<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>

from typing import List
import copy

class Solution:
    def minDays(self, grid: List[List[int]]) -> int:
        # Step 1: Count total land cells
        res = sum(sum(i) for i in grid)
        if res == 0:
            return 0
        if res == 1:
            return 1

        r, c = len(grid), len(grid[0])
        
        # Helper function to backtrack and mark connected land as visited
        def back(i, j):
            if i < 0 or i >= r or j < 0 or j >= c or grid[i][j] == 0:
                return
            grid[i][j] = 0
            back(i + 1, j)
            back(i - 1, j)
            back(i, j + 1)
            back(i, j - 1)

        # Helper function to count the number of islands in the grid
        def count_islands():
            temp_islands = 0
            for a in range(r):
                for b in range(c):
                    if grid[a][b] == 1:
                        back(a, b)
                        temp_islands += 1
            return temp_islands
        
        # Step 2: Count the initial number of islands
        original_grid = copy.deepcopy(grid)
        islands = count_islands()
        if islands > 1:
            return 0

        # Step 3: Try removing each land cell and see if it disconnects the grid
        for a in range(r):
            for b in range(c):
                if original_grid[a][b] == 1:
                    # Reset grid to original state and remove one cell
                    grid = copy.deepcopy(original_grid)
                    grid[a][b] = 0

                    # Count islands after removing the cell
                    if count_islands() > 1:
                        return 1

        # If no single land removal disconnects the grid, return 2 days
        return 2

842