Number of Ways to Split a String

Problem Description

Given a binary string s, you can split s into 3 non-empty strings s1, s2, and s3 where s1 + s2 + s3 = s. Return the number of ways s can be split such that the number of ones is the same in s1, s2, and s3. Since the answer may be too large, return it modulo 10^9 + 7.

Key Insights

• The string can only be split into 3 parts if the total number of '1's in the string is divisible by 3.
• If the total number of '1's is zero, any split of '0's is valid.
• The valid splits can be counted by tracking the positions of '1's and calculating the combinations of indices to form the three parts.
• The answer is computed as the product of the number of ways to choose the split points for the second and third segments.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we can use the following approach:

1. Count the total number of '1's in the string. If it's not divisible by 3, return 0.
2. If the total count of '1's is 0, return the number of ways to split the string of '0's into 3 parts.
3. Track the positions of '1's as we iterate through the string.
4. Calculate the number of ways to choose the split points for segments s2 and s3 based on the positions of '1's using combinatorial counting.
5. Return the result modulo 10^9 + 7.

Code Solutions