Groups of Special-Equivalent Strings

To find the number of groups of special-equivalent strings, we can represent each string by a specific pattern and then use a set to count the unique patterns.

A pattern for a special-equivalent string can be represented by sorting the characters at even indices and sorting the characters at odd indices. This is because we can only swap characters at even indices with each other and characters at odd indices with each other.

Here’s the code:

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class Solution:
    def numSpecialEquivGroups(self, words: List[str]) -> int:
        # Create a set to store unique patterns of special-equivalent strings
        special_equiv_groups = set()

        # Iterate through each word and find its pattern
        for word in words:
            # Separate even and odd indexed characters
            even_chars = ''.join(word[i] for i in range(0, len(word), 2))
            odd_chars = ''.join(word[i] for i in range(1, len(word), 2))

            # Sort the even and odd indexed characters and concatenate to form the pattern
            pattern = ''.join(sorted(even_chars)) + ''.join(sorted(odd_chars))

            # Add the pattern to the set of special-equivalent groups
            special_equiv_groups.add(pattern)

        # The number of unique patterns represents the number of groups of special-equivalent strings
        return len(special_equiv_groups)

This code works by defining a pattern for each special-equivalent string and counting the unique patterns. The time complexity is O(n * m * log(m)), where n is the number of words, and m is the length of each word. The space complexity is O(n * m), as we are storing a pattern for each word in the input list.