<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:
    
    def __init__(self, n):
        self.rank = [0 for i in range(n)]
        self.root = [i for i in range(n)]
        self.n = n
        
    def find(self, a):
        if self.root[a] == a:
            return a
        self.root[a] = self.find(self.root[a])
        return self.root[a]
        
    def union(self, a, b):
        aroot = self.find(a)
        broot = self.find(b)
        if aroot == broot:
            return
    
        arank = self.rank[aroot]
        brank = self.rank[broot]
        
        if arank > brank:
            self.root[broot] = aroot
        elif arank < brank:
            self.root[aroot] = broot
        else:
            self.root[aroot] = broot
            self.rank[broot] += 1
        self.n -= 1
            
class Solution:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        n = len(s)
        uf = UnionFind(n)
        
        for a, b in pairs:
            uf.union(a, b)
        
        # print(uf.root)
        
        mp = {}
        for i in range(n):
            root = uf.find(i)
            if root in mp:
                mp[root].append(s[i])
            else:
                mp[root] = [s[i]]

        sorted_mp = {k: sorted(v) for k, v in mp.items()}
        # print(sorted_mp)
        
        res = []
        for i in range(n):
            root = uf.find(i)
            res.append(sorted_mp[root].pop(0))
        return "".join(res)
        
        
        
790