<p>You are given two integer arrays, <code>source</code> and <code>target</code>, both of length <code>n</code>. You are also given an array <code>allowedSwaps</code> where each <code>allowedSwaps[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that you are allowed to swap the elements at index <code>a<sub>i</sub></code> and index <code>b<sub>i</sub></code> <strong>(0-indexed)</strong> of array <code>source</code>. Note that you can swap elements at a specific pair of indices <strong>multiple</strong> times and in <strong>any</strong> order.</p>

<p>The <strong>Hamming distance</strong> of two arrays of the same length, <code>source</code> and <code>target</code>, is the number of positions where the elements are different. Formally, it is the number of indices <code>i</code> for <code>0 &lt;= i &lt;= n-1</code> where <code>source[i] != target[i]</code> <strong>(0-indexed)</strong>.</p>

<p>Return <em>the <strong>minimum Hamming distance</strong> of </em><code>source</code><em> and </em><code>target</code><em> after performing <strong>any</strong> amount of swap operations on array </em><code>source</code><em>.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> source = [1,2,3,4], target = [2,1,4,5], allowedSwaps = [[0,1],[2,3]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> source can be transformed the following way:
- Swap indices 0 and 1: source = [<u>2</u>,<u>1</u>,3,4]
- Swap indices 2 and 3: source = [2,1,<u>4</u>,<u>3</u>]
The Hamming distance of source and target is 1 as they differ in 1 position: index 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> source = [1,2,3,4], target = [1,3,2,4], allowedSwaps = []
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are no allowed swaps.
The Hamming distance of source and target is 2 as they differ in 2 positions: index 1 and index 2.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> source = [5,1,2,4,3], target = [1,5,4,2,3], allowedSwaps = [[0,4],[4,2],[1,3],[1,4]]
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == source.length == target.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= source[i], target[i] &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= allowedSwaps.length &lt;= 10<sup>5</sup></code></li>
	<li><code>allowedSwaps[i].length == 2</code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= n - 1</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
</ul>

class Solution {
public:
    int minHelper(vector<int>& source, vector<int>& target) {
        int same_count = 0;
        std::unordered_map<int, int> source_map;
        for (int i = 0; i < source.size(); i++) {
            source_map[source[i]]++;
        }
        for (int i = 0; i < source.size(); i++) {
            if (source_map.count(target[i]) > 0) {
                if (source_map[target[i]] > 0) {
                    source_map[target[i]]--;
                    same_count++;
                }
            }
        }
        return (source.size() - same_count);
    }
    int minimumHammingDistance(vector<int>& source, vector<int>& target, vector<vector<int>>& allowedSwaps) {
        vector<set<int>*> merged(source.size(), nullptr);
        for (auto& swap : allowedSwaps) {
            int a= swap[0];
            int b = swap[1];
            if (merged[a] && merged[b] && (merged[a] != merged[b])) {
                set<int>* other = merged[b];
                for (auto it = other->begin(); it != other->end(); it++) {
                    merged[a]->insert(*it);
                    merged[*it] = merged[a];
                }
                delete other;
            } else if (!merged[a] && !merged[b]) {
                merged[a] = new set<int>();
                merged[a]->insert(a);
                merged[a]->insert(b);
                merged[b] = merged[a];
            } else if (merged[a] && !merged[b]) {
                merged[a]->insert(b);
                merged[b] = merged[a];
            } else if (merged[b] && !merged[a]) {
                merged[b]->insert(a);
                merged[a] = merged[b];
            }
        }

        int distance = 0;
        vector<int> osrc, odst;
        for (int i = 0; i < merged.size(); i++) {
            if (merged[i]) {
                auto set_ptr = merged[i];
                vector<int> tsrc, tdst;
                for (auto it = set_ptr->begin(); it != set_ptr->end(); it++) {
                    tsrc.push_back(source[*it]);
                    tdst.push_back(target[*it]);
                }
                set_ptr->clear();
                distance += minHelper(tsrc, tdst);
            } else {
                osrc.push_back(source[i]);
                odst.push_back(target[i]);
            }
        }
        for (int i =0; i < osrc.size(); i++) {
            if (osrc[i] != odst[i]) {
                distance++;
            }
        }
        return distance;
    }
};
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