days should be a list of integers'				)

      if len(_UpperCAmelCase				) != 3 or not all(isinstance(_UpperCAmelCase ,_UpperCAmelCase				) for cost in costs				):
            raise ValueError('The parameter costs should be a list of three integers'				)

      if len(_UpperCAmelCase				) == 0:
            return 0

      if min(_UpperCAmelCase				) <= 0:
            raise ValueError('All days elements should be greater than 0'				)

      if max(_UpperCAmelCase				) >= 3_66:
            raise ValueError('All days elements should be less than 366'				)

      __snake_case :   str													=    set(_UpperCAmelCase				)

      @functools.cache
      def dynamic_programming(_UpperCAmelCase    :      int				) -> int:
            if index > 3_65:
                  return 0

            if index not in days_set:
                  return dynamic_programming(index + 1				)

            return min(
                costs[0] + dynamic_programming(index + 1				) ,costs[1] + dynamic_programming(index + 7				) ,costs[2] + dynamic_programming(index + 30				) ,)

      return dynamic_programming(1				)


if __name__ == "__main__":
    import doctest

    doctest.testmod()



