<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 visit(const vector<vector<int>>& grid,vector<vector<vector<int>>>& visited, int x, int y, vector<pair<int,int>>&ans){
        visited[x][y][0]=1;
        ans.push_back({x,y});
        int dx[4]={-1,0,1,0}, dy[4]={0,1,0,-1};
        for(int i=0;i<4;i++){
            int newx=x+dx[i], newy=y+dy[i];
            if (newx>-1 && newx<grid.size() && newy>-1 && newy<grid[0].size() && !visited[newx][newy][0]){
                if(grid[newx][newy]){
                    visit(grid, visited,newx,newy,ans);
                }
            }
        }
    }

    int largestIsland(vector<vector<int>>& grid) {
        int ans=0,size=0;
        vector<vector<vector<int>>>visited(grid.size(),vector<vector<int>>(grid[0].size(),{0,-1,-1}));
        for(int i=0;i<grid.size();i++){
            for(int j=0;j<grid[0].size();j++){
                if(!visited[i][j][0] && grid[i][j]){
                    vector<pair<int,int>>res;
                    visit(grid,visited, i, j, res);
                    size=res.size();
                    ans=max(ans,size);
                    for(auto cord:res){
                        visited[cord.first][cord.second][0]=size;
                        visited[cord.first][cord.second][1]=i;
                        visited[cord.first][cord.second][2]=j;
                    }
                }
            }
        }
        int dx[4]={-1,0,1,0}, dy[4]={0,1,0,-1};
        for(int i=0;i<grid.size();i++){
            for(int j=0;j<grid[0].size();j++){
                if(!grid[i][j]){
                    size=1;
                    map<pair<int,int>,int> marked;
                    for(int k=0;k<4;k++){
                        int newx=i+dx[k], newy=j+dy[k];
                        if (newx>-1 && newx<grid.size() && newy>-1 && newy<grid[0].size()){
                            if(grid[newx][newy] && marked[{visited[newx][newy][1],visited[newx][newy][2]}]==0) size+=visited[newx][newy][0],marked[{visited[newx][newy][1],visited[newx][newy][2]}]=1;
                        }
                    }
                    ans=max(ans,size);
                }
            }
        }
    return ans;
    }
};
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