<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 DisjointSet{
    vector<int>rank,par,size;
public:
    DisjointSet(int n)
    {
        rank.resize(n+1,0);
        size.resize(n+1);
        par.resize(n+1);
        for(int i=0;i<=n;i++)
        {
            par[i]=i;
            size[i]=1;
        }
    }

    int findPar(int u)
    {
        if(u==par[u])
        return u;

        return par[u] = findPar(par[u]);
    }

    void unionByRank(int u, int v)
    {
        int ult_pu=findPar(u);
        int ult_pv=findPar(v);
        if(ult_pu==ult_pv) return;

        if(rank[ult_pu]<rank[ult_pv])
        par[ult_pu]=ult_pv;

        else if(rank[ult_pv]<rank[ult_pv])
        par[ult_pv]=ult_pu;

        else
        {
            par[ult_pu]=ult_pv;
            rank[ult_pv]++;
        }  
    }

    void unionBySize(int u, int v)
    {
        int ult_pu=findPar(u);
        int ult_pv=findPar(v);
        if(ult_pu==ult_pv) return;

        if(size[ult_pu]<ult_pv)
        {
            par[ult_pu]=ult_pv;
            size[ult_pv]+=size[ult_pu];
        }
        else
        {
            par[ult_pv]=ult_pu;
            size[ult_pu]+=size[ult_pv];
        }

    }
};
class Solution {
public:
    string smallestStringWithSwaps(string s, vector<vector<int>>& pairs) {
        int n=s.size();

        DisjointSet ds(n);
        for(int i=0;i<pairs.size();i++)
        ds.unionBySize(pairs[i][0],pairs[i][1]);

        unordered_map<int, multiset<char>>m;
        for(int i=0;i<n;i++)
        {
            m[ds.findPar(i)].insert(s[i]);
        }

        for(int i=0;i<n;i++)
        {
            auto it=m[ds.findPar(i)].begin();
            s[i]=*it;
            m[ds.findPar(i)].erase(it);
        } 
        return s;
         
    }
};
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