<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:
    # Maximum number of vertices
    N = 100001

    def __init__(self):
        # Initialize adjacency list and visited list
        self.adj = [[] for _ in range(self.N)]
        self.visited = [False] * self.N

    def DFS(self, s, vertex, characters, indices):
        # Add the character and index to the list
        characters.append(s[vertex])
        indices.append(vertex)
        
        # Mark the current vertex as visited
        self.visited[vertex] = True
        
        # Traverse the adjacent vertices
        for adjacent in self.adj[vertex]:
            if not self.visited[adjacent]:
                self.DFS(s, adjacent, characters, indices)

    def smallestStringWithSwaps(self, s, pairs):
        # Build the adjacency list
        for edge in pairs:
            source = edge[0]
            destination = edge[1]
            
            # Undirected edge
            self.adj[source].append(destination)
            self.adj[destination].append(source)
        
        # Convert the string to a list for easier manipulation
        s = list(s)
        
        # Perform DFS for each unvisited vertex
        for vertex in range(len(s)):
            if not self.visited[vertex]:
                characters = []
                indices = []
                
                # Perform DFS and collect characters and indices
                self.DFS(s, vertex, characters, indices)
                
                # Sort the list of characters and indices
                characters.sort()
                indices.sort()

                # Place sorted characters at their respective indices
                for i in range(len(characters)):
                    s[indices[i]] = characters[i]
        
        # Convert the list back to a string and return it
        return ''.join(s)
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