(16 pts) This problem is related to disjoint set operations. Assume that we are using union by rank and find with path compression. Suppose that you are given a disjoint set structure described by the following array representation.

i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10| 11| 12| 13| 14| 15| 16|

A |-3 | 9 | 9 | 3 | 9 | 5 | 5 | 7 |-3 | 1 | 1 | 11| 1 | 13| 13| 15|

(a) Draw the tree structure(view) of the given disjoint sets.

(b) Write the resulting array representation of the disjoint set structure after applying union(2, 10) to the given disjoint set structure.

(c) Write the resulting array representation of the disjoint set structure after applying union(8, 14) to the given disjoint set structure (not the one after your operation).

(d) Assume that you are dealing with n elements and m disjoint set operations including n make-set operations. Use asymptotic notation to denote the total time complexity of these m operations if union is by rank and find is with path compression.

Please don't copy the answer from another post. Any help is much appreciated!