<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 DSU {
	vector<int> p;
	vector<int> s;
	
  	// constructor initilisation
	DSU(int size) : p(size), s(size, 1) {
		for (int i = 0; i < size; i++) { p[i] = i; }
	}

    // finding the identifer of set containing element x
	int find(int x) {
		return p[x] == x ? x : (p[x] = find(p[x]));
	}
	
	// union of two sets set containing x & set containing y
	bool unite(int x, int y) {
		x = find(x);
		y = find(y);
		if (x == y) return false;
		if(s[x] > s[y]) swap(x, y);
		s[y] += s[x];
		s[x] = s[y]; 
		p[x] = y;
		return true;  
	}
	
	// return true if the element x and y belongs to same set else false
	bool sameSet(int x, int y) { return find(x) == find(y); }
	
	// returns size of set containing element x
	int sizeOfSet(int x){ return s[find(x)]; }
};
class Solution {
public:
    string smallestStringWithSwaps(string s, vector<vector<int>>& a) {
        int n = s.size();
        DSU dsu(n);
        map<int, set<int>> m;
        for(int i = 0; i < (int)a.size(); i++){
            int x = a[i][0];
            int y = a[i][1];
            if(!dsu.sameSet(x, y)){
                dsu.unite(x, y);
            }
        }
        for(int i = 0; i < n; i++){
            int p = dsu.find(i);
            m[p].insert(i);
        }
        map<int, char> resm;
        for(auto v : m){
            string t = "";
            for(auto x : v.second){
                t += s[x];
            }
            sort(t.begin(), t.end());
            int i = 0;
            for(auto x : v.second){
                resm[x] = t[i];
                i++;
            }
        }
        string res = "";
        for(auto x : resm){
            res += x.second;
        }
        return res;
    }
};
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