Assume that you are using union by rank and FIND with path compression. Also assume that we start out with 10 singleton sets from the first 10 positive integers (1, 2, , 10). Show the disjoint sets (use disjoint-set forest representation; draw the trees) after each of the following operations [when there is a tie (of rank), use the root of the second forest as the new root]:

union(1, 2); union(3, 4); union(5, 6); union(7, 8); union(9, 10);

link(2, 4); link(6, 8);

union(10, 5); union(1, 10)

Note: Use the rank definition from the lecture slides.

Definition from lecture slides:

rank: Upper bound on height of the tree: <= floor(log2 (# of nodes in tree)) if union by rank.