The gcd angle clicked pretty fast but I underestimated how much work comes after that.
For each prefix, compute the character frequency counts and the total length. Then find the greatest common divisor (GCD) of all non-zero frequencies; the maximum number of equal-length blocks is the number of divisors of the GCD that also divide the prefix length. Alternatively, iterate over possible block counts from largest to smallest and check if the prefix can be partitioned into that many blocks with equal character frequencies.
Pro tip: Start by explaining the brute-force approach and its O(n^2) complexity, then optimize using GCD and divisor enumeration to O(n * sqrt(n)) or better. This shows you understand trade-offs and can scale solutions.
Restate the problem in your own words and confirm with the interviewer: for each prefix, we need the maximum k such that the prefix can be split into k contiguous blocks of equal length, and within each block, every character appears the same number of times.
For each prefix, try all possible block counts from largest to smallest. For each candidate k, check if the prefix length is divisible by k, then verify if each block has identical character frequency distributions.
Observe that the maximum number of blocks is limited by the GCD of the character frequencies in the prefix. Compute the GCD of all non-zero frequencies, then find the largest divisor of the prefix length that is also a divisor of this GCD.
Maintain frequency counts incrementally as you extend the prefix. Update the GCD of frequencies efficiently (e.g., using a running GCD). For each prefix, compute the answer by checking divisors of the current GCD that also divide the prefix length.
Discuss time and space complexity. Handle edge cases: empty prefix, single character, all characters same, etc. Consider if further optimization is needed for very large strings.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.