<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:
     vector<pair<int,int>>dir = {{0,1},{1,0},{-1,0},{0,-1}};
    void helper(int i,int j,vector<vector<int>>&grid,vector<vector<int>>&vis,vector<vector<int>>&parent,int p,int &count){
         
         
         count += 1;
         parent[i][j] = p;
         vis[i][j] = 1;
         for(auto d : dir){
             int x = d.first + i;
             int y = d.second + j;
             if(x>=0 && x <grid.size() && y>=0 && y<grid[0].size() && grid[x][y]==1 &&  vis[x][y]==0){  
                 helper(x,y,grid,vis,parent,p,count);
             }
         }
    }
    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<vector<int>>parent = vis;
        int ans = 0;
        unordered_map<int,int>mp;
        int p = 0;
        for(int i = 0;i<n;i++){ 
            for(int j = 0;j<m;j++){
                if(grid[i][j] && vis[i][j] == 0){
                     int count = 0;
                     p+=1;
                     helper(i,j,grid,vis,parent,p,count);
                     mp[p] = count;
                     ans = max(ans,count);
                    //  cout<<i<<" "<<j<<"  : "<<count<<endl;
                }
            }
        }
        for(int i = 0;i<n;i++){ 
            for(int j = 0;j<m;j++){
                if(grid[i][j] == 0 ){
                     unordered_map<int,int>mp1;
                  for(auto d : dir){
                        int x = d.first + i;
                        int y = d.second + j;
                       
                        if(x>=0 && x <grid.size() && y>=0 && y<grid[0].size() && grid[x][y]){  
                                mp1[parent[x][y]]++;
                    }
                  }
                  int cal = 1;
                    for(auto x : mp1){
                         cal  += mp[x.first];
                    }
                    
                    ans = max(ans,cal);
                }
            }
        }
        return ans;
    }
};
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