Number of Ways to Split a String - Solution & Explanation

This approach primarily involves the calculation of the number of '1's in the string and then leveraging prefix sums to determine viable partition points:

• First, count the total number of '1's in the string. If this number is not divisible by 3, return 0 as it's impossible to split the string as required. Let's denote the total number of '1's as totalOnes.
• Compute the number of '1's that each partition should have: onesPerPart = totalOnes / 3.
• Traverse the string to count where these partitions can occur. Maintain two counts: firstPartEnds and secondPartStarts.
• For the first partition, count how many ending points there are at the point where exactly onesPerPart '1's have been seen.
• Similarly, for the second partition, count how many starting points there are after the first partition where the same condition holds.
• The number of ways to split is the product of these two counts.

The Python solution reads the entire string to count the '1's initially. Using modular arithmetic, if the ones count is zero, it calculates combinations of splitting zeroes correctly. For non-zero ones, it identifies break points based on index locations for effectively segmenting the string post-sufficient counts of '1's.

This approach uses a combinatorial logic to find the possible splits:

• Calculate the total number of '1's and ensure it's divisible by 3; otherwise, return 0.
• For a case with zero '1's, the potential splits are computed using combinatorial mathematics regarding zero positions.
• Divide the task into finding partitions that place the required '1's in each segment based logically on zero interspersal between calculated divisions.
• Combining counts of zero placement spans for multiplicity represents valid configurations for splitting.

The C++ implementation uses standard library functions to simplify the counting process and leverages modulus arithmetic to handle large output, ensuring integer overflow does not occur.