<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:
    def minDays(self, grid):
        rows = len(grid)
        cols = len(grid[0])

        def count_islands():
            gr = [-2 if c==0 else -1 for r in grid for c in r]
            def get_group(i):
                while gr[i] != -1:
                    i = gr[i]
                return i
            gr
            for r in range(rows-1):
                for c in range(cols-1):
                    if grid[r][c] == 0:
                        continue
                    this_gr = get_group(r * cols + c)
                    right = r * cols + c + 1
                    if gr[right] != -2:
                        right_gr = get_group(right)
                        if this_gr != right_gr:
                            gr[right_gr] = this_gr
                    bottom = (r+1) * cols + c
                    if gr[bottom] != -2:
                        bottom_gr = get_group(bottom)
                        if this_gr != bottom_gr:
                            gr[bottom_gr] = this_gr

                if grid[r][cols - 1] == 0:
                    continue
                this_gr = get_group(r * cols + cols-1)
                bottom = (r+1) * cols + cols-1
                if gr[bottom] != -2:
                    bottom_gr = get_group(bottom)
                    if this_gr != bottom_gr:
                        gr[bottom_gr] = this_gr

            for c in range(cols-1):
                if grid[rows - 1][c] == 0:
                    continue
                this_gr = get_group((rows-1) * cols + c)
                right = (rows-1) * cols + c + 1
                if gr[right] != -2:
                    right_gr = get_group(right)
                    if this_gr != right_gr:
                        gr[right_gr] = this_gr
            return sum(1 for i in gr if i == -1)

        if count_islands() != 1:
            return 0

        for r in range(rows):
            for c in range(cols):
                if grid[r][c] == 0:
                    continue
                grid[r][c] = 0
                if count_islands() != 1:
                    return 1
                grid[r][c] = 1
        return 2





if __name__ == '__main__':
    print(Solution().minDays([[0,1,1,0],[0,1,1,0],[0,0,0,0]]))  # 2
    print(Solution().minDays([[1,1,1],[1,0,1],[1,1,1]]))  # 2
    print(Solution().minDays([[1,1],[1,0]]))  # 1
    print(Solution().minDays([[1,1]]))   # 2
    print(Solution().minDays([[1,1,1,0],[1,1,1,0],[0,1,0,0],[1,1,1,1],[1,1,1,1]]))  # 1
    print(Solution().minDays([[1,0,1,0],[0,0,0,0],[0,0,0,1],[1,0,1,0]]))  # 0

521