Let be some constant. Consider running the Partition subroutine on an array with no duplicate

elements and with the pivot element chosen uniformly at random $($as in QuickSort and RSelect$).$

What is the probability that, after partitioning, both subarrays $($elements to the left of the pivot, and elements

to the right of the pivot$)$ have size at least alpha $$ times that of the original array?

$$

$2-2$

$1-$

$1-2$