2. Assume a union-find data structure with the following initial setting: 10 Assume that the following operations (in that order from left to right) are applied on the initial setting union(1, 2), union(3, 4), union(4, 5), unio(6, 8), union(5, 8), unio( 6), union(7, 9), union (1e, 11), union(11, union(1, 11). Show the sequence of union-find data structures that result from applying the above-mentioned sequence of operations. Answer this question for each of the three following parts separately: (a) The unions are performed by height (same as union-by-rank) and finds are simple. (b) The unions are performed by size and finds are simple (c) he unions are performed by height and finds use path compression. Note: There could be more than one correct answer sequence for each part. You just need to give one