A159325 Median number of comparisons used by insertion sort on n (distinct) elements.

0, 1, 3, 5, 8, 11, 15, 19, 24, 30, 36, 42, 49, 56, 64, 73, 82, 91, 101, 111, 122, 134, 146, 158, 171, 185

Offset: 1

Author

Harmen Wassenaar (towr(AT)ai.rug.nl), Apr 10 2009

Keywords

• nonn

Comments

The frequencies of the number of comparisons are given by sequence A129178, so if Sum_{k=0..i-1} A129178(n,k) < n!/2 and Sum_{k=0..i} A129178(n,k) > n!/2, then the median is entry i, which corresponds to n(n-1)/2-i comparisons.

Close to average number of comparisons: A159324(n)/n!

Examples

			For n=3, permutations 123,132,213,231,312,321 require 3,3,3,2,3,2 comparisons respectively, so the median is 3.
		

Crossrefs

Cf. A129178, A159323, A159324.