<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) -> None:
        self.root=[i for i in range(n)]
        self.rank = [1]*n
        self.count = n

    def find(self,x):
        if(self.root[x]==x):
            return x
        self.root[x] = self.find(self.root[x])
        return self.root[x]
    
    def union(self,x,y):
        rootX = self.find(x)
        rootY = self.find(y)
        if(rootX!=rootY):
            if(self.rank[rootX]>self.rank[rootY]):
                self.root[rootY] = rootX
            elif(self.rank[rootX]<self.rank[rootY]):
                self.root[rootX] = rootY
            else:
                self.root[rootY] = rootX
                self.rank[rootX]+=1
            self.count-=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)
        
        roots = {}
        for i in range(n):
            r = uf.find(i)
            if(r not in roots):
                roots[r] =[i]
            else:
                roots[r].append(i)
        ans  =[""]*n
        for r in roots:
            indexes = roots[r]
            arr = []
            for i in indexes:
                arr.append(s[i])
            arr.sort()
            for i in indexes:
                ans[i] = arr.pop(0)

        return "".join(ans)
738