# Show that the best case time complexity of Quicksort is $\Omega(n \log n)$

I am trying to show that the best case time complexity of Quicksort is $$\Omega(n \log n)$$.

The following recurrence describes the best-case time complexity of Quicksort:

$$T(n) = \min_{0 \le q \le n-1} \left(T(q) + T(n-q-1) \right) + \Theta(n).$$

But I have difficulty in proving that $$T(n) = \Omega(n \log n)$$ using the recurrence above.

So how to solve this recurrence?