<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 {
public:
    void dfs(int i,int j,vector<vector<int>>& grid,vector<vector<int>>&vis,int n,int m,int k,vector<int>&num){
        vis[i][j]=1;
        grid[i][j]=k;
        num[k]++;
        int a[4]={1,-1,0,0};
        int b[4]={0,0,-1,1};
        for(int l=0;l<4;l++){
            int r=i+a[l];
            int c=j+b[l];
            if(r>=0&&r<n&&c>=0&&c<m&&vis[r][c]==0&&grid[r][c]!=0){
                dfs(r,c,grid,vis,n,m,k,num);
            }
        } 
    }
    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        vector<vector<int>>vis(n,vector<int>(m,0));
        vector<int>num(250000,0);
        int k=1;
        int ans=1;
        for(int i=0; i<n; i++){
          for(int j=0; j<n;j++){
              if(grid[i][j]==1&&vis[i][j]==0){
                dfs(i,j,grid,vis,n,m,k,num);
               ans=max(ans,num[k]);
               k++;
              }
          }
        }
        
        int a[4]={1,-1,0,0};
        int b[4]={0,0,-1,1};
        vector<int>vis2(25000,-1);
      for(int i=0;i<n;i++){
        for(int j=0;j<m;j++){
            int x=0;
            set<int>s;
            if(grid[i][j]==0){
              for(int l=0;l<4;l++){
                int r=i+a[l];
                int c=j+b[l];
                if(r>=0&&r<n&&c>=0&&c<m&&grid[r][c]!=0){
                    s.insert(grid[r][c]);
                }
              }
            }
            for(auto p:s){
                x+=num[p];
            }
            ans=max(ans,1+x);
        }
      }
      return ans;
    }
};
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