<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 numberOfIslands(self, grid: List[List[int]]) -> int:
        res = 0
        rows, cols = len(grid), len(grid[0])

        def isInBoundary(r: int, c: int) -> bool:
            return -1 < r < rows and -1 < c < cols

        def dfs(r: int, c: int) -> None:
            if not isInBoundary(r, c) or (r, c) in visited or grid[r][c] == 0:
                return
            visited.add((r, c))
            dfs(r + 1, c)
            dfs(r - 1, c)
            dfs(r, c + 1)
            dfs(r, c - 1)

        visited = set()
        def isNewIsland(r: int, c: int) -> bool:
            return isInBoundary(r, c) and (r, c) not in visited and grid[r][c] == 1

        for r in range(rows):
            for c in range(cols):
                if isNewIsland(r, c):
                    res += 1
                    dfs(r, c)
        return res
    
    def minDays(self, grid: List[List[int]]) -> int:
        islandCount = self.numberOfIslands(grid)
        if islandCount == 0 or islandCount >= 2:
            return 0

        for r in range(len(grid)):
            for c in range(len(grid[0])):
                if grid[r][c] == 0:
                    continue
                grid[r][c] = 0
                islandCount = self.numberOfIslands(grid)
                if islandCount == 0 or islandCount >= 2:
                    return 1
                grid[r][c] = 1
        
        return 2

1376