The minimum number of comparisons occurs when the array is already in

sorted order. Now look at the tree of splits of the array into sub-arrays

and count the number of comparisons needed in the merge step when

the left sub-array contains elements all less than each of the elements of the

right-sub array.

If the sub-arrays both contain single elements 1 comparison is made

If the left sub-array contains 1 element and the right sub-array 2 elements then 1 comparison is made

If both sub-arrays contain 3 elements then 3 comparisons are needed.

The merges in the decomposition tree for an array of size 6 is comprised

of merges from the above list, and by adding up the comparisons for the

required merges you will get the answer you need.

(I make it 2 merges of type (1,1), two merges of type (1,2), and one

merge of type (3,3) to give a total of 7 comparisons).

RonL