Sorting arrays (Bubble Sort)

Question

I have a small doubt while sorting arrays and yeah I am new to programming. Take a look at this code for example:

public void bubbleSort(int[] array) {
boolean swapped = true;
int j = 0;
int tmp;
while (swapped) {
    swapped = false;
    j++;
    for (int i = 0; i < array.length - j; i++) {
        if (array[i] > array[i + 1]) {
            tmp = array[i];
            array[i] = array[i + 1];
            array[i + 1] = tmp;
            swapped = true;
        }
    }
}

In the above code, why do we have to use j++ and i < (array.length-j) as the test expression? We could have rather used i < (array.length) as the test expression while omitting the variable j . Any answers?

Answer 1

"Why do we have to use j++ and i < (array.length-j) as the test expression?"

The reason behind is at any time elements array[ array.length -j ] to array[array.length - 1] are already sorted.

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Example: Say you have array of length n .

So after the first iteration the biggest element will be placed at array[n - 1] .
So because the largest element is already sorted on the next iteration we will only sort array of length n - 1 .

After the second iteration the second biggest element will be placed at array[ n - 2] .

So because the 1st largest and 2nd largest elements are already sorted on the next iteration we will only sort array of length n - 2 , and so on...

The running time of the algorithm will be which is

As you said it we could have used i < (array.length - 1) but we will be just doing a lot of work for nothing. If we do this the running time will be (n n) which is O(n n). But though the running time is still O(n*n) but it is obvious that is smaller than , hence the first one is efficient.