<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 dfsArea(vector<vector<int>>& grid, int x, int y, vector<vector<int>>& visited, int id)
    {
        stack<pair<int, int>> s;
        s.push({x, y});
        int area = 0;
        while(!s.empty())
        {
            int x = s.top().first;
            int y = s.top().second;
            s.pop();
            if(visited[x][y]) continue;
            visited[x][y] = 1;
            area++;
            grid[x][y] = id;
            if(x > 0 && visited[x - 1][y] == 0 && grid[x - 1][y] == 1) s.push({x - 1, y});
            if(x + 1 < grid.size() && visited[x + 1][y] == 0 && grid[x + 1][y] == 1) s.push({x + 1, y});
            if(y > 0 && visited[x][y - 1] == 0 && grid[x][y - 1] == 1) s.push({x, y - 1});
            if(y + 1 < grid.size() && visited[x][y + 1] == 0 && grid[x][y + 1] == 1) s.push({x, y + 1});
        }
        // cout << "ID: " << id << " Area: " << area << endl;
        return area;
    }
    int largestIsland(vector<vector<int>>& grid) {
        unordered_map<int, int> area;
        int n = grid.size();
        vector<vector<int>> visited(n, vector<int>(n, 0));
        set<int> neighbours;
        area[0] = 0;
        int id = 2;
        for(int i = 0; i < n; i++)
        {
            for(int j = 0; j < n; j++)
            {
                if(grid[i][j] == 1 && !visited[i][j])
                {
                    area[id] = dfsArea(grid, i, j, visited, id);
                    id++;
                }
            }
        }
        int ans = 0;
        int currArea = 0;
        for(int i = 0; i < n; i++)
        {
            for(int j = 0; j < n; j++)
            {
                // cout << grid[i][j] << " ";
                if(grid[i][j] == 0)
                {
                    if(i > 0) neighbours.insert(grid[i - 1][j]);
                    if(j > 0) neighbours.insert(grid[i][j - 1]);
                    if(i + 1 < n) neighbours.insert(grid[i + 1][j]);
                    if(j + 1 < n) neighbours.insert(grid[i][j + 1]);
                    for(int id: neighbours)
                    {
                        currArea = currArea + area[id];
                    }
                    ans = max(ans, currArea + 1);
                    currArea = 0;
                    neighbours.clear();
                }
                else
                {
                    ans = max(ans, area[grid[i][j]]);
                }
            }
            // cout << endl;
        }
        return ans;
    }
};
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