<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:

    vector<int> parent;
    int getParent(int a) {
        if (a == parent[a]) return a;
        parent[a] = getParent(parent[a]);
        return parent[a];
    }

    void make_union(int a, int b) {
        int pa = getParent(a);
        int pb = getParent(b);
        if (pa != pb) parent[pa] = pb;
    }

    int minimumHammingDistance(vector<int>& source, vector<int>& target, vector<vector<int>>& allowedSwaps) {
        parent = vector<int>(100005, 0);
        for(int i=0; i<100005; i++) parent[i] = i;
        for(auto a: allowedSwaps) {
            make_union(a[0], a[1]);
        }
        unordered_map<int, vector<int>> cont1, cont2;
        for(int i=0; i<source.size(); i++) {
            cont1[getParent(i)].push_back(source[i]);
            cont2[getParent(i)].push_back(target[i]);
        }
        // cout<<"source: "<<endl;
        for(unordered_map<int, vector<int>>::iterator itr = cont1.begin(); itr != cont1.end(); itr++) {
            vector<int>&temp = itr->second;
            sort(temp.begin(), temp.end());
            // cout<<itr->first<<endl;
            // for(auto a: itr->second) {
            //     cout<<a<<" ";
            // }
            // cout<<endl;
        }
        // cout<<"target: "<<endl;
        for(unordered_map<int, vector<int>>::iterator itr = cont2.begin(); itr != cont2.end(); itr++) {
            vector<int>&temp = itr->second;
            sort(temp.begin(), temp.end());
            // cout<<itr->first<<endl;
            // for(auto a: itr->second) {
            //     cout<<a<<" ";
            // }
            // cout<<endl;
        }

        int ans = 0;
        for(auto a: cont1) {
            // for(auto b: a.second) {
            //     if (find(cont2[a.first].begin(), cont2[a.first].end(), b) == cont2[a.first].end()) ans++;
            // }
            int left = 0, right = 0, nn = a.second.size(), temp = 0;
            vector<int>& temp1 = a.second;
            vector<int>& temp2 = cont2[a.first];
            
            while(left < nn && right < nn) {
                if (temp1[left] == temp2[right]) {
                    left++;
                    right++;
                    temp++;
                } else if (temp1[left] < temp2[right]) {
                    left++;
                } else {
                    right++;
                }
            }
            ans += nn - temp;
        }
        return ans;
    }
};
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