<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:
        from collections import defaultdict
        
        # Maximum size of the string
        n = len(s)
        
        # Visited array to mark nodes
        visited = [False] * n
        
        # Adjacency list to represent the graph
        adj = defaultdict(list)
        
        # Depth-first search function
        def dfs(i):
            chars.append(s[i])  # Add the character of the current index to chars
            idxs.append(i)  # Add the index to idxs
            visited[i] = True  # Mark the node as visited
            
            # Traverse all the adjacent nodes
            for nei in adj[i]:
                if not visited[nei]:
                    dfs(nei)

        # Build the adjacency list from the pairs
        for src, dest in pairs:
            adj[src].append(dest)
            adj[dest].append(src)

        # Result array, initialized with empty strings
        res = [""] * n

        # Traverse all nodes
        for i in range(n):
            if visited[i]:  # If node is already visited, skip it
                continue

            # For connected components, collect chars and their indices
            chars, idxs = [], []
            dfs(i)  # Perform DFS to collect connected component
            
            # Sort the characters and indices to form the smallest possible lexicographical order
            chars.sort()
            idxs.sort()

            # Place the sorted characters back to their correct positions
            for j in range(len(chars)):
                res[idxs[j]] = chars[j]

        return "".join(res)

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