Search for a substring of a number with a specific property

Question

I am assigned a string consisting only of numbers from 0 to 9. I want to calculate how many substrings of them have a power of 2.

For example, for substation 2560616, substring 256 and 16 are 2. I need to calculate how many such substrings are in any given substring.

Note that the substring is very large, so brute force cannot work. Therefore, I basically want to solve two problems.

• How to efficiently count all substrings that have power 2
• How to efficiently calculate if a substring is power 2

I think there might be a DP approach, but I'm not sure about that.

Answer 1

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