Depth-first search can be used to detect whether a graph has any cycles. How would you augment the pseudo-code for depth-first search, given below, to determine if the graph has a cycle? You can assume that the graph is connected.

Depth-first-search

Input: An undirected, connected graph G. A start vertex v1

Output: T, a depth-first search tree.

Add v1 to T. visit(v1)

visit(v)

For every neighbor w of v:

If w is not already in T

visit(w);

Add w and {w, v} to T.

End-for