Final answer:
False. The claim that an unsorted array can be sorted in linear time using the buildheap operation is false; buildheap is linear, but heapsort, which includes the buildheap operation, has a time complexity of O(n log n).
Step-by-step explanation:
The statement that an unsorted array can be sorted in linear time using the buildheap operation is false. While it's true that a buildheap operation, which creates a heap from an array, can be performed in linear time (O(n)), the sorting process itself requires additional steps. Specifically, once you have a heap, you would typically use the heapsort algorithm, which involves repeatedly removing the largest element from the heap and rebuilding the heap until it is empty. This process has a time complexity of O(n log n) due to the log n complexity of heapifying after each removal of the largest element. Therefore, it is not possible to sort an unsorted array in linear time using the buildheap operation alone.