

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)


4



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

2,2


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. AddisonWesley, Reading, MA, 1998.


LINKS



CROSSREFS

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


KEYWORD

nonn,more


AUTHOR



STATUS

approved



