Advantage to depth first search:

It just looks like it will be a long period it finds 'DAN' until. This highlights an important drawback for depth first search. It can regularly go deep down paths for which we have no solutions, when there may be we get any solution much higher ups the tree, although on a different branch. Also, depth for first search is not, in generally, may be complete. 

Rather than basically adding the next agenda item directly needs to the top of the agenda, it might be a superior idea to make sure that every node in the tree is fully expanded before moving on to the next depth in the search. This is other kind of depth first search which the Russell and Norvig explain in their rules and regulation. For our DNA example we see that, if we did this, the search tree would like this: 

And the big advantage to depth first search is just that it requires very much less memory to operate and control than breadth first search. If we just count the number of 'alive' nodes in the figure above, it amounts to only 4, just because the ones on them in the bottom row are not to be expanded due to the depth edge. However, it can be shown that if there an agent wants to search for all solutions then up to a depth of d in a space with branching factor b, and in a depth first search its only needs to remember up to a more maximum of b*d states at any one time easily. 

To put this in the perspective, if there our professor wanted to search for all names up to length 8, she would only have to remember that 3 * 8 = 24 for different strings to complete the procedure a depth first search is rather than 2187 in a breadth first search.