Earlier quoted context omitted.
Not sure if that's really relevant. Unless you are applying for a job where time is money stock trading or some such I don't see how knowing a method you are writing is O(log N) rather then O(N2) is useful. Its something to keep in mind sure, but I would rather have the slower method integrated into the code base faster. Yes performance is a feature but realistically you can get away with some fairly awfully performi…
Knowing the time complexity a given function you write is generally not important. However, the skill to analyze the complexity is an important one to have, because when performance issues to come up, it is often a very powerful tool to have.
If they can tell you in Big O notation why its bad for large inputs then great, but so long as they can tell you why that's what really matters.