<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 UnionFind:
    def __init__(self) -> None:
        self.parents = {}  # item -> item (parent)
        self.ranks = {}

    def find(self, item):
        parent = self.parents[item]
        if parent != item:
            return self.find(parent)
        return parent

    def union(self, item1, item2):
        parent1 = self.find(item1)
        parent2 = self.find(item2)

        if parent1 != parent2:
            if self.ranks[parent1] > self.ranks[parent2]:
                self.parents[parent2] = self.parents[parent1]
                self.ranks[parent1] += self.ranks[parent2]
            else:
                self.parents[parent1] = self.parents[parent2]
                self.ranks[parent2] += self.ranks[parent1]

    def add(self, item):
        if item not in self.parents:
            self.parents[item] = item
            self.ranks[item] = 1


class Solution:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        if not pairs:
            return s
        union_find = UnionFind()
        for a, b in pairs:
            union_find.add(a)
            union_find.add(b)
            union_find.union(a, b)

        for i in range(len(s)):
            union_find.add(i)

        unions = defaultdict(list)
        for i in range(len(s)):
            unions[union_find.find(i)].append((s[i], i))

        groups: list[tuple[str, list[int]]] = []
        for v in unions.values():
            curr_s = ''
            indices = []
            for l, n in v:
                curr_s += l
                indices.append(n)
            groups.append((sorted(curr_s), sorted(indices)))

        if len(groups) == 1:
            return ''.join(sorted(s))

        ret = [None] * len(s)
        for i in range(len(groups)):
            group = groups[i]
            for c, idx in zip(*group):
                ret[idx] = c
        return ''.join(ret)

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