Question

I have a few questions so please bear with me. I need some help to clarify Big O and run time. As I understand it Big O is a way of presenting the run time of an algorithm correct? From reading I’ve been trying to figure out how to calculate the Big O of an algorithm. So far I’ve figured out that something like this has a Big O of O(N^2)

for(i = 0; i < N, i++)
    for(j = 0; j < N; j++)
      //code

But what happens if it is this:

for(i = 0; i < N, i++)
    for(j = 0; j < M; j++)
      //code

Where N isnt always equal to M.

Also what is the Big O if you have two of these added together?

for(i = 0; i < N, i++)
    for(j = 0; j < N; j++)
      //code
for(i = 0; i < N, i++)
    for(j = 0; j < N; j++)
      //code

Is the big O equal to N^2 + N^2 = 2N^2?

Answer 1

Where N isnt always equal to M.

Then it is O(NM), unless M is dependent on N or vice versa. If they are independent, then it is also true to say that it is O(N) and O(M).

Is the big O equal to N^2 + N^2 = 2N^2?

O(2N^2) is equivalent to O(N^2).