John has maintained a union-find data structure for a set using trees. The following is the current status of the trees, so that the set is currently partitioned into two subsets: x 2 b d (a) Suppose John is using Union-By-Size strategy to perform union, and the Path- Compression heuristic to perform find. Describe what will happen after (i) union(a,x), and (ii) then find(y). (b) Suppose John is using Union-By-Rank strategy to perform union, and the Path- Compression heuristic to perform find. Suppose the rank of î is 2 and the rank of a is 1. Describe what will happen after (i) union(a,x), and (ii) then find(y). (c) John has maintained another union-find data structure for a set using trees. At this moment, the trees contain k edges in total. Show that if John next performs any n find operations, together with the path compression heuristic, the total time for these find operations is bounded by O(n + k). Y