In the interview format it is most certainly not possible. It is a dance where both sides pretend that the interviewee is going to invent, in ~30 minutes, under intense interview stress, on a whiteboard, some algorithm that took usually years of research to originally develop.

If that were even remotely possible, why isn't that person cranking out multiple novel algorithm research papers per day? They should be outpublishing Knuth, for sure.

So, no. The only road is to memorize extensively and practice acting skills on the delivery.

Most leetcode problems I have seen are not research problem statements and usually require applying one or two algorithms taught in any CS program. So I have to disagree.

EDIT: Obviously even some of the most elementary Algo 101 problems were research questions at some point, and led to published papers, but that's the reason people write textbooks and use them in college, so newcomers don't have to redo the foundational work.