<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 largestIsland(vector<vector<int>>& grid) {
        unordered_map<int,int> idtosize;
        int id=2;
        int res=0;
        vector<pair<int,int>> dir={{-1,0}, {0,-1}, {1,0}, {0,1}};
        for(int i=0;i<grid.size();i++)
        {
            for(int j=0;j<grid[0].size();j++)
            {
                if(grid[i][j]!=1)
                    continue;
                queue<pair<int,int>> q;
                q.push({i,j});
                int size=0;
                while(!q.empty())
                {
                    pair<int,int> p=q.front();
                    q.pop();
                    grid[i][j]=id;
                    size++;
                    for(pair<int,int> d:dir)
                    {
                        int x=p.first+d.first;
                        int y=p.second+d.second;
                        if(x>=0 && y>=0 && x<grid.size() && y<grid[0].size() && grid[x][y]==1)
                        {
                            grid[x][y]=id;
                            q.push({x,y});
                        }
                    }
                }
                idtosize[id]=size;
                res=max(res, size);
                id++;
            }
        }
        for(int i=0;i<grid.size();i++)
        {
            for(int j=0;j<grid[0].size();j++)
            {
                if(grid[i][j]!=0)
                    continue;
                unordered_set<int> neighbors;
                for(pair<int,int> d:dir)
                {
                    int x=i+d.first;
                    int y=j+d.second;
                    if(x>=0 && y>=0 && x<grid.size() && y<grid[0].size() && grid[x][y]!=0)
                    {
                        neighbors.insert(grid[x][y]);
                    }
                }
                int size=1;
                for(int id:neighbors)
                {
                    size+=idtosize[id];
                }
                res=max(res, size);
            }
        }
        return res;
    }
};
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