Logic or Pseudo code for filling territories?

I have been told that using "flood fill" in games isn't usually done because it's too slow or something like that. So here's my question...

If I'm making a game similar to Risk, where territories on a map are "conquered" by other players and territory shapes are irregular (such as a map of the USA divided by state borders), how do professional programmers recolor a given territory?
closed account (18hRX9L8)
Well that depends on what graphics library you are using.
Allegro 5
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