There are two main techniques we can adopt to improve the performance of bubble sort. It's important to realize that although both of these strategies improve the overall performance of bubble sort in the average case; in the worst case, the algorithm still has the same poor runtime complexity of O(n²).

The first small enhancement we can make to the original bubble sort is to make use of the fact that a sorted "bubble" is building at the end of the list. With every pass we make, another item is added at the end portion of this bubble. This is the reason why (n - 1) passes are needed.

This is also shown in Figure 2.1. In this diagram, the items shown in the dotted circle are already sorted in the correct place:

We can use this fact so we don't try to sort the elements inside this bubble. We can do this by slightly modifying our Java code, as shown in Snippet 2.3. In the inner loop, instead of processing until the end of the list, we can stop just before the sorted bubble, until numbers.length - i. For brevity, in Snippet 2.3 we have replaced the swap logic with a method as follows:

public void sortImprovement1(int[] numbers) {
  for (int i = 1; i < numbers.length; i++) {
    for (int j = 0; j < numbers.length - i; j++) {
      if (numbers[j] > numbers[j + 1]) {
        swap(numbers, j, j + 1);
      }
    }
  }
}  

If we give a sorted list to our bubble sort algorithm, we will still make multiple passes on it without modifying it. We can further improve the algorithm by cutting short the outer loop when the list inside the array is fully sorted. We can check that the array is sorted by checking if any swaps were done during our last pass. In this manner, if we give our method an already sorted list, we just need to do one pass on the array and leave it untouched. This means that the best case is now O(n), although the worst case stays the same.