A Complete Worst-Case Analysis of Heapsort with Experimental Verification of Its Results, A manuscript (MS)

Main results. A rigorous proof that the number of comparisons of keys performed in the worst case by Heapsort on any array of size N ≥ 2 is equal to: 2(N − 1) ( lg N − 1 2 + ε )− 2s2(N)− e2(N) + min(blg(N − 1)c, 2) + 6 + c, where ε, given by: ε = 1 + dlg (N − 1)e − lg (N − 1)− 2dlg (N−1)e−lg (N−1), is a function of N with the minimum value 0 and and the supremum value δ = 1− lg e+ lg lg e ≈ 0.0860713320559342, s2(N) is the sum of all digits of the binary representation of N , e2(N) is the exponent of 2 in the prime factorization of N , and c is a binary function on the set of integers defined by: c =  1 if N ≤ 2 dlgNe − 4