Consider the following algorithm to check connectivity of a graph defined by its adjacency matrix.

Does this algorithm work correctly for every undirected graph with n > 0 vertices?

If yes, indicate the algorithm's efficiency class in the worst case: if no, explain why.

ALGORITHM Connected(0..n-1, 0..n-1]) //Input: Adjacency matrix A[0.n - 1, 0..n - 1] of an undirected graph G //Output: 1 (true) if G is connected and 0 (false) if it is not if n = l return l //one-vertex graph is connected by definition else if not Connected(AIO.n-2, 0..n-2) return 0 else for j 0 to n-2 do if Aln 1, j]return 1 return 0