<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

class DisjointSet:
    def __init__(self, size):
        self.parents = [i for i in range(size)]
        self.ranks = [0] * size

    def find(self, i):
        if self.parents[i] == i:
            return i
        self.parents[i] = self.find(self.parents[i])
        return self.parents[i]

    def union(self, a, b):
        parent_a = self.find(a)
        parent_b = self.find(b)
        if parent_a == parent_b:
            return

        rank_a = self.ranks[parent_a]
        rank_b = self.ranks[parent_b]
        if rank_a > rank_b:
            self.parents[parent_b] = parent_a
        elif rank_b > rank_a:
            self.parents[parent_a] = parent_b
        else:
            self.parents[parent_b] = parent_a
            self.ranks[parent_a] += 1


class Solution:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        disjoint_set = DisjointSet(len(s))
        for a, b in pairs:
            disjoint_set.union(a, b)

        parent_lists = defaultdict(list)
        for i, c in enumerate(s):
            parent_lists[disjoint_set.find(i)].append(c)
        for k in parent_lists.keys():
            parent_lists[k].sort(reverse=True)
        result = []
        for i in range(len(s)):
            result.append(parent_lists[disjoint_set.find(i)].pop())
        return "".join(result)

497