Time Complexity of Simple Algo

Question

I'm trying to figure out the running time of the code below.

If add and trimToSize are both O(n), the interior of the block would run in 2N time, and then since the loop takes N time, the whole program would run in N*(2N) time?... O(n^2)?

ArrayList a = new ArrayList();

for (int i = 0; i< N; i++){
    a.add(i);
    a.trimToSize();
}

Answer 1

Yes. But ArrayList#add is usually O(1) except for the case when the internal storage array has to be increased.

If you want to optimize your code, do it as follows:

ArrayList a = new ArrayList(N); // reserve space for N elements

for (int i = 0; i < N; i++) {
    a.add(i); // O(1)
}

// no need for trimToSize

This now has only O(n) !

Answer 2

You are correct, it would be O(n^2). The for loop executes N times, and like you said, add and trimToSize take O(n) time, so it would be:

N * (N + N) = N * (2N) = 2 * N^2

but the constant factor of 2 does not matter for big-O notation because the n^2 is the dominating part of the function. Therefore, it is O(n^2).