<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 __init__(self):
        self.father: List[int] = []

    def find(self, x) -> int:
        if x != self.father[x]:
            self.father[x] = self.find(self.father[x])
        return self.father[x]

    def union(self, x, y):
        fx = self.find(x)
        fy = self.find(y)

        if fx != fy:
            self.father[fx] = fy

    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        charArr: List[str] = list(s)
        res: List[str] = ["" for _ in range(len(charArr))]
        self.father = [i for i in range(len(charArr))]

        # construct the graph
        for edge in pairs:
            self.union(edge[0], edge[1])

        print(self.father)

        # find each sub-graph
        # graph -> [[indexes, charArr]]
        subGraph: List[List[int]] = [[[],[]] for _ in range(len(charArr))]
        for i in range(len(charArr)):
            father = self.find(i)
            subGraph[father][0].append(i)
            subGraph[father][1].append(charArr[i])

        # sort to combine each sub-graph then combine the whole string
        for i in range(len(charArr)):
            if len(subGraph[i][0]) > 0:
                subGraph[i][0].sort()
                subGraph[i][1].sort()
                
                print(subGraph[i])
                for index, char in zip(subGraph[i][0], subGraph[i][1]):
                    res[index] = char
        
        return ''.join(res)
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