<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 minDays(vector<vector<int>>& grid) 
    {
        lands_.clear();
        int landCount = bfs(grid, true);

        if (landCount > 1 || landCount == 0)
            return 0;

        for (int i = 0; i < lands_.size(); ++i)
        {
            auto [x, y] = lands_[i];
            
            grid[x][y] = 0;
            landCount = bfs(grid, false);

            if (landCount > 1 || landCount == 0)
                return 1;

            grid[x][y] = 1;
        }

        return 2;
    }

private:
    int bfs(std::vector<std::vector<int>>& grid, bool recordLand = false)
    {
        std::memset(visited_, 0, sizeof(visited_));
        int m = grid.size(), n = grid[0].size(), count = 0;

        for (int i = 0; i < m; ++i)
        {
            for (int j = 0; j < n; ++j)
            {
                if (grid[i][j] == 1)
                {
                    if (visited_[i][j] == 1)
                        continue;

                    count++;

                    std::queue<std::pair<int, int>> queue;
                    queue.push({ i, j });
                    visited_[i][j] = 1;

                    while (!queue.empty())
                    {
                        int len = queue.size();
                        while (len--)
                        {
                            auto [x, y] = queue.front();
                            queue.pop();

                            if (recordLand)
                                lands_.push_back({ x, y });

                            for (auto&& dir : dirs_)
                            {
                                int xx = x + dir.first;
                                int yy = y + dir.second;

                                if (xx < 0 || xx >= m || yy < 0 || yy >= n)
                                    continue;

                                if (visited_[xx][yy] == 1)
                                    continue;

                                if (grid[xx][yy] == 0)
                                    continue;

                                visited_[xx][yy] = 1;
                                queue.push({ xx, yy });
                            }
                        }
                    }
                }
            }
        }

        return count;
    }

private:
    int visited_[35][35];
    std::vector<std::pair<int, int>> dirs_ = {
        { 0, 1 },
        { 1, 0 },
        { 0, -1 },
        { -1, 0 }
    };

    std::vector<std::pair<int, int>> lands_;
};
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