It could overheat and break
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Answer:
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Explanation:
All you know is that an
algorithm is eventually (a lot) faster than an
algorithm, but for any specific value of n, you can't say anything. Indeed, the asymptotic growth of the function doesn't depend on its value on
. This means that if
then for all
, the following function is also
:

So asymptotic notation is completely uninformative regarding the performance of algorithms on specific values of n.
You could say that functions such as
are artificial and never really occur in practice. This is not quite true (you can hard-code some auxiliary information for small n, for example), but even if you consider "natural" functions, asymptotic notation doesn't help you to determine anything other than asymptotic's: consider for example
against
(such examples definitely happen in practice, for example in fast matrix multiplication).
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