<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 {
public:
    class UnionFind {
        vector<int> ids, sz;
        int num_components;

    public:
        UnionFind(int n) : ids(n), sz(n, 1), num_components(n) {
            for (int i = 0; i < n; ++i) {
                ids[i] = i;
            }
        }

        int find(int p) {
            if (p == ids[p]) return p;
            return find(ids[p]);
        }

        void merge(int p, int q) {
            p = find(p), q = find(q);
            if (p == q) return;
            if (sz[p] < sz[q]) {
                sz[q] += sz[p];
                ids[p] = q;
            } else {
                sz[p] += sz[q];
                ids[q] = p;
            }
            --num_components;
        }

        int get_components() const {
            return num_components;
        }
    };

    string smallestStringWithSwaps(string s, vector<vector<int>>& pairs) {
        const int n = s.size();
        UnionFind uf(n);
        for (const auto& p : pairs) {
            uf.merge(p[0], p[1]);
        }
        unordered_map<int, pair<vector<int>, vector<char>>> groups;
        for (int i = 0; i < n; ++i) {
            groups[uf.find(i)].first.push_back(i);
            groups[uf.find(i)].second.push_back(s[i]);
        }
        string smallest = s;
        for (auto itr : groups) {
            auto& indexes = itr.second.first;
            auto& chars = itr.second.second;
            sort(indexes.begin(), indexes.end());
            sort(chars.begin(), chars.end());
            for (int i = 0; i < indexes.size(); ++i) {
                smallest[indexes[i]] = chars[i];
            }
        }
        return smallest;
    }
};

/*

dcab

0,3
1,2

bd ac
bacd

collecting the pairs in a group
    dfs
    visited indexes
sort the indexes in the group

*/
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