<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 Union(int x, int y) {
        int rx = find(x);
        int ry = find(y);
        if(rx!=ry) {
            if(rank[rx] > rank[ry]) root[ry] = rx;
            else if(rank[rx] < rank[ry]) root[rx] = ry;
            else {
                root[rx] = ry;
                rank[ry] += 1;
            }
        }
    }
    string smallestStringWithSwaps(string s, vector<vector<int>>& pairs) {
        int n = s.size();
        for(int i=0;i<n;i++) {
            root.push_back(i);
            rank.push_back(1);
        }
        for(auto & ele : pairs) {
            Union(ele[0], ele[1]);
        }
        // find root of each node
        map<int,vector<int>> children; // {root, all_children} children including root self
        for(int i=0;i<n;i++) children[find(i)].push_back(i);

        for (auto & [k, v] : children) {
            string child;
            for(auto idx : v) child.push_back(s[idx]);
            sort(child.begin(), child.end());
            int i = 0;
            for(auto c: child) {
                s[v[i]] = c;
                i++;
            }
        }
        return s;
    }
};
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