Solution Explanation:

This problem asks whether two sentences are similar based on a given set of similar word pairs. Two sentences are considered similar if they have the same length and each word at a given index in one sentence is either identical to or considered similar to the word at the same index in the other sentence. Similarity is not transitive (e.g., A is similar to B, B is similar to C does not imply A is similar to C).

The most efficient approach uses a hash table (or set) to store the similar word pairs. This allows for quick lookups to determine if two words are similar.

Algorithm:

1. Length Check: First, compare the lengths of sentence1 and sentence2. If they are different, the sentences cannot be similar, so return false.

2. Hash Table Initialization: Create a hash table (or set) to store the similar word pairs from similarPairs. The key can be a concatenation of both words (e.g., "word1#word2") to handle both orders easily.

3. Word-by-Word Comparison: Iterate through the words of both sentences simultaneously using zip (Python) or an index-based loop (other languages). For each pair of words at the same index (word1 from sentence1 and word2 from sentence2):

   • If the words are identical (word1 == word2), continue to the next pair.
   • If the words are different, check if either "word1#word2" or "word2#word1" exists in the hash table. If neither exists, it means the words are not similar, so return false.

4. Similarity Confirmed: If the loop completes without returning false, it means all word pairs at corresponding indices are either identical or similar. Therefore, the sentences are similar, and the function returns true.

Time Complexity: O(M + N + P), where M is the length of sentence1, N is the length of sentence2, and P is the length of similarPairs. The dominant operations are iterating through the sentences and the similar pairs. The hash table lookups are generally O(1) on average.

Space Complexity: O(P), where P is the length of similarPairs. This is the space used to store the similar word pairs in the hash table.

Code Examples (with detailed comments):

The code examples provided in the previous response demonstrate this algorithm in various languages. Let's highlight the key parts of the Python example:

class Solution:
    def areSentencesSimilar(
        self, sentence1: List[str], sentence2: List[str], similarPairs: List[List[str]]
    ) -> bool:
        if len(sentence1) != len(sentence2):  # Length check
            return False
        s = {(x, y) for x, y in similarPairs}  # Efficient set creation for lookups
        for x, y in zip(sentence1, sentence2):  # Iterate simultaneously
            if x != y and (x, y) not in s and (y, x) not in s:  # Check for similarity
                return False
        return True

The other language examples follow the same core logic, differing only in syntax and data structure specifics. The use of sets (or hash sets) is crucial for efficient similarity checking.