|
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
![](v3_space.gif) |
|
Induction
step
|
|
|
|
|
assume
for i, prove for i+1.
|
|
|
|
|
consider two numbers: X, Y. Say Xi
is ith digit
|
|
|
|
|
of X (from the right)
|
|
|
|
|
Xi+1 < Yi+1 then i+1th
BinSort will put them in order
|
|
|
|
|
|
|
Xi+1 > Yi+1 , same thing
|
|
|
|
|
|
|
Xi+1 = Yi+1 , order depends on last i digits. Induction
|
|
|
hypothesis
says already sorted for these digits.
|
|
|
(Careful
about ensuring that your BinSort preserves
|
|
|
order
aka stable
)
|
|
|
|