How to optimally solve the flood fill puzzle?

Question

I like playing the puzzle game Flood-It, which can be played online at:

https://www.lemoda.net/javascript/flood-it/game.html

It\'s also available as an iGoog

Answer 1

A naive 'greedy' algorithm is to pick the next step that maximizes the overall perimeter of the main region.

(A couple of smart friends of mine were thinking about this the other day and decided the optimium may be NP-hard (e.g. you must brute force it) - I do not know if they're correct (wasn't around to hear the reasoning and haven't thought through it myself).)

Note that for computing steps, I presume the union-find algorithm is your friend, it makes computing 'one step' very fast (see e.g. this blog post).