I am not certain I am asking this question correctly, but essentially I have written an algorithm to search a string for any sequential characters or sequences of characters. The algorithm works, but I suspect it can be written more efficiently by someone much smarter than I am.
That being said, I would like to know how to describe the efficiency for the algorithm given the set of results I have shown here. I know the algorithm could be O(N^2) because I have two nested loops but I limit the outer loop by the length of the string divided in half, so its really not that expensive. In the worst-case event that the given string has no sequential matching sequences of characters, here are the number of cycles I am seeing:
I don't need an exact answer here, I just need to be able to give a ball-park estimate of the efficiency.
Thanks for any help offered.
You cannot make a (mathematically) strong argument that the data indicate that your algorithm has such-and-such time complexity, since you will only have a finite amount of data and you could never show the data for arbitrarily large input values.
You can, however, compare your data to some function and make a qualitative argument that it looks like a quadratic. This is not mathematically rigorous, but it might be the answer you're looking for. I can tell you for sure that your function is a quadratic. To find out which one, you might try to compute a quadratic regression over your data and see how close the fit is.