<p>You are given a string <code>s</code>, and an array of pairs of indices in the string&nbsp;<code>pairs</code>&nbsp;where&nbsp;<code>pairs[i] =&nbsp;[a, b]</code>&nbsp;indicates 2 indices(0-indexed) of the string.</p>

<p>You can&nbsp;swap the characters at any pair of indices in the given&nbsp;<code>pairs</code>&nbsp;<strong>any number of times</strong>.</p>

<p>Return the&nbsp;lexicographically smallest string that <code>s</code>&nbsp;can be changed to after using the swaps.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;dcab&quot;, pairs = [[0,3],[1,2]]
<strong>Output:</strong> &quot;bacd&quot;
<strong>Explaination:</strong> 
Swap s[0] and s[3], s = &quot;bcad&quot;
Swap s[1] and s[2], s = &quot;bacd&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;dcab&quot;, pairs = [[0,3],[1,2],[0,2]]
<strong>Output:</strong> &quot;abcd&quot;
<strong>Explaination: </strong>
Swap s[0] and s[3], s = &quot;bcad&quot;
Swap s[0] and s[2], s = &quot;acbd&quot;
Swap s[1] and s[2], s = &quot;abcd&quot;</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;cba&quot;, pairs = [[0,1],[1,2]]
<strong>Output:</strong> &quot;abc&quot;
<strong>Explaination: </strong>
Swap s[0] and s[1], s = &quot;bca&quot;
Swap s[1] and s[2], s = &quot;bac&quot;
Swap s[0] and s[1], s = &quot;abc&quot;
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 10^5</code></li>
	<li><code>0 &lt;= pairs.length &lt;= 10^5</code></li>
	<li><code>0 &lt;= pairs[i][0], pairs[i][1] &lt;&nbsp;s.length</code></li>
	<li><code>s</code>&nbsp;only contains lower case English letters.</li>
</ul>

class UnionSet{
    public:
    UnionSet(int nodesCount) : islands(nodesCount) {
        rank = vector<int>(nodesCount, 1);
        root.resize(nodesCount);
        std::iota(root.begin(), root.end(), 0);
    }
    
    int FindRoot(int node){
        if (node == root[node])
            return root[node];
        return root[node] = FindRoot(root[node]);
    }
    
    void Union(int firstNode, int secondNode){
        auto firstRoot = FindRoot(firstNode);
        auto secondRoot = FindRoot(secondNode);
        
        if (firstRoot != secondRoot){
            if (rank[firstRoot] > rank[secondRoot]){
                root[secondRoot] = firstRoot;
            }
            else if (rank[firstRoot] < rank[secondRoot]){
                root[firstRoot] = secondRoot;
            }
            else{
                root[secondRoot] = firstRoot;
                ++rank[firstRoot];
            }
            --islands;
        }
    }
    
    bool IsConnected(int left, int right){
        return FindRoot(left) == FindRoot(right);
    }
    
    int Islands(){
        return islands;
    }
    
    std::unordered_map<int, set<int>> GetIsLands(){
        std::unordered_map<int, set<int>> islands;
        for (int i = 0; i < root.size(); ++i){
            islands[FindRoot(i)].insert(i);
        }
        return islands;
    }
    

    int islands = 0;
    vector<int> rank;
    vector<int> root;
    
};

class Solution {
public:
    string smallestStringWithSwaps(string s, vector<vector<int>>& pairs) {
        string answer;
        answer.resize(s.size());
        UnionSet disjointSet(s.size());
        for (const auto& elem : pairs){
            disjointSet.Union(elem[0], elem[1]);
        }
        auto islands = disjointSet.GetIsLands();
        for (const auto& [key, value] : islands){
                vector<int> sortedIndexes(value.begin(), value.end());
                vector<int> sortedLetters(value.begin(), value.end());
                std::sort(sortedLetters.begin(), sortedLetters.end(), [&s] (int left, int right){
                    return s[left] < s[right];
                });
                for (int i = 0; i < sortedIndexes.size(); ++i){
                    answer[sortedIndexes[i]] = s[sortedLetters[i]];
                }
        }
        return answer;
    }
};
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