<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 Solution {
    private:
    void dfs(int i,int j ,vector<vector<int>>&vis,vector<vector<int>>&grid,int n,vector<int>row,vector<int>col,int &count,
                    set<pair<int,int>> &nn){

            vis[i][j]=1;
            count++;
            for(int k=0;k<4;k++){
                int r=i+row[k];
                int c=j+col[k];
                if(r>=0 && c>=0 && r<n && c<n ){
                    if(!vis[r][c] && grid[r][c]){
                        dfs(r,c,vis,grid,n,row,col,count,nn);
                    }
                    else if(grid[r][c]==0){
                        nn.insert({r,c});
                    }
                }
            }
    }


    void makeNeigh(set<pair<int,int>> nn,vector<vector<int>>& neigh,int count,int &maxi){
        for(auto it:nn){
            int i =it.first;
            int j =it.second;
            neigh[i][j]+=count;
            maxi=max(maxi,neigh[i][j]);
        }
    }
public:
    int largestIsland(vector<vector<int>>& grid) {
        int n =grid.size();
        vector<vector<int>>vis(n,vector<int>(n,0));
        vector<vector<int>>neigh(n,vector<int>(n,0));
        vector<int> row={-1,0,1,0};
        vector<int> col={0,1,0,-1};
        int maxi=0;
        int mm=0;
        for(int i =0;i<n;i++){
            for(int j=0;j<n;j++){
                if(!vis[i][j] && grid[i][j]){
                    int count=0;
                    set<pair<int,int>> nn;
                    dfs(i,j,vis,grid,n,row,col,count,nn);
                    mm=max(mm,count);
                    makeNeigh(nn,neigh,count,maxi);
                }
            }
        }
        return max(maxi+1,mm);
    }
};
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