<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> area;
        int n = grid.size();
        vector<vector<int>> dirs = {{0,1}, {1,0}, {-1,0}, {0,-1}};
        int island = 2;
        int res = 1;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 1) {
                    int count = 1;
                    queue<vector<int>> q;
                    q.push({i, j});
                    grid[i][j] = island;
                    while (!q.empty()) {
                        int x = q.front()[0];
                        int y = q.front()[1];
                        q.pop();
                        
                        
                        for (vector<int>& d : dirs) {
                            int nx = x+d[0];
                            int ny = y+d[1];
                            if (nx < 0 || nx >= n || ny < 0 || ny >= n || grid[nx][ny] != 1)
                                continue;
                            q.push({nx, ny});
                            grid[nx][ny] = island;
                            count++;
                        }
                    }
                    area[island++] = count;
                    //cout << count;
                    res = max(res, count);
                }
            }
        }
        
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 0) {
                    int count = 1;
                    unordered_set<int> islands;
                    for (vector<int>& d : dirs) {
                        int x = i+d[0];
                        int y = j+d[1];
                        if (x < 0 || x >= n || y < 0 || y >= n || grid[x][y] == 0 || islands.count(grid[x][y]))
                            continue;
                        islands.insert(grid[x][y]);
                        count += area[grid[x][y]];
                    }
                    res = max(res, count);
                }
            }
        }
        return res;
    }
};
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