

from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403



def   __UpperCAmelCase					(      __a :     Optional[int]						,__a :     int						,__a :     List[Any] = "x"						,__a :     Dict = 10**-10						,__a :     Tuple = 1						,)     ->	List[Any]:

					"""simple docstring"""

					_a      :       Union[str, Any]   =						symbols(snake_case__      )
					_a      :       List[str]   =						lambdify(snake_case__						,snake_case__      )
					_a      :       Dict   =						lambdify(snake_case__						,diff(snake_case__						,snake_case__      )      )

					_a      :       List[Any]   =						starting_point

					while True:
										if diff_function(snake_case__      ) != 0:
															_a      :       Dict   =						prev_guess - multiplicity * func(snake_case__      ) / diff_function(
															    snake_case__      )
										else:
															raise ZeroDivisionError('''Could not find root'''      ) from None

										# Precision is checked by comparing the difference of consecutive guesses
										if abs(next_guess - prev_guess      ) < precision:
															return next_guess

										_a      :       Union[str, Any]   =						next_guess


# Let's Execute
if __name__ == "__main__":
			# Find root of trigonometric function
			# Find value of pi
			print(f'''The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}''')

			# Find root of polynomial
			# Find fourth Root of 5
			print(f'''The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5J)}''')

			# Find value of e
			print(
			    '''The root of log(y) - 1 = 0 is ''',
			    f'''{newton_raphson("log(y) - 1", 2, variable="y")}''',
			)

			# Exponential Roots
			print(
			    '''The root of exp(x) - 1 = 0 is''',
			    f'''{newton_raphson("exp(x) - 1", 10, precision=0.005)}''',
			)

			# Find root of cos(x)
			print(f'''The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}''')





'''simple docstring'''




from random import randint, random







def 						lowerCAmelCase_							(  snake_case__						,							snake_case__						,							snake_case__						,							snake_case__ = False						,							snake_case__ = False						,							snake_case__ = 5						,							):




    '''simple docstring'''



    A			:  List[str]   =		[[-1] * number_of_cells]  # Create a highway without any car
    A			:  Optional[Any]   =		0
    A			:  Tuple   =		max(snake_case__						,							0		)
    while i < number_of_cells:
        A			:  Optional[int]   =		(
            randint(0						,							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 						lowerCAmelCase_							(  snake_case__						,							snake_case__		):




    '''simple docstring'''



    A			:  Dict   =		0
    A			:  str   =		highway_now[car_index + 1 :]
    for cell in range(len(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(snake_case__						,							-1		)







def 						lowerCAmelCase_							(  snake_case__						,							snake_case__						,							snake_case__		):




    '''simple docstring'''



    A			:  int   =		len(snake_case__		)
    # Beforce calculations, the highway is empty
    A			:  int   =		[-1] * number_of_cells

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







def 						lowerCAmelCase_							(  snake_case__						,							snake_case__						,							snake_case__						,							snake_case__		):




    '''simple docstring'''



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

    for i in range(snake_case__		):
        A			:  int   =		update(highway[i]						,							snake_case__						,							snake_case__		)
        A			:  Any   =		[-1] * number_of_cells

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

    return highway


if __name__ == "__main__":
      import doctest

      doctest.testmod()




