


from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np


class 		_SCREAMING_SNAKE_CASE     (						A     ):


     def        __snake_case(  self							,					A_    ):
       return 0.0




def    a__    (		snake_case__					:							np.ndarray						,   snake_case__					:							int     ):
  _UpperCAmelCase		:							List[Any]							=     min([-20, np.min(fft_results[1 : samplerate // 2 - 1]     )]     )
  _UpperCAmelCase		:							Optional[int]							=     max([20, np.max(fft_results[1 : samplerate // 2 - 1]     )]     )
  return lowest, highest




def    a__    (		snake_case__					:							FilterType						,   snake_case__					:							int     ):
  _UpperCAmelCase		:							List[str]							=     512
  _UpperCAmelCase		:							Tuple							=     [1] + [0] * (size - 1)
  _UpperCAmelCase		:							Optional[Any]							=     [filter_type.process(snake_case__     ) for item in inputs]

  _UpperCAmelCase		:							Union[str, Any]							=     [0] * (samplerate - size)  # zero-padding
  outputs += filler
  _UpperCAmelCase		:							List[str]							=     np.abs(np.fft.fft(snake_case__     )     )
  _UpperCAmelCase		:							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
  _UpperCAmelCase		:							int							=     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    a__    (		snake_case__					:							FilterType						,   snake_case__					:							int     ):
  _UpperCAmelCase		:							Any							=     512
  _UpperCAmelCase		:							int							=     [1] + [0] * (size - 1)
  _UpperCAmelCase		:							Dict							=     [filter_type.process(snake_case__     ) for item in inputs]

  _UpperCAmelCase		:							List[str]							=     [0] * (samplerate - size)  # zero-padding
  outputs += filler
  _UpperCAmelCase		:							Optional[Any]							=     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()









def    a__    (		snake_case__					:							Tuple     ):  # noqa: E741
  _UpperCAmelCase		:							Dict							=     len(snake_case__     )
  _UpperCAmelCase		:							Tuple							=     0
  _UpperCAmelCase		:							Union[str, Any]							=     [0] * n
  _UpperCAmelCase		:							Union[str, Any]							=     [False] * n
  _UpperCAmelCase		:							Tuple							=     [False] * n

  def dfs(snake_case__					:							List[str]						,   snake_case__					:							int						,   snake_case__					:							str						,   snake_case__					:							int     ):
    if parent == root:
      out_edge_count += 1
    _UpperCAmelCase		:							List[Any]							=     True
    _UpperCAmelCase		:							List[str]							=     at

    for to in l[at]:
      if to == parent:
        pass
      elif not visited[to]:
        _UpperCAmelCase		:							Optional[Any]							=     dfs(snake_case__						,   snake_case__						,   snake_case__						,   snake_case__     )
        _UpperCAmelCase		:							Optional[Any]							=     min(low[at]						,   low[to]     )

        # AP found via bridge
        if at < low[to]:
          _UpperCAmelCase		:							List[str]							=     True
        # AP found via cycle
        if at == low[to]:
          _UpperCAmelCase		:							Optional[Any]							=     True
      else:
        _UpperCAmelCase		:							str							=     min(low[at]						,   snake_case__     )
    return out_edge_count

  for i in range(snake_case__     ):
    if not visited[i]:
      _UpperCAmelCase		:							List[Any]							=     0
      _UpperCAmelCase		:							List[str]							=     dfs(snake_case__						,   snake_case__						,   -1						,   snake_case__     )
      _UpperCAmelCase		:							Optional[Any]							=     out_edge_count > 1

  for x in range(len(snake_case__     )     ):
    if is_art[x] is True:
      print(snake_case__     )


# Adjacency list of graph
SCREAMING_SNAKE_CASE__					:     Optional[Any]       =     {
    0: [1, 2],
    1: [0, 2],
    2: [0, 1, 3, 5],
    3: [2, 4],
    4: [3],
    5: [2, 6, 8],
    6: [5, 7],
    7: [6, 8],
    8: [5, 7],
}





compute_ap(data)





