No. I knew nothing about computer science when I got that interview. I had programmed (self-taught) but knew nothing of Big O and had never heard of Dijkstra or the Dutch National Flag problem.
These questions were less about testing my knowledge more about testing my ability to figure stuff out. The latter is highly prized in my experience by Oxford.
Yes I went up to Oxford in 1983 to read Natural Science and although I was mad on computers that meant simply that I had done some z80 and BASIC programming and read a few books on e.g. PL/1 programming and AI (i.e. lisp) from the local library. There was no internet then :-)