How dominant term helps determine time complexity using Big-O?

algorithm, big-o

Solution

The dominant term is the term the one that gets biggest (i.e. dominates) as N gets bigger.

For example:

 N(100N + 200N^3) + N^3

can be rewritten as

 (100 * N^2) + (200 * N^4) + N^3

and as N gets very large, the N^4 is going to get biggest (irrespective of the 200 that you multiply it by).

So that would be O(N^4).

Problem

I don't quite understand the concept of dominant terms and how to determine the time complexity using big o. Like, for example, the dominant term of N(100N + 200N^3) + N^3. If anyone could explain it, that would be very helpful.

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