Why does heap sort have a space complexity of O(1)?

Question

I understand that both quick sort and merge sort need O(n) auxiliary space for the temporary sub-arrays that are constructed, and in-place quick sort requires <

Answer 1

HEAP-SORT(A)
{
BUILD-MAX-HEAP(A)
if(i= A.length down to 2)
    exchange A[i] with A[1]
    A.heapSize = A.heapSize-1
    MAX-HEAPIFY(A,1)

}

i/p is stored in array which is passed to heap sort algorithm- HEAP-SORT(A). Array A is interpreted as tree and after BUILD-MAX-HEAP out of it and swapping last element with root and reducing size of heap each time by one and then call MAX-HEAPIFY(A,1) on it.

this all operations we are performing inside that array(A) only - which is given as i/p to algorithm. we are not using any extra space while performing this operation.. So space complexity - O(1).