The 2-stage of the algorithm puts the X’s in order among themselves and the Y ’s in
order among themselves. Let Sn be the number of comparisons that .2; 1/-Shell Sort
makes to sort n random keys, and let Cn be the number of comparisons that insertion
sort makes to sort n random keys. The 2-stage of .2; 1/-Shell Sort makes two runs of
insertion sort on the subarrays X1; : : : ; Xdn=2e and Y1; : : : ; Ybn=2c, thus requiring