# Questions about a k-means variant : recompute centroids after each point is reasigned

I have a variant of k-means, where the points are reassigned incrementally and I have a few questions about it.

Each time we reassign a point (we move the point from cluster $$C_1$$to $$C_2$$), we recompute both the centroids of $$C_1$$and $$C_2$$. The centroid of a cluster $$C$$ is computed as the mean of the points in $$C$$.

1) Why does it produces k non-empty clusters ?

2) Can you find an exemple where a different order of processing the input points gives different clusterings ?