Big O from Timing Ratio

Another method that can often be used to find Big O is to look at the ratio of times as the size of input is doubled. Ratios that are approximately powers of 2 are easily recognized:

Ratio	Power of 2	Big O
2	21	n
2+	21+	n * log(n) ?
4	22	n2
8	23	n3

Example:

n	Time	Ratio
4000	0.01779
8000	0.06901	3.8785
16000	0.27598	3.9991
32000	1.10892	4.0180
64000	4.44222	4.0059

Since the ratio is about 4, this function is O(n²).