<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:
        # map index to character
        N = len(s)
        iToC = {i:c for i,c in enumerate(s)}
        
        # get disjoint sets
        reps = [i for i in range(N)]
        rank = [1]*N
        
        # use path compression, otherwise times out
        def find(u):
            if u == reps[u]:
                return u
            reps[u] = find(reps[u])
            return reps[u]
      
        # use union by rank, otherwise times out
        def union(u, v):
            rU, rV = find(u), find(v)
            
            if rU == rV:
                return # not doing the union
            
            bot, top = rU, rV
            if rank[rU] == rank[rV]:
                rank[top] += 1
            elif rank[rV] < rank[rU]:
                bot, top = rV, rU
            
            reps[bot] = top
        
        # set rep of each node to the actual root
        def toRoot(u):
            rep = reps[u]
            while u != rep:
                u = rep
                rep = reps[u]
            return u
        
        # make disjoint sets
        for u, v in pairs:
            union(u, v)
        
        # set all reps to the actual root
        for i, rep in enumerate(reps):
            reps[i] = toRoot(rep)
        
        # create disjoint sets including their characters
        repToSet = defaultdict(list)
        for i, rep in enumerate(reps):
            repToSet[rep].append((i, iToC[i]))
        
        # minimize strings 
        # THE MAIN IDEA IS THAT IF COMPONENTS ARE CONNECTED THEY CAN BE SWAPPED
        # SO IF ALL CHARACTERS ARE CONNNECTED THE MIN STRING IS THE SORTED LIST OF CHARACTERS
        for rep, ds in repToSet.items():  
            # get indices by themselves
            idxs = [i for i,_ in ds]
            # get chars by themselves
            chars = [c for _,c in ds]
            
            # sort ds (list of tuples) by character
            idxs.sort()
            chars.sort()
            repToSet[rep] = zip(idxs, chars)
            
          
        # build min string
        res = ['']*N
        for rep, ds in repToSet.items():
            for i, c in ds:
                res[i] = c
        
        return ''.join(res)
                
            
        
        
        
"""
1) get disjoint sets
2) minimize disjoint sets
    sort w/ characters
3) combine disjoint sets

btw using "quick find" times out... that was the previous submission

"""
60374