<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 DisjointSet:
    from collections import defaultdict
    import heapq
    def __init__(self, size):
        self.parents = [i for i in range(0, size)]
        self.rank = [1] * size
        self.heaps = defaultdict(list)
        self.visited = set()
    
    def find(self, x):
        #print(f"find {x}")
        #print(self.parents)
        if x == self.parents[x]:
            return x
        self.parents[x] = self.find(self.parents[x])
        return self.parents[x]

    def union(self, x, y, c1, c2):
        parentX = self.find(x)
        parentY = self.find(y)
        if parentX != parentY:
            if self.rank[parentX] > self.rank[parentY]:
                self.parents[parentY] = parentX
                self.rank[parentX] += 1
                #transfer heap
                parentYHeap = self.heaps[parentY]
                for child in parentYHeap:
                    heapq.heappush(self.heaps[parentX], child)
                if parentY in self.heaps:
                    del self.heaps[parentY]
                if not (x, c1) in self.visited:
                    heapq.heappush(self.heaps[parentX], c1)
                    self.visited.add((x, c1))
                if not (y, c2) in self.visited:
                    heapq.heappush(self.heaps[parentX], c2)
                    self.visited.add((y, c2))
            else:
                self.parents[parentX] = parentY
                self.rank[parentY] += 1
                parentXHeap = self.heaps[parentX]
                for child in parentXHeap:
                    heapq.heappush(self.heaps[parentY], child)
                if parentX in self.heaps:
                    del self.heaps[parentX]
                if not (x, c1) in self.visited:
                    heapq.heappush(self.heaps[parentY], c1)
                    self.visited.add((x, c1))
                if not (y, c2) in self.visited:
                    heapq.heappush(self.heaps[parentY], c2)
                    self.visited.add((y, c2))

    
    def get_char(self, indx):
        if indx in self.heaps and self.heaps[indx]:
            return heapq.heappop(self.heaps[indx])
        return ""


class Solution:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        if not pairs:
            return s
        dsu = DisjointSet(len(s))
        for pair in pairs:
            dsu.union(pair[0], pair[1], s[pair[0]], s[pair[1]])
        final_ans = []
        for i in range(0, len(s)):
            #print(f"finding {i}")
            parent = dsu.find(i)
            candidate = dsu.get_char(parent)
            final_ans.append(candidate if candidate else s[i])
        return "".join(final_ans)
        
            
628