Build-Max-Heap vs. HeapSort

I'm not sure whether my definition for these 2 terms are correct. Hence, could you help me verify that:

HeapSort: A procedure which sorts an array in place.

Build-Max-Heap: A procedure which runs in linear time, produces a max- heap from an unordered input array.

Is worst-case input = worst-case running time?

If so, given the size n for Build-Max-Heap, would its worst case input be the same as the HeapSort which is $\mathcal{O}(n \log n)$?

• Famously, building a heap is possible in linear time.
– Raphael
Feb 25, 2015 at 15:21