





from __future__ import annotations
class      UpperCamelCase_						:




					def __init__(						self			,  lowerCAmelCase_					)						->							None:
										_snake_case													=			order

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

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




					def 		lowerCAmelCase     (						self			,  lowerCAmelCase_			,  lowerCAmelCase_					)						->							None:
										if len(lowerCAmelCase_					) < self.order:
															_snake_case													=			[1.0, *a_coeffs]

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

										_snake_case													=			a_coeffs
										_snake_case													=			b_coeffs






					def 		lowerCAmelCase     (						self			,  lowerCAmelCase_					)						->							float:
										_snake_case													=			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]
															)

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

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

										_snake_case													=			sample
										_snake_case													=			result

										return result










from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst





def   lowerCamelCase__       (       )     ->	List[str]:



					'''simple docstring'''




					_snake_case							,       _snake_case													=			9, 14  # noqa: F841
					_snake_case													=			[
					    [0, 1, 4],
					    [0, 7, 8],
					    [1, 2, 8],
					    [7, 8, 7],
					    [7, 6, 1],
					    [2, 8, 2],
					    [8, 6, 6],
					    [2, 3, 7],
					    [2, 5, 4],
					    [6, 5, 2],
					    [3, 5, 14],
					    [3, 4, 9],
					    [5, 4, 10],
					    [1, 7, 11],
					]

					_snake_case													=			defaultdict(UpperCamelCase__  )
					for nodea, nodea, cost in edges:
										adjancency[nodea].append([nodea, cost]  )
										adjancency[nodea].append([nodea, cost]  )

					_snake_case													=			mst(UpperCamelCase__  )

					_snake_case													=			[
					    [7, 6, 1],
					    [2, 8, 2],
					    [6, 5, 2],
					    [0, 1, 4],
					    [2, 5, 4],
					    [2, 3, 7],
					    [0, 7, 8],
					    [3, 4, 9],
					]

					for answer in expected:
										_snake_case													=			tuple(answer[:2]  )
										_snake_case													=			tuple(edge[::-1]  )
										assert edge in result or reverse in result



