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

Smashery's answer can be slightly tweaked. For the total number of moves estimate, if there are 'k' colors at maximum distance, add 'k-1' to the number of moves estimate.

More generally, for each color, consider the maximum distance at which the color can be cleared. This gives us a dictionary mapping some maximum distances to a non-zero number of colors that can be cleared at that distance. Sum value-1 across the keys and add this to the maximum distance to get a number of moves estimate.

Also, there are certain free cases. If at any point we can clear a color in one move, we can take that move without considering the other moves.