Using tree implementation of disjoint sets: (a) Describe a sequence of make-set and union operations that builds a tree such that the longest path has length 3 (3 edges on the path). Use the fewest number of elements possible and draw the resulting tree. (b) In general, what is the min number of nodes needed for the longest path length to be k? (c) What is the max number of nodes possible in a tree for the longest path length Using tree implementation of disjoint sets: (a) Describe a sequence of make-set and union operations that builds a tree such that the longest path has length 3 (3 edges on the path). Use the fewest number of elements possible and draw the resulting tree. (b) In general, what is the min number of nodes needed for the longest path length to be k? (c) What is the max number of nodes possible in a tree for the longest path length