




'''simple docstring'''






from __future__ import annotations

__UpperCAmelCase       =							'''#'''




class 		a__    :





							'''simple docstring'''






							def __init__(		self       )	->							None:
														lowerCAmelCase__	       =     {}







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_       )	->							None:
														lowerCAmelCase__	       =     self._trie
														for char in text:
																					if char not in trie:
																												lowerCAmelCase__	       =     {}
																					lowerCAmelCase__	       =     trie[char]
														lowerCAmelCase__	       =     True







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_       )	->							tuple | list:
														lowerCAmelCase__	       =     self._trie
														for char in prefix:
																					if char in trie:
																												lowerCAmelCase__	       =     trie[char]
																					else:
																												return []
														return self._elements(lowerCamelCase_       )







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_       )	->							tuple:
														lowerCAmelCase__	       =     []
														for c, v in d.items():
																					lowerCAmelCase__	       =     [''' '''] if c == END else [(c + s) for s in self._elements(lowerCamelCase_       )]
																					result.extend(lowerCamelCase_       )
														return tuple(lowerCamelCase_       )

__UpperCAmelCase       =							Trie()
__UpperCAmelCase       =							('''depart''', '''detergent''', '''daring''', '''dog''', '''deer''', '''deal''')
for word in words:
		trie.insert_word(word)


def  _snake_case       (					A	)						->   tuple:
							lowerCAmelCase__	       =     trie.find_word(A	)
							return tuple(string + word for word in suffixes	)


def  _snake_case       (					)						->   None:
							print(autocomplete_using_trie('''de'''	)	)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		main()



'''simple docstring'''






from __future__ import annotations




class 		a__    :





							'''simple docstring'''






							def __init__(		self ,   lowerCamelCase_       )	->							None:
														lowerCAmelCase__	       =     order

														# a_{0} ... a_{k}
														lowerCAmelCase__	       =     [1.0] + [0.0] * order
														# b_{0} ... b_{k}
														lowerCAmelCase__	       =     [1.0] + [0.0] * order

														# x[n-1] ... x[n-k]
														lowerCAmelCase__	       =     [0.0] * self.order
														# y[n-1] ... y[n-k]
														lowerCAmelCase__	       =     [0.0] * self.order







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_ ,   lowerCamelCase_       )	->							None:
														if len(lowerCamelCase_       ) < self.order:
																					lowerCAmelCase__	       =     [1.0, *a_coeffs]

														if len(lowerCamelCase_       ) != self.order + 1:
																					lowerCAmelCase__	       =     (
																					    F"""Expected a_coeffs to have {self.order + 1} elements """
																					    F"""for {self.order}-order filter, got {len(lowerCamelCase_       )}"""
																					)
																					raise ValueError(lowerCamelCase_       )

														if len(lowerCamelCase_       ) != self.order + 1:
																					lowerCAmelCase__	       =     (
																					    F"""Expected b_coeffs to have {self.order + 1} elements """
																					    F"""for {self.order}-order filter, got {len(lowerCamelCase_       )}"""
																					)
																					raise ValueError(lowerCamelCase_       )

														lowerCAmelCase__	       =     a_coeffs
														lowerCAmelCase__	       =     b_coeffs







							def   __SCREAMING_SNAKE_CASE							(		self ,   lowerCamelCase_       )	->							float:
														lowerCAmelCase__	       =     0.0

														# Start at index 1 and do index 0 at the end.
														for i in range(1 ,   self.order + 1       ):
																					result += (
																					    self.b_coeffs[i] * self.input_history[i - 1]
																					    - self.a_coeffs[i] * self.output_history[i - 1]
																					)

														lowerCAmelCase__	       =     (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

														lowerCAmelCase__	       =     self.input_history[:-1]
														lowerCAmelCase__	       =     self.output_history[:-1]

														lowerCAmelCase__	       =     sample
														lowerCAmelCase__	       =     result

														return result