A350567 a(n) is the maximum number of key comparisons required to perform an indirect sort of n records with distinct keys using a two-way merge (A. D. Woodall's mergesort).

1, 4, 6, 10, 13, 17, 20, 25, 29, 34, 38, 43, 47, 52

Offset

2,2

Comments

There are six places in the Algol 60 procedure mergesort where the keys are compared. The sequence shows the maxima of the counts of these comparisons, determined over all n! possible orders of the records.

a(16) >= 56.

References

D. E. Knuth, The Art of Computer Programming Second Edition. Vol. 3, Sorting and Searching. Chapter 5.2.4 Sorting by Merging, Pages 164-166. Addison-Wesley, Reading, MA, 1998.

Links

Table of n, a(n) for n=2..15.

A. D. Woodall, An internal sorting procedure using a two-way merge, Algorithm 45, The Computer Journal, Volume 13, Number 1, February 1970, Algorithms Supplement, pp. 110-111.

Crossrefs

A350568 provides the corresponding average numbers and a comparison table.

Cf. A001768, A001855, A350569.

Sequence in context: A246439 A186514 A184402 * A079524 A141740 A088135

Adjacent sequences: A350564 A350565 A350566 * A350568 A350569 A350570

Keyword

nonn,more

Author

Hugo Pfoertner, Jan 09 2022

Status

approved