<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.root = {i : i for i in range(n)}
        self.rank = [1] * n
        
    def find(self,node):
        if node == self.root[node]:
            return node
        self.root[node] = self.find(self.root[node])
        return self.root[node]
    
    def union(self,node1,node2):
        root1 = self.find(node1)
        root2 = self.find(node2)
        if root1 != root2:
            if self.rank[root1] > self.rank[root2]:
                self.root[root2] = root1
            elif self.rank[root2] > self.rank[root1]:
                self.root[root1] = root2
            else:
                self.root[root2] = root1
                self.rank[root1] += 1
        
    
class Solution:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        # figure out each set of strings that can be swapped and swap them in lexicographical order.
        
        uf = UnionFind(len(s))
        
        for i,j in pairs:
            uf.union(i,j)
        
        rootToComp = collections.defaultdict(list)
        for i in range(len(s)):
            root = uf.find(i)
            rootToComp[root].append(s[i])

        for k in rootToComp.keys():
            rootToComp[k].sort()

        res = ''
        for i in range(len(s)):
            res += rootToComp[uf.root[i]].pop(0)


        return res
        
        
        
784