Grouping / equivalence (Union-Find (DSU) Sub-pattern)

// Grouping by "is equivalent to": union every given pair, then collect each root's members.
// Uses the DSU from the Union-Find template. Here: Smallest String With Swaps.
string smallestStringWithSwaps(string s, const vector<vector<int>>& pairs) {
    int n = s.size();
    DSU dsu(n);
    for (auto& p : pairs) dsu.unite(p[0], p[1]);  // swaps chain: (0,3) and (3,1) let 0, 1, 3 trade freely
    unordered_map<int, vector<int>> members;       // root → indices in that group, increasing
    for (int i = 0; i < n; i++) members[dsu.find(i)].push_back(i);
    for (auto& [root, idx] : members) {
        string chars;
        for (int i : idx) chars += s[i];
        sort(chars.begin(), chars.end());          // inside a group any arrangement is reachable
        for (int k = 0; k < (int)idx.size(); k++) s[idx[k]] = chars[k];
    }
    return s;
}