<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:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        
        from collections import deque
        class UnionFind:

            def __init__(self, size):
                self.root = [i for i in range(size)]
                self.rank = [0] * size

            def find(self, x):
                if x == self.root[x]:
                    return x
                self.root[x] = self.find(self.root[x])
                return self.root[x]
        
            def union(self, x, y):
                root_x = self.find(x)
                root_y = self.find(y)
                if root_x != root_y:
                    if self.rank[root_x] > self.rank[root_y]:
                        self.root[root_y] = root_x
                    elif self.rank[root_x] < self.rank[root_y]:
                        self.root[root_x] = root_y
                    else:
                        self.root[root_y] = root_x
                        self.rank[root_y] += 1

            def isConnected(self, x, y):
                return self.find(x) == self.find(y)

        uf = UnionFind(len(s))

        for pair in pairs:
            uf.union(pair[0], pair[1])

        d = {}
        for i, char in enumerate(s):
            root = uf.find(i)
            if root not in d.keys():
                d[root] = [char]
            else:
                d[root].append(char)

        for key, chars in d.items():
            d[key] = deque(sorted(chars))

        res = [''] * len(s)
        for j in range(len(res)):
            root = uf.root[j]
            res[j] = d[root].popleft()
        
        return ''.join(res)

                
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