Interview 1: For the algorithms question, I first stated the most obvious solution I could think of, which ran in O(nlogn) time. I did NOT code this solution, since it definitely wasn't optimal. The interviewer asked if I could think of a better solution (O(n) time). I asked different questions about the problem, such as: is there enough memory to hold multiple arrays? Are there any restrictions on the entries of the array? Is there a max/min value?
At some point I explained a more generalized version of the intended algorithm, due to an ambiguity in the problem statement that I did not catch--at which point, the interviewer explained that ambiguity, which led me to the more specific correct solution. He asked me to code it up, which took a few minutes, including checking through the code, considering edge cases, and making sure nothing was redundant or off by one.
Interview 2: I'm actually not sure how I made it to round 2, since I said in round 1 that I didn't have any data science experience. This interview went about as well as you'd expect--badly. :/
But hey, experiences, right?