<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:
    int dfs(vector<vector<int>>&grid,vector<vector<int>>&vis,int i,int j,map<pair<int,int>,int>&m,int comp)
    {
        if(i==grid.size() || j==grid[0].size() || i<0 || j<0)return 0;
        if(grid[i][j]==0)return 0;
        if(vis[i][j]==1)return 0;
        vis[i][j]=1;
        m[{i,j}]=comp;
        return 1+dfs(grid,vis,i+1,j,m,comp)+dfs(grid,vis,i,j+1,m,comp)+dfs(grid,vis,i-1,j,m,comp)+dfs(grid,vis,i,j-1,m,comp);

    }
    int largestIsland(vector<vector<int>>& grid) {
        vector<int>size;
        vector<pair<int,int>>direc={{-1,0},{1,0},{0,-1},{0,1}};
        vector<vector<int>>vis(grid.size(),vector<int>(grid[0].size(),0));
        map<pair<int,int>,int>m;
        int comp=0;
        for(int i=0;i<grid.size();i++)
        {
            for(int j=0;j<grid[0].size();j++)
            {
                if(grid[i][j]==0 || vis[i][j])continue;
                int a=dfs(grid,vis,i,j,m,comp);
                size.push_back(a);
                comp++;
            }
        }

        if(m.size()==0)return 1;
        for(auto it:size)cout<<it<<" ";
        cout<<endl;
        int ans=0;

        for(int i=0;i<grid.size();i++)
        {
            for(int j=0;j<grid[0].size();j++)
            {
                if(grid[i][j]==1)continue;
                unordered_set<int>s;
                int temp=1;
                for(auto it:direc)
                {
                    int a=i+it.first;
                    int b=j+it.second;
                    if(a>=0 && b>=0 && a<grid.size() && b<grid[0].size() && grid[a][b]==1)
                    {
                        if(!s.count(m[{a,b}]))
                        {
                            temp+=size[m[{a,b}]];
                            s.insert(m[{a,b}]);
                        }
                        
                    }
                }
                ans=max(ans,temp);
            }
        }

        if(size[0]==grid.size()*grid[0].size())
        {
            return size[0];
        }
        return ans;
    }
};
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