Amazon·Software Engineer·Online Assessment (OA)·Intermediate

Intermediate

Jul 2026

Summary

Amazon SWE online assessment with a string/prefix problem that looks deceptively simple but has a tricky frequency-equality constraint baked in.

Questions Asked (1)

Given a string of uppercase letters, for each prefix compute the maximum number of equal-length contiguous blocks such that every character appears the same number of times in every block.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The problem statement reads cleanly but I kept second-guessing the frequency constraint.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

First, clarify the problem: for each prefix, we need to partition it into the maximum number of contiguous blocks of equal length such that in each block, every character appears the same number of times. Then, derive an efficient algorithm by analyzing the constraints and using prefix sums or frequency counts to check validity of block sizes, aiming for O(n^2) or better.

Pro tip: Start by discussing the brute-force approach and its complexity, then optimize by noting that the block length must divide the prefix length and that the character frequencies in each block must be uniform. This shows you can iterate from naive to optimal, a key skill at Amazon.

1. Clarify the problem

Restate the problem in your own words and ask clarifying questions: Does 'every character appears the same number of times' mean each character's frequency is equal to every other character's frequency within a block? Are blocks contiguous and non-overlapping? Confirm that we need the maximum number of blocks for each prefix.

2. Brute-force approach

For each prefix, try all possible block lengths that divide the prefix length. For each block length, partition the prefix into blocks and check if each block has uniform character frequencies. Track the maximum number of blocks. Analyze time complexity: O(n^3) or O(n^2 * alphabet) depending on implementation.

3. Optimize with prefix sums

Precompute prefix sums of character frequencies to quickly get the frequency of any character in any substring. For a given block length L, we need to check if for each block, the frequency of each character is the same. This can be done by comparing the frequency vector of each block to the first block's frequency vector, or by ensuring that the difference between prefix sums at block boundaries is consistent.

4. Iterate over block lengths efficiently

For each prefix length i, iterate over all divisors L of i. For each L, check if the prefix can be partitioned into i/L blocks each satisfying the condition. Use the prefix sums to check each block in O(1) per character, but we can optimize by noting that the condition implies that the total frequency of each character in the prefix must be divisible by the number of blocks, and the frequency in each block must be exactly total_freq / num_blocks. So we can check if each block has exactly that frequency for each character.

5. Implement and test

Write code to compute the answer for each prefix. Test with small examples and edge cases (e.g., all same characters, all distinct characters). Discuss potential further optimizations or trade-offs (e.g., using a hash of frequency vectors to compare blocks quickly).

Key Points to Mention

Definition of the problem: maximum number of equal-length contiguous blocks per prefix where each block has uniform character frequencies.
Brute-force approach and its time complexity, then moving to an optimized solution using prefix sums.
Key observation: For a valid partition with k blocks, each character's total frequency in the prefix must be divisible by k, and each block must contain exactly total_freq/k of that character.
Using prefix sums to compute character frequencies in any substring in O(1) time.
Iterating over divisors of the prefix length to find possible block lengths.
Time and space complexity analysis of the final algorithm, and potential trade-offs (e.g., precomputation vs. on-the-fly checks).

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.