<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 Solution:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        # Union-Find data structure
        def find(x, root):
            if x != root[x]:
                root[x] = find(root[x], root)
            return root[x]
        
        def union(x, y, root, rank):
            root_x = find(x, root)
            root_y = find(y, root)
            if root_x != root_y:
                if rank[root_x] > rank[root_y]:
                    root[root_y] = root_x
                elif rank[root_x] < rank[root_y]:
                    root[root_x] = root_y
                else:
                    root[root_y] = root_x
                    rank[root_x] += 1
        
        # Initialize union-find structures
        n = len(s)
        root = list(range(n))
        rank = [0] * n
        
        # Perform union for each pair
        for u, v in pairs:
            union(u, v, root, rank)
        
        # Group characters by their root index
        groups = {}
        for i in range(n):
            r = find(i, root)
            if r not in groups:
                groups[r] = []
            groups[r].append(s[i])
        
        # Sort characters in each group
        for r in groups:
            groups[r].sort(reverse=True)
        
        # Construct the result string
        result = []
        for i in range(n):
            r = find(i, root)
            result.append(groups[r].pop())
        
        return ''.join(result)

# Example usage:
solution = Solution()
s = "dcab"
pairs = [[0,3],[1,2]]
print(solution.smallestStringWithSwaps(s, pairs))  # Output: "bacd"
491