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 Big O
2 n
2+ n * log(n) ?
4 n2
8 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).

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