Groups of Special-Equivalent Strings

You are given an array A of strings.

A move onto S consists of swapping any two even indexed characters of S, or any two odd indexed characters of S.

Two strings S and T are special-equivalent if after any number of moves onto S, S == T.

For example, S = "zzxy" and T = "xyzz" are special-equivalent because we may make the moves "zzxy" -> "xzzy" -> "xyzz" that swap S[0] and S[2], then S[1] and S[3].

Now, a group of special-equivalent strings from A is a non-empty subset of A such that:

1.Every pair of strings in the group are special equivalent, and;

2.The group is the largest size possible (ie., there isn't a string S not in the group such that S is special equivalent to every string in the group)

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

Example:

Input: ["abcd","cdab","cbad","xyzz","zzxy","zzyx"]
Output: 3
Explanation: 
One group is ["abcd", "cdab", "cbad"], since they are all pairwise special equivalent, and none of the other strings are all pairwise special equivalent to these.

The other two groups are ["xyzz", "zzxy"] and ["zzyx"].  Note that in particular, "zzxy" is not special equivalent to "zzyx".

Approach:

C++

#include <bits/stdc++.h>
using namespace std;

int numSpecialEquivGroups(vector<string> &A)
{
    unordered_set<string> set;
    for (auto &str : A)
    {
        string upper = "", lower = "";
        for (int i = 0; i < str.size(); ++i)
        {
            if (i & 1)
            {
                lower += str[i];
            }
            else
            {
                upper += str[i];
            }
        }
        sort(lower.begin(), lower.end());
        sort(upper.begin(), upper.end());
        str = lower + upper;
        if (set.find(str) == set.end())
        {
            set.insert(str);
        }
    }
    return set.size();
}
int main()
{
    vector<string> A = {"abcd", "cdab", "cbad",
                        "xyzz", "zzxy", "zzyx"};

    cout << numSpecialEquivGroups(A);

    return 0;
}