<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 {
    class unionFind {
        vector<int> root;
        vector<int> rank;
        
    public:
        unionFind(int sz) : root(sz), rank(sz, 1) {
            for (int i = 0; i < sz; i++) {
                root[i] = i;
            }
        }

        int find(int x) {
            if (x == root[x]) return x;
            return root[x] = find(root[x]);
        }

        void unionf(int x, int y) {
            int rootx = find(x);
            int rooty = find(y);
            if (rootx != rooty) {
                if (rank[rootx] > rank[rooty]) {
                    root[rooty] = rootx;
                } else if (rank[rooty] > rank[rootx]) {
                    root[rootx] = rooty;
                } else {
                    root[rootx] = rooty;
                    rank[rooty] += 1;
                }
            }
        }

        vector<vector<int>> connectedComponents(int n) {
            unordered_map<int, vector<int>> components;
            for (int i = 0; i < n; i++) {
                int t = find(i);
                components[t].push_back(i);
            }

            vector<vector<int>> res;
            for (auto& comp : components) {
                res.push_back(comp.second);
            }
            return res;
        }
    };
    
public:
    string smallestStringWithSwaps(string s, vector<vector<int>>& pairs) {
        int n = s.size();
        unionFind uf(n);
        for (auto& pair : pairs) {
            uf.unionf(pair[0], pair[1]);
        }

        string resStr(s);
        vector<vector<int>> res = uf.connectedComponents(n);
        for (auto& v : res) {
            sort(v.begin(), v.end());
            vector<char> tmp;
            for (int i = 0; i < v.size(); i++) {
                tmp.push_back(s[v[i]]);
            }
            sort(tmp.begin(), tmp.end());
            for (int i = 0; i < v.size(); i++) {
                resStr[v[i]] = tmp[i];
            }
        }
        return resStr;
    }
};

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