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

Transcribed Image Text:

4.1.5 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 undirected graph G //Output: 1 (true) if G is connected and 0 (false) if it is not if n = 1 return 1 //one-vertex graph is connected by definition else if not Connected (A[0..n-2, 0..n-2]) return 0 else for j +0 ton - 2 do if A[n 1, j] return 1 return 0 Does this algorithm work correctly for every undirected graph with n > o vertices? If you answer yes, indicate the algorithm's efficiency class in the worst case; if you answer no, explain why. 4.1.5 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 undirected graph G //Output: 1 (true) if G is connected and 0 (false) if it is not if n = 1 return 1 //one-vertex graph is connected by definition else if not Connected (A[0..n-2, 0..n-2]) return 0 else for j +0 ton - 2 do if A[n 1, j] return 1 return 0 Does this algorithm work correctly for every undirected graph with n > o vertices? If you answer yes, indicate the algorithm's efficiency class in the worst case; if you answer no, explain why.