Final answer:
The disadvantage of Heapsort among the given options is that it is not stable, which means records with equal keys might not maintain their order after sorting. It has an average-case running time of O(n log n) and doesn't require much auxiliary storage.
Step-by-step explanation:
The student is asking about the disadvantages of Heapsort, which is an algorithm used in computer science for sorting elements. Among the options given, Heapsort is indeed not a stable sort. This means that equal elements might not necessarily remain in the same order as they were in the input; that is, if two objects with equal keys appear in a certain order in the input, they might end up in a different order after Heapsort is applied.
Heapsort has a worst-case and average-case running time of O(n log n), not O(n²) as one of the options incorrectly suggests. It does not need a lot of auxiliary storage because it is an in-place algorithm. In fact, one of the main advantages of Heapsort is that it requires only a constant amount of additional storage space, which is O(1). So the correct answer is: a. It is not stable (i.e., records with equal keys might not remain in the same order after sorting).