Problem 2. (8 points) Show that the total running time of performing n union and find operations in amortized union-find data structure (i.e one using Tar- jans algorithm) is O(n) if all the union operations are performed before all the finds in the sequence of n operations. Hint : Use accounting method where for a Find operation, one cost unit is al- located to Find operation itself and one cost unit is allocated to every element involved in the path compression of Find operation