def doubling_algorithm(points, k): centers = [] radius = 0 while True: for point in points: # Check if point is within 2*radius of any center if not any(is_within_distance_2r(center, point, radius) for center in centers): centers.append(point) if len(centers) > k: # Double the radius and restart with empty centers radius *= 2 centers = [] break else: # Exit loop if we didn't hit the break (meaning we have <= k centers) break return centers, radius def is_within_distance_2r(center, point, radius): return distance(center, point) <= 2 * radius def distance(p1, p2): # Implement the distance function based on your data pass