You are given an undirected graph G=(V,E). We say that a subgraph G= (V,E),EE,VV is a connected component of G if every vertex vi V,vi=vj, is a) connected to every other vertex vjV in the same subgraph by at least one path, b) disconnected from all vertices vkVV outside of the subgraph. We say that a connected component G is a tree if every two vertices vi,vjV are connected by exactly one path. Equivalently, G is a tree if it contains no cycles. For example, the graph below has three connected components, of which only one is a tree. Devise an algorithm that computes how many connected components in G are trees. Prove its correctness. Your algorithm should run in (amortized) O(V+ E+E(V)) time, where (n) is the inverse Ackermann function. Note that the V+E term in the runtime is simply the time that we need to read the input. Hint: Use the data structure for disjoint sets that we have studied. Specifically use the variant with union-by-rank with path compression that has efficient implementation (you don't have to know exactly how union-by-rank with path compression exactly work to use it, just employ Theorem 21.14 from the slides or from CLRS)