Time complexity 2n^2

Question

I have algorithm that has time complexity of 2n^2, and on some machine it takes x time to execute it. The question is: if my machine is 32 times faster and time stays the same how mutch data will it process?

ty <3

Answer 1

Realistically, this question does not make any sense, because complexity does not determine exact runtime, operations etc.

However, here we don't have big-O notation (asymptotic representation), I will work with the assumption that:

1. This is purely theoretical
2. Changing machines doesn't impact time taken per operation (the change remains same across machines and that is exactly by a factor of 32)

So, lets say you process D, d data points on M1, M2, taking x time

If complexity here represents exact time taken for operations,

2 * D^2 = x = 2 * d^2

Since M2 is 32 times faster,

32 * 2 * D^2 = 2 * d^2
=> d = 4 * D * sqrt(2)