<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>

import random
class Solution:
    def minDays(self, grid: List[List[int]]) -> int:
        m, n = len(grid), len(grid[0])

        def is_valid(i, j):
            return 0 <= i < m and 0 <= j < n
        
        def get_neis(i, j):
            return [(i+1,j), (i-1,j), (i,j+1), (i,j-1)]
        
        def dfs(i, j, visited):
            visited.add((i,j))
            for x, y in get_neis(i, j):
                if is_valid(x, y) and (x,y) not in visited and grid[x][y] == 1:
                    dfs(x, y, visited)
        
        islands = []
        seen = set()
        for i in range(m):
            for j in range(n):
                if (i,j) not in seen and grid[i][j] == 1:
                    visited = set()
                    dfs(i, j, visited)
                    islands.append(visited)
                    seen.update(visited)

        if len(islands) > 1 or len(islands) == 0:
            return 0
        
        island_indices = islands[0]
        if len(island_indices) == 1:
            return 1

        island_copy = copy.copy(island_indices)
        for index in island_indices:
            i, j = index
            island_copy.remove(index)
            grid[i][j] = 0
            visited = set()
            x, y = random.choice(list(island_copy))
            dfs(x, y, visited)
            if len(visited) != len(island_copy):
                return 1

            island_copy.add(index)
            grid[i][j] = 1

        return 2
        
1590