<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>

#include <vector>
#include <string>
#include <algorithm>
#include <unordered_map>
using namespace std;

class Solution {
public:
    // Union-Find (Disjoint Set Union) Helper functions
    int find(int x, vector<int>& parent) {
        if (parent[x] != x) {
            parent[x] = find(parent[x], parent);  // Path compression
        }
        return parent[x];
    }
    
    void unionSet(int x, int y, vector<int>& parent, vector<int>& rank) {
        int rootX = find(x, parent);
        int rootY = find(y, parent);
        
        if (rootX != rootY) {
            if (rank[rootX] > rank[rootY]) {
                parent[rootY] = rootX;
            } else if (rank[rootX] < rank[rootY]) {
                parent[rootX] = rootY;
            } else {
                parent[rootY] = rootX;
                rank[rootX]++;
            }
        }
    }
    
    string smallestStringWithSwaps(string s, vector<vector<int>>& pairs) {
        int n = s.size();
        vector<int> parent(n);
        vector<int> rank(n, 0);
        
        // Initialize the parent array where each element is its own parent
        for (int i = 0; i < n; ++i) {
            parent[i] = i;
        }
        
        // Union-Find to connect the pairs
        for (const auto& pair : pairs) {
            unionSet(pair[0], pair[1], parent, rank);
        }
        
        // Group the indices by their root parent (connected components)
        unordered_map<int, vector<int>> components;
        for (int i = 0; i < n; ++i) {
            int root = find(i, parent);
            components[root].push_back(i);
        }
        
        // Sort each component's characters and place them back in the string
        for (auto& component : components) {
            vector<int>& indices = component.second;
            string chars;
            
            // Collect characters at the indices of this component
            for (int idx : indices) {
                chars.push_back(s[idx]);
            }
            
            // Sort the characters and the indices
            sort(chars.begin(), chars.end());
            sort(indices.begin(), indices.end());
            
            // Reassign sorted characters to the sorted indices
            for (int i = 0; i < indices.size(); ++i) {
                s[indices[i]] = chars[i];
            }
        }
        
        return s;
    }
};

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