


from random import randint, random






def 		_A		(		_lowercase					,  _lowercase					,  _lowercase					,  _lowercase = False					,  _lowercase = False					,  _lowercase = 5					,  )					-> list:


     """simple docstring"""


     __UpperCamelCase =			[[-1] * number_of_cells]  # Create a highway without any car
     __UpperCamelCase =			0
     __UpperCamelCase =			max(_lowercase					,  0 )
     while i < number_of_cells:
          __UpperCamelCase =			(
              randint(0					,  _lowercase ) 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 		_A		(		_lowercase					,  _lowercase )					-> int:


     """simple docstring"""


     __UpperCamelCase =			0
     __UpperCamelCase =			highway_now[car_index + 1 :]
     for cell in range(len(_lowercase ) ):  # 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(_lowercase					,  -1 )






def 		_A		(		_lowercase					,  _lowercase					,  _lowercase )					-> list:


     """simple docstring"""


     __UpperCamelCase =			len(_lowercase )
     # Beforce calculations, the highway is empty
     __UpperCamelCase =			[-1] * number_of_cells

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






def 		_A		(		_lowercase					,  _lowercase					,  _lowercase					,  _lowercase )					-> list:


     """simple docstring"""


     __UpperCamelCase =			len(highway[0] )

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

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

     return highway


if __name__ == "__main__":
    import doctest

    doctest.testmod()






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

from collections import namedtuple
from dataclasses import dataclass
@dataclass
class   lowercase      :

		"""simple docstring"""

		_a       					=							42
		_a       					=							None
		_a       					=							None



__snake_case				 =	namedtuple('''CoinsDistribResult''', '''moves excess''')


def      a (     __a  )    ->      int:



					'''simple docstring'''






					if root is None:
										return 0

					# Validation
					def count_nodes(__a  ) -> int:
										if node is None:
															return 0

										return count_nodes(node.left  ) + count_nodes(node.right  ) + 1

					def count_coins(__a  ) -> int:
										if node is None:
															return 0

										return count_coins(node.left  ) + count_coins(node.right  ) + node.data

					if count_nodes(__a  ) != count_coins(__a  ):
										raise ValueError('''The nodes number should be same as the number of coins'''  )

					# Main calculation
					def get_distrib(__a  ) -> CoinsDistribResult:

										if node is None:
															return CoinsDistribResult(0					,   1  )

										UpperCamelCase__   ,							UpperCamelCase__  :Optional[Any]				   =					get_distrib(node.left  )
										UpperCamelCase__   ,							UpperCamelCase__  :Union[str, Any]				   =					get_distrib(node.right  )

										UpperCamelCase__  :Tuple				   =					1 - left_distrib_excess
										UpperCamelCase__  :Optional[int]				   =					1 - right_distrib_excess

										UpperCamelCase__  :int				   =					(
										    left_distrib_moves
										    + right_distrib_moves
										    + abs(__a  )
										    + abs(__a  )
										)
										UpperCamelCase__  :Optional[Any]				   =					node.data - coins_to_left - coins_to_right

										return CoinsDistribResult(__a					,   __a  )

					return get_distrib(__a  )[0]


if __name__ == "__main__":
		import doctest

		doctest.testmod()