Final answer:
The MaxHeapPercolateDown function is called 9 times while sorting the given 7-element array with heapsort. Three times during the initial max heap creation for the non-leaf nodes, and six times for each of the root removals (except the last element).
Step-by-step explanation:
The question revolves around the use of the MaxHeapPercolateDown function in the heapsort algorithm. Heapsort is a comparison-based sorting technique based on a binary heap data structure. When sorting an array using heapsort, the MaxHeapPercolateDown is called once for the creation of the max heap and then for each element that is removed from it. This operation is critical for maintaining the heap property after removing the root of the heap.
To calculate the number of times MaxHeapPercolateDown is called, we need to build the max heap from the array and then perform the sort. The initial build of the max heap calls MaxHeapPercolateDown once for each non-leaf node, which is n/2 - 1 times for an array of n elements. In our case, there are 7 elements, so the initial heap creation calls MaxHeapPercolateDown 3 times (since 7/2 - 1 = 2.5, which rounds down to 2 for non-leaf nodes, and we start counting from 0).
After the initial heap is built, heapsort calls MaxHeapPercolateDown each time the root is removed and the last element is swapped into the root's position. With 7 elements, this means that after the initial build, the function is called 6 more times (for every element except the last one, since the heap shrinks by one each time). The total number of calls to MaxHeapPercolateDown is therefore 3 (initial build) + 6 = 9.
The correct answer is 9 times for the given array, which corresponds to option b).