In my experience teaching 1st year undergrad algorithms, I'd be surprised if the average 1st year student that has just passed an "Introduction to algorithms" course would even be able to solve Problem Set 0.
However I don't think we should delay teaching algorithms until several years into the CS university curriculum. It's too important and central a topic to miss out on. We really need an intro algorithms curriculum that can teach both the basics (as in Problem Set 0) and the algorithms and data structures in the textbook.
[1] https://ocw.mit.edu/courses/6-006-introduction-to-algorithms...
[2] https://ocw.mit.edu/courses/6-006-introduction-to-algorithms...