<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 DSU:
    def __init__(self, n):
        self.ranks = [1 for _ in range(n)]
        self.parents = [i for i in range(n)]
        self.num_components = n
    def find(self, i):
        if self.parents[i] == i:
            return i
        # route compression
        self.parents[i] = self.find(self.parents[i])
        return self.parents[i]

    def union(self, i, j):
        pi = self.find(i)
        pj = self.find(j)
        if pi == pj:
            return
        rpi, rpj = self.ranks[pi], self.ranks[pj]
        if rpi > rpj:
            self.parents[pj] = pi
        elif rpj > rpi:
            self.parents[pi] = pj
        else:
            self.parents[pi] = pj
            self.ranks[pj] += 1
        self.num_components -= 1
	


class Solution:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        n = len(s)
        dsu = DSU(n)
        ans = [""] * n
        for x,y in pairs:
            dsu.union(x,y)
        components = defaultdict(list)
        for i in range(n):
            components[dsu.find(i)].append((s[i], i))
        for component_list in components.values():
            indices = [cmp[1] for cmp in component_list]
            sorted_vals = sorted(cmp[0] for cmp in component_list)
            for i,c in zip(indices, sorted_vals):
                ans[i] = c
        return "".join(ans)
        
536