Let $0 < a < 0.5$ be some constant. We have an $n$-element array as input. Randomized quicksort chooses one element from array uniformly at random as a pivot and partitions. With probability $1-2a$ the smallest section be greater than $an$.How we can Calculate this probability?after 72 hours try i reach to following that means valid area is (1-a)n-an=n(1-2a). by dividing n(1-2a)/ n we get 1-2a.
Probability bounds on size of smaller partition in randomized quicksort
algorithms;sorting;probability theory;probabilistic algorithms;quicksort