Final answer:
Heapsort has a consistent time complexity of O(n log n) for the worst, average, and best cases. This means that the time complexities are the same across all cases, option d is the correct answer.
Step-by-step explanation:
The question asks about the cases in which time complexities are the same for Heapsort. Heapsort is a comparison-based sorting algorithm and has a time complexity of O(n log n) for the worst, average, and best cases. Unlike other comparison sorts such as quicksort, which has a worst case time complexity of O(n²), the time complexity of Heapsort does not change significantly with the nature of the input data.
Therefore, the correct answer to the question is d. Worst, Average and Best. The time complexity of Heapsort is O(n log n) regardless of how the input data is structured, making it consistent across all cases.