<p>You are given an <code>n x n</code> binary matrix <code>grid</code>. You are allowed to change <strong>at most one</strong> <code>0</code> to be <code>1</code>.</p>

<p>Return <em>the size of the largest <strong>island</strong> in</em> <code>grid</code> <em>after applying this operation</em>.</p>

<p>An <strong>island</strong> is a 4-directionally connected group of <code>1</code>s.</p>

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

<pre>
<strong>Input:</strong> grid = [[1,0],[0,1]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> Change one 0 to 1 and connect two 1s, then we get an island with area = 3.
</pre>

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

<pre>
<strong>Input:</strong> grid = [[1,1],[1,0]]
<strong>Output:</strong> 4
<strong>Explanation: </strong>Change the 0 to 1 and make the island bigger, only one island with area = 4.</pre>

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

<pre>
<strong>Input:</strong> grid = [[1,1],[1,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> Can&#39;t change any 0 to 1, only one island with area = 4.
</pre>

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

<ul>
	<li><code>n == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 500</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>


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

         }
         int findPar(int node){
            if(par[node]==node)return node;
            return par[node]=findPar(par[node]);
         }
         void unionBy_size(int &u,int &v){
            int up_u=findPar(u);
            int up_v=findPar(v);
            if(up_u==up_v)return;
            if(size[up_u]<size[up_v]){
                par[up_u]=up_v;
                size[up_v]+=size[up_u];
            }
            else{
                par[up_v]=up_u;
                size[up_u]+=size[up_v];
            }
         }
         int getSize(int node){
            return size[node];
         }
         int getMaxSize(){
            int mx=0;
            for(int i=0;i<size.size();i++){
                mx=max(mx,size[i]);
            }
            return mx;
         }


};
class Solution {
public:
    
    int largestIsland(vector<vector<int>>& grid) {
        int n=grid.size();
        int size=n*n;
        Disjoint ds(size);
        int a[]={-1,1,0,0};
        int b[]={0,0,-1,1};
        vector<vector<bool>> vis(n,vector<bool>(n,false));
        
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==1 && !vis[i][j]){
                    vis[i][j]=true;
                    int u=i*n+j;
                    for(int k=0;k<4;k++){
                        int row=i+a[k];
                        int col=j+b[k];
                        if(row<n && row>=0 && col<n && col>=0 && vis[row][col]){
                            int v=row*n+col;
                            if(ds.findPar(u)!=ds.findPar(v)){
                                ds.unionBy_size(u,v);
                            }

                        }
                    }
                }


            }
        }
        int ans=ds.getMaxSize();
        cout<<"ans"<<ans<<endl;
        unordered_map<int,bool> mp;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                int counter=0;
                if(grid[i][j]==0){
                    counter++;
                    
                    for(int k=0;k<4;k++){
                        int row=i+a[k];
                        int col=j+b[k];
                        
                        if(row<n && row>=0 && col<n && col>=0 && grid[row][col]==1){
                           int node=row*n+col;
                           int up=ds.findPar(node);
                        //    cout<<"up"<<up<<endl;
                           if(mp.find(up)==mp.end()){
                            int res=ds.getSize(up);
                            counter+=res;
                            mp[up]=1;

                           }
                           
                                     
                        }
                    }

                    
                }
                mp.clear();
                ans=max(ans,counter);
                // cout<<i<<"->"<<j<<"->"<<"ans "<<ans<<endl;
            }
        }
        return ans;
        
    }
};
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