<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>

from collections import defaultdict
class Solution:
    def smallestStringWithSwaps(self, s: str, pairs: List[List[int]]) -> str:
        # build the graph using pairs
        # for any connected components, all indices can always be swapped to any position in the connected components
        # we just sort all the letters within each connnected components
        # finally concatenate them together

        if len(pairs) == 0:
            return s

        G = defaultdict(list)
        for pair in pairs:
            G[pair[0]].append(pair[1])
            G[pair[1]].append(pair[0])

        # get each connected components using DFS
        connected_components = [] # list of lists for each component
        visited = [False for _ in range(len(s))]

        def dfs(currIdx, visited, component):
            for nextIdx in G[currIdx]:
                if not visited[nextIdx]:
                    visited[nextIdx] = True
                    component.append(nextIdx)
                    dfs(nextIdx, visited, component)

        for i in range(len(s)):
            if not visited[i]:
                visited[i] = True
                component = [i]
                dfs(i, visited, component)
                connected_components.append(component)

        # get the smallest string within each component
        # use a hashmap to store index -> letter after the sorting
        hashmap = {}
        for component in connected_components:
            tmpLetterList = []
            tmpIndexList = []
            for index in component:
                tmpLetterList.append(s[index])
                tmpIndexList.append(index)
            tmpLetterList.sort()
            tmpIndexList.sort()
            for index, letter in zip(tmpIndexList, tmpLetterList):
                hashmap[index] = letter

        # return smallest string by iterating the hashmap index from 0 to L-1
        res = ""
        for i in range(len(s)):
            res += hashmap[i]
            
        return res
        
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