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

2,2

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.

Links

Table of n, a(n) for n=2..14.

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.

Sequence in context: A299638 A189474 A184483 * A310239 A189797 A310240

Adjacent sequences: A350424 A350425 A350426 * A350428 A350429 A350430

Keyword

nonn,more

Author

Hugo Pfoertner, Jan 05 2022

Status

approved