






"""simple docstring"""



from random import randint, random

def 			_snake_case    (					lowerCamelCase__     :   int    ,						lowerCamelCase__     :   int    ,						lowerCamelCase__     :   int    ,						lowerCamelCase__     :   bool = False    ,						lowerCamelCase__     :   bool = False    ,						lowerCamelCase__     :   int = 5    ,						)    ->     list:
							lowerCamelCase_	:							Dict									=[[-1] * number_of_cells]  # Create a highway without any car
							lowerCamelCase_	:							int									=0
							lowerCamelCase_	:							int									=max(lowerCamelCase__    ,						0  )
							while i < number_of_cells:
														lowerCamelCase_	:							List[str]									=(
														    randint(0    ,						lowerCamelCase__  ) 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 			_snake_case    (					lowerCamelCase__     :   list    ,						lowerCamelCase__     :   int  )    ->     int:
							lowerCamelCase_	:							List[Any]									=0
							lowerCamelCase_	:							Any									=highway_now[car_index + 1 :]
							for cell in range(len(lowerCamelCase__  )  ):  # 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(lowerCamelCase__    ,						-1  )

def 			_snake_case    (					lowerCamelCase__     :   list    ,						lowerCamelCase__     :   float    ,						lowerCamelCase__     :   int  )    ->     list:
							lowerCamelCase_	:							List[str]									=len(lowerCamelCase__  )
							# Beforce calculations, the highway is empty
							lowerCamelCase_	:							Optional[int]									=[-1] * number_of_cells

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

def 			_snake_case    (					lowerCamelCase__     :   list    ,						lowerCamelCase__     :   int    ,						lowerCamelCase__     :   float    ,						lowerCamelCase__     :   int  )    ->     list:
							lowerCamelCase_	:							List[str]									=len(highway[0]  )

							for i in range(lowerCamelCase__  ):
														lowerCamelCase_	:							Optional[int]									=update(highway[i]    ,						lowerCamelCase__    ,						lowerCamelCase__  )
														lowerCamelCase_	:							List[Any]									=[-1] * number_of_cells

														for car_index in range(lowerCamelCase__  ):
																					lowerCamelCase_	:							Union[str, Any]									=next_speeds_calculated[car_index]
																					if speed != -1:
																												# Change the position based on the speed (with % to create the loop)
																												lowerCamelCase_	:							Dict									=(car_index + speed) % number_of_cells
																												# Commit the change of position
																												lowerCamelCase_	:							Tuple									=speed
														highway.append(lowerCamelCase__  )

							return highway


if __name__ == "__main__":
						import doctest

						doctest.testmod()











"""simple docstring"""



def 			_snake_case    (					lowerCamelCase__     :   list[list[int]]    ,						lowerCamelCase__     :   int    ,						lowerCamelCase__     :   int    ,						lowerCamelCase__     :   list[int]  )    ->     bool:

							# 1. Validate that path exists between current and next vertices
							if graph[path[curr_ind - 1]][next_ver] == 0:
														return False

							# 2. Validate that next vertex is not already in path
							return not any(vertex == next_ver for vertex in path  )

def 			_snake_case    (					lowerCamelCase__     :   list[list[int]]    ,						lowerCamelCase__     :   list[int]    ,						lowerCamelCase__     :   int  )    ->     bool:

							# Base Case
							if curr_ind == len(lowerCamelCase__  ):
														# return whether path exists between current and starting vertices
														return graph[path[curr_ind - 1]][path[0]] == 1

							# Recursive Step
							for next_ver in range(0    ,						len(lowerCamelCase__  )  ):
														if valid_connection(lowerCamelCase__    ,						lowerCamelCase__    ,						lowerCamelCase__    ,						lowerCamelCase__  ):
																					# Insert current vertex  into path as next transition
																					lowerCamelCase_	:							Tuple									=next_ver
																					# Validate created path
																					if util_hamilton_cycle(lowerCamelCase__    ,						lowerCamelCase__    ,						curr_ind + 1  ):
																												return True
																					# Backtrack
																					lowerCamelCase_	:							int									=-1
							return False

def 			_snake_case    (					lowerCamelCase__     :   list[list[int]]    ,						lowerCamelCase__     :   int = 0  )    ->     list[int]:
							lowerCamelCase_	:							Optional[Any]									=[-1] * (len(lowerCamelCase__  ) + 1)
							# initialize start and end of path with starting index
							lowerCamelCase_	:							Optional[int]									=start_index
							# evaluate and if we find answer return path either return empty array
							return path if util_hamilton_cycle(lowerCamelCase__    ,						lowerCamelCase__    ,						1  ) else []



