Google Software Engineer New Grad interview questions

I was contacted by a recruiter out of the blue. I had no idea when I applied for the position as the last time i sent out resumes was at least 6 months prior. The recruiter set me up for a phone interview which lasts about 45mins. Ideally they ask two questions one easy and one hard and you are asked to code in Google Doc. After I was done with the phone interview I got a call the immediate next day saying I got selected for On-Site interview at Mountain View. Was pretty excited and set three weeks aside. On-Site there were 5 rounds one of which supposedly does not count. 1. The first one was for the SWE position.One interviewer and one shadow. System design question. Bombed this one. 2. The second one was for SWE and SWET position. A Matrix navigation kind of problem. Did well towards the end, maybe I took too much time. 3. The third one was for SWET, binary AVL Tree based question. I was asked to write code solving a specific problem based on AVL trees, Once I was done with that I was asked to solve for the reverse case of the problem. solved both just in time. 4. The third one had an easy question to start things off and then a tough question. the easy question is just to warm up, the tough one was the proper one. It's essentially reading a tree off of a file. I offered a a couple of solutions before the end of the interview. Towards the end I somehow stumbled towards an optimal one.