<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) {
        const vector dir4 {0,1,0,-1,0};
        const int n = (int)grid.size();
        int ret = 0, id = 2;
        vector<int> sizes;
        unordered_map<int, unordered_set<int>> zeroes;
        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 1) {
                    int sz = 0;
                    queue<pair<int,int>> q;
                    q.emplace(i, j);
                    while (!q.empty()) {
                        const int x = q.front().first, y = q.front().second;
                        q.pop();
                        grid[x][y] = id;
                        sz++;
                        for (int k = 0; k < 4; k++) {
                            const int x1 = x + dir4[k], y1 = y + dir4[k + 1];
                            if (x1 < 0 || y1 < 0 || x1 == n || y1 == n) continue;
                            if (grid[x1][y1] == 1) {
                                grid[x1][y1] = id;
                                q.emplace(x1, y1);
                            } else if (grid[x1][y1] == 0)
                                zeroes[x1 * n + y1].insert(id);
                        }
                    }
                    ret = max(ret, sz);
                    sizes.push_back(sz);
                    id++;
                }
            }
        if (zeroes.empty()) return ret ? ret : 1;
        for (auto &x : zeroes) {
            int sum = 0;
            for (auto i : x.second) sum+= sizes[i - 2];
            ret = max(ret, sum);
        }
        return ret + 1;
    }
};
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