A350428 2*a(n)/n! is the average number of key comparisons required to sort n records with distinct keys using heapsort (Algorithm H in Don Knuth's TAOCP Vol. 3).

1, 9, 78, 657, 5448, 49869, 520416, 5901138, 70092000, 902850273, 12416814432, 183763314090, 2854581512832

Offset: 2

Author

Hugo Pfoertner, Jan 05 2022

Keywords

• nonn
• more

Comments

There are two places in the algorithm where the keys are compared. The first is in step H4 [Find larger child.] and the second in step H6 [Larger than K?]. The sequence is the sum, divided by 2, of the counts of these comparisons, taken 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, Page 145. Addison-Wesley, Reading, MA, 1998.

Crossrefs

Cf. A350426, A350427.

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