Quick sort analysis confusion Is randomized quick sort runtime is independent of the sequence of input? but depends on the numbers in the input?

Let say A1 = [1,2,3,4,5] , A2 = [5,2,3,4,1] A3 = [5,4,3,2,1] , Will the randomized Quick sort will have same runtime in terms of big O for A1, A2, A2

but for B1 = [1,2,3,4,5] B2 = [11,12,13,14,15] will have different runtime i.e. depends on the digits in the input?
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 $\Theta(n^2)$.