0
$\begingroup$

Between what two common time complexities would you place $n^c lg n, 0<c<1$?

The following table illustrates the common time complexities. Source: wikipedia Source: https://en.wikipedia.org/wiki/Time_complexity#Table_of_common_time_complexities

$\endgroup$
2
$\begingroup$

$O(n^c \log n)$ is above $O(n^c)$ but below $O(n^{c+\varepsilon})$ for any $\varepsilon > 0$. This is true for any $c \geq 0$, including $c < 1$.

For example, $n^{0.5} \log n$ is not in $O(n^{0.5})$ but is in $O(n^{0.500001})$.

This is one of the reasons for the invention of the "soft O" notation $\tilde{O}(n^c)$, defined as the union of $O(n^c (\log n)^d)$ for all $d \geq 0$. Soft O allows you to fudge log factors and focus on the most important part, which is the highest-order polynomial exponent.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.