Solution

The difference between Quicksort and Randomized Quicksort lies mainly in the way the pivot element is chosen. Let’s analyze each option:

1. Selection of Pivot element ✅

   • Quicksort: Pivot is chosen deterministically (e.g., always first element, last element, or middle element).

   • Randomized Quicksort: Pivot is chosen randomly (uniformly among available elements).
     → This is the key difference.

2. Worst case time complexity ❌

   • For both, the worst case is still O(n²).

   • Randomization only reduces the chance of hitting the worst case often, but it does not eliminate it.

3. Best case time Complexity ❌

   • Both have the same best case: O(n log n) (when pivot splits the array evenly).

   • Randomization doesn’t change the best case.

4. Final Output ❌

   • Both produce the same sorted output.

   • Randomization only affects the process, not the final result.