$2$-sorted array. How to sort it in minimal number of comparisons ?
Hint:Show that the algorithm must compare the following pairs:
$$ (a[1],a[2]), (a[2],a[3]), (a[3],a[4]), \ldots, (a[n-1],a[n]). $$

For each comparison $(a[i],a[i+1])$, assume that you haven't compares $a[i]$ to $a[i+1]$ but you have done all other comparisons. Show that you still don't know the correct sorted order of the array.