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The best-, average-, and worst case time complexity of Heapsort for $n$ distinct keys are all $\Theta(n \lg n)$.

What are the worst-case inputs for heapsort?

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Please check the paper@arXiv2015: A Complete Worst-Case Analysis of Heapsort by M. A. Suchenek.

This paper gives a rather involved lower bound; see Abstract and Theorem 12.2 on page 94.

To the specific question,

Example of a 500-node worst-case array for Heapsort, created by my Java program, is included in Appendix A.3 page 110.

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