Sorting n elements in worst case of $\sqrt{n}\log n$
This is impossible. You cannot sort $n$ elements without examining each element at least once, which takes at least $n$ operations.

$n=\sqrt{n}\cdot\sqrt{n}\ge\sqrt{n}\cdot\log{n}$ for all $n&gt;1$, assuming the logarithmic base is at least 2. (Of course, if you assume something completely asinine like $\log_{1.000001}n$, it would be technically possible for some values of $n$.)