"""simple docstring"""







def     lowercase__( __SCREAMING_SNAKE_CASE							:  Union[str, Any]   ):
     lowercase_			:       int									=			0
     lowercase_			:       str									=			len(__SCREAMING_SNAKE_CASE   )

     for i in range(n - 1   ):
          for j in range(i + 1  ,    __SCREAMING_SNAKE_CASE   ):
               if arr[i] > arr[j]:
                    num_inversions += 1

     return num_inversions



def     lowercase__( __SCREAMING_SNAKE_CASE							:  Union[str, Any]   ):
     if len(__SCREAMING_SNAKE_CASE   ) <= 1:
          return arr, 0
     lowercase_			:       Optional[Any]									=			len(__SCREAMING_SNAKE_CASE   ) // 2
     lowercase_			:       str									=			arr[0:mid]
     lowercase_			:       Tuple									=			arr[mid:]

     lowercase_							,						lowercase_			:       Dict									=			count_inversions_recursive(__SCREAMING_SNAKE_CASE   )
     lowercase_							,						lowercase_			:       List[str]									=			count_inversions_recursive(__SCREAMING_SNAKE_CASE   )
     lowercase_							,						lowercase_			:       List[str]									=			_count_cross_inversions(__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE   )

     lowercase_			:       str									=			inversion_p + inversions_q + cross_inversions
     return c, num_inversions



def     lowercase__( __SCREAMING_SNAKE_CASE							:  str  ,    __SCREAMING_SNAKE_CASE							:  int   ):
     lowercase_			:       List[Any]									=			[]
     lowercase_			:       str									=			0
     while i < len(__SCREAMING_SNAKE_CASE   ) and j < len(__SCREAMING_SNAKE_CASE   ):
          if p[i] > q[j]:
               # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
               # These are all inversions. The claim emerges from the
               # property that P is sorted.
               num_inversion += len(__SCREAMING_SNAKE_CASE   ) - i
               r.append(q[j]   )
               j += 1
          else:
               r.append(p[i]   )
               i += 1

     if i < len(__SCREAMING_SNAKE_CASE   ):
          r.extend(p[i:]   )
     else:
          r.extend(q[j:]   )

     return r, num_inversion



def     lowercase__( ):
     lowercase_			:       int									=			[10, 2, 1, 5, 5, 2, 11]

     # this arr has 8 inversions:
     # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

     lowercase_			:       int									=			count_inversions_bf(__SCREAMING_SNAKE_CASE   )
     lowercase_							,						lowercase_			:       Optional[Any]									=			count_inversions_recursive(__SCREAMING_SNAKE_CASE   )

     assert num_inversions_bf == num_inversions_recursive == 8

     print('number of inversions = '  ,    __SCREAMING_SNAKE_CASE   )

     # testing an array with zero inversion (a sorted arr_1)

     arr_a.sort()
     lowercase_			:       int									=			count_inversions_bf(__SCREAMING_SNAKE_CASE   )
     lowercase_							,						lowercase_			:       int									=			count_inversions_recursive(__SCREAMING_SNAKE_CASE   )

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '  ,    __SCREAMING_SNAKE_CASE   )

     # an empty list should also have zero inversions
     lowercase_			:       str									=			[]
     lowercase_			:       Union[str, Any]									=			count_inversions_bf(__SCREAMING_SNAKE_CASE   )
     lowercase_							,						lowercase_			:       Dict									=			count_inversions_recursive(__SCREAMING_SNAKE_CASE   )

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '  ,    __SCREAMING_SNAKE_CASE   )


if __name__ == "__main__":
       main()


"""simple docstring"""







from random import randint, random



def     lowercase__( __SCREAMING_SNAKE_CASE							:  int  ,    __SCREAMING_SNAKE_CASE							:  int  ,    __SCREAMING_SNAKE_CASE							:  int  ,    __SCREAMING_SNAKE_CASE							:  bool = False  ,    __SCREAMING_SNAKE_CASE							:  bool = False  ,    __SCREAMING_SNAKE_CASE							:  int = 5  ,    ):
     lowercase_			:       Union[str, Any]									=			[[-1] * number_of_cells]  # Create a highway without any car
     lowercase_			:       str									=			0
     lowercase_			:       List[Any]									=			max(__SCREAMING_SNAKE_CASE  ,    0   )
     while i < number_of_cells:
          lowercase_			:       Union[str, Any]									=			(
              randint(0  ,    __SCREAMING_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     lowercase__( __SCREAMING_SNAKE_CASE							:  list  ,    __SCREAMING_SNAKE_CASE							:  int   ):
     lowercase_			:       Union[str, Any]									=			0
     lowercase_			:       Dict									=			highway_now[car_index + 1 :]
     for cell in range(len(__SCREAMING_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(__SCREAMING_SNAKE_CASE  ,    -1   )



def     lowercase__( __SCREAMING_SNAKE_CASE							:  list  ,    __SCREAMING_SNAKE_CASE							:  float  ,    __SCREAMING_SNAKE_CASE							:  int   ):
     lowercase_			:       List[Any]									=			len(__SCREAMING_SNAKE_CASE   )
     # Beforce calculations, the highway is empty
     lowercase_			:       Dict									=			[-1] * number_of_cells

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



def     lowercase__( __SCREAMING_SNAKE_CASE							:  list  ,    __SCREAMING_SNAKE_CASE							:  int  ,    __SCREAMING_SNAKE_CASE							:  float  ,    __SCREAMING_SNAKE_CASE							:  int   ):
     lowercase_			:       Union[str, Any]									=			len(highway[0]   )

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

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

     return highway


if __name__ == "__main__":
       import doctest

       doctest.testmod()

