This caught me mid-explanation and I had to pause.
Clarify that the run-length encoding (RLE) signature key already captures the sequence of characters, so storing full strings in each bucket is redundant. Explain that you can store only the count vectors (run lengths) for each word, and matching reduces to comparing count vectors within the same signature bucket. Discuss the memory savings and the trade-off in matching complexity.
Pro tip: Emphasize that this optimization is only valid if the signature is a canonical representation of the character sequence; otherwise, you risk incorrect grouping. Also, mention that while memory decreases, the matching step may require comparing vectors of varying lengths, which can affect time complexity.
Explain that the RLE signature is a string like 'a2b1c3' that encodes both the characters and their run lengths. The key uniquely identifies the sequence of characters and their counts.
Point out that if the key already contains the character identities in order, storing the full words in the bucket duplicates that information. Instead, you can store only the count vectors (e.g., [2,1,3]) extracted from each word.
Discuss that storing count vectors instead of full strings reduces memory usage, especially for long words with few runs. The savings depend on the average run length and word length.
Explain that matching two words now requires comparing their count vectors, not the full strings. Since they share the same signature, the character sequence is identical, so only the counts need to be compared.
Mention that while memory is saved, matching may become slightly more complex because you need to compare vectors of different lengths. However, the time complexity remains O(k) where k is the number of runs, which is often smaller than the word length.
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