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%I #5 Jan 06 2022 08:17:10
%S 1,3,7,12,16,20,27,34,39,44,51,57,63
%N a(n) is the maximum number of key comparisons required to sort n records with distinct keys using a modified heapsort (Algorithm H in Don Knuth's TAOCP Vol. 3, answer to exercise 18).
%C There are two places in R. W. Floyd's modified algorithm where the keys are compared. The first is in step H4 [Find larger child.] and the second in step H9' [Does K fit?]. The sequence shows the maxima of the counts of these comparisons, determined over all n! possible orders of the records.
%D D. E. Knuth, The Art of Computer Programming Second Edition. Vol. 3, Sorting and Searching. Chapter 5.2.3 Sorting by Selection, Pages 145, 156 and 642. Addison-Wesley, Reading, MA, 1998.
%Y Cf. A350426, A350428.
%Y A350569 contains a table with the maximum and average number of comparisons for the original algorithm and for its modified version.
%K nonn,more
%O 2,2
%A _Hugo Pfoertner_, Jan 05 2022
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