runtime to a BFS flood-fill with multiple centres?
Suppose there are n pixels on the screen.

We add the neighbours onto the queue only if they haven't yet been processed.

This way a pixel is added onto the colouring queue only if it hasn't been coloured yet.

Thus a pixel can be added onto the queue for a maximum of 1 time.

So if there are n pixels, then at most n additions would be done to the queue and thus n operations would be needed to colour the entire display.

It doesn't matter if number of centres are increased or decreased since each pixel would need to be added onto the queue at most once.

Thus the complexity would remain O(n) in both the cases.

Sources that claim the complexity to be O(4^n) are considering a brute force approach where we don't remember the pixels we have already coloured and end up colouring it over and over again.