Performance analysis of 3 sum

Question

I have a method that finds 3 numbers in an array that add up to a desired number.

code:

public static void threeSum(int[] arr, int sum) {
    quicksort(arr, 0, arr.length - 1);
    for (int i = 0; i < arr.length - 2; i++) {
        for (int j = 1; j < arr.length - 1; j++) {
            for (int k = arr.length - 1; k > j; k--) {
                if ((arr[i] + arr[j] + arr[k]) == sum) {
                    System.out.println(Integer.toString(i) + "+" + Integer.toString(j) + "+" + Integer.toString(k) + "="  + sum);
                }
            }
        }
    }
}

I'm not sure about the big O of this method. I have a hard time wrapping my head around this right now. My guess is O(n^2) or O(n^2logn). But these are complete guesses. I can't prove this. Could someone help me wrap my head around this?

Answer 1

It's an O(n^3) complexity because there are three nested forloops. The inner forloop only runs if k>j so you can think of n^2*(n/2) but in big O notation you can ignore this.