Quick-Union with Union-by-Rank (10 marks) In class, we saw the Weighted Quick-Union algorithm, which performs UNION in the following way: make the root of the tree containing less elements the child of the root of the tree containing more elements (with ties resolved arbitrarily). Let's call this version of UNION "Union-by-Weight". We w now look at a similar algorithm, which instead uses a version of UNION we will call "Union-by-Rank". Union-by-Rank proceeds by making the root of the tree of smaller height a child of the root of the tree of greater height (with ties resolved arbitrarily) Let n be the number of vertices. Prove that when using Quick-Union with Union-by Rank, a call to CONNECTED takes time O(log n) in the worst case