5
AAAAA
ans:5.000

6
CBDCBD
ans:3.600

6
DDADDD
ans:2.000
They helped me to solve this problem~
Hope they can help you
o(∩_∩)o...

Test "DDADDD"  is really nice.
My program shows different results for different shifts of that string.  For first two shifts it shows 2.0 and for the next four it shows 1.4,1.8,2.2 and 1.2 respectively