Consider the following set of one-dimensional points: {0.1, 0.2, 0.45, 0.55, 0.8, 0.9}. All the points are located in the range between [0,1]. a) Suppose we apply k-means clustering to obtain three clusters, A, B, and C. If the initial centroids are located at {0, 0.4, 1}, respectively, show the cluster assignments and locations of the centroids after the first three iterations by filling out the following table. (3 points) Cluster assignment of data points 0.10 0.20 0.45 0.55 0.80 0.90 Centroid Locations A B ТС 0.00 0.40 1.00 Iter 0 1 2 3 b) For the dataset given in part (a), is it possible to obtain empty clusters? If possible, what are the values of the initial centroids? If not, state why.