How Could One Implement the K-Means++ Algorithm?

Question

I am having trouble fully understanding the K-Means++ algorithm. I am interested exactly how the first k centroids are picked, namely the initialization as the

Answer 1

One Liner.

Say we need to select 2 cluster centers, instead of selecting them all randomly{like we do in simple k means}, we will select the first one randomly, then find the points that are farthest to the first center{These points most probably do not belong to the first cluster center as they are far from it} and assign the second cluster center nearby those far points.