I knew the formula going in but fumbled the implementation a bit.
Start by clarifying the problem: confirm that strings are tokenized into words and that cosine similarity is computed on term frequency vectors. Then outline the algorithm: build vocabulary, compute term frequencies, calculate dot product and norms, and return similarity. Finally, discuss trade-offs like handling of unseen words, normalization, and efficiency for large datasets.
Pro tip: Mention that in production, you'd likely use TF-IDF or embeddings instead of raw counts, and that cosine similarity is scale-invariant but sensitive to tokenization choices. This shows you understand practical limitations beyond the textbook algorithm.
Ask whether strings should be tokenized by whitespace, lowercased, or stripped of punctuation. Confirm that the output should be a float between 0 and 1, and discuss handling of empty strings or zero vectors.
Explain that you'll create a combined vocabulary from both strings, then represent each string as a term frequency vector. Mention that using a dictionary or Counter is efficient for sparse vectors.
Compute the dot product of the two vectors and the product of their Euclidean norms. Return the dot product divided by the norms, with a guard for zero norms.
Discuss time complexity O(n+m) for tokenization and vector operations, and space complexity O(v) where v is vocabulary size. Mention alternatives like using scipy or sklearn for production, and the impact of tokenization on results.
Walk through examples: identical strings (similarity 1), disjoint vocabularies (similarity 0), and one empty string (similarity 0). This demonstrates thoroughness.
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