You don't need randomized pivoting for this, there are deterministic ones like median of median that will also result in a O(nlogn) worst case.
Also note that with a randomized pivoting you _might_ hit a O(n^2) worst case, it's just that it's incredibly rare and cannot be forced by an attacker controlling your input, so for most practical purposes can be ignored.
alt Hacker News
You don't need randomized pivoting for this, there are deterministic ones like median of median that will also result in a O(nlogn) worst case.
Also note that with a randomized pivoting you _might_ hit a O(n^2) worst case, it's just that it's incredibly rare and cannot be forced by an attacker controlling your input, so for most practical purposes can be ignored.