What is the time complexity of the bubble sort algorithm?

The bubble sort algorithm has a time complexity:

• In the worst and average case: O(n²), where n is the number of elements in the array.
• In the best case (if the array is already sorted): O(n), thanks to an optimization with a flag that stops the sorting if no swaps were made during a pass.

Example in Java:

void bubbleSort(int[] arr) {
    int n = arr.length;
    boolean swapped;
    for (int i = 0; i < n - 1; i++) {
        swapped = false;
        for (int j = 0; j < n - i - 1; j++) {
            if (arr[j] > arr[j + 1]) {
                int temp = arr[j];
                arr[j] = arr[j + 1];
                arr[j + 1] = temp;
                swapped = true;
            }
        }
        if (!swapped) break; // array is already sorted
    }
}