Programmatically obtaining Big-O efficiency of code

Question

I wonder whether there is any automatic way of determining (at least roughly) the Big-O time complexity of a given function?

If I graphed an O(n) function vs. an O(n

Answer 1

As others have said, this is theoretically impossible. But in practice, you can make an educated guess as to whether a function is O(n) or O(n^2), as long as you don't mind being wrong sometimes.

First time the algorithm, running it on input of various n. Plot the points on a log-log graph. Draw the best-fit line through the points. If the line fits all the points well, then the data suggests that the algorithm is O(n^k), where k is the slope of the line.

I am not a statistician. You should take all this with a grain of salt. But I have actually done this in the context of automated testing for performance regressions. The patch here contains some JS code for it.