<p>You are given an <code>m x n</code> binary grid <code>grid</code> where <code>1</code> represents land and <code>0</code> represents water. An <strong>island</strong> is a maximal <strong>4-directionally</strong> (horizontal or vertical) connected group of <code>1</code>&#39;s.</p>

<p>The grid is said to be <strong>connected</strong> if we have <strong>exactly one island</strong>, otherwise is said <strong>disconnected</strong>.</p>

<p>In one day, we are allowed to change <strong>any </strong>single land cell <code>(1)</code> into a water cell <code>(0)</code>.</p>

<p>Return <em>the minimum number of days to disconnect the grid</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/24/land1.jpg" style="width: 500px; height: 169px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,1,0],[0,1,1,0],[0,0,0,0]]

<strong>Output:</strong> 2
<strong>Explanation:</strong> We need at least 2 days to get a disconnected grid.
Change land grid[1][1] and grid[0][2] to water and get 2 disconnected island.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/24/land2.jpg" style="width: 404px; height: 85px;" />
<pre>
<strong>Input:</strong> grid = [[1,1]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Grid of full water is also disconnected ([[1,1]] -&gt; [[0,0]]), 0 islands.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 30</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution
{
public:
    int countLand(const vector<vector<int>>& grid, vector<vector<int>>& u)
    {
        const int n = grid.size();
        const int m = grid[0].size();
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < m; ++j)
                u[i][j] = 0;
        int result = 0;
        queue<pair<int, int>> q;
        const int dx[4] = {1, 0, -1, 0};
        const int dy[4] = {0, 1, 0, -1};
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < m; ++j)
                if (grid[i][j] && !u[i][j])
                {
                    ++result;
                    u[i][j] = 1;
                    q.emplace(i, j);
                    while (!q.empty())
                    {
                        const auto v = q.front();
                        q.pop();
                        for (int d = 0; d < 4; ++d)
                        {
                            const int ni = v.first + dx[d];
                            const int nj = v.second + dy[d];
                            if (ni < 0 || nj < 0 || ni >= n || nj >= m || !grid[ni][nj] || u[ni][nj])
                                continue;
                            u[ni][nj] = 1;
                            q.emplace(ni, nj);
                        }
                    }
                }
        if (result == 0)
            return 2;
        return result;
    }

    int minDays(vector<vector<int>>& grid)
    {
        const int n = grid.size();
        const int m = grid[0].size();
        vector<vector<int>> u(n, vector<int>(m));
        if (countLand(grid, u) > 1)
            return 0;
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < m; ++j)
            {
                if (!grid[i][j])
                    continue;
                grid[i][j] = 0;
                if (countLand(grid, u) > 1)
                    return 1;
                grid[i][j] = 1;
            }
        return min(n * m, 2);
    }
};
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