<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

class Solution:
    def minDays(self, grid: List[List[int]]) -> int:
        self.grid = grid
        # self.visited = [[False] * len(grid[0]) for _ in range(len(grid))]
        if(not self.isConnected()):
            return 0
        
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 1 and not self.is_surrounded(i, j):
                    grid[i][j] = 0
                    if(not self.isConnected()):
                        return 1
                    grid[i][j] = 1
            
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 1 and not self.is_surrounded(i, j):
                    grid[i][j] = 0

                    direction = [(0, 1), (1, 1), (1, 0)]
                    for dx, dy in direction:
                        x, y = i + dx, j + dy
                        if 0 <= x < len(grid) and 0 <= y < len(grid[0]) and grid[x][y] == 1 and not self.is_surrounded(x, y):
                            grid[x][y] = 0
                            if not self.isConnected():
                                return 2
                            grid[x][y] = 1
            

                    if(not self.isConnected()):
                        return 1
                    grid[i][j] = 1

        
    def isConnected(self):
        n_islands = 0
        visited = [[False] * len(self.grid[0]) for _ in range(len(self.grid))]

        for i in range(len(self.grid)):
            for j in range(len(self.grid[0])):
                if self.grid[i][j] == 1 and not visited[i][j]:
                    n_islands += 1
                    if n_islands > 1:
                        return False
                    self.dfs(i, j, visited)
        return n_islands == 1
    
    def dfs(self, i, j, visited):
        visited[i][j] = True

        for dx, dy in [(0, 1), (0, -1), (1, 0), (-1, 0)]:
            x, y = i + dx, j + dy
            if 0 <= x < len(self.grid) and 0 <= y < len(self.grid[0]) and self.grid[x][y] == 1 and not visited[x][y]:
                self.dfs(x, y, visited)

    def try_cuts(self, n_cuts):
        return self.recursive_cut(n_cuts, 0, 0)


    def recursive_cut(self, n_cuts, i, j):
        if n_cuts == 0:
            if(not self.isConnected()):
                print(end="")
            return not self.isConnected()

        if i == len(self.grid):
            return False

        
        
        if self.grid[i][j] == 1 and not self.is_surrounded(i, j):
            self.grid[i][j] = 0

            (x, y) = (i-1, j)
            if self.validCoord(x, y) and self.recursive_cut(n_cuts - 1, x, y):
                return True
            (x, y) = (i+1, j)
            if self.validCoord(x, y) and self.recursive_cut(n_cuts - 1, x, y):
                return True
            (x, y) = (i, j-1)
            if self.validCoord(x, y) and self.recursive_cut(n_cuts - 1, x, y):
                return True
            (x, y) = (i, j+1)
            if self.validCoord(x, y) and self.recursive_cut(n_cuts - 1, x, y):
                return True
            (x, y) = (i-1, j-1)
            if self.validCoord(x, y) and self.recursive_cut(n_cuts - 1, x, y):
                return True
            (x, y) = (i-1, j+1)
            if self.validCoord(x, y) and self.recursive_cut(n_cuts - 1, x, y):
                return True
            (x, y) = (i+1, j-1)
            if self.validCoord(x, y) and self.recursive_cut(n_cuts - 1, x, y):
                return True
            (x, y) = (i+1, j+1)
            if self.validCoord(x, y) and self.recursive_cut(n_cuts - 1, x, y):
                return True
            self.grid[i][j] = 1

        if(j == len(self.grid[0])-1):
            i+=1
            j = 0
        else:
            j+=1

        return self.recursive_cut(n_cuts, i, j)
    
    def validCoord(self, x, y):
        return 0<=x<len(self.grid) and 0<=y<len(self.grid[0])


    def search_cuts(self, update_coords):
        for i in range(len(self.grid)):
            for j in range(len(self.grid[0])):
                if self.grid[i][j] == 1 and not self.visited[i][j] and not self.is_surrounded(i, j):
                    cnt=0
                    (x, y) = (i, j)
                    while self.validCoord(x, y) and self.grid[x][y] == 1 and not self.visited[x][y]:
                        cnt+=1
                        self.grid[x][y] = 0
                        self.visited[x][y] = True
                        if not self.isConnected():
                            self.cur_min = min(self.cur_min, cnt)
                            break
                        (x, y) = update_coords(x, y)
                    (x, y) = (i, j)
                    for _ in range(cnt):
                        self.grid[x][y] = 1
                        if(not self.isConnected()):
                            self.cur_min = min(self.cur_min, cnt)
                        (x, y) = update_coords(x, y)
        self.visited = [[False] * len(self.grid[0]) for _ in range(len(self.grid))]

    def is_surrounded(self, i, j):
        for dx, dy in [(0, 1), (0, -1), (1, 0), (-1, 0), (-1, -1), (-1, 1), (1, -1), (1, 1)]:
            x, y = i + dx, j + dy
            if 0 <= x < len(self.grid) and 0 <= y < len(self.grid[0]) and self.grid[x][y] == 0:
                return False
            if not self.validCoord(x, y):
                return False
        return True

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