<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 {
private:
    vector<int> root;
    vector<int> rank;
public:
    // Initialize the array root and rank
    // Each vertex is representative of itself with rank 1
    UnionFind(int sz) : root(sz), rank(sz) {
        for (int i = 0; i < sz; i++) {
            root[i] = i;
            rank[i] = 1;
        }
    }
    
    // Get the root of a vertex
    int find(int x) {
        if (x == root[x]) {
            return x;
        }
        return root[x] = find(root[x]);
    }

    // Perform the union of two components
    void unionSet(int x, int y) {
        int rootX = find(x);
        int rootY = find(y);
        if (rootX != rootY) {
            if (rank[rootX] >= rank[rootY]) {
                root[rootY] = rootX;
                rank[rootX] += rank[rootY];
            } else {
                root[rootX] = rootY;
                rank[rootY] += rank[rootX];
            }
        }
    }
};

class Solution {
public:
    string smallestStringWithSwaps(string s, vector<vector<int>>& pairs) {
        UnionFind uf(s.size());
        
        // Iterate over the edges
        for (vector<int> edge : pairs) {
            int source = edge[0];
            int destination = edge[1];
            
            // Perform the union of end points
            uf.unionSet(source, destination);
        }
        
        
        unordered_map<int, vector<int>> rootToComponent;
        // Group the vertices that are in the same component
        for (int vertex = 0; vertex < s.size(); vertex++) {
            int root = uf.find(vertex);
            // Add the vertices corresponding to the component root
            rootToComponent[root].push_back(vertex);
        }
        
        // String to store the answer
        string smallestString(s.length(), ' ');
        // Iterate over each component
        for (auto component : rootToComponent) {
            vector<int> indices = component.second;
            
            // Sort the characters in the group
            vector<char> characters;
            for (int index : indices) {
                characters.push_back(s[index]);
            }
            sort(characters.begin(), characters.end());
            
            // Store the sorted characters
            for (int index = 0; index < indices.size(); index++) {
                smallestString[indices[index]] = characters[index];
            }
        }
        
        return smallestString;
    }
};



// class Solution {
// public:
//     // Maximum number of vertices
//     static const int N = 100001;
//     vector<int> adj[N];
//     bool visited[N];
    
//     void DFS(string& s, int vertex, vector<char>& characters, vector<int>& indices) {
//         // Add the character and index to the list
//         characters.push_back(s[vertex]);
//         indices.push_back(vertex);
//         visited[vertex] = true;
        
//         // Traverse the adjacents
//         for (int adjacent : adj[vertex]) {
//             if (!visited[adjacent]) {
//                 DFS(s, adjacent, characters, indices);
//             }
//         }
//     }
    
//     string smallestStringWithSwaps(string s, vector<vector<int>>& pairs) {
        
//         // Build the adjacency list
//         for (vector<int> edge : pairs) {
//             int source = edge[0], destination = edge[1];
//             // Undirected edge
//             adj[source].push_back(destination);
//             adj[destination].push_back(source);
//         }
        
//         for (int vertex = 0; vertex < s.size(); vertex++) {
//             // If not covered in the DFS yet
//             if (!visited[vertex]) {
//                 vector<char> characters;
//                 vector<int> indices;
                
//                 // DFS, get all vertices that are connected with curr vertex
//                 DFS(s, vertex, characters, indices);
//                 // Sort the list of characters and indices
//                 sort(characters.begin(), characters.end());
//                 sort(indices.begin(), indices.end());

//                 // Store the sorted characters corresponding to the index
//                 for (int index = 0; index < characters.size(); index++) {
//                     s[indices[index]] = characters[index];
//                 }
//             }
//         }
//         return s;
//     }
// };












// ////////


// //////



60537