<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.parents = [i for i in range(n)]
        self.ranks = [1] * n
    def find(self, i):
        p = self.parents[i]
        if p == i:
            return i
        p = self.find(p)
        self.parents[i] = p
        return p
    def union(self, i, j):
        p1 = self.find(i)
        p2 = self.find(j)

        if p1 != p2:
            if self.ranks[p1] >= self.ranks[p2]:
                self.parents[p2] = p1
                self.ranks[p1] += int(self.ranks[p1] == self.ranks[p2])
            else:
                self.parents[p1] = p2

class Solution:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        n = len(s)
        u_find = UnionFind(n)

        for s_,e_ in pairs:
            u_find.union(s_,e_)
        all_parents = list(u_find.find(i) for i in range(n))
        conn_groups = defaultdict(list)

        for i in range(n):
            p = all_parents[i]
            conn_groups[p].append(s[i])

        for k in conn_groups.keys():
            conn_groups[k] = sorted(conn_groups[k])
        group_last_ind = defaultdict(int)
        '''
        For each group, sort the elements and start building the resulting string
        '''
        res = []
        for i in range(n):
            g_ind = all_parents[i]
            sub_g_ind = group_last_ind[g_ind]
            res.append(conn_groups[g_ind][sub_g_ind])
            group_last_ind[g_ind] += 1
        return "".join(res)



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