I am curious though, what were the more mechanical aspects of how you made that transition? Did you have a plan to practice algorithms in a certain way and then wait till you were contacted by the right recruiter? How did you go about it? Did you more simply just try and do 1 problem a day and then build that up, or did you find useful projects to apply more obscure algorithms to, that might be more interesting and motivating?
As far as interviews go, I think I tend to interview pretty well when it comes to social skills. Problem solving is tough. I had to do a lot of whiteboard practicing. I probably over practiced this part because, in my experience, you're not really writing tons of code on the whiteboard. Yes, you need to write some, but it's typically short snippets or pseudocode.
I remember telling my interviewers that I didn't think I was a good fit for the job. It seemed more 'CS' than I could handle. I don't know why they went with me. I know the company was rapidly growing at the time so I probably just got lucky. Not what you want to hear, I know.