"""
Simulate the evolution of a highway with only one road that is a loop.
The highway is divided in cells, each cell can have at most one car in it.
The highway is a loop so when a car comes to one end, it will come out on the other.
Each car is represented by its speed (from 0 to 5).

Some information about speed:
    -1 means that the cell on the highway is empty
    0 to 5 are the speed of the cars with 0 being the lowest and 5 the highest

highway: list[int]  Where every position and speed of every car will be stored
probability         The probability that a driver will slow down
initial_speed       The speed of the cars a the start
frequency           How many cells there are between two cars at the start
max_speed           The maximum speed a car can go to
number_of_cells     How many cell are there in the highway
number_of_update    How many times will the position be updated

More information here: https://en.wikipedia.org/wiki/Nagel%E2%80%93Schreckenberg_model

Examples for doctest:
>>> simulate(construct_highway(6, 3, 0), 2, 0, 2)
[[0, -1, -1, 0, -1, -1], [-1, 1, -1, -1, 1, -1], [-1, -1, 1, -1, -1, 1]]
>>> simulate(construct_highway(5, 2, -2), 3, 0, 2)
[[0, -1, 0, -1, 0], [0, -1, 0, -1, -1], [0, -1, -1, 1, -1], [-1, 1, -1, 0, -1]]
"""
from random import randint, random


def construct_highway(
    number_of_cells: int,
    frequency: int,
    initial_speed: int,
    random_frequency: bool = False,
    random_speed: bool = False,
    max_speed: int = 5,
) -> list:
    """
    Build the highway following the parameters given
    >>> construct_highway(10, 2, 6)
    [[6, -1, 6, -1, 6, -1, 6, -1, 6, -1]]
    >>> construct_highway(10, 10, 2)
    [[2, -1, -1, -1, -1, -1, -1, -1, -1, -1]]
    """

    highway = [[-1] * number_of_cells]  # Create a highway without any car
    i = 0
    if initial_speed < 0:
        initial_speed = 0
    while i < number_of_cells:
        highway[0][i] = (
            randint(0, max_speed) 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 get_distance(highway_now: list, car_index: int) -> int:
    """
    Get the distance between a car (at index car_index) and the next car
    >>> get_distance([6, -1, 6, -1, 6], 2)
    1
    >>> get_distance([2, -1, -1, -1, 3, 1, 0, 1, 3, 2], 0)
    3
    >>> get_distance([-1, -1, -1, -1, 2, -1, -1, -1, 3], -1)
    4
    """

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


def update(highway_now: list, probability: float, max_speed: int) -> list:
    """
    Update the speed of the cars
    >>> update([-1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 3], 0.0, 5)
    [-1, -1, -1, -1, -1, 3, -1, -1, -1, -1, 4]
    >>> update([-1, -1, 2, -1, -1, -1, -1, 3], 0.0, 5)
    [-1, -1, 3, -1, -1, -1, -1, 1]
    """

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

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


def simulate(
    highway: list, number_of_update: int, probability: float, max_speed: int
) -> list:
    """
    The main function, it will simulate the evolution of the highway
    >>> simulate([[-1, 2, -1, -1, -1, 3]], 2, 0.0, 3)
    [[-1, 2, -1, -1, -1, 3], [-1, -1, -1, 2, -1, 0], [1, -1, -1, 0, -1, -1]]
    >>> simulate([[-1, 2, -1, 3]], 4, 0.0, 3)
    [[-1, 2, -1, 3], [-1, 0, -1, 0], [-1, 0, -1, 0], [-1, 0, -1, 0], [-1, 0, -1, 0]]
    """

    number_of_cells = len(highway[0])

    for i in range(number_of_update):
        next_speeds_calculated = update(highway[i], probability, max_speed)
        real_next_speeds = [-1] * number_of_cells

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

    return highway


if __name__ == "__main__":
    import doctest

    doctest.testmod()