Amazon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Amazon coding round, one algorithmic problem the whole session. The problem looked like a string manipulation warmup but turned into something way more involved once you actually think about the constraints.

Questions Asked (1)

Given a string, for each prefix of that string compute the maximum number of equal-length contiguous blocks you can split it into such that every block has the same character frequency multiset.

Algorithms & Data Structures

Author's notes

I stared at the example with 'ABBA' for a solid minute before I even understood what 'same frequency multiset' meant in context.

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AI HintsAI Generated

Suggested Approach

For each prefix, the block length must divide the prefix length. For each divisor, check if the prefix can be split into blocks with identical character frequency multisets by comparing frequency vectors. Optimize by precomputing prefix frequency counts and using hashing or canonical representations of frequency multisets.

Pro tip: Clarify the definition of 'maximum number of blocks'—it means the smallest block length that works. Also, mention that the frequency multiset condition is equivalent to all blocks having the same sorted frequency vector, which can be hashed for O(1) comparisons.

1. Understand the problem and constraints

Restate the problem: for each prefix, find the smallest block length L such that the prefix can be divided into equal-length blocks, each with the same character frequency multiset. Discuss input size and expected complexity.

2. Brute-force approach

For each prefix, iterate over all divisors L of the prefix length. For each L, split the prefix into blocks and compute the frequency multiset of each block. Check if all multisets are equal. Keep track of the maximum number of blocks (i.e., smallest L).

3. Optimize with prefix frequency arrays

Precompute prefix frequency arrays for the entire string to quickly get the frequency multiset of any substring. For a block from i to i+L-1, compute its frequency vector by subtracting prefix frequencies. Compare vectors efficiently using hashing or by encoding the sorted frequency vector into a string or integer.

4. Handle each prefix efficiently

For each prefix length n, iterate over divisors L of n. For each L, check all blocks using the precomputed prefix frequencies. Use a hash set to store the frequency multiset of the first block, then compare subsequent blocks. If all match, record n/L as a candidate and break (since we want the maximum number of blocks, i.e., smallest L).

5. Analyze complexity and edge cases

Time complexity: O(N * sqrt(N) * alphabet_size) or better with hashing. Space complexity: O(N * alphabet_size) for prefix frequencies. Discuss edge cases: empty string, single character, all characters same, etc.

Key Points to Mention

The block length must divide the prefix length.
The frequency multiset condition means all blocks have the same multiset of character counts, not necessarily the same order.
Use prefix frequency arrays to compute block frequencies in O(alphabet_size) time.
Hash the frequency multiset (e.g., sorted tuple or polynomial hash) for O(1) comparisons.
Iterate over divisors of the prefix length to find the smallest valid block length.
Consider trade-offs between time and space; precomputation can speed up repeated queries.

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