


"""simple docstring"""






from __future__ import annotations





def 				A_       ( snake_case__       ,					snake_case__		)					->  list[tuple[int, int]]:
			_UpperCamelCase     ,      _UpperCamelCase					:List[Any]					     =	position
			_UpperCamelCase					:Dict					     =	[
			    (y + 1, x + 2),
			    (y - 1, x + 2),
			    (y + 1, x - 2),
			    (y - 1, x - 2),
			    (y + 2, x + 1),
			    (y + 2, x - 1),
			    (y - 2, x + 1),
			    (y - 2, x - 1),
			]
			_UpperCamelCase					:Optional[Any]					     =	[]

			for position in positions:
						_UpperCamelCase     ,      _UpperCamelCase					:Any					     =	position
						if 0 <= y_test < n and 0 <= x_test < n:
									permissible_positions.append(snake_case__		)

			return permissible_positions





def 				A_       ( snake_case__		)					->  bool:
			return not any(elem == 0 for row in board for elem in row		)





def 				A_       ( snake_case__       ,					snake_case__       ,					snake_case__		)					->  bool:

			if is_complete(snake_case__		):
						return True

			for position in get_valid_pos(snake_case__       ,					len(snake_case__		)		):
						_UpperCamelCase     ,      _UpperCamelCase					:Tuple					     =	position

						if board[y][x] == 0:
									_UpperCamelCase					:List[Any]					     =	curr + 1
									if open_knight_tour_helper(snake_case__       ,					snake_case__       ,					curr + 1		):
												return True
									_UpperCamelCase					:int					     =	0

			return False





def 				A_       ( snake_case__		)					->  list[list[int]]:
			_UpperCamelCase					:Union[str, Any]					     =	[[0 for i in range(snake_case__		)] for j in range(snake_case__		)]

			for i in range(snake_case__		):
						for j in range(snake_case__		):
									_UpperCamelCase					:List[str]					     =	1
									if open_knight_tour_helper(snake_case__       ,					(i, j)       ,					1		):
												return board
									_UpperCamelCase					:Tuple					     =	0

			_UpperCamelCase					:Optional[int]					     =	f"Open Kight Tour cannot be performed on a board of size {n}"
			raise ValueError(snake_case__		)


if __name__ == "__main__":
					import doctest

					doctest.testmod()





"""simple docstring"""






from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np






class      A(  lowerCamelCase__		):

		"""simple docstring"""





		def   _UpperCamelCase( self					,				SCREAMING_SNAKE_CASE__   )      ->	float:

					"""simple docstring"""



					return 0.0





def 				A_       ( snake_case__       ,					snake_case__		)					->  tuple[int | float, int | float]:
			_UpperCamelCase					:Union[str, 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__       ,					snake_case__		)					->  None:
			_UpperCamelCase					:List[str]					     =	5_12
			_UpperCamelCase					:int					     =	[1] + [0] * (size - 1)
			_UpperCamelCase					:Union[str, Any]					     =	[filter_type.process(snake_case__		) for item in inputs]

			_UpperCamelCase					:Any					     =	[0] * (samplerate - size)  # zero-padding
			outputs += filler
			_UpperCamelCase					:int					     =	np.abs(np.fft.fft(snake_case__		)		)
			_UpperCamelCase					:str					     =	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					:Tuple					     =	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__       ,					snake_case__		)					->  None:
			_UpperCamelCase					:Tuple					     =	5_12
			_UpperCamelCase					:Union[str, Any]					     =	[1] + [0] * (size - 1)
			_UpperCamelCase					:List[Any]					     =	[filter_type.process(snake_case__		) for item in inputs]

			_UpperCamelCase					:str					     =	[0] * (samplerate - size)  # zero-padding
			outputs += filler
			_UpperCamelCase					:Tuple					     =	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()

