<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 dx[4]={0,1,-1,0};
    int dy[4]={1,0,0,-1};
    vector<vector<bool>> vis;
    vector<vector<int>> area;
    vector<vector<int>> gid;
    int n,id;

    void dfs(int cx, int cy, vector<vector<int>>& grid){
        if(cx < 0 || cx >= n || cy < 0 || cy >= n) return;
        if(vis[cx][cy] || grid[cx][cy] == 0) return;
        
        vis[cx][cy]=true;
        area.push_back({cx,cy});
        
        for(int i=0;i<4;i++){
            int x = cx + dx[i];
            int y = cy + dy[i];
            dfs(x,y,grid);
        }
    }
    void updateGridArea(vector<vector<int>>& grid){
        id++;
        int sz=area.size();
        for(auto i:area){
            grid[i[0]][i[1]]=sz;
            gid[i[0]][i[1]]=id;
        }
    }

    int largestIsland(vector<vector<int>>& grid) {
        n = grid.size();
        id=0;
        vis.resize(n,vector<bool>(n,false));
        gid.resize(n,vector<int>(n,0));

        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==1 && !vis[i][j]){
                    area.clear();
                    dfs(i,j,grid);
                    updateGridArea(grid);
                }
            }
        }
        int ans=0,flag=false;

        
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==0){
                    flag=true;
                    int tmp=1;
                    map<int,bool> mp;
                    for(int k=0;k<4;k++){
                        int x = i+dx[k];
                        int y = j+dy[k];
                        if(x < 0 || x >= n || y < 0 || y >= n) continue;
                        if(mp[gid[x][y]]) continue;
                        //cout<<x<< " "<<y<< "\n";
                        mp[gid[x][y]]=true;
                        tmp+=grid[x][y];
                    }
                    //cout<< "\n";
                    ans=max(ans,tmp);
                }
            }
        }
        if(!flag) return n*n;
        return ans;
    }
};
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