<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 {
public:
    vector<int> parent, rank;
    
    string smallestStringWithSwaps(string s, vector<vector<int>>& pairs) {
        int n = s.size();
        parent.resize(n), rank.resize(n, 1);
        for(int i=0; i<n; i++) {
            parent[i] = i;
        }
        
        for(auto pair : pairs) {
            unionFind(pair[0], pair[1]);
        }
        
        unordered_map<int, vector<int>> components;
        for(int i=0; i<n; i++) {
            components[find(i)].push_back(i);
        }
        
        unordered_map<int, vector<pair<char, int>>> sortedComponents;
        for(auto component : components) {
            for(auto element : component.second) {
                sortedComponents[component.first].push_back({s[element], element});
            }
            sort(components[component.first].begin(), components[component.first].end());
            sort(sortedComponents[component.first].begin(), sortedComponents[component.first].end());
        }
        
        for(auto component : components) {
            int n = component.second.size();
            for(int i=0; i<n; i++) {
                s[component.second[i]] = sortedComponents[component.first][i].first;
            }
        }
        return s;
    }
    
    int find(int x) {
        if(x == parent[x]) {
            return x;
        }
        return parent[x] = find(parent[x]);
    }
    
    bool unionFind(int x, int y) {
        int px = find(x), py = find(y);
        if(px == py) return false;
        
        if(rank[px] < rank[py]) {
            parent[px] = py;
        } else if(rank[px] > rank[py]) {
            parent[py] = px;
        } else {
            rank[py]++;
            parent[px] = py;
        }
        return true;
    }
};

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