I had almost exactly this same engineering test when google interviewed me in 2006. It was terrible, and left a bad taste in my mouth. Given the complexity of the work I was doing at the time, the entire thing seemed ridiculous.
replies(2):
I had the same a couple of years ago, at the time I was a Rails developer at a small startup. The first screening they asked me some basic technical questions (I guess it was a recruiter), then the second screening they asked me to walk through some data structures and algorithms off the top of my head.
I knew they would do this, and hadn't looked at any CS algorithms since university, so got a copy of Programming Pearls and studied through that every evening for the week before. I picked a few that I hoped would come up, and it turned out that's what they asked for. I think first a linked list (maybe doubly linked?) and then a tree sort.
I surprisingly passed, but the attitude of the interviewer really put me off. He said he knew Python, Java and Go - none of which I had used - and wasn't too happy when I said I wanted to use Ruby (which the first guy I spoke to, said was fine). Then throughout the interview it seemed very much like he was fighting against me and trying to prove me wrong.
After that I couldn't be bothered any more, I didn't really want a job at Google, it's just a recruiter contacted me and I decided to try it out. I guess this style of interviewing must work for Google, but it's just not the way I like a company to introduce itself to me. It just seems like they are approaching it with so much ego, as if I would be privileged to work there, but to me a job should be mutually beneficial.