Question

Hi I am using the following generic bubble sort algorithm and I would like to display the time complexity. I understand that the best/worst case for this algorithm is fixed but I was wondering, can it be specific for my array?

For example the worst case for this sort is O(n^2), can that be specific for my array?

For example, worst case can be sorting 100 of the 120 elements (thats what i mean by specific for my array).

public static <E extends Comparable<? super E>> void bubbleSort(E[] comparable) {
    boolean changed = false;
    do {
        changed = false;
        for (int a = 0; a < comparable.length - 1; a++) {
            if (comparable[a].compareTo(comparable[a + 1]) > 0) {
                E tmp = comparable[a];
                comparable[a] = comparable[a + 1];
                comparable[a + 1] = tmp;
                changed = true;
            }
        }
    } while (changed);
}

Answer 1

Complexity is an asymptotic property of a function (or an algorithm), and not of an actual execution path. Complexity expresses the relation between input size and computation time (or space requirement). As such, this concept has no meaning when applied to one single, concrete computation.

In other words, you can ask about the complexity of computing f(n) depending on n, but not of computing f(5). The latter is just a number. The former is a function.

What you can do instead is count the actual number of operations. Every time you perform an operation that you want to include (for example “comparisons”), just increment some global counter, and check its value afterwards. (The algorithmic complexity should tell you bounds for the values that this counter may take.)