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Leetcode 893. Groups of Special

Problem Statement

You are given an array A of strings. Two strings S and T are considered special-equivalent if after any number of moves, S can become T.

A move consists of choosing two indices i and j with the same parity (both even or both odd) and swapping S[i] with S[j].

Return the number of groups of special-equivalent strings from A.

Clarifying Questions

  1. Input Constraints:
    • How large can the strings in the array A be?
    • Are all characters lowercase English letters?
  2. Output:
    • Do we need to return the count of unique special-equivalent groups or the actual groups?

For the sake of this problem, we assume:

Strategy

  1. Character Grouping by Parity:
    • Each string can be divided into two substrings: one containing characters at even indices and another containing characters at odd indices.
  2. Normalization:
    • For any given string, sort the characters at even indices and characters at odd indices separately.
    • Concatenate these sorted substrings to form a normalized representation of the string.
  3. Using a Set for Uniqueness:
    • Use a set to store these normalized forms because sets inherently avoid duplicates.
    • The size of the set at the end gives the number of unique groups.

Code

#include <iostream>
#include <vector>
#include <unordered_set>
#include <algorithm>

int numSpecialEquivGroups(std::vector<std::string>& A) {
    std::unordered_set<std::string> unique_groups;

    for (const auto &s : A) {
        std::string even, odd;

        // Separate characters by even and odd indices
        for (int i = 0; i < s.size(); ++i) {
            if (i % 2 == 0)
                even += s[i];
            else
                odd += s[i];
        }

        // Sort both parts
        std::sort(even.begin(), even.end());
        std::sort(odd.begin(), odd.end());

        // Concatenate sorted parts and add to the set
        unique_groups.insert(even + odd);
    }

    return unique_groups.size();
}

int main() {
    std::vector<std::string> A = {"abc","acb","bac","bca","cab","cba"};
    std::cout << "Number of groups: " << numSpecialEquivGroups(A) << std::endl;
    return 0;
}

Time Complexity

This approach ensures we effectively group all special-equivalent strings and then determine the count of such groups.

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