Quick sort analysis confusion
Will the randomized Quick sort will have same runtime in terms of big O for A1, A2, A2


Statements like this do not make any sense. For any given input, any algorithm has running time O(1).

Note that Landau notation (here) inherently contains a "for size to infinity" clause. Therefore, it makes only sense for infinite input sets.

Then, yes, the result depends a lot on the input sequences you consider. If you average over all inputs, you get $\Theta(n \log n)$. If you average over all worst-case inputs, you get $\Theta(n^2)$.