<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:
        def binary_search(l, c):
            left = 0
            right = len(l)
            
            while left < right:
                mid = (left + right)//2
                if l[mid] > c:
                    right = mid
                else:
                    left = mid + 1
            return left
        
        my_dict = defaultdict(list)
        n = len(s)
        
        # Union find
        root = [i for i in range(n)]
        rank = [1] * n
        
        def find(x):
            if x == root[x]:
                return x
            root[x] = find(root[x])
            return root[x]
        def union(x, y):
            rootx = find(x)
            rooty = find(y)
            if rootx != rooty:
                if rank[rootx] > rank[rooty]:
                    root[rooty] = rootx
                elif rank[rootx] < rank[rooty]:
                    root[rootx] = rooty
                else:
                    root[rooty] = rootx
                    rank[rootx] +=1
                    
        for x, y in pairs:
            union(x, y)
        
        for i, c in enumerate(s):
            index = binary_search(my_dict[find(i)], c)
            my_dict[find(i)].insert(index, c)
            
        for l in my_dict.values():
            l.reverse()
        print(my_dict)
        ans = []
        for i, c in enumerate(s):
            ans.append(my_dict[find(i)].pop())
        return "".join(ans)
        
823