<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) {
        if (isDisconnected(grid))
        {
            return 0;
        }

        int m = grid.size();
        int n = grid[0].size();
        for (int i = 0; i < m; i++)
        {
            for (int j = 0; j < n; j++)
            {
                if (grid[i][j] == 1)
                {
                    grid[i][j] = 0;
                    if (isDisconnected(grid))
                    {
                        return 1;
                    }

                    grid[i][j] = 1;
                }
            }
        }

        return 2;
    }

private:
    bool isDisconnected(const vector<vector<int>>& grid)
    {
        if (countIslands(grid) == 1)
        {
            return false;
        }

        return true;
    }

    int countIslands(vector<vector<int>> grid)
    {
        int islands = 0;

        int m = grid.size();
        int n = grid[0].size();
        for (int i = 0; i < m; i++)
        {
            for (int j = 0; j < n; j++)
            {
                if (grid[i][j] == 1)
                {
                    islands++;
                    destroyIsland(grid, i, j, m, n);
                }
            }
        }

        return islands;
    }

    void destroyIsland(vector<vector<int>>& grid, int i, int j, int m, int n)
    {
        if ((i < 0) || (i >= m) || (j < 0) || (j >= n) || (grid[i][j] != 1))
        {
            return;
        }

        grid[i][j] = 0;

        for (auto& adj : adjacencies)
        {
            destroyIsland(grid, i + adj.first, j + adj.second, m, n);
        }
    }

    const vector<pair<int, int>> adjacencies = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
};
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