<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 Solution:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        n = len(s)
        uf = UF(n, s)
        for num1, num2 in pairs:
            uf.union(num1, num2)
        
        return uf.rearrange()
        
class UF:
    def __init__(self, n, s):
        self.parents = {x: x for x in range(n)}
        self.indices = collections.defaultdict(list)
        self.string = collections.defaultdict(list)
        self.n = n
        self.s = s
        self.ranks = {x: 0 for x in range(n)}
    
    def find(self, x):
        if self.parents[x] == x: return x
        return self.find(self.parents[x])
    
    def union(self, x1, x2):
        p1 = self.find(x1)
        p2 = self.find(x2)
        if p1 == p2: return
        self.parents[max(p1, p2)] = min(p1, p2)
        # self.parents[x1] = min(p1, p2)
        # self.parents[x2] = min(p1, p2)
        # if self.ranks[p1] > self.ranks[p2]:
        #     self.parents[p2] = p1
        # else:
        #     self.parents[p1] = p2
        #     if self.ranks[p1] == self.ranks[p2]:
        #         self.ranks[p2] += 1
            
        
    def rearrange(self):
        for k, v in self.parents.items():
            v = self.find(v)
            self.indices[v].append(k)
            self.string[v].append(self.s[k])
                
        for k, v in self.string.items():
            v.sort(reverse = True)
        
        res = ''
        for i in range(self.n):
            res += self.string[self.find(self.parents[i])].pop()
        return res
595