<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>

typedef int const& T;

class Solution {
private:
    std::vector<std::vector<int>> graph;
    std::vector<bool> visited;

    void add_undirected_edge(T from, T to) {
        graph[from].push_back(to);
        graph[to].push_back(from);
    }

    void dfs(T node, std::vector<int>& cc_indices) {
        visited[node] = true;
        cc_indices.push_back(node);

        for (auto const& neighbour : graph.at(node))
            if (!visited[neighbour])
                dfs(neighbour, cc_indices);
    }

public:
    // O(V) time and space
    std::string smallestStringWithSwaps(std::string str,
                                        std::vector<std::vector<int>>& pairs) {
        graph.resize(str.length()); // Adjacency List representaion
        visited.resize(str.length());

        // build graph
        for (auto const& edge : pairs)
            add_undirected_edge(edge[0], edge[1]);

        for (int i{}; i < static_cast<int>(str.length()); ++i)
            if (!visited[i]) // new CC
            {
                std::vector<int> cc_indices;
                dfs(i, cc_indices);

                // get letter's from cc of indices
                std::string cc_letters;
                for (auto const& idx : cc_indices)
                    cc_letters += str[idx];

                std::sort(cc_indices.begin(), cc_indices.end());
                std::sort(cc_letters.begin(), cc_letters.end());

                // this wrong, don't do that
                // for (auto const &idx : cc_indices)
                //         str[idx] = cc_letters[idx];

                for (int j{}; j < static_cast<int>(cc_indices.size()); ++j)
                    str[cc_indices[j]] = cc_letters[j];
            }
        return str;
    }
};
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