





"""simple docstring"""






from __future__ import annotations

def      __A   (      a_    :list[int] ,							a_    :list[int] ,							a_    :list[int] ,							a_    :list[list[str]] ,							a_    :int ,							)		->		None:
				__a			:    Tuple      							=	len(a_)

				# If row is equal to the size of the board it means there are a queen in each row in
				# the current board (possible_board)
				if row == n:
								# We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
								# this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
								boards.append(['''. ''' * i + '''Q ''' + '''. ''' * (n - 1 - i) for i in possible_board])
								return

				# We iterate each column in the row to find all possible results in each row
				for col in range(a_):
								# We apply that we learned previously. First we check that in the current board
								# (possible_board) there are not other same value because if there is it means
								# that there are a collision in vertical. Then we apply the two formulas we
								# learned before:
								#
								# 45º: y - x = b or 45: row - col = b
								# 135º: y + x = b or row + col = b.
								#
								# And we verify if the results of this two formulas not exist in their variables
								# respectively.  (diagonal_right_collisions, diagonal_left_collisions)
								#
								# If any or these are True it means there is a collision so we continue to the
								# next value in the for loop.
								if (
								    col in possible_board
								    or row - col in diagonal_right_collisions
								    or row + col in diagonal_left_collisions
								):
												continue

								# If it is False we call dfs function again and we update the inputs
								depth_first_search(
								    [*possible_board, col] ,							[*diagonal_right_collisions, row - col] ,							[*diagonal_left_collisions, row + col] ,							a_ ,							a_ ,							)

def      __A   (      a_    :int)		->		None:
				__a			:    list[list[str]]      							=	[]
				depth_first_search([] ,							[] ,							[] ,							a_ ,							a_)

				# Print all the boards
				for board in boards:
								for column in board:
												print(a_)
								print('''''')

				print(len(a_) ,							'''solutions were found.''')


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		n_queens_solution(4)




"""simple docstring"""







from random import randint, random

def  __SCREAMING_SNAKE_CASE		(			lowerCamelCase_:							int     ,		lowerCamelCase_:							int     ,		lowerCamelCase_:							int     ,		lowerCamelCase_:							bool = False     ,		lowerCamelCase_:							bool = False     ,		lowerCamelCase_:							int = 5     ,		):
						"""simple docstring"""






						snake_case   :			str						    = [[-1] * number_of_cells]  # Create a highway without any car
						snake_case   :			str						    = 0
						snake_case   :			Any						    = max(lowerCamelCase_     ,		0 )
						while i < number_of_cells:
												snake_case   :			Optional[int]						    = (
												    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  __SCREAMING_SNAKE_CASE		(			lowerCamelCase_:							list     ,		lowerCamelCase_:							int ):
						"""simple docstring"""






						snake_case   :			Any						    = 0
						snake_case   :			int						    = 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  __SCREAMING_SNAKE_CASE		(			lowerCamelCase_:							list     ,		lowerCamelCase_:							float     ,		lowerCamelCase_:							int ):
						"""simple docstring"""






						snake_case   :			List[str]						    = len(lowerCamelCase_ )
						# Beforce calculations, the highway is empty
						snake_case   :			Dict						    = [-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
																		snake_case   :			Tuple						    = min(highway_now[car_index] + 1     ,		lowerCamelCase_ )
																		# Number of empty cell before the next car
																		snake_case   :			int						    = get_distance(lowerCamelCase_     ,		lowerCamelCase_ ) - 1
																		# We can't have the car causing an accident
																		snake_case   :			str						    = min(next_highway[car_index]     ,		lowerCamelCase_ )
																		if random() < probability:
																								# Randomly, a driver will slow down
																								snake_case   :			Optional[Any]						    = max(next_highway[car_index] - 1     ,		0 )
						return next_highway

def  __SCREAMING_SNAKE_CASE		(			lowerCamelCase_:							list     ,		lowerCamelCase_:							int     ,		lowerCamelCase_:							float     ,		lowerCamelCase_:							int ):
						"""simple docstring"""






						snake_case   :			Optional[Any]						    = len(highway[0] )

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

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

						return highway


if __name__ == "__main__":
			import doctest

			doctest.testmod()



