<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 UnionFind{
    public : 
    vector<int> par, sz;
    UnionFind(int n): par(n) , sz(n,1) {
        iota(par.begin(),par.end(),0);
    }
    int find(int x){
        if(par[x]==x) return x;
        return par[x] = find(par[x]);
    }
    
    bool Union(int x,int y){
        int xp = find(x);
        int yp = find(y);
        
        if(xp==yp) return false;
        
        if(sz[xp]>sz[yp]) {par[yp] = xp; sz[xp]+=sz[yp];}
        else {par[xp]=yp; sz[yp]+=sz[xp];}
        return true;
    }
};
class Solution {
public:
    string smallestStringWithSwaps(string s, vector<vector<int>>& pairs) {
       string ans(s.size(),' '); 
       UnionFind uf(s.size()+1);
       for(auto x:pairs)
           uf.Union(x[0],x[1]);
       unordered_map<int,multiset<char>> m;
       for(int i=0;i<s.size();i++){
           m[uf.find(i)].insert(s[i]);
       } 
       for(int i=0;i<s.size();i++){
           auto it = m[uf.find(i)].begin();
           ans[i]=*it;
           m[uf.find(i)].erase(it);
       } 
        return ans;
    }
};
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