The transitivity part is what makes this tricky.
Model the similarity relationships as a graph and use union-find (disjoint set union) to group words that are transitively similar. Then iterate through both sentences, checking that lengths match and each word pair is either identical or belongs to the same similarity group.
Pro tip: Mention that you can optimize by only building groups for words that appear in the sentences, and use path compression and union by rank for near-constant time operations. This shows you consider practical performance beyond the basic algorithm.
Confirm that similarity is transitive, that sentences must be of equal length, and that identical words are always similar. Ask about case sensitivity and whether similarity pairs are bidirectional.
Select union-find (disjoint set union) to efficiently group words based on the given similar pairs, leveraging transitivity. Alternatively, build an adjacency list and run BFS/DFS, but union-find is simpler and faster for this use case.
Initialize each unique word as its own set, then union each pair from the similar word pairs list. After processing all pairs, words in the same set are considered similar.
First check if the sentences have the same length; if not, return false. Then iterate through corresponding words: if they are identical, continue; otherwise, check if they belong to the same similarity group using find operations.
State the time complexity: O(N + P α(N)) where N is total words and P is number of pairs, with near-constant α due to path compression. Walk through examples, including edge cases like empty sentences or words not in any pair.
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