Question about Problem F: Posterize

My question is, can we solve this problem using algorithms like k-means or something? After all, all we're trying to do is minimize the error for each pixel with respect to the nearest cluster/value out of the K values, right? this idea hit me first before the straightforward dynamic programming solution which passes nicely here link, but when I tried this solution link I got WA on test #9 and I have no idea if the error is from my implementation or that the algorithm doesn't even fit here, in which case I'd very much like to know explicitly why?

Thanks in advance.