I'm trying to understand the approach to calculating an answer to the following question.
I need to do some processing on a list of n items. I know that the total processing time takes $\log_2 (n)$ milliseconds.
Problem: What is the maximum number of items that can be processed in $10$ seconds (i.e., $10,000$ milliseconds) ?
What is the right general approach / technique? I should mention that I am a math neophyte.
It's clear that if I have a list of $1,000,000$ items it will take $13.8$ milliseconds, as $\log_2(1000000) = 13.8$.
What's not clear is how to compute the maximum n that can be processed in $10,0000$ milliseconds. I know it's a gigantic number, but I am not sure how to calculate it. If the number was small I could probably find it by trial and error, but:
A) It's a giant number such that trial and error seems impractical.
B) Even if it was not so huge, I'd really like to understand how to compute it deterministically rather than by experiment.
Thanks very much for any pointers.