Question

(Assuming no duplicate key values:) The order of the input records has what impact on the number of comparisons required by Heapsort (as presented in this module)?

a. None
b. There is a constant factor difference
c. There is a big difference, the asymptotic running time can change

Answer 1

Heapsort's number of comparisons is not affected by the initial order of the input. It depends on the tree's height, which is consistent regardless of the input sequence. So, the correct option is a. None.

Step-by-step explanation:

The order of the input records has no impact on the number of comparisons required by Heapsort. Heapsort is a comparison-based sorting algorithm that builds a heap from the input data and then repeatedly extracts the maximum element and rebuilds the heap until all elements are sorted. Regardless of the initial order of the input, the process of building and adjusting the heap results in a complete binary tree, and the number of comparisons depends on the number of nodes in the tree, which is a property of heap construction, not the initial order of input.

This is because Heapsort's performance is determined by its ability to organize elements into a heap, which requires several comparisons that depend on the tree's height (logarithmic in the number of elements) rather than the initial order of the input.