add implementation of Nagel and Schrekenberg algo (TheAlgorithms#5584)

* add implementation of Nagel and Schrekenberg algo

* Update cellular_automata/nasch.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update nasch.py

* Update and rename nasch.py to nagel_schrekenberg.py

* Update cellular_automata/nagel_schrekenberg.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update nagel_schrekenberg.py

* Update nagel_schrekenberg.py

* Update nagel_schrekenberg.py

* update nagel_schrekenberg.py

* Update nagel_schrekenberg.py

Co-authored-by: Christian Clauss <cclauss@me.com>

Author: Leoriem-code

cellular_automata/nagel_schrekenberg.py

@@ -0,0 +1,140 @@
+"""
+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()