Question

I’m testing out some functions I made and I am trying to figure out the time complexity.
My problem is that even after reading up on some articles on Big O I can’t figure out what the following should be:

1000 loops : 15000 objects : time 6

1000 loops : 30000 objects : time 9

1000 loops : 60000 objects : time 15

1000 loops : 120000 objects : time 75

The difference between the first 2 is 3 ms, then 6 ms, and then 60, so the time doubles up with each iteration. I know this isn’t O(n), and I think it’s not O(log n).

When I try out different sets of data, the time doesn’t always go up. For example take this sequence (ms): 11-17-26-90-78-173-300

The 78 ms looks out of place. Is this even possible?

Edit:
NVM, I’ll just have to talk this over with my college tutor.
The output of time differs too much with different variables.
Thanks for those who tried to help though!

Answer 1

Big O notation is not about how long it takes exactly for an operation to complete. It is a (very rough) estimation of how various algorithms compare asymptotically with respect to changing input sizes, expressed in generic “steps”. That is “how many steps does my algorithm do for an input of N elements?”.

Having said this, note that in the Big O notation constants are ignored. Therefore a loop over N elements doing 100 calculations at each iteration would be 100 * N but still equal to O(N). Similarly, a loop doing 10000 calculations would still be O(N).

Hence in your example, if you have something like:

for(int i = 0; i < 1000; i++)
   for(int j = 0; j < N; j++)
      // computations

it would be 1000 * N = O(N).

Big O is just a simplified algorithm running time estimation, which basically says that if an algorithm has running time O(N) and another one has O(N^2) then the first one will eventually be faster than the second one for some value of N. This estimation of course does not take into account anything related to the underlying platform like CPU speed, caching, I/O bottlenecks, etc.