Topcoder 550-Point problem from SRM 355, Division 2
James S. Plank
Tue Apr 9 12:12:53 EDT 2013
Definition from Topcoder: http://community.topcoder.com/stat?c=problem_statement&pm=7759&rd=10712
Skeleton: NoEights.cpp
Main: NoEights-Main.cpp

As always, feel free to solve this problem on your own. However, I would like you to think about the problem recursively. That may not be the most natural way for you to think about it, but it's good practice.

One of the keys to this problem is to turn low and high into strings and work on the strings. Here's how you can do it.

Turn low and high into the strings l and h.
If the two strings differ in size, you can return instantly. Think about it.
Otherwise, let's define a function NE(l, h), where l and h are strings that are the same size. We'll define NE as follows:
- If l and h are empty strings, then NE(l, h) equals zero.
- Otherwise, let l be l₀ + l_end, where l₀ is the first character of l and l_end is the rest of the characters. Similarly, let h be h₀ + h_end. If l₀ does not equal h₀, then NE(l, h) equals zero.
- Otherwise, we know that l₀ equals h₀. If l₀ equals '8', then NE(l, h) equals (1 + NE(l_end, h_end)).
- Otherwise, NE(l, h) equals NE(l_end, h_end).

Go ahead and turn this definition into a recursive solution.

I know you can do this with one for loop after you've created l and h. However, I'd like you to structure it with recursion. It's good practice.