<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>

import heapq
class Solution:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        roots = [ [i, [s[i]], [i]]for i in range(len(s))]
        for i,j in pairs:
            self.union(i,j,roots)
        res = ['']*len(s)
        for i in range(len(s)):
            if i == roots[i][0]:
                char_heap, idx_heap = roots[i][1], roots[i][2]
                heapq.heapify(roots[i][1]), heapq.heapify(roots[i][2])
                while char_heap:
                    char, idx = heapq.heappop(char_heap), heapq.heappop(idx_heap)
                    res[idx] = char
        return ''.join(res)
        
    def union(self, i, j, roots):
        parent_i, parent_j = self.find_parent(i, roots), self.find_parent(j, roots)
        if parent_i == parent_j:
            return
        if len(roots[parent_i][1]) > len(roots[parent_j][1]):
            roots[parent_j][0] = parent_i
            roots[parent_i][1].extend(roots[parent_j][1])
            roots[parent_i][2].extend(roots[parent_j][2])
        else:
            roots[parent_i][0] = parent_j
            roots[parent_j][1].extend(roots[parent_i][1])
            roots[parent_j][2].extend(roots[parent_i][2])
        
    def find_parent(self, i, roots):
        if i == roots[i][0]:
            return i
        roots[i][0] = self.find_parent(roots[i][0], roots)
        return roots[i][0]
        
        
641