When I interviewed at Google in 2015 I was asked a Depth-first search question. I couldn't believe it! I actually giggled about it - but not in a condescending way - I had just read an article that stated flatly "if you interview at Google, you better know your binary tree algorithms" and boom! There it was.
The question had to do with lines of succession in a royal family tree and it was a lot of fun to work through it. Believe it or not I enjoyed it and the interviewer seemed to be happy with my answer!
Another super popular interview is question is about balancing a binary tree. You usually find these questions in the screening phase - they're considered a little easier to deal with than the more complex questions we'll tackle later on.
To balance a binary tree you'll need to know how to efficiently traverse it - that's where depth-first and it's couterpart breadth-first search come in.