Randomized Quicksort

Why it matters

Randomization avoids worst-case input attacks. Understanding shapes robust sorting.

The architecture

Random pivot from range.

Partition around pivot.

Recurse both sides.

How it works end to end

Random pivot: uniform in range.

Expected comparisons: 2n ln n.

Worst case: exponentially rare.

In-place partition (Lomuto or Hoare).