<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>>& g) {
        n = g.size();
        p = vector<int>(n*n, -2);
        int cntz = 0, cnto = 0;
        for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) {
            if (g[i][j] == 1) {
                cnto++;
                p[i*n+j] = -1;
                if (i-1 >= 0 && g[i-1][j] == 1) u(i*n+j, (i-1)*n+j);
                if (j-1 >= 0 && g[i][j-1] == 1) u(i*n+j, i*n+j-1);
            } else {
                cntz++;
            }
        }
        if (cntz == n * n) return 1;
        if (cnto == n * n) return n * n;

        // for (int i = 0; i < p.size(); i++) {
        //     if (i % n == 0) cout<<endl;
        //     cout<<p[i]<<" ";
        // } cout<<endl; cout<<endl;
        
        unordered_map<int, int> p2s;
        int ans = 0;
        for (int i = 0; i < p.size(); i++) if (p[i] != -2) p2s[f(i)]++;

        vector<vector<int>> dirs = {{0, -1}, {0, 1}, {-1, 0}, {1, 0}};
        for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) if (g[i][j] == 0) {
            unordered_map<int, int> s;
            for (auto dir : dirs) {
                int ii = i + dir[0];
                int jj = j + dir[1];
                // cout<<ii<<"-"<<jj<<endl;
                if (0 <= ii && ii < n && 0 <= jj && jj < n && g[ii][jj] == 1) {
                    int r = f(ii*n+jj);
                    int size = p2s[r];
                    // cout<<r<<" "<<size<<endl;
                    s[r] = size;
                }
            }
            int sum = s.empty() ? 0 : 1;
            for (auto& [k, v] : s) sum += v;
            ans = max(ans, sum);
        }
        return ans;
    }

private:
    vector<int> p;
    int n;

    int f(int x) {
        if (p[x] == -1) return x;
        return f(p[x]);
    }

    void u(int x, int y) {
        int xp = f(x), yp = f(y);
        if (xp != yp) p[xp] = yp;
    }
};
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