Quicksort Algorithm not assigning pivot correctly

Question

I watched this fantastic visualization of a quick sort algorithm: http://www.youtube.com/watch?v=Z5nSXTnD1I4

I felt I really understood the principles behind quick sort and, with the help of some guides online, set about creating my own quick sort.
This is what I came up with:

public void quickSort(int[] a, int left, int right) {

    int index = partition(a, left, right);
    if (left < index - 1)
      quickSort(a, left, index);
    if (index < right)
      quickSort(a, index + 1, right);
}

private int partition (int[] a, int left, int right) {
    int i = left - 1;
    int j = right + 1;
    int pivot = a[0];

    while (i < j) {

        i++;

        while (a[i] < pivot)
            i++;

        j--;

        while (a[j] > pivot)
            j--;

        if (i < j)
            swap (a, i, j);
    }
return i;
}   

private void swap (int[] a, int i, int j) {
    int temp = a[i];
    a[i] = a[j];
    a[j] = temp;
}

The values of left and right are the following:

left = 0
right = array size - 1

Unfortunately the output isn't correct. The problem appears to lie in my treatment of the pivot. In the visualization I watched, the instructor physically removed the pivot and left the pointer pointing at nothing. He carried on with the tutorial and when he got to the point where i and j (what I call left and right) both pointed at the same empty spot, he inserted the pivot and carried on.

As I am physically keeping the pivot in place, I am finding it difficult to properly sort it.

In this code, I am working with the input:

4 8 1 6 3 7 2 5

I get the output:

1 3 2 6 8 7 4 5

Once the "4" value (i.e. the pivot) is sorted at the very start of the algorithm, I never resort it, which throws everything off. Additionally, I think there is something wrong with the quickSort method.

Could someone give me a few pointers? Thanks.

Edit: Two edits that were here have been removed as they contained unnecessary and incorrect information. One of them changed the pivot to: (left + right) / 2. This was of course wrong for the reasons explained in the answers below.

Answer 1

I had to get rid of partition, because you need both i and j. It should look like this:

public void quickSort(int[] a, int left, int right) {

    int i = left; // Was -1 
    int j = right; // Was +1
    int pivot = a[left + (right - left) / 2]; // Pivot is the value of the middle index, not the index itself
    while (i <= j) { // Changed terminating condition
        //   i++;  Not needed
        while (a[i] < pivot) { 
            i++;
        }
        //    j++; Not needed
        while (a[j] > pivot) {
            j--;
        }
        if (i <= j) {  // Changed terminating condition
            swap(a, i, j);
            i++;  // You need to progress the indexes after the swap
            j--;
        }
    }

    System.out.println(Arrays.toString(a));
    if (left < j) {  // Changed condition
        quickSort(a, left, j);
    }
    if (i < right) { 
        quickSort(a, i, right); // was i + 1
    }
}

Output:

[4, 5, 1, 2, 3, 7, 6, 8]
[1, 5, 4, 2, 3, 7, 6, 8]
[1, 3, 2, 4, 5, 7, 6, 8]
[1, 2, 3, 4, 5, 7, 6, 8]
[1, 2, 3, 4, 5, 7, 6, 8]
[1, 2, 3, 4, 5, 6, 7, 8]
[1, 2, 3, 4, 5, 6, 7, 8]
[1, 2, 3, 4, 5, 6, 7, 8]

Answer 2

well obviously that you have got your accepted answer. however I would mention that your partition logic could be implemented easier, with only one for (or while) loop, without nest loop either:

int partition(final int[] a, final int left, final int right) {
        // set the last element as pivot
        final int pivot = a[right];
        int i = left - 1, j = left;
        for (; j < right; j++) 
            if (a[j] < pivot) {
                i++;
                swap(a, i, j);
            }       
        // swap a[i+1] and pivot
        swap(a, i + 1, right);
        return i + 1;
    }

and in your quickSort method:

if (left < index)
  quickSort(a, left, index-1);
if (index < right)
  quickSort(a, index + 1, right);

hope it helps