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Bloomberg·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jun 2026

Summary

Bloomberg follow-up design question on the bigram next-word predictor. The focus shifted from building the thing to interrogating whether the space complexity was actually necessary, which I wasn't fully prepared for.

Questions Asked (1)

Q1

Your bigram next-word predictor stores full count maps for every prefix. Does it have to use O(N) space relative to total training tokens, and what are your options for reducing that?

Algorithms & Data StructuresTechnical Trade-offsSystem Design
Author's notes

I knew the basic answer (store only the argmax per prefix after training, toss the counts) but then they pushed on what you lose by doing that and I kind of fumbled.

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AI HintsAI Generated

Suggested Approach

First, clarify that the space complexity depends on the number of unique bigrams, not total tokens, but in the worst case (all bigrams unique) it is O(N). Then, discuss trade-offs of different reduction techniques such as pruning, hashing, and compression, emphasizing that the choice depends on accuracy, latency, and memory constraints.

Pro tip: Quantify the impact: e.g., 'Pruning to top 10k bigrams can reduce memory by 90% with minimal accuracy loss on typical text.' This shows you think in terms of real-world trade-offs, not just theory.

1. Clarify the space complexity

Explain that the space is O(V^2) in the worst case where V is vocabulary size, but often O(N) if N is the number of unique bigrams. Distinguish between total tokens and unique bigrams.

2. Identify reduction goals

State that the goal is to reduce memory while maintaining acceptable prediction quality and latency. Consider the constraints of the deployment environment (e.g., embedded vs. server).

3. List reduction techniques

Discuss techniques like pruning low-frequency bigrams, using hashing with collisions, quantization of counts, and compression (e.g., variable-length encoding).

4. Evaluate trade-offs

For each technique, mention the impact on memory, accuracy, and speed. For example, pruning saves memory but may hurt recall; hashing saves memory but introduces collisions.

5. Recommend a solution

Suggest a combined approach (e.g., pruning + quantization) and justify based on typical requirements. Mention that the best choice depends on the specific use case.

Key Points to Mention

  • Space complexity is O(U) where U is number of unique bigrams, which can be O(N) in worst case.
  • Pruning: remove bigrams with count below a threshold, or keep only top-K per prefix.
  • Hashing: use a fixed-size hash table, accepting collisions; can use multiple hash functions to reduce false positives.
  • Quantization: store counts in fewer bits (e.g., 8-bit) or use logarithmic bucketing.
  • Compression: use techniques like Elias gamma coding or dictionary encoding for counts.
  • Trade-offs: memory vs. accuracy vs. speed; consider the impact on prediction quality and latency.

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