





from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np


class      A       (	__lowercase						):



      def 	lowerCAmelCase__    (	self:						Union[str, Any]		,  _lowerCAmelCase:						float       )						->    float:
         '''simple docstring'''

         return 0.0




def     a__ (					lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   UpperCAmelCase_											=min([-2_0, np.min(fft_results[1 : samplerate // 2 - 1]  )]  )
   UpperCAmelCase_											=max([2_0, np.max(fft_results[1 : samplerate // 2 - 1]  )]  )
   return lowest, highest




def     a__ (					lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   UpperCAmelCase_											=5_1_2
   UpperCAmelCase_											=[1] + [0] * (size - 1)
   UpperCAmelCase_											=[filter_type.process(_UpperCamelCase  ) for item in inputs]

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

   # 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
   UpperCAmelCase_											=get_bounds(_UpperCamelCase  ,    _UpperCamelCase  )
   plt.ylim(max([-8_0, bounds[0]]  )  ,    min([8_0, bounds[1]]  )  )
   plt.ylabel("Gain (dB)"  )

   plt.plot(_UpperCamelCase  )
   plt.show()





def     a__ (					lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   UpperCAmelCase_											=5_1_2
   UpperCAmelCase_											=[1] + [0] * (size - 1)
   UpperCAmelCase_											=[filter_type.process(_UpperCamelCase  ) for item in inputs]

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

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











from __future__ import annotations




def     a__ (					lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   UpperCAmelCase_						,       UpperCAmelCase_											=set(lowercase__  ), [start]

   while stack:
      UpperCAmelCase_											=stack.pop()
      explored.add(lowercase__  )
      # Differences from BFS:
      # 1) pop last element instead of first one
      # 2) add adjacent elements to stack without exploring them
      for adj in reversed(graph[v]  ):
         if adj not in explored:
            stack.append(lowercase__  )
   return explored


__lowercase  :   Dict						      ={
    """A""": ["""B""", """C""", """D"""],
    """B""": ["""A""", """D""", """E"""],
    """C""": ["""A""", """F"""],
    """D""": ["""B""", """D"""],
    """E""": ["""B""", """F"""],
    """F""": ["""C""", """E""", """G"""],
    """G""": ["""F"""],
}

if __name__ == "__main__":
     import doctest

     doctest.testmod()
     print(depth_first_search(G, """A"""))




