<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, size) -> None:
        self.head = [i for i in range(size)]
        self.rank = [1] * size

    def find(self, x):
        # find the root
        root = x
        while root != self.head[root]:
            root = self.head[root]

        # set each node to point directly at x as we go
        while x != root:
            old_root = self.head[x]
            self.head[x] = root
            x = old_root

        return root

    def union(self, x, y):
        head_x = self.find(x)
        head_y = self.find(y)

        if head_x != head_y:
            if self.rank[head_x] > self.rank[head_y]:
                self.head[head_y] = head_x
            elif self.rank[head_x] < self.rank[head_y]:
                self.head[head_x] = head_y
            else:
                self.head[head_y] = head_x
                self.rank[head_x] += 1

class Solution:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        uf = UnionFind(len(s))
        
        for i, j in pairs:
            uf.union(i, j)
        
        head_to_component = {i: [] for i in range(len(s))}
        
        for i in range(len(s)):
            head_to_component[uf.find(i)].append(i)
        
        answer = [0]*len(s)
        for head, indices in head_to_component.items():
            characters = sorted([s[i] for i in indices])
            for i, index in enumerate(indices):
                answer[index] = characters[i]
        
        return "".join(answer)
        
57779