My question arises from the post "Plain English Explanation of Big O". I don't know the exact meaning for logarithmic complexity. I know that I can make a regression between the time and the number of operations and calculate the X-squared value, and determine so the complexity. However, I want to know a method to determine it quickly on paper.
How do you determine logarithmic complexity? Are there some good benchmarks?
Not sure if this is what you mean, but... logarithmic complexity usually arises when you're working with a spread-out data structure like a balanced binary tree, which contains 1 node at the root, 2 children, 4 grandchildren, 8 great-grandchildren, etc. Basically at each level the number of nodes gets multiplied by some factor (2) but still only one of those is involved in the iteration. Or as another example, a loop in which the index doubles at each step:
for (int i = 1; i < N; i *= 2) { ... }
Things like that are the signatures of logarithmic complexity.