A350427 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).

1, 3, 7, 12, 16, 20, 27, 34, 39, 44, 51, 57, 63

Offset: 2

Author

Hugo Pfoertner, Jan 05 2022

Keywords

• nonn
• more

Comments

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.

References

• 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.

Crossrefs

Cf. A350426, A350428.

A350569 contains a table with the maximum and average number of comparisons for the original algorithm and for its modified version.