Final answer:
Quicksort is typically considered faster than Merge sort and Heapsort, especially for large datasets, due to its O(n log n) average-case time complexity and in-place sorting feature. However, Merge sort offers consistent performance and stability, while Heapsort has a higher operational overhead. Choice of sorting method often depends on various factors beyond just speed.
Step-by-step explanation:
When comparing sorting algorithms such as Quicksort, Merge sort, and Heapsort, we find that their performance can differ based on the data and specific use cases. Generally, Quicksort is considered faster on average, especially for large datasets, because its operations can be better optimized by modern computer architectures. It typically has the best performance thanks to its average-case time complexity of O(n log n) and its in-place sort feature which saves space. However, Merge sort also shares the same average-case time complexity of O(n log n) and provides consistent performance and stability with the added benefit of being a stable sort. On the other hand, Heapsort is also O(n log n), but it is usually a bit slower due to more overhead from operations. Nevertheless, in the worst-case scenario, Quicksort can degrade to O(n^2); hence why Merge sort and Heapsort can sometimes be preferred as they maintain a worst-case time complexity of O(n log n).
It is essential to consider that when algorithm performance is close, the choice of sorting methods may be decided by other factors such as ease of implementation, memory constraints, and the need for a stable sort.