
'''simple docstring'''
from __future__ import annotations


class       _lowerCAmelCase   :







							'''simple docstring'''

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

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

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

														_snake_case       =  a_coeffs
														_snake_case       =  b_coeffs





							def 	lowercase							(self  ,  UpperCAmelCase  )					->       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

'''simple docstring'''
from random import randint, random






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE = False							, _SCREAMING_SNAKE_CASE = False							, _SCREAMING_SNAKE_CASE = 5							, ):
							_snake_case       =  [[-1] * number_of_cells]  # Create a highway without any car
							_snake_case       =  0
							_snake_case       =  max(_SCREAMING_SNAKE_CASE							, 0				)
							while i < number_of_cells:
														_snake_case       =  (
														    randint(0							, _SCREAMING_SNAKE_CASE				) if random_speed else initial_speed
														)  # Place the cars
														i += (
														    randint(1							, max_speed * 2				) if random_frequency else frequency
														)  # Arbitrary number, may need tuning
							return highway






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				):
							_snake_case       =  0
							_snake_case       =  highway_now[car_index + 1 :]
							for cell in range(len(_SCREAMING_SNAKE_CASE				)				):  # May need a better name for this
														if cells[cell] != -1:  # If the cell is not empty then
																					return distance  # we have the distance we wanted
														distance += 1
							# Here if the car is near the end of the highway
							return distance + get_distance(_SCREAMING_SNAKE_CASE							, -1				)






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				):
							_snake_case       =  len(_SCREAMING_SNAKE_CASE				)
							# Beforce calculations, the highway is empty
							_snake_case       =  [-1] * number_of_cells

							for car_index in range(_SCREAMING_SNAKE_CASE				):
														if highway_now[car_index] != -1:
																					# Add 1 to the current speed of the car and cap the speed
																					_snake_case       =  min(highway_now[car_index] + 1							, _SCREAMING_SNAKE_CASE				)
																					# Number of empty cell before the next car
																					_snake_case       =  get_distance(_SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				) - 1
																					# We can't have the car causing an accident
																					_snake_case       =  min(next_highway[car_index]							, _SCREAMING_SNAKE_CASE				)
																					if random() < probability:
																												# Randomly, a driver will slow down
																												_snake_case       =  max(next_highway[car_index] - 1							, 0				)
							return next_highway






def  __SCREAMING_SNAKE_CASE				(  _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				):
							_snake_case       =  len(highway[0]				)

							for i in range(_SCREAMING_SNAKE_CASE				):
														_snake_case       =  update(highway[i]							, _SCREAMING_SNAKE_CASE							, _SCREAMING_SNAKE_CASE				)
														_snake_case       =  [-1] * number_of_cells

														for car_index in range(_SCREAMING_SNAKE_CASE				):
																					_snake_case       =  next_speeds_calculated[car_index]
																					if speed != -1:
																												# Change the position based on the speed (with % to create the loop)
																												_snake_case       =  (car_index + speed) % number_of_cells
																												# Commit the change of position
																												_snake_case       =  speed
														highway.append(_SCREAMING_SNAKE_CASE				)

							return highway


if __name__ == "__main__":
				import doctest

				doctest.testmod()