(a)Show the following array as it goes through in-place Heap Sort (from smallest to largest).

{3, 4, 1, 0, 9, 2}

(b) Explain in detail the worst-case runtime of Heap Sort. Your explanation should include a summation.

(c)What is the best-case runtime for Heap Sort? Be specific about the input that would result in the best case and explain your reasoning.