$1.$Nadha Skolar read online at $$Geeks for Geeks$$ that $\backslash$Omega $($nlogn$)$ is the supposed lower bound for all comparison$-$based sorting algorithms in the worst case. Skeptical about this claim, Nadha asks his little five$-$year$-$old sister, Stellar, to tackle the problem $($unlike her brother, Stellar is naturally gifted in CS$).$ Using an unusual technique, Stellar devises a comparison$-$based sorting algorithm with a worst$-$case running time of O $($ log $).$ Based on this result, Nadha quickly writes up a research paper claiming the two Skolars have just vanquished the lower$-$bound of nlogn for comparison based$-$sorting. Nadha believes these results are stunning enough that his paper should get published in an upcoming issue of the Journal of the ACM, ensuring him of his long$-$awaited fame.

Is it possible that Nadha and Stellar shattered the glass floor on comparison$-$based sorting algorithms? If so$,$ briefly explain why and how their algorithm can be asymptotically faster than every known comparison$-$based sorting algorithm. If not, assuming Stellar is correct, explain why Nadha$$s enthusiasm for Stellar$$s results is misguided. Be sure to state your reasoning clearly and concisely in no more than a single short paragraph.