That sounds like a Depth-First-Search[1] (which wasn't included exactly). In DFS you'll go all the way out one way, until you reach the end, and then go back to when you last had a choice, and go out a new way, etc (a bit like the mouse did).
It is worth mentioning though, that this approach probably isn't so good if the map level is very large, since the BFS is way more likely to catch something around the player first.
It is worth mentioning though, that this approach probably isn't so good if the map level is very large, since the BFS is way more likely to catch something around the player first.
[1] http://en.wikipedia.org/wiki/Depth-first_search