In case of merge sort with unequal balance, where at each step we divide the array into $\sqrt{n}$ and $n-\sqrt{n}$, then find the time complexity in this case.
Time complexity is defined as $$T(n) = T(\sqrt{n}) + T(n-\sqrt{n}) + O(n)$$ which can be written as $$f(n) = f(\sqrt{n})+f(n-\sqrt{n})+cn$$. I have solved such problems before like where we have $\frac{n}{b}$ in place of $\sqrt{n}$ but I have no idea how many tree levels it will have in this case. Please help!