Take the 2-minute tour ×  Is Big-O notation always reliable?
For example:  Algorithm A: $n * 10^{100} =
\mathcal{O}\left(n\right)$  Algorithm B: $n^{1.001} =
\mathcal{O}\left(n^{1.001}\right)$  According to
Big-$\mathcal{O}$ notation, Algorithm $A$ would be more
efficient, yet for all practical purposes Algorithm $B$ is more
efficient. In a situation like this, wouldn't Big-O notation
fail? Is there a way to avoid such problems?  share|improve this
question The notation is "reliable", in that it denotes a
perfectly consistent, well-defined mathematical idea. It just
doesn't provide the information you would like it to provide. – 
Zev Chonoles May 12 '12 at 20:51 Theoretically $n \times
10^{100}$ is still better than $n^{1.001}$ for large enough $n$.
On the other hand, practical computer science is hardly a part
mathematics. –  Levon Haykazyan May 12 '12 at 20:52 Asymptotic
complexity analysis is seldom about practice. It is, as the name
implies, about asymptotic behaviour of the algorithm. In
practice, howev