<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 DisjointSet
{
    int nodes;
    vector<int>par,sz;
    public:
    DisjointSet(int n)
    {
        nodes=n;
        par.resize(n,1);
        sz.resize(n,1);
        for(int i=0;i<nodes;i++)
            par[i]=i;
    }


    int findUPar(int v)
    {
        if(par[v]==v)
            return v;
        return par[v]=findUPar(par[v]);
    }


    void unionBySize(int u,int v)
    {
        int upar_u=findUPar(u);
        int upar_v=findUPar(v);

        if(upar_u==upar_v)
            return;
        if(sz[upar_u]>=sz[upar_v])
        {
            par[upar_v]=upar_u;
            sz[upar_u]+=sz[upar_v];
        }
        else
        {
              par[upar_u]=upar_v;
            sz[upar_v]+=sz[upar_u];
        }
    }

    unordered_map<int,vector<int>>getAllComp()
    {

         unordered_map<int,vector<int>>comps;   
        for(int i=0;i<nodes;i++)
        {
            if(par[i]==i)
                comps[i].push_back(i);
            else
            {
                int upar=findUPar(i);
                comps[upar].push_back(i);
            }
        }
        return comps;
    }

};
class Solution {
public:
    int minimumHammingDistance(vector<int>& source, vector<int>& target, vector<vector<int>>& allowedSwaps) {
        
      
        int n=source.size();

        DisjointSet ds(n);

        for(auto swap:allowedSwaps)
        {
            ds.unionBySize(swap[0],swap[1]);
        }

        unordered_map<int,vector<int>>compos=ds.getAllComp();
        int ans=0;
        for(auto it:compos)
        {

            multiset<int>st;
            for(auto index:it.second)
            {
                   
                    st.insert(source[index]);
            }
            
            for(auto index:it.second)
            {
              
                auto pos=st.find(target[index]);
                if(pos==st.end())
                {
                      cout<<target[index]<<" ";
                    ans++;
                }
                else
                    st.erase(pos);
            }


        }
        return ans;
    }
};
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