Performance analysis of 3 digits sum I have a method that finds 3 numbers in an array that add up to a desired number.

public static void threeSum(int[] arr, int sum) {
    quicksort(arr, 0, arr.length - 1);
    for (int i = 0; i &lt; arr.length - 2; i++) {
        for (int j = 1; j &lt; arr.length - 1; j++) {
            for (int k = arr.length - 1; k &gt; 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(n2) or O(n2logn). But these are complete guesses. I can't prove this. Could someone help me wrap my head around this?
The running time is O(n3).  You have three nested loops:


Approximately n iterations of i
For each i, approximately n iterations of j
For each (i, j) pair, up to about n iterations of k.  On average, it take just 0.5 * n iterations of k, but the constant factor doesn't matter.


Quicksort is generally O(n log n).  So the total is O(n log n + 0.5 n × n × n), which is O(n3).

Since you took the trouble to sort the array, the innermost loop could be replaced by a binary search, which is O(log n).  Therefore, an improved algorithm could work in O(n2 log n).