Prove by induction that the maximum height of a union-find tree built using the weighted quick-union method is log2n where n is the total number of elements in the tree. hint: let p(j) be the claim that a union-find tree with at most 2jelements built using the weighted quick-union method is at most j. show that p(k)p(k+1) and don’t forget your base case! keep in mind that a tree with one element (just the root) is considered to have a height of 0.