Start by clarifying requirements and edge cases, then outline a simple frequency-based approach using a hash map. Discuss how to handle ties, unseen words, and scalability, and finally provide clean code for training and prediction.
Pro tip: Demonstrate awareness of real-world complexities by mentioning smoothing techniques (e.g., add-one smoothing) and how to extend to n-grams, showing you think beyond the basic solution.
Ask about input size, whether to consider case sensitivity, punctuation, and how to handle unseen words or ties. Confirm the expected output format.
Propose using a hash map (dictionary) where each key is a word and the value is another hash map mapping next words to their frequencies. This allows efficient updates and lookups.
Iterate through each sentence, tokenize into words, and for each adjacent pair, increment the count of the next word in the inner map for the current word.
For a given word, look up its inner map and return the next word with the highest frequency. Handle cases where the word is not in the map or has no successors.
Mention time/space complexity, potential improvements like using a heap for top-k predictions, and extensions to n-grams or smoothing for better generalization.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify that the O(k) cost comes from scanning k candidate next words to find the maximum probability. Then propose precomputing a data structure—such as a max-heap or sorted list—per context so the top candidate is always at the front, enabling O(1) retrieval. Discuss trade-offs like update cost and memory overhead, and mention that O(1) is achievable if the context is fixed and the distribution is static or updated infrequently.
Pro tip: Emphasize that O(1) lookup requires O(k) preprocessing or update time, so the real trade-off is between query latency and update cost—this shows you understand system design, not just algorithms.
Explain that the current O(k) comes from linearly scanning all k possible next words to find the one with the highest probability. This is the operation we need to eliminate.
For each context, store the most likely next word (and its probability) in a hash map or dictionary. Then lookup is O(1) because it's a direct key access.
If the model updates, recompute the top word for affected contexts. For ties, define a deterministic tie-breaking rule (e.g., alphabetical or random) and store it.
Precomputing uses extra memory (O(number of contexts)) and updates become O(k) per context. If updates are frequent, consider a heap or balanced tree for O(log k) updates while keeping O(1) peek.
Mention that if k is small, O(k) might be fine; but for large k or latency-critical systems, precomputation is worth it. Also note that approximate methods (e.g., caching top-N) can reduce cost.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Explain that you need to convert the model's raw scores into a probability distribution using softmax, then sample from that distribution. Discuss how to implement sampling efficiently, such as using cumulative distribution function (CDF) and binary search, and mention trade-offs like temperature scaling for controlling randomness.
Pro tip: Mention that sampling introduces nondeterminism, so for reproducibility you should allow setting a random seed. Also, note that in production you might want to cache the CDF or use alias tables for O(1) sampling when the vocabulary is large.
Apply softmax to the model's output logits to obtain a valid probability distribution over the vocabulary. Ensure numerical stability by subtracting the max logit before exponentiation.
Compute the cumulative sum of the probabilities to create a CDF array. This allows mapping a uniform random number to a word index.
Generate a random number between 0 and 1, then find the first index where the CDF exceeds this value. This can be done via linear scan or binary search for efficiency.
Address cases like zero probabilities, floating-point precision, and large vocabularies. Consider optimizations like precomputing the CDF or using alias sampling for O(1) time.
Talk about how temperature affects the distribution, the impact on text generation quality, and potential need for reproducibility via random seeds.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.