<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 DisjointSet{

//     public:
//      vector<int>parent,sizee;
    
//      DisjointSet(int n){
//         parent.resize(n+1);
//         sizee.resize(n+1,1);
//         for(int i=0;i<=n;i++){
//             parent[i]=i;
//         }
//     }
        
//         int findUPar(int node){
//             if(node==parent[node])return node;
            
//             parent[node]=findUPar(parent[node]);
//             return parent[node];
//         }
        
//         void unionBySize(int u,int v){
//             int ulp=findUPar(u);
//             int vlp=findUPar(v);
//             if(ulp==vlp)return;
//             if(sizee[ulp]<sizee[vlp]){
//                 parent[ulp]=vlp;
//                 sizee[ulp]+=sizee[vlp];
//             }else{
//                 parent[vlp]=ulp;
//                 sizee[vlp]+=sizee[ulp];
//             }
//         }
// };
class DisjointSet{
    
 public:
 vector<int> sizee,parent;
    DisjointSet(int n){
        sizee.resize(n+1,1);
        parent.resize(n+1);
        for(int i=0;i<=n;i++){
            parent[i]=i;
        }
    }

    int findUPar(int node){
        if(node==parent[node])
        return node;
        return parent[node]=findUPar(parent[node]);
    }

    void unionBySize(int u,int v){
        int ulp_u=findUPar(u);
        int ulp_v=findUPar(v);
        if(ulp_u==ulp_v)return;
        if(sizee[ulp_u]<sizee[ulp_v]){
            parent[ulp_u]=ulp_v;
            sizee[ulp_v]+=sizee[ulp_u];
        }else{
            parent[ulp_v]=ulp_u;
            sizee[ulp_u]+=sizee[ulp_v];
        }
    }

};
class Solution {
public:
    int largestIsland(vector<vector<int>>& grid) {
        int n=grid.size();
        int ans=0;
        DisjointSet ds(n*n);
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==1){
                    ans=max(ans,1);
                    int ar[]={0,-1,0,1};
                int ac[]={1,0,-1,0};
                for(int k=0;k<4;k++){
                    int r=i+ar[k];
                    int c=j+ac[k];
                    if(r>=0&&r<n&&c>=0&&c<n&&grid[r][c]==1){
                        int node=i*n+j;
                        int adjnode=r*n+c;
                        ds.unionBySize(node,adjnode);
                         int p=ds.findUPar(adjnode);
                         ans=max(ans,ds.sizee[p]);
                }
                }
            }
        }
    }
        
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==1)continue;
                int ar[4]={0,-1,0,1};
                int ac[4]={1,0,-1,0};
                int tmparea=0;
                map<int,bool>mp;
                for(int k=0;k<4;k++){
                    int r=i+ar[k];
                    int c=j+ ac[k];
                    if(r>=0&&r<n&&c>=0&&c<n&&grid[r][c]==1){
                        int adjnode=r*n+c;
                        int p=ds.findUPar(adjnode);
                        if(mp[p]==false){
                            tmparea+=ds.sizee[p];
                            mp[p]=true;
                        }
                    }
            }
            ans=max(ans,tmparea+1);
        }
         
        }
        return ans;
    }
    
};
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