<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>

from collections import defaultdict
from typing import List

class Solution:
    def find(self, parent, i):
        if parent[i] != i:
            parent[i] = self.find(parent, parent[i])
        return parent[i]
    
    def union(self, parent, rank, x, y):
        rootX = self.find(parent, x)
        rootY = self.find(parent, y)
        
        if rootX != rootY:
            if rank[rootX] > rank[rootY]:
                parent[rootY] = rootX
            elif rank[rootX] < rank[rootY]:
                parent[rootX] = rootY
            else:
                parent[rootY] = rootX
                rank[rootX] += 1
    
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        n = len(s)
        parent = list(range(n))
        rank = [1] * n
        
        # Union-Find: Grouping connected indices
        for x, y in pairs:
            self.union(parent, rank, x, y)
        
        # Group all characters by their connected component
        groups = defaultdict(list)
        for i in range(n):
            root = self.find(parent, i)
            groups[root].append(s[i])
        
        # Sort characters in each group lexicographically
        for key in groups.keys():
            groups[key].sort(reverse=True)
        
        # Build the lexicographically smallest string by picking the smallest characters from each group
        result = []
        for i in range(n):
            root = self.find(parent, i)
            result.append(groups[root].pop())
        
        return ''.join(result)

484