<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: List[List[int]]) -> int:
        """
        1/ count number of islands. if it is != 1, return 0
        """
        island_ct = self.num_islands(grid)
        if island_ct != 1:
            return 0
        return self.calculate_min_days(grid)
    
    def num_islands(self, grid: List[List[int]]) -> int:
        m = len(grid)
        n = len(grid[0])
        count = 0
        visited = set()
        for start_row in range(m):
            for start_col in range(n):
                if grid[start_row][start_col] == 1 and (start_row, start_col) not in visited:
                    count += 1
                    stack = [(start_row, start_col)]
                    visited.add((start_row, start_col))
                    while stack:
                        r, c = stack.pop()
                        for adj_r, adj_c in [(r - 1, c), (r + 1, c), (r, c - 1), (r, c + 1)]:
                            if 0 <= adj_r < m and 0 <= adj_c < n and grid[adj_r][adj_c] == 1 and (adj_r, adj_c) not in visited:
                                visited.add((adj_r, adj_c) )
                                stack.append((adj_r, adj_c))
        return count
    
    def calculate_min_days(self, grid: List[List[int]]) -> int:
        m = len(grid)
        n = len(grid[0])
        min_surrounding = 4
        island_size = 0
        row_counts = [0] * m
        col_counts = [0] * n
        diag_counts = defaultdict(int)
        anti_diag_counts = defaultdict(int)

        for r in range(m):
            can_reach_above_ct = 0
            for c in range(n):
                if grid[r][c] == 1:
                    island_size += 1
                    grid[r][c] = 0
                    if self.num_islands(grid) == 2:
                        return 1
                    grid[r][c] = 1

                    row_counts[r] += 1
                    col_counts[c] += 1
                    diag_counts[r + c] += 1
                    anti_diag_counts[r - c] += 1

                    if 0 < r and grid[r - 1][c] == 1:
                        can_reach_above_ct += 1

                    surrounding = 0
                    for adj_r, adj_c in [(r - 1, c), (r + 1, c), (r, c - 1), (r, c + 1)]:
                        if 0 <= adj_r < m and 0 <= adj_c < n and grid[adj_r][adj_c] == 1:
                            surrounding += 1
                    min_surrounding = min(min_surrounding, surrounding)
            
            if can_reach_above_ct == 1:
                min_surrounding = min(min_surrounding, 1)
        
        if 1 in row_counts or 1 in col_counts:
            min_surrounding = min(min_surrounding, 1)
        min_diag = min(diag_counts)
        max_diag = max(diag_counts)
        min_anti_diag = min(anti_diag_counts)
        max_anti_diag = max(anti_diag_counts)
        for diag in diag_counts:
            if diag_counts[diag] == 1 and min_diag < diag < max_diag:
                min_surrounding = min(min_surrounding, 1)
        for anti_diag in anti_diag_counts:
            if anti_diag_counts[anti_diag] == 1 and min_anti_diag < anti_diag < max_anti_diag:
                min_surrounding = min(min_surrounding, 1)

        if min_surrounding + 1 == island_size:
            return island_size

        return min_surrounding
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