public static void extendHeap(int[] A, int i){
        int size = A.length;
        int max = i;
        int left = 2 * i;
        int right = 2 * i + 1;
        if (left < size && A[left] > A[max])
            max = left;

        if (right < size && A[right] > A[max])
            max = right;

        if (max != i) {
            int temp = A[i];
            A[i] = A[max];
            A[max] = temp;

            extendHeap(A, max);
        }

    }

    /**
     * Input:
     *      array A of integers
     * Expected output:
     *      the array A is now a max-heap under the tree view;
     */
    public static void buildHeapTopDown(int[] A){
        int size = A.length;
        int index = (size / 2);


        for (int i = index; i >= 0; i--) {
            extendHeap(A, i);
        }
    }