Solve Question 13 with matrices

solution_matrix.py

def calculate_pushes(a_x, b_x, a_y, b_y, prize_x, prize_y) -> tuple[int, int]:
    """
    Using matrix multiplication
    if A . [x,y] = [prize_x, prize_y]
    then [x,y] = A^-1 . [prize_x, prize_y[]
    """

    A = np.array([[a_x, b_x], [a_y, b_y]])
    P = np.array([prize_x, prize_y])
    a_pushes, b_pushes = np.linalg.solve(A, P).round().astype(int)

    ## double check integer versions work
    if (a_x*a_pushes + b_x*b_pushes) == prize_x and (a_y*a_pushes + b_y*b_pushes) == prize_y:
        return (a_pushes, b_pushes)
    else:
        return (None, None)