<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>

struct UnionFind {
    vector<int> parents;
    
    UnionFind(size_t n): parents(n) {
        iota(parents.begin(), parents.end(), 0);
    }
    
    int find(int i) {
        while (i != parents[i]) {
            i = parents[i] = parents[parents[i]];
        }
        return i;
    }
    
    void do_union(const int i, const int j) {
        const int parent_i = find(i);
        const int parent_j = find(j);
        
        parents[parent_j] = parents[j] = parents[i];
    }
    
};

class Solution {
public:
    string smallestStringWithSwaps(string s, vector<vector<int>>& pairs) {
        int n = size(s);
        UnionFind uf(n);
        
        for (auto &p : pairs)  {
            uf.do_union(p[0], p[1]);
        }
        
        /* 
         * countTable represent 2d of array 
         * the first dimension is for parent of the union find node if the slot idx is not parent then we don't use it
         * the second dimension is represent number of character depend on the index. 0 = a, 1 = b, ..., 25 = z
         *
         * cursors represent current character of the countTable we from 0..=25, or we could say 'a' to 'z'
         */
        vector<vector<int>> countTable(n, vector<int>(26));
        vector<int> cursors(n);
        for (int i = 0; i < n; i++) {
            countTable[uf.find(i)][s[i] - 'a']++;
        }
        
        for (int i = 0; i < n; i++) {
            int j = uf.find(i);
            
            // move cursor until we find next character in the bucket
            while (countTable[j][cursors[j]] == 0) cursors[j]++;
            countTable[j][cursors[j]]--;
            
            // reuse input as a result
            s[i] = cursors[j] + 'a';
        }
        return s;
    }
};
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