Hey, counter example here:

5
3 4 2 1 5

the expected output is 3, but with your logic:

3 4 2 1 5
1 2 3 4 5
---------
1 1 1 1 0

&&

3 4 2 1 5
5 4 3 2 1
---------
1 0 1 1 1

the output is ceil(4/2) = 2

The flaw in your logic is that you assume that two different positions between the input array and the sorted input array are fixed with only 1 swap, when in reality it's a bit more complex than that.