<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 SafeGrid:
    def __init__(self, grid):
        self.grid = grid
        w, h = len(grid[0]), len(grid)
        self.w = w
        self.h = h
    def __getitem__(self, idx):
        y, x = idx
        if 0 <= x < self.w and 0 <= y < self.h:
            return self.grid[y][x]
        return 0

    
class Solution:
    def minDays(self, grid: List[List[int]]) -> int:
        w, h = len(grid[0]), len(grid)
        unvisited = set([(x,y) for x in range(w) for y in range(h) if grid[y][x] == 1])

        islands = []
        while unvisited:
            x,y = unvisited.pop()
            stack = [(x,y)]
            island = [(x,y)]
            islands.append(island)
            while stack:
                x,y = stack.pop()

                for dx, dy in ((0,1), (0,-1), (1,0), (-1,0)):
                    if (x+dx, y+dy) not in unvisited:
                        continue
                    unvisited.remove((x+dx, y+dy))
                    stack.append((x+dx, y+dy))
                    island.append((x+dx, y+dy))
        # [print(l) for l in grid]
        # print(islands)
        if len(islands) == 0 or len(islands) > 1:
            return 0
        else:
            if len(islands[0]) == 1:
                return 1
            island = set(islands[0])
            nipples = 0
            bridges = []
            grid = SafeGrid(grid)
            for x,y in island:
                if (
                    (grid[y,x+1] == grid[y,x-1] == 0 and grid[y+1,x] == grid[y-1,x] == 1)
                    or
                    (grid[y+1,x] == grid[y-1,x] == 0 and grid[y,x+1] == grid[y,x-1] == 1)
                    or
                    (grid[y+1,x] == grid[y-1,x] == grid[y,x+1] == grid[y,x-1] == 1 and grid[y+1,x+1] == grid[y-1,x-1] == 0)
                    or
                    (grid[y+1,x] == grid[y-1,x] == grid[y,x+1] == grid[y,x-1] == 1 and grid[y+1,x-1] == grid[y+1,x-1] == 0)
                ):
                    bridges.append((x,y))
                if (
                    (grid[y,x+1] == grid[y,x-1] == grid[y+1,x] == 0 and grid[y-1,x] == 1)
                    or 
                    (grid[y,x+1] == grid[y,x-1] == grid[y-1,x] == 0 and grid[y+1,x] == 1)
                    or 
                    (grid[y,x+1] == grid[y+1,x] == grid[y-1,x] == 0 and grid[y,x-1] == 1)
                    or 
                    (grid[y,x-1] == grid[y+1,x] == grid[y-1,x] == 0 and grid[y,x+1] == 1)
                ):
                    nipples += 1
                
            if nipples > 0 and len(island) > 2:
                return 1
            else:
                # print(bridges)
                if not bridges:
                    return 2
                island_copy = set(island)
                bridge = bridges[0]
                # print(island_copy)
                island_copy.remove(bridge)
                x, y = bridge
                for dx, dy in ((0,1), (0,-1), (1,0), (-1,0)):
                    if (x+dx, y+dy) not in island_copy:
                        continue

                    stack = [(x+dx, y+dy)]
                    island_copy.remove((x+dx, y+dy))
                    break
                # print(stack)
                # print(island_copy)
                # G = [[0]*w for _ in range(h)]
                # for x,y in island_copy:
                #     G[y][x] = 1
                # [print(l) for l in G]
                while stack:
                    x,y = stack.pop()
                    for dx, dy in ((0,1), (0,-1), (1,0), (-1,0)):
                        if (x+dx, y+dy) not in island_copy:
                            continue
                        island_copy.remove((x+dx, y+dy))
                        stack.append((x+dx, y+dy))
                # print(island_copy)

                if len(island_copy) > 0:
                    return 1
                return 2
            
           




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