<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 dsu{
    public:
    vector<int>rank,parent;
    dsu(int n){
        rank.resize(n);
        parent.resize(n);
        for(int i=0;i<n;i++) parent[i]=i;
    }
    int find(int u){
        if(parent[u]==u) return u;
        return parent[u]=find(parent[u]);
    }
    void unite(int u,int v){
        int U=find(u),V=find(v);
        if (U==V) return;
        if(rank[U]>rank[V]) parent[V]=U;
        else if(rank[V]>rank[U]) parent[U]=V;
        else{
            parent[V]=U;
            rank[U]++;
        }
    }
};
class Solution {
public:
    int minimumHammingDistance(vector<int>& source, vector<int>& target, vector<vector<int>>& allowedSwaps) {
        int n=source.size();
        dsu ds(n);
        for(auto it:allowedSwaps) {
            ds.unite(it[0],it[1]);
        }
        unordered_map<int,vector<int>>mpp_s,mpp_tg;
        for(int i=0;i<n;i++){
            int root=ds.find(i);
            mpp_s[root].push_back(source[i]);
            mpp_tg[root].push_back(target[i]);
        }
        for(auto it:mpp_s){
            cout<<it.first<<"=";
            for(auto i:it.second){
                cout<<i<<" "; 
            } 
            cout<<endl;
        }
        cout<<"second_map"<<endl;
         for(auto it:mpp_tg){
            cout<<it.first<<"=";
            for(auto i:it.second){
                cout<<i<<" "; 
            } 
            cout<<endl;
        }
        int ans=0;
      for(const auto& [root,src_g]:mpp_s) {
        vector<int>sg=src_g;
        vector<int>tg=mpp_tg[root];
        sort(sg.begin(),sg.end());
        sort(tg.begin(),tg.end());
        cout << "Sorted Source Group for Root " << root << ": ";
            for (int x : sg) cout << x << " ";
            cout << "\n";

            cout << "Sorted Target Group for Root " << root << ": ";
            for (int x : tg) cout << x << " ";
            cout << "\n";
        int i=0,j=0;
        int match=0;
        while(i<sg.size()&&j<tg.size()){
            if(sg[i]==tg[j]){
                match++;
                i++;
                j++;
            }
            else if(tg[j]>sg[i]) i++;
            else{
                j++;
            }
            
        }
        ans+=sg.size()-match;
       }
       return ans;
    }
};
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