Consider the following algorithm to check connectivity of a graph defined by its adjacency matrix. ALGORITHM Connected(A[0..n - 1, 0..n - 1]) //Input: Adjacency matrix A[0..n - 1, 0..n - 1]) of an un //Output: 1 (true) if G is connected and 0 (false) if it is n if n = 1 return 1//one-vertex graph is connected by def else if not Connected(A[0..n - 2, 0..n - 2]) return 0 else for j leftarrow 0 to n - 2do if A[n - 1, j] return1 return 0 Does this algorithm work correctly for every undirected graph with n > 0 vertices? If you answer yes, indicate the algorithm's efficiency class in the worst case: if you answer no, explain why