1. Show the result of the following sequence of instructions: union(1,2), union(3,4), union(3,5), union(1,7), union(3,6), union(8,9), union(1,8), union(3,10), union (3,11), union(3,12), union(3,13), union(14,15), union(16,0), union(14,16), union (1,3), union(1, 14) when the unions are
a. performed arbitrarily
b. performed by height
c. performed by size
4. For each of the trees in the previous exercise, perform a find with path compression on the deepest node.
3. Write a program to determine the effects of path compression and the various unioning strategies. Your program should process a long sequence of equivalence operations using all six of the possible strategies.