<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:
    string smallestStringWithSwaps(string s, vector<vector<int>>& pairs) {
        int n = s.size();
        vector<vector<int>> adj(n,vector<int>());
        for(auto it:pairs){
            adj[it[0]].push_back(it[1]);
            adj[it[1]].push_back(it[0]);
        }
        vector<int> vis(n,0);
        vector<char> ans(n);
        for(int i=0; i<n; i++){
            if(!vis[i]){
                vector<int> es;    //indices of the CC
                bfs(i , adj , es , vis);
                sort(es.begin() , es.end());
                vector<char> c;  //characters at the indices of a CC
                for(auto it:es){
                    c.push_back(s[it]);  
                }
                // sorted letters mapped to sorted index sequence of the CC
                sort(c.begin() , c.end());
                int k = 0;
                for(auto it:es){
                    ans[it] = c[k]; k++;
                }
            }
        }
        string finn = "";
        for(int i=0; i<n; i++){
            finn += ans[i];
        }
        return finn;
    }
    void bfs(int st, vector<vector<int>>& adj, vector<int>& es , vector<int>& vis){
        queue<int> q;
        q.push(st);
        vis[st] = 1;
        es.push_back(st);
        while(!q.empty()){
            int par = q.front();
            q.pop();
            for(auto it:adj[par]){
                if(!vis[it]){
                    vis[it] = 1;
                    q.push(it);
                    es.push_back(it);
                }
            }
        }
    }
};
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