## 734. Sentence Similarity

Given two sentences `words1, words2` (each represented as an array of strings), and a list of similar word pairs `pairs`, determine if two sentences are similar.

For example, "great acting skills" and "fine drama talent" are similar, if the similar word pairs are ```pairs = [["great", "fine"], ["acting","drama"], ["skills","talent"]]```.

Note that the similarity relation is not transitive. For example, if "great" and "fine" are similar, and "fine" and "good" are similar, "great" and "good" are not necessarily similar.

However, similarity is symmetric. For example, "great" and "fine" being similar is the same as "fine" and "great" being similar.

Also, a word is always similar with itself. For example, the sentences `words1 = ["great"], words2 = ["great"], pairs = []` are similar, even though there are no specified similar word pairs.

Finally, sentences can only be similar if they have the same number of words. So a sentence like `words1 = ["great"]` can never be similar to `words2 = ["doubleplus","good"]`.

Note:

• The length of `words1` and `words2` will not exceed `1000`.
• The length of `pairs` will not exceed `2000`.
• The length of each `pairs[i]` will be `2`.
• The length of each `words[i]` and `pairs[i][j]` will be in the range `[1, 20]`.

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#### Approach #1: Set [Accepted]

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Intuition and Algorithm

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To check whether `words1[i]` and `words2[i]` are similar, either they are the same word, or `(words1[i], words2[i])` or `(words2[i], words1[i])` appear in `pairs`.

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To check whether `(words1[i], words2[i])` appears in `pairs` quickly, we could put all such pairs into a Set structure.

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Complexity Analysis

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Time Complexity: , where is the maximum length of `words1` and `words2`, and is the length of `pairs`.

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Space Complexity: , the size of `pairs`. Intermediate objects created in evaluating whether a pair of words are similar are created one at a time, so they don\'t take additional space.

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Analysis written by: @awice.

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