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Bottom-Up-Heapsort is a variant of Heapsort. Its worst-case complexity for the number of comparisons is known to be bounded from above by 3/2n logn+0(n), wheren is the number of elements to be sorted. There is also an example of a heap which needs 5/4n logn-0(n log logn) comparisons. We show in this paper that the upper bound is asymptotically tight, i.e., we prove for largen the existence of heaps which need at least 3/2n logn-O(n log logn) comparisons. This result also proves the old conjecture that the best case for classical Heapsort needs only asymptotic n logn + O(n log logn) comparisons.

A tight lower bound for the worst case of Bottom-Up-Heapsort