



from random import randint, random






def      _A				(UpperCamelCase		:      int      ,			UpperCamelCase		:      int      ,			UpperCamelCase		:      int      ,			UpperCamelCase		:      bool = False      ,			UpperCamelCase		:      bool = False      ,			UpperCamelCase		:      int = 5      ,			)  ->list:



			'''simple docstring'''







			lowerCamelCase__ :      str								=		[[-1] * number_of_cells]  # Create a highway without any car
			lowerCamelCase__ :      int								=		0
			lowerCamelCase__ :      str								=		max(UpperCamelCase      ,			0 )
			while i < number_of_cells:
						lowerCamelCase__ :      Tuple								=		(
						    randint(0      ,			UpperCamelCase ) 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				(UpperCamelCase		:      list      ,			UpperCamelCase		:      int )  ->int:



			'''simple docstring'''







			lowerCamelCase__ :      List[str]								=		0
			lowerCamelCase__ :      Dict								=		highway_now[car_index + 1 :]
			for cell in range(len(UpperCamelCase ) ):  # 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(UpperCamelCase      ,			-1 )






def      _A				(UpperCamelCase		:      list      ,			UpperCamelCase		:      float      ,			UpperCamelCase		:      int )  ->list:



			'''simple docstring'''







			lowerCamelCase__ :      Optional[Any]								=		len(UpperCamelCase )
			# Beforce calculations, the highway is empty
			lowerCamelCase__ :      int								=		[-1] * number_of_cells

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






def      _A				(UpperCamelCase		:      list      ,			UpperCamelCase		:      int      ,			UpperCamelCase		:      float      ,			UpperCamelCase		:      int )  ->list:



			'''simple docstring'''







			lowerCamelCase__ :      int								=		len(highway[0] )

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

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

			return highway


if __name__ == "__main__":
				import doctest

				doctest.testmod()








import unittest

from .lib import (
    Matrix,
    Vector,
    axpy,
    square_zero_matrix,
    unit_basis_vector,
    zero_vector,
)
class 				__A					( unittest.TestCase      ):





			def        _snake_case    (self				):
						lowerCamelCase__ :      List[str]								=		Vector([1, 2, 3]				)
						self.assertEqual(x.component(0				)							,    1				)
						self.assertEqual(x.component(2				)							,    3				)
						lowerCamelCase__ :      str								=		Vector()





			def        _snake_case    (self				):
						lowerCamelCase__ :      Dict								=		Vector([0, 0, 0, 0, 0, 1]				)
						self.assertEqual(str(__magic_name__				)							,    """(0,0,0,0,0,1)"""				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Tuple								=		Vector([1, 2, 3, 4]				)
						self.assertEqual(len(__magic_name__				)							,    4				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Dict								=		Vector([1, 2]				)
						lowerCamelCase__ :      str								=		Vector([1, 2, 3, 4, 5]				)
						lowerCamelCase__ :      int								=		Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]				)
						lowerCamelCase__ :      int								=		Vector([1, -1, 1, -1, 2, -3, 4, -5]				)
						self.assertAlmostEqual(x.euclidean_length()							,    2.2_36							,    3				)
						self.assertAlmostEqual(y.euclidean_length()							,    7.4_16							,    3				)
						self.assertEqual(z.euclidean_length()							,    0				)
						self.assertAlmostEqual(w.euclidean_length()							,    7.6_16							,    3				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      str								=		Vector([1, 2, 3]				)
						lowerCamelCase__ :      Union[str, Any]								=		Vector([1, 1, 1]				)
						self.assertEqual((x + y).component(0				)							,    2				)
						self.assertEqual((x + y).component(1				)							,    3				)
						self.assertEqual((x + y).component(2				)							,    4				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Optional[int]								=		Vector([1, 2, 3]				)
						lowerCamelCase__ :      Any								=		Vector([1, 1, 1]				)
						self.assertEqual((x - y).component(0				)							,    0				)
						self.assertEqual((x - y).component(1				)							,    1				)
						self.assertEqual((x - y).component(2				)							,    2				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Dict								=		Vector([1, 2, 3]				)
						lowerCamelCase__ :      int								=		Vector([2, -1, 4]				)  # for test of dot product
						lowerCamelCase__ :      List[Any]								=		Vector([1, -2, -1]				)
						self.assertEqual(str(x * 3.0				)							,    """(3.0,6.0,9.0)"""				)
						self.assertEqual((a * b)							,    0				)





			def        _snake_case    (self				):
						self.assertEqual(str(zero_vector(10				)				).count("""0"""				)							,    10				)





			def        _snake_case    (self				):
						self.assertEqual(str(unit_basis_vector(3							,    1				)				)							,    """(0,1,0)"""				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Any								=		Vector([1, 2, 3]				)
						lowerCamelCase__ :      str								=		Vector([1, 0, 1]				)
						self.assertEqual(str(axpy(2							,    __magic_name__							,    __magic_name__				)				)							,    """(3,4,7)"""				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Optional[Any]								=		Vector([1, 0, 0, 0, 0, 0]				)
						lowerCamelCase__ :      int								=		x.copy()
						self.assertEqual(str(__magic_name__				)							,    str(__magic_name__				)				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      int								=		Vector([1, 0, 0]				)
						x.change_component(0							,    0				)
						x.change_component(1							,    1				)
						self.assertEqual(str(__magic_name__				)							,    """(0,1,0)"""				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Optional[Any]								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						self.assertEqual("""|1,2,3|\n|2,4,5|\n|6,7,8|\n"""							,    str(__magic_name__				)				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      int								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						lowerCamelCase__ :      int								=		[[-3, -14, -10], [-5, -10, -5], [-2, -1, 0]]
						for x in range(a.height()				):
									for y in range(a.width()				):
												self.assertEqual(minors[x][y]							,    a.minor(__magic_name__							,    __magic_name__				)				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Any								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						lowerCamelCase__ :      Optional[Any]								=		[[-3, 14, -10], [5, -10, 5], [-2, 1, 0]]
						for x in range(a.height()				):
									for y in range(a.width()				):
												self.assertEqual(cofactors[x][y]							,    a.cofactor(__magic_name__							,    __magic_name__				)				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Optional[int]								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						self.assertEqual(-5							,    a.determinant()				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      List[str]								=		Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]							,    3							,    3				)
						lowerCamelCase__ :      Optional[int]								=		Vector([1, 2, 3]				)
						self.assertEqual("""(14,32,50)"""							,    str(a * x				)				)
						self.assertEqual("""|2,4,6|\n|8,10,12|\n|14,16,18|\n"""							,    str(a * 2				)				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      str								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						a.change_component(0							,    2							,    5				)
						self.assertEqual("""|1,2,5|\n|2,4,5|\n|6,7,8|\n"""							,    str(__magic_name__				)				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      List[Any]								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						self.assertEqual(7							,    a.component(2							,    1				)							,    0.01				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      Tuple								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						lowerCamelCase__ :      int								=		Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]							,    3							,    3				)
						self.assertEqual("""|2,4,10|\n|4,8,10|\n|12,14,18|\n"""							,    str(a + b				)				)





			def        _snake_case    (self				):
						lowerCamelCase__ :      str								=		Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]							,    3							,    3				)
						lowerCamelCase__ :      Optional[Any]								=		Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]							,    3							,    3				)
						self.assertEqual("""|0,0,-4|\n|0,0,0|\n|0,0,-2|\n"""							,    str(a - b				)				)





			def        _snake_case    (self				):
						self.assertEqual(
						    """|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n"""							,    str(square_zero_matrix(5				)				)							,    )


if __name__ == "__main__":
				unittest.main()



