We would like to clusters the numbers from 1 to 1024 using hierarchical clustering. We will use Euclidian distance as our distance measure. We break ties by combining the two clusters in which the lowest number resides. For example, if the distance between clusters A and B is the same as the distance between clusters C and D we would chose A and B as the next two clusters to combine if min{A,B} < min{C,D} where {A,B} are the set of numbers assigned to A and B.

We would like to compare the results of the three linkage methods discussed in class for this dataset. For each of the three methods, specify the number of elements ( numbers) assigned to each of the two clusters defined by the root (that is, what are the sizes of the two clusters if we cut the hierarchical clustering tree at the root or in other words what are the sizes of the last two clusters that we combine)