When building heap, is heap unique?

Question

I'm studying heap & heap sorting.
There is a array : arr[8] = {6,9,3,1,8,7,2,11}
When I'm trying to build the heap, using code and pencil, I faced two kinds of heap.

When using code, MaxHeap : 11 9 7 6 8 3 2 1

When using insertion theory, MaxHeap : 11 9 7 8 6 3 2 1

The code that i'm using :

int[] DoHeapSort(int[] value) {
    int length = value.length;

    for (int i = length / 2; i > 0; i--) {
        maxHeapify(value, i, length);
    }

    //print Heap
    for(int i = 0 ; i<value.length; i++)
        System.out.println(value[i]);

    return (value);
}


void maxHeapify(int[] array, int index, int heapSize) {
    int left = index * 2;
    int right = left + 1;
    int max = index;

    if (left <= heapSize && array[left - 1] > array[index - 1]) {
        max = left;
    }

    if (right <= heapSize && array[right - 1] > array[max - 1]) {
        max = right;
    }

    if (max != index) {
        swap(array, index - 1, max - 1);
        maxHeapify(array, max, heapSize);
    }
}

Theory, in this case, create another array for heap and insert from 6 to 11 in order. (On the other hand, code is in-place heap)

Both maxHeap results satisfied heap definition. Then Heap is not unique ? Thanks

Answer 1

That's correct. The heap constraint (which is that children are not greater than their parents) does not completely specify the heap, so there is usually more than one possible arrangement.