<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:
    vector<pair<int, int>> neighbors(int r, int c, int n) {
        vector<pair<int, int>> result;
        int nb[4][2] = {{1, 0}, {0, 1}, {0, -1}, {-1, 0}};
        for (int i = 0; i < 4; i++) {
            int nr = r + nb[i][0];
            int nc = c + nb[i][1];
            if (nr < 0 || nc < 0 || nr >= n || nc >= n) continue;
            result.push_back({nr, nc});
        }
        return result;    
    }

    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        int group = 2;
        int answer = 0;
        unordered_map<int, int> island_size;
        for (int r = 0; r < n; r++) {
            for (int c = 0; c < n; c++) {
                if (grid[r][c] != 1) continue;
                int cur_size = 0;
                grid[r][c] = group;
                vector<pair<int, int>> q;
                q.push_back({r, c});
                while (q.size() > 0) {
                    vector<pair<int, int>> nq;
                    for (auto &[cr, cc] : q) {
                        cur_size++;
                        for (auto [nr, nc] : neighbors(cr, cc, n)) {
                            if (grid[nr][nc] != 1) continue;
                            grid[nr][nc] = group;
                            nq.push_back({nr, nc});
                        }
                    }
                    q = std::move(nq);
                }

                answer = max(answer, cur_size);
                island_size[group] = cur_size;
                group++;
                // cout << uf.Find(r, c) << " " << cur_size << endl;
            }
        }

        for (int r = 0; r < n; r++) {
            for (int c = 0; c < n; c++) {
                if (grid[r][c] != 0) continue;
                int new_size = 1;
                vector<int> groups;
                for (auto &[nr, nc] : neighbors(r, c, n)) {
                    if (grid[nr][nc] == 0) continue;
                    bool found = false;
                    for (int g : groups)
                        if (g == grid[nr][nc]) found = true;
                    if (!found) {
                        new_size += island_size[grid[nr][nc]];
                        groups.push_back(grid[nr][nc]);
                    }
                }
                answer = max(answer, new_size);
            }
        }
        
        return answer;
    }
};
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