

"""simple docstring"""






from __future__ import annotations







class       snake_case__  :







			def __init__(			self			: List[str]			,  lowercase			: int  ):





								'''simple docstring'''



								UpperCAmelCase			:   List[str]      =				order

								# a_{0} ... a_{k}
								UpperCAmelCase			:   int      =				[1.0] + [0.0] * order
								# b_{0} ... b_{k}
								UpperCAmelCase			:   List[Any]      =				[1.0] + [0.0] * order

								# x[n-1] ... x[n-k]
								UpperCAmelCase			:   Any      =				[0.0] * self.order
								# y[n-1] ... y[n-k]
								UpperCAmelCase			:   Optional[Any]      =				[0.0] * self.order







			def 			__lowerCAmelCase				(			self			: List[Any]			,  lowercase			: list[float]			,  lowercase			: list[float]  ):





								'''simple docstring'''



								if len(lowercase  ) < self.order:
													UpperCAmelCase			:   List[Any]      =				[1.0, *a_coeffs]

								if len(lowercase  ) != self.order + 1:
													UpperCAmelCase			:   List[str]      =				(
													    f"""Expected a_coeffs to have {self.order + 1} elements """
													    f"""for {self.order}-order filter, got {len(lowercase  )}"""
													)
													raise ValueError(lowercase  )

								if len(lowercase  ) != self.order + 1:
													UpperCAmelCase			:   int      =				(
													    f"""Expected b_coeffs to have {self.order + 1} elements """
													    f"""for {self.order}-order filter, got {len(lowercase  )}"""
													)
													raise ValueError(lowercase  )

								UpperCAmelCase			:   List[str]      =				a_coeffs
								UpperCAmelCase			:   Optional[Any]      =				b_coeffs







			def 			__lowerCAmelCase				(			self			: Optional[Any]			,  lowercase			: float  ):





								'''simple docstring'''



								UpperCAmelCase			:   Optional[int]      =				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]
													)

								UpperCAmelCase			:   Union[str, Any]      =				(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

								UpperCAmelCase			:   Optional[Any]      =				self.input_history[:-1]
								UpperCAmelCase			:   List[Any]      =				self.output_history[:-1]

								UpperCAmelCase			:   Optional[int]      =				sample
								UpperCAmelCase			:   str      =				result

								return result





"""simple docstring"""






def   lowercase_	(    _lowercase       :		List[str]							,      _lowercase       :		Tuple							,      _lowercase       :		int							,      _lowercase       :		Optional[Any]	):




					'''simple docstring'''






					UpperCAmelCase			:   int      =				[False] * len(_lowercase	)
					UpperCAmelCase			:   List[str]      =				[]
					queue.append(_lowercase	)
					UpperCAmelCase			:   List[Any]      =				True

					while queue:
										UpperCAmelCase			:   Any      =				queue.pop(0	)
										for ind in range(len(graph[u]	)	):
															if visited[ind] is False and graph[u][ind] > 0:
																				queue.append(_lowercase	)
																				UpperCAmelCase			:   Optional[int]      =				True
																				UpperCAmelCase			:   int      =				u

					return visited[t]



def   lowercase_	(    _lowercase       :		Tuple							,      _lowercase       :		Dict							,      _lowercase       :		Optional[int]	):




					'''simple docstring'''






					UpperCAmelCase			:   List[Any]      =				[-1] * (len(_lowercase	))
					UpperCAmelCase			:   List[Any]      =				0
					while bfs(_lowercase							,      _lowercase							,      _lowercase							,      _lowercase	):
										UpperCAmelCase			:   List[str]      =				float("Inf"	)
										UpperCAmelCase			:   str      =				sink

										while s != source:
															# Find the minimum value in select path
															UpperCAmelCase			:   Tuple      =				min(_lowercase							,      graph[parent[s]][s]	)
															UpperCAmelCase			:   Optional[Any]      =				parent[s]

										max_flow += path_flow
										UpperCAmelCase			:   List[str]      =				sink

										while v != source:
															UpperCAmelCase			:   Dict      =				parent[v]
															graph[u][v] -= path_flow
															graph[v][u] += path_flow
															UpperCAmelCase			:   Dict      =				parent[v]
					return max_flow


snake_case_   :   Optional[Any]        =       [
    [0, 1_6, 1_3, 0, 0, 0],
    [0, 0, 1_0, 1_2, 0, 0],
    [0, 4, 0, 0, 1_4, 0],
    [0, 0, 9, 0, 0, 2_0],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]

snake_case_     ,      snake_case_   :   str        =       0, 5




print(ford_fulkerson(graph, source, sink))


