




'''simple docstring'''





from collections.abc import Callable







class a :
						"""simple docstring"""

						def __init__( self :     Union[str, Any]				,							lowerCamelCase__ :     Callable | None = None				)    ->						None:
													"""simple docstring"""


													__lowercase      =    []
													# Stores indexes of each item for supporting updates and deletion.
													__lowercase      =    {}
													# Stores current size of heap.
													__lowercase      =    0
													# Stores function used to evaluate the score of an item on which basis ordering
													# will be done.
													__lowercase      =    key or (lambda lowerCamelCase__				: x)






						def     UpperCAmelCase_      ( self :     Optional[Any]				,							lowerCamelCase__ :     int				)    ->						int | None:
													"""simple docstring"""


													return int((i - 1) / 2				) if i > 0 else None






						def     UpperCAmelCase_      ( self :     Optional[int]				,							lowerCamelCase__ :     int				)    ->						int | None:
													"""simple docstring"""


													__lowercase      =    int(2 * i + 1				)
													return left if 0 < left < self.size else None






						def     UpperCAmelCase_      ( self :     Tuple				,							lowerCamelCase__ :     int				)    ->						int | None:
													"""simple docstring"""


													__lowercase      =    int(2 * i + 2				)
													return right if 0 < right < self.size else None






						def     UpperCAmelCase_      ( self :     str				,							lowerCamelCase__ :     int				,							lowerCamelCase__ :     int				)    ->						None:
													"""simple docstring"""


													__lowercase     ,     __lowercase      =    (
													    self.pos_map[self.arr[j][0]],
													    self.pos_map[self.arr[i][0]],
													)
													# Then swap the items in the list.
													__lowercase     ,     __lowercase      =    self.arr[j], self.arr[i]






						def     UpperCAmelCase_      ( self :     str				,							lowerCamelCase__ :     int				,							lowerCamelCase__ :     int				)    ->						bool:
													"""simple docstring"""


													return self.arr[i][1] < self.arr[j][1]






						def     UpperCAmelCase_      ( self :     Any				,							lowerCamelCase__ :     int				)    ->						int:
													"""simple docstring"""


													__lowercase      =    self._left(lowerCamelCase__				)
													__lowercase      =    self._right(lowerCamelCase__				)
													__lowercase      =    i

													if left is not None and not self._cmp(lowerCamelCase__				,							lowerCamelCase__				):
																				__lowercase      =    left
													if right is not None and not self._cmp(lowerCamelCase__				,							lowerCamelCase__				):
																				__lowercase      =    right

													return valid_parent






						def     UpperCAmelCase_      ( self :     List[str]				,							lowerCamelCase__ :     int				)    ->						None:
													"""simple docstring"""


													__lowercase      =    self._parent(lowerCamelCase__				)
													while parent is not None and not self._cmp(lowerCamelCase__				,							lowerCamelCase__				):
																				self._swap(lowerCamelCase__				,							lowerCamelCase__				)
																				__lowercase     ,     __lowercase      =    parent, self._parent(lowerCamelCase__				)






						def     UpperCAmelCase_      ( self :     Dict				,							lowerCamelCase__ :     int				)    ->						None:
													"""simple docstring"""


													__lowercase      =    self._get_valid_parent(lowerCamelCase__				)
													while valid_parent != index:
																				self._swap(lowerCamelCase__				,							lowerCamelCase__				)
																				__lowercase     ,     __lowercase      =    valid_parent, self._get_valid_parent(lowerCamelCase__				)






						def     UpperCAmelCase_      ( self :     Union[str, Any]				,							lowerCamelCase__ :     int				,							lowerCamelCase__ :     int				)    ->						None:
													"""simple docstring"""


													if item not in self.pos_map:
																				return
													__lowercase      =    self.pos_map[item]
													__lowercase      =    [item, self.key(lowerCamelCase__				)]
													# Make sure heap is right in both up and down direction.
													# Ideally only one of them will make any change.
													self._heapify_up(lowerCamelCase__				)
													self._heapify_down(lowerCamelCase__				)






						def     UpperCAmelCase_      ( self :     Tuple				,							lowerCamelCase__ :     int				)    ->						None:
													"""simple docstring"""


													if item not in self.pos_map:
																				return
													__lowercase      =    self.pos_map[item]
													del self.pos_map[item]
													__lowercase      =    self.arr[self.size - 1]
													__lowercase      =    index
													self.size -= 1
													# Make sure heap is right in both up and down direction. Ideally only one
													# of them will make any change- so no performance loss in calling both.
													if self.size > index:
																				self._heapify_up(lowerCamelCase__				)
																				self._heapify_down(lowerCamelCase__				)






						def     UpperCAmelCase_      ( self :     Any				,							lowerCamelCase__ :     int				,							lowerCamelCase__ :     int				)    ->						None:
													"""simple docstring"""


													__lowercase      =    len(self.arr				)
													if arr_len == self.size:
																				self.arr.append([item, self.key(lowerCamelCase__				)]				)
													else:
																				__lowercase      =    [item, self.key(lowerCamelCase__				)]
													__lowercase      =    self.size
													self.size += 1
													self._heapify_up(self.size - 1				)






						def     UpperCAmelCase_      ( self :     Optional[Any]				)    ->						tuple | None:
													"""simple docstring"""


													return self.arr[0] if self.size else None






						def     UpperCAmelCase_      ( self :     Dict				)    ->						tuple | None:
													"""simple docstring"""


													__lowercase      =    self.get_top()
													if top_item_tuple:
																				self.delete_item(top_item_tuple[0]				)
													return top_item_tuple







def 		_A(       )    -> None:
							'''simple docstring'''






if __name__ == "__main__":
			import doctest

			doctest.testmod()












from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np







class a (     __SCREAMING_SNAKE_CASE  ):
						"""simple docstring"""

						def     UpperCAmelCase_      ( self :     List[str]				,							lowerCamelCase__ :     float				)    ->						float:
													"""simple docstring"""


													return 0.0







def 		_A(       UpperCamelCase__							:			np.ndarray				,       UpperCamelCase__							:			int				)    -> tuple[int | float, int | float]:
							'''simple docstring'''


							__lowercase      =    min([-20, np.min(fft_results[1 : samplerate // 2 - 1]				)]				)
							__lowercase      =    max([20, np.max(fft_results[1 : samplerate // 2 - 1]				)]				)
							return lowest, highest







def 		_A(       UpperCamelCase__							:			FilterType				,       UpperCamelCase__							:			int				)    -> None:
							'''simple docstring'''


							__lowercase      =    512
							__lowercase      =    [1] + [0] * (size - 1)
							__lowercase      =    [filter_type.process(UpperCamelCase__				) for item in inputs]

							__lowercase      =    [0] * (samplerate - size)  # zero-padding
							outputs += filler
							__lowercase      =    np.abs(np.fft.fft(UpperCamelCase__				)				)
							__lowercase      =    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
							__lowercase      =    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:
							'''simple docstring'''


							__lowercase      =    512
							__lowercase      =    [1] + [0] * (size - 1)
							__lowercase      =    [filter_type.process(UpperCamelCase__				) for item in inputs]

							__lowercase      =    [0] * (samplerate - size)  # zero-padding
							outputs += filler
							__lowercase      =    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()






