<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 Solution {
public:
    vector<int>root;
    vector<int>rank;
    int find(int x){
        if(x == root[x])
            return x;
        root[x] = find(root[x]);
        return root[x];
    }
    void unionPair(int x, int y){
        int rootX = find(x);
        int rootY = find(y);
        
        if(rootX != rootY){
            if(rank[rootX] > rank[rootY]){
                root[rootY] = rootX;
            }
            else if(rank[rootY] < rank[rootX]){
                root[rootX] = rootY;
            }
            else{
                root[rootY] = rootX;
                rank[rootX]++;
            }
        }
    }
    string smallestStringWithSwaps(string s, vector<vector<int>>& pairs) {
        int n = s.length();
        for(int i = 0; i < n; i++ ){
            root.push_back(i);
            rank.push_back(1);
        }
        
        for(auto pair : pairs){
            unionPair(pair[0], pair[1]);
        }

        map<int, vector<int>> roottoComp;

        for(int vertex = 0; vertex < n; vertex++){
            int root = find(vertex);
            roottoComp[root].push_back(vertex);
        }

        string output(n, ' ');

        for(auto component : roottoComp ){
            vector<int> indices = component.second;

            vector<char> chars;
            for(int idx : indices){
                chars.push_back(s[idx]);
            }
            sort(chars.begin(), chars.end());

            for(int idx = 0; idx < indices.size(); idx++){
                output[indices[idx]] = chars[idx];
            }
        }

        return output;
    }
};
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