How to solve the recurrence equation $T(n)=2T(n/2) + n \lg n$
For ex: I implemented "Counting inversions" with a full mergesort instead of just using merge part, So the outer complexity will be $n \lg n$.
Also, What is the $O$(complexity) of above ?
Introduction to Algorithms, 3rd edition (p.95) has an example of how to solve the a similar recurrence $T(n)= 3T\left(\frac{n}{4}\right) + n \log(n)$ using master theorem by showing $f(n)$ is polynomially larger than $n^{\log_b a}$. But I am not sure about this one.
