Final answer:
The claim that an unsorted array can be sorted in linear time with the buildheap operation is B. false. While building a heap is linear.
Step-by-step explanation:
The statement that an unsorted array can be sorted in linear time using the buildheap operation is false. To clarify, a heap can indeed be built from an unsorted array in O(n) time, which is the buildheap operation. However, sorting an array requires additional steps beyond just building a heap. Once a heap has been built, the process of heap sort needs to extract the maximum element and re-heapify the remaining elements, progressively building a sorted list. This extraction and re-heapification must occur for each element in the array. As each operation takes logarithmic time (O(log n)), when performed for 'n' elements, the overall time complexity of heap sort becomes O(n log n). Therefore, while the buildheap operation is linear, the entire process of sorting is not linear, but rather O(n log n) in complexity.
An unsorted array can be sorted in linear time using the build heap operation.
Build heap is an efficient algorithm that creates a heap from an unsorted array. A heap is a binary tree structure that follows certain rules: every parent node is greater than or equal to its child nodes in a max heap, or every parent node is less than or equal to its child nodes in a min heap.
The build heap operation works by starting with the last parent node in the array and sifting down each node to its proper position until the heap property is satisfied.