<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 typing import List, Dict
from collections import defaultdict

class UnionFind:
    def __init__(self, s: str):
        self.root = [i for i in range(len(s))]
        self.rank = [1] * len(s)        
        
    def find(self, x) -> int:
        if x == self.root[x]:
            return x
        
        self.root[x] = self.find(self.root[x])
        
        return self.root[x]
    
    def union(self, x, y):
        
        rx = self.find(x)
        ry = self.find(y)
        
        if rx != ry:
            if self.rank[rx] > self.rank[ry]:
                self.root[ry] = rx
            elif self.rank[rx] < self.rank[ry]:
                self.root[rx] = ry
            else:
                self.root[ry] = rx
                self.rank[rx] += 1
                
    def get_groups(self) -> Dict[int, List[int]]:
        
        groups = defaultdict(list)
        
        for pos in range(len(self.root)):
            
            groups[self.find(pos)].append(pos)
            
        return groups
        

class Solution:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        
        uf = UnionFind(s)
        
        for pair in pairs:
            uf.union(*pair)
            
        groups = uf.get_groups()
        
        s_list = list(s)
        ans = list(s)
        
        for group in groups.values():
            
            lex_sorted = sorted(group, key=lambda x: ord(s_list[x]))
            group_sorted = sorted(group)
            
            for i, pos in enumerate(group_sorted):
                ans[pos] = s_list[lex_sorted[i]]
            
        return "".join(ans)
        
        
        
478