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The Two Pointers technique involves using two indices that move towards each other from the start and end of the lists. This approach effectively captures the prefixes and suffixes.
By using two pointers, we move from the start to the first words that don't match and from the end to the first words that also don't match. If the pointers end up crossing or are equal, the sentences are considered similar. We exploit the fact that any dissimilar portion in the middle, if any, can be 'inserted'.
Time Complexity: O(n + m), where n and m are the lengths of sentence1 and sentence2 respectively.
Space Complexity: O(n + m) for storing words.
1def areSentencesSimilar(sentence1: str, sentence2: str) -> bool:
2 s1_words = sentence1.split()
3 s2_words = sentence2.split()
4
5 i, j = 0, 0
6
7 while i < len(s1_words) and i < len(s2_words) and s1_words[i] == s2_words[i]:
8 i += 1
9
10 while j < len(s1_words) - i and j < len(s2_words) - i and
11 s1_words[-1-j] == s2_words[-1-j]:
12 j += 1
13
14 return i + j >= len(s1_words) or i + j >= len(s2_words)
15The Python implementation uses list slicing for word extraction and a combination of loops to implement the two-pointer approach to match sequences of words.
Another approach is to utilize a dynamic programming table to store sub-problems results. You can construct a DP table where dp[i][j] indicates whether the first i words from sentence1 can match the first j words from sentence2. This could be expanded using insertion strategies for any non-matching sub-sequences.
This approach relies more on systematic computation than geometric traversal, but can be more memory intensive.
Time Complexity: O(n*m)
Space Complexity: O(n*m)
This solution uses dynamic programming where a table is constructed to store sub-computations. The logic draws from comparing and setting DP cells based on direct match or feasibility of insertion.