What is Big O of a loop?

Question

I was reading about Big O notation. It stated,

The big O of a loop is the number of iterations of the loop into number of statements within the loop.

Here is a code snippet,

for (int i=0 ;i<n; i++)
{
    cout <<"Hello World"<<endl;
    cout <<"Hello SO";
}

Now according to the definition, the Big O should be O(n*2) but it is O(n). Can anyone help me out by explaining why is that?

Answer 1

If you check the definition of the O() notation you will see that (multiplier) constants doesn't matter.

The work to be done within the loop is not 2. There are two statements, for each of them you have to do a couple of machine instructions, maybe it's 50, or 78, or whatever, but this is completely irrelevant for the asymptotic complexity calculations because they are all constants. It doesn't depend on n. It's just O(1).

O(1) = O(2) = O(c) where c is a constant.
O(n) = O(3n) = O(cn)