Final answer:
Heapsort requires only a constant amount of auxiliary space beyond the array holding the records, which is ϴ(1). This minimal space requirement is due to the in-place nature of the algorithm, where rearrangement occurs within the input array.
Step-by-step explanation:
The auxiliary space required by Heapsort is not dependent on the number of records being sorted, but rather on the operations necessary to maintain the heap structure. During the sorting process, Heapsort uses a given array to create a heap and then sort it. The significant aspect of Heapsort with regard to space complexity is that it requires only a constant amount of additional space beyond the input array.
Therefore, the correct answer is b. ϴ(1), which means that Heapsort requires a constant amount of auxiliary space. This is one of the primary reasons why Heapsort is considered an in-place sorting algorithm. No additional arrays or significant extra storage is needed, as the elements of the input array are rearranged within the array itself.