As @emory pointed out, it is provably impossible to determine the big-O time complexity of an arbitrary piece of code automatically (the proof is a reduction from the halting problem). However, there are tools that can attempt to measure the complexity of a piece of code empirically by running it on several different inputs. One such tool is described in the paper “Measuring Empirical Computational Complexity” by Goldsmith, Aiken, and Wilkerson. It works by attempting to do a regression on the program’s runtime versus its input size. The tool, called trend-prof, has been discontinued, but is archived here for reference.
